wpmath0000010_0

(+)-abscisic_acid_8'-hydroxylase.html

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(+)-borneol_dehydrogenase.html

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(+)-neomenthol_dehydrogenase.html

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(+)-sabinol_dehydrogenase.html

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(+)-trans-carveol_dehydrogenase.html

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(-)-borneol_dehydrogenase.html

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(-)-menthol_dehydrogenase.html

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(-)-menthol_monooxygenase.html

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(1-hydroxycyclohexan-1-yl)acetyl-CoA_lyase.html

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(3S,4R)-3,4-dihydroxycyclohexa-1,5-diene-1,4-dicarboxylate_dehydrogenase.html

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(a,b,0)_class_of_distributions.html

  1. N N
  2. p k p k - 1 = a + b k , k = 1 , 2 , 3 , \frac{p_{k}}{p_{k-1}}=a+\frac{b}{k},\qquad k=1,2,3,\dots
  3. p k = P ( N = k ) p_{k}=P(N=k)
  4. a a
  5. b b
  6. W N ( x ) W_{N}(x)\,
  7. P [ N = k ] P[N=k]\,
  8. a a\,
  9. b b\,
  10. p 0 p_{0}\,
  11. W N ( x ) W_{N}(x)\,
  12. E [ N ] E[N]\,
  13. V a r ( N ) Var(N)\,
  14. ( n k ) p k ( 1 - p ) n - k {\left({{n}\atop{k}}\right)}p^{k}(1-p)^{n-k}
  15. - p 1 - p \frac{-p}{1-p}
  16. p ( n + 1 ) 1 - p \frac{p(n+1)}{1-p}
  17. ( 1 - p ) n (1-p)^{n}\,
  18. ( p x + ( 1 - p ) ) n (px+(1-p))^{n}\,
  19. n p np\,
  20. n p ( 1 - p ) np(1-p)\,
  21. e - λ λ k k ! e^{-\lambda}\frac{\lambda^{k}}{k!}\,
  22. 0 0\,
  23. λ \lambda\,
  24. e - λ e^{-\lambda}\,
  25. e λ ( x - 1 ) e^{\lambda(x-1)}\,
  26. λ \lambda\,
  27. λ \lambda\,
  28. Γ ( r + k ) k ! Γ ( r ) p r ( 1 - p ) k \frac{\Gamma(r+k)}{k!\,\Gamma(r)}\,p^{r}\,(1-p)^{k}\,
  29. 1 - p 1-p\,
  30. ( 1 - p ) ( r - 1 ) (1-p)(r-1)\,
  31. p r p^{r}\,
  32. ( p 1 - x ( 1 - p ) ) r \left(\frac{p}{1-x(1-p)}\right)^{r}\,
  33. r ( 1 - p ) p \frac{r(1-p)}{p}\,
  34. r ( 1 - p ) p 2 \frac{r(1-p)}{p^{2}}\,
  35. k k
  36. k p k p k - 1 = a k + b , k\,\frac{p_{k}}{p_{k-1}}=ak+b,
  37. k k
  38. n n
  39. p k p_{k}
  40. n k n_{k}
  41. k k
  42. p ^ k = n k n \hat{p}_{k}=\frac{n_{k}}{n}
  43. p k p_{k}
  44. a a
  45. b b

(cytochrome_c)-arginine_N-methyltransferase.html

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(cytochrome_c)-lysine_N-methyltransferase.html

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(cytochrome_c)-methionine_S-methyltransferase.html

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(Formate-C-acetyltransferase)-activating_enzyme.html

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(heparan_sulfate)-glucosamine_3-sulfotransferase_1.html

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(heparan_sulfate)-glucosamine_3-sulfotransferase_2.html

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(heparan_sulfate)-glucosamine_3-sulfotransferase_3.html

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(heparan_sulfate)-glucosamine_N-sulfotransferase.html

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(hydroxyamino)benzene_mutase.html

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(Iso)eugenol_O-methyltransferase.html

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(Methionine_synthase)_reductase.html

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(Myelin_basic_protein)-arginine_N-methyltransferase.html

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(R)-2-haloacid_dehalogenase.html

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(R)-2-hydroxy-fatty-acid_dehydrogenase.html

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(R)-2-hydroxyacid_dehydrogenase.html

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(R)-3-hydroxyacid-ester_dehydrogenase.html

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(R)-4-hydroxyphenyllactate_dehydrogenase.html

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(R)-6-hydroxynicotine_oxidase.html

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(R)-aminopropanol_dehydrogenase.html

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(R)-dehydropantoate_dehydrogenase.html

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(R)-limonene_6-monooxygenase.html

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(R)-pantolactone_dehydrogenase_(flavin).html

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(R,R)-butanediol_dehydrogenase.html

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(Ribulose-bisphosphate_carboxylase)-lysine_N-methyltransferase.html

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(RS)-1-benzyl-1,2,3,4-tetrahydroisoquinoline_N-methyltransferase.html

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(RS)-norcoclaurine_6-O-methyltransferase.html

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(S)-2-haloacid_dehalogenase.html

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(S)-2-hydroxy-acid_oxidase.html

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(S)-2-hydroxy-fatty-acid_dehydrogenase.html

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(S)-3-hydroxyacid-ester_dehydrogenase.html

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(S)-6-hydroxynicotine_oxidase.html

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(S)-canadine_synthase.html

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(S)-carnitine_3-dehydrogenase.html

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(S)-cheilanthifoline_synthase.html

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(S)-coclaurine-N-methyltransferase.html

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(S)-limonene_3-monooxygenase.html

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(S)-limonene_6-monooxygenase.html

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(S)-limonene_7-monooxygenase.html

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(S)-mandelate_dehydrogenase.html

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(S)-scoulerine_9-O-methyltransferase.html

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(S)-stylopine_synthase.html

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(S)-tetrahydroprotoberberine_N-methyltransferase.html

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(S)-usnate_reductase.html

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(S,S)-butanediol_dehydrogenase.html

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1,2-dehydroreticulinium_reductase_(NADPH).html

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1,2-dihydrovomilenine_reductase.html

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1,2-dihydroxy-6-methylcyclohexa-3,5-dienecarboxylate_dehydrogenase.html

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1,3-propanediol_dehydrogenase.html

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1,5-anhydro-D-fructose_reductase.html

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1,5-anhydro-D-fructose_reductase_(1,5-anhydro-D-mannitol-forming).html

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1,6-dihydroxycyclohexa-2,4-diene-1-carboxylate_dehydrogenase.html

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1-aminocyclopropane-1-carboxylate_synthase.html

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1-hydroxy-2-naphthoate_1,2-dioxygenase.html

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1-Pyrroline-5-carboxylate_dehydrogenase.html

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10-hydroxydihydrosanguinarine_10-O-methyltransferase.html

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12-hydroxydihydrochelirubine_12-O-methyltransferase.html

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12alpha-hydroxysteroid_dehydrogenase.html

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12beta-hydroxysteroid_dehydrogenase.html

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15,16-dihydrobiliverdin:ferredoxin_oxidoreductase.html

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15-hydroxyicosatetraenoate_dehydrogenase.html

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15-hydroxyprostaglandin-D_dehydrogenase_(NADP+).html

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15-hydroxyprostaglandin-I_dehydrogenase_(NADP+).html

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15-hydroxyprostaglandin_dehydrogenase_(NAD+).html

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15-hydroxyprostaglandin_dehydrogenase_(NADP+).html

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15-oxoprostaglandin_13-oxidase.html

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16-alpha-hydroxysteroid_dehydrogenase.html

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16-hydroxysteroid_epimerase.html

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17-alpha-hydroxyprogesterone_aldolase.html

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2'-deoxymugineic-acid_2'-dioxygenase.html

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2'-hydroxybiphenyl-2-sulfinate_desulfinase.html

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2'-hydroxydaidzein_reductase.html

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2'-Hydroxyisoflavone_reductase.html

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2,2-dialkylglycine_decarboxylase_(pyruvate).html

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2,3-dihydro-2,3-dihydroxybenzoate_dehydrogenase.html

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2,3-dihydroxy-2,3-dihydro-p-cumate_dehydrogenase.html

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2,3-dihydroxybenzoate_2,3-dioxygenase.html

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2,3-dihydroxybenzoate_3,4-dioxygenase.html

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2,3-dihydroxyindole_2,3-dioxygenase.html

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2,3-dimethylmalate_lyase.html

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2,4'-dihydroxyacetophenone_dioxygenase.html

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2,4-diaminopentanoate_dehydrogenase.html

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2,4-dichlorobenzoyl-CoA_reductase.html

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2,4-dichlorophenol_6-monooxygenase.html

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2,5-didehydrogluconate_reductase.html

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2,5-dihydroxypyridine_5,6-dioxygenase.html

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2,5-dioxovalerate_dehydrogenase.html

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2,6-dihydroxypyridine_3-monooxygenase.html

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2,6-dioxo-6-phenylhexa-3-enoate_hydrolase.html

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2-(R)-hydroxypropyl-CoM_dehydrogenase.html

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2-(S)-hydroxypropyl-CoM_dehydrogenase.html

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2-acetolactate_mutase.html

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2-alkenal_reductase.html

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2-alkyn-1-ol_dehydrogenase.html

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2-aminobenzenesulfonate_2,3-dioxygenase.html

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2-aminohexano-6-lactam_racemase.html

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2-C-methyl-D-erythritol_2,4-cyclodiphosphate_synthase.html

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2-chloro-4-carboxymethylenebut-2-en-1,4-olide_isomerase.html

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2-chlorobenzoate_1,2-dioxygenase.html

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2-coumarate_reductase.html

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2-dehydro-3-deoxy-6-phosphogalactonate_aldolase.html

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2-dehydro-3-deoxy-D-gluconate_5-dehydrogenase.html

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2-dehydro-3-deoxy-D-gluconate_6-dehydrogenase.html

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2-dehydro-3-deoxy-D-pentonate_aldolase.html

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2-dehydro-3-deoxy-L-pentonate_aldolase.html

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2-dehydro-3-deoxy-phosphogluconate_aldolase.html

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2-dehydro-3-deoxyglucarate_aldolase.html

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2-dehydropantoate_2-reductase.html

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2-dehydropantoate_aldolase.html

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2-dehydropantolactone_reductase_(A-specific).html

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2-dehydropantolactone_reductase_(B-specific).html

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2-deoxy-D-gluconate_3-dehydrogenase.html

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2-enoate_reductase.html

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2-furoyl-CoA_dehydrogenase.html

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2-hexadecenal_reductase.html

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2-hydroxy-1,4-benzoquinone_reductase.html

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2-hydroxy-3-oxopropionate_reductase.html

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2-hydroxy-6-oxo-6-phenylhexa-2,4-dienoate_reductase.html

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2-hydroxybiphenyl_3-monooxygenase.html

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2-hydroxycyclohexanone_2-monooxygenase.html

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2-hydroxyglutarate_dehydrogenase.html

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2-hydroxymethylglutarate_dehydrogenase.html

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2-hydroxymuconate-semialdehyde_hydrolase.html

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2-hydroxypyridine_5-monooxygenase.html

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2-hydroxyquinoline_5,6-dioxygenase.html

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2-hydroxyquinoline_8-monooxygenase.html

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2-methyl-branched-chain-enoyl-CoA_reductase.html

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2-methylacyl-CoA_dehydrogenase.html

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2-methyleneglutarate_mutase.html

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2-nitrophenol_2-monooxygenase.html

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2-nitropropane_dioxygenase.html

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2-oxo-acid_reductase.html

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2-oxoadipate_reductase.html

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2-oxoaldehyde_dehydrogenase_(NAD+).html

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2-oxoaldehyde_dehydrogenase_(NADP+).html

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2-oxobutyrate_synthase.html

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2-oxoglutarate_decarboxylase.html

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2-oxoglutarate_synthase.html

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2-oxoisovalerate_dehydrogenase_(acylating).html

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2-oxopropyl-CoM_reductase_(carboxylating).html

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20000_(number).html

  1. 13 4 = 169 2 = 119 2 + 120 2 13^{4}=169^{2}=119^{2}+120^{2}

20alpha-hydroxysteroid_dehydrogenase.html

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21-hydroxysteroid_dehydrogenase_(NAD+).html

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21-hydroxysteroid_dehydrogenase_(NADP+).html

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24-hydroxycholesterol_7alpha-hydroxylase.html

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24-methylenesterol_C-methyltransferase.html

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27-hydroxycholesterol_7alpha-monooxygenase.html

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3'-demethylstaurosporine_O-methyltransferase.html

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3'-hydroxy-N-methyl-(S)-coclaurine_4'-O-methyltransferase.html

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3,4-dihydroxy-9,10-secoandrosta-1,3,5(10)-triene-9,17-dione_4,5-dioxygenase.html

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3,4-dihydroxyphenylacetate_2,3-dioxygenase.html

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3,4-dihydroxyphthalate_decarboxylase.html

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3,7-dimethylquercetin_4'-O-methyltransferase.html

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3,9-dihydroxypterocarpan_6a-monooxygenase.html

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3-(hydroxyamino)phenol_mutase.html

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3-(imidazol-5-yl)lactate_dehydrogenase.html

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3-aci-nitropropanoate_oxidase.html

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3-aminobutyryl-CoA_ammonia-lyase.html

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3-carboxy-cis,cis-muconate_cycloisomerase.html

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3-carboxyethylcatechol_2,3-dioxygenase.html

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3-chloro-D-alanine_dehydrochlorinase.html

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3-dehydro-L-gulonate-6-phosphate_decarboxylase.html

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3-dehydro-L-gulonate_2-dehydrogenase.html

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3-dehydrosphinganine_reductase.html

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3-demethylubiquinone-9_3-O-methyltransferase.html

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3-deoxy-D-manno-octulosonate_aldolase.html

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3-hydroxy-16-methoxy-2,3-dihydrotabersonine_N-methyltransferase.html

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3-hydroxy-2-methylbutyryl-CoA_dehydrogenase.html

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3-hydroxy-2-methylpyridine-4,5-dicarboxylate_4-decarboxylase.html

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3-hydroxy-2-methylpyridinecarboxylate_dioxygenase.html

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3-hydroxy-2-methylquinolin-4-one_2,4-dioxygenase.html

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3-hydroxy-3-isohexenylglutaryl-CoA_lyase.html

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3-hydroxy-4-oxoquinoline_2,4-dioxygenase.html

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3-hydroxyacyl-CoA_dehydrogenase.html

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3-hydroxyanthranilate_3,4-dioxygenase.html

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3-hydroxyanthranilate_4-C-methyltransferase.html

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3-hydroxyanthranilate_oxidase.html

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3-hydroxyaspartate_aldolase.html

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3-hydroxybenzoate_2-monooxygenase.html

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3-hydroxybenzoate_4-monooxygenase.html

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3-hydroxybenzoate_6-monooxygenase.html

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3-hydroxybenzyl-alcohol_dehydrogenase.html

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3-hydroxybutyrate_dehydrogenase.html

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3-hydroxybutyryl-CoA_dehydrogenase.html

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3-hydroxybutyryl-CoA_epimerase.html

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3-hydroxycyclohexanone_dehydrogenase.html

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3-hydroxyisobutyrate_dehydrogenase.html

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3-hydroxymethylcephem_carbamoyltransferase.html

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3-hydroxyphenylacetate_6-hydroxylase.html

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3-hydroxypimeloyl-CoA_dehydrogenase.html

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3-hydroxypropionate_dehydrogenase.html

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3-keto-steroid_reductase.html

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3-ketovalidoxylamine_C-N-lyase.html

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3-mercaptopyruvate_sulfurtransferase.html

  1. \rightleftharpoons
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3-methyl-2-oxobutanoate_dehydrogenase.html

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3-methyl-2-oxobutanoate_dehydrogenase_(ferredoxin).html

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3-methyl-2-oxobutanoate_hydroxymethyltransferase.html

  1. \rightleftharpoons

3-methylbutanal_reductase.html

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3-methyleneoxindole_reductase.html

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3-methylquercetin_7-O-methyltransferase.html

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3-oxo-5beta-steroid_4-dehydrogenase.html

  1. \rightleftharpoons

3-oxoacid_CoA-transferase.html

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3-oxoacyl-(acyl-carrier-protein)_reductase.html

  1. \rightleftharpoons

3-oxoacyl-(acyl-carrier-protein)_reductase_(NADH).html

  1. \rightleftharpoons

3-oxoadipate_CoA-transferase.html

  1. \rightleftharpoons

3-oxolaurate_decarboxylase.html

  1. \rightleftharpoons

3-oxosteroid_1-dehydrogenase.html

  1. \rightleftharpoons

3-phenylpropanoate_dioxygenase.html

  1. \rightleftharpoons

30000_(number).html

  1. 181 2 181^{2}
  2. 2 15 - 1 2^{15}-1
  3. 2 15 2^{15}

3alpha(17beta)-hydroxysteroid_dehydrogenase_(NAD+).html

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3alpha(or_20beta)-hydroxysteroid_dehydrogenase.html

  1. \rightleftharpoons

3alpha,7alpha,12alpha-trihydroxy-5beta-cholestanoyl-CoA_24-hydroxylase.html

  1. \rightleftharpoons

3alpha,7alpha,12alpha-trihydroxycholestan-26-al_26-oxidoreductase.html

  1. \rightleftharpoons

3alpha-hydroxy-5beta-androstane-17-one_3alpha-dehydrogenase.html

  1. \rightleftharpoons

3alpha-hydroxycholanate_dehydrogenase.html

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3alpha-hydroxyglycyrrhetinate_dehydrogenase.html

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3alpha-hydroxysteroid_dehydrogenase_(A-specific).html

  1. \rightleftharpoons

3alpha-hydroxysteroid_dehydrogenase_(B-specific).html

  1. \rightleftharpoons

3beta(or_20alpha)-hydroxysteroid_dehydrogenase.html

  1. \rightleftharpoons

3beta-hydroxy-5alpha-steroid_dehydrogenase.html

  1. \rightleftharpoons

3beta-hydroxy-5beta-steroid_dehydrogenase.html

  1. \rightleftharpoons

4'-methoxyisoflavone_2'-hydroxylase.html

  1. \rightleftharpoons

4,5-dihydroxyphthalate_decarboxylase.html

  1. \rightleftharpoons

4-(2-carboxyphenyl)-2-oxobut-3-enoate_aldolase.html

  1. \rightleftharpoons

4-(dimethylamino)phenylazoxybenzene_reductase.html

  1. \rightleftharpoons

4-(hydroxymethyl)benzenesulfonate_dehydrogenase.html

  1. \rightleftharpoons

4-aminobenzoate_1-monooxygenase.html

  1. \rightleftharpoons

4-carboxy-2-hydroxymuconate-6-semialdehyde_dehydrogenase.html

  1. \rightleftharpoons

4-carboxymethyl-4-methylbutenolide_mutase.html

  1. \rightleftharpoons

4-carboxymuconolactone_decarboxylase.html

  1. \rightleftharpoons

4-chlorobenzoate_dehalogenase.html

  1. \rightleftharpoons

4-chlorobenzoyl-CoA_dehalogenase.html

  1. \rightleftharpoons

4-chlorophenylacetate_3,4-dioxygenase.html

  1. \rightleftharpoons

4-Cresol_dehydrogenase_(hydroxylating).html

  1. \rightleftharpoons

4-deoxy-L-threo-5-hexosulose-uronate_ketol-isomerase.html

  1. \rightleftharpoons

4-formylbenzenesulfonate_dehydrogenase.html

  1. \rightleftharpoons

4-hydroxy-2-oxoglutarate_aldolase.html

  1. \rightleftharpoons

4-hydroxy-2-oxovalerate_aldolase.html

  1. \rightleftharpoons

4-hydroxy-3-methylbut-2-en-1-yl_diphosphate_synthase.html

  1. \rightleftharpoons

4-hydroxy-4-methyl-2-oxoglutarate_aldolase.html

  1. \rightleftharpoons

4-hydroxyacetophenone_monooxygenase.html

  1. \rightleftharpoons

4-hydroxybenzaldehyde_dehydrogenase.html

  1. \rightleftharpoons

4-hydroxybenzoate_1-hydroxylase.html

  1. \rightleftharpoons

4-hydroxybenzoate_3-monooxygenase.html

  1. \rightleftharpoons

4-hydroxybenzoate_3-monooxygenase_(NAD(P)H).html

  1. \rightleftharpoons

4-hydroxybenzoate_decarboxylase.html

  1. \rightleftharpoons

4-hydroxybenzoyl-CoA_reductase.html

  1. \rightleftharpoons

4-Hydroxybutyrate_dehydrogenase.html

  1. \rightleftharpoons

4-Hydroxycyclohexanecarboxylate_dehydrogenase.html

  1. \rightleftharpoons

4-hydroxymandelate_oxidase.html

  1. \rightleftharpoons

4-hydroxymandelate_synthase.html

  1. \rightleftharpoons

4-hydroxymuconic-semialdehyde_dehydrogenase.html

  1. \rightleftharpoons

4-hydroxyphenylacetaldehyde_dehydrogenase.html

  1. \rightleftharpoons

4-hydroxyphenylacetaldehyde_oxime_monooxygenase.html

  1. \rightleftharpoons

4-hydroxyphenylacetate_1-monooxygenase.html

  1. \rightleftharpoons

4-Hydroxyphenylacetate_3-monooxygenase.html

  1. \rightleftharpoons

4-hydroxyphenylacetate_decarboxylase.html

  1. \rightleftharpoons

4-hydroxyphenylpyruvate_decarboxylase.html

  1. \rightleftharpoons

4-hydroxyphenylpyruvate_oxidase.html

  1. \rightleftharpoons

4-hydroxyproline_epimerase.html

  1. \rightleftharpoons

4-hydroxyquinoline_3-monooxygenase.html

  1. \rightleftharpoons

4-hydroxythreonine-4-phosphate_dehydrogenase.html

  1. \rightleftharpoons

4-methoxybenzoate_monooxygenase_(O-demethylating).html

  1. \rightleftharpoons

4-nitrophenol_2-monooxygenase.html

  1. \rightleftharpoons

4-oxalocrotonate_decarboxylase.html

  1. \rightleftharpoons

4-oxoproline_reductase.html

  1. \rightleftharpoons

4-phosphoerythronate_dehydrogenase.html

  1. \rightleftharpoons

4-sulfobenzoate_3,4-dioxygenase.html

  1. \rightleftharpoons

4-trimethylammoniobutyraldehyde_dehydrogenase.html

  1. \rightleftharpoons

40000_(number).html

  1. 6 6 6^{6}

5,10-methylenetetrahydromethanopterin_reductase.html

  1. \rightleftharpoons

5,6-dihydroxy-3-methyl-2-oxo-1,2,5,6-tetrahydroquinoline_dehydrogenase.html

  1. \rightleftharpoons

5-(carboxyamino)imidazole_ribonucleotide_mutase.html

  1. \rightleftharpoons

5-amino-6-(5-phosphoribosylamino)uracil_reductase.html

  1. \rightleftharpoons

5-carboxymethyl-2-hydroxymuconate_Delta-isomerase.html

  1. \rightleftharpoons

5-carboxymethyl-2-hydroxymuconic-semialdehyde_dehydrogenase.html

  1. \rightleftharpoons

5-dehydro-2-deoxyphosphogluconate_aldolase.html

  1. \rightleftharpoons

5-guanidino-2-oxopentanoate_decarboxylase.html

  1. \rightleftharpoons

5-hydroxypentanoate_CoA-transferase.html

  1. \rightleftharpoons

5-methyltetrahydropteroyltriglutamate—homocysteine_S-methyltransferase.html

  1. \rightleftharpoons

5-O-(4-coumaroyl)-D-quinate_3'-monooxygenase.html

  1. \rightleftharpoons

5-oxopent-3-ene-1,2,5-tricarboxylate_decarboxylase.html

  1. \rightleftharpoons

5-pyridoxate_dioxygenase.html

  1. \rightleftharpoons

50000_(number).html

  1. 51984 = 228 2 = 37 3 + 11 3 51984=228^{2}=37^{3}+11^{3}
  2. 3 10 3^{10}

5beta-cholestane-3alpha,7alpha-diol_12alpha-hydroxylase.html

  1. \rightleftharpoons

6,7-dihydropteridine_reductase.html

  1. \rightleftharpoons

6-endo-hydroxycineole_dehydrogenase.html

  1. \rightleftharpoons

6-hydroxyhexanoate_dehydrogenase.html

  1. \rightleftharpoons

6-hydroxymellein_O-methyltransferase.html

  1. \rightleftharpoons

6-hydroxynicotinate_dehydrogenase.html

  1. \rightleftharpoons

6-hydroxynicotinate_reductase.html

  1. \rightleftharpoons

6-methylsalicylate_decarboxylase.html

  1. \rightleftharpoons

6-O-methylnorlaudanosoline_5'-O-methyltransferase.html

  1. \rightleftharpoons

6-oxocineole_dehydrogenase.html

  1. \rightleftharpoons

6-oxohexanoate_dehydrogenase.html

  1. \rightleftharpoons

6-pyruvoyltetrahydropterin_2'-reductase.html

  1. \rightleftharpoons

60000_(number).html

  1. 2 16 2^{16}

6beta-hydroxyhyoscyamine_epoxidase.html

  1. \rightleftharpoons

7,8-dihydroxykynurenate_8,8a-dioxygenase.html

  1. \rightleftharpoons

7-cubic_honeycomb.html

  1. C ~ 7 {\tilde{C}}_{7}
  2. C ~ 7 {\tilde{C}}_{7}
  3. B ~ 7 {\tilde{B}}_{7}
  4. D ~ 7 {\tilde{D}}_{7}

7-demicubic_honeycomb.html

  1. B ~ 7 {\tilde{B}}_{7}
  2. D ~ 7 {\tilde{D}}_{7}
  3. 7 + {}^{+}_{7}
  4. 7 2 {}^{2}_{7}
  5. n + {}^{+}_{n}
  6. 7 * {}^{*}_{7}
  7. 7 4 {}^{4}_{7}
  8. 7 2 {}^{2}_{7}
  9. 7 * {}^{*}_{7}
  10. B ~ 7 {\tilde{B}}_{7}
  11. D ~ 7 {\tilde{D}}_{7}
  12. C ~ 7 {\tilde{C}}_{7}

7-deoxyloganin_7-hydroxylase.html

  1. \rightleftharpoons

7-methylxanthosine_synthase.html

  1. \rightleftharpoons

70000_(number).html

  1. 15 * 16 * 17 * 18 15*16*17*18
  2. 42 3 42^{3}
  3. 5 7 5^{7}
  4. 43 3 43^{3}

7alpha-hydroxycholest-4-en-3-one_12alpha-hydroxylase.html

  1. \rightleftharpoons

7alpha-hydroxysteroid_dehydrogenase.html

  1. \rightleftharpoons

7beta-hydroxysteroid_dehydrogenase_(NADP+).html

  1. \rightleftharpoons

8-cubic_honeycomb.html

  1. C ~ 8 {\tilde{C}}_{8}
  2. C ~ 8 {\tilde{C}}_{8}
  3. B ~ 8 {\tilde{B}}_{8}
  4. D ~ 8 {\tilde{D}}_{8}

8-demicubic_honeycomb.html

  1. B ~ 8 {\tilde{B}}_{8}
  2. D ~ 8 {\tilde{D}}_{8}
  3. E ~ 8 {\tilde{E}}_{8}
  4. D ~ 8 {\tilde{D}}_{8}
  5. E ~ 8 {\tilde{E}}_{8}
  6. D ~ 8 {\tilde{D}}_{8}
  7. D 8 D_{8}
  8. 8 + {}^{+}_{8}
  9. 8 2 {}^{2}_{8}
  10. 8 * {}^{*}_{8}
  11. 8 4 {}^{4}_{8}
  12. 8 2 {}^{2}_{8}
  13. 8 * {}^{*}_{8}

8-dimethylallylnaringenin_2'-hydroxylase.html

  1. \rightleftharpoons

8-hydroxyquercetin_8-O-methyltransferase.html

  1. \rightleftharpoons

8-oxocoformycin_reductase.html

  1. \rightleftharpoons

A_Disappearing_Number.html

  1. 1 + 2 + 3 + = - 1 12 ( ) 1+2+3+\cdots=-\frac{1}{12}\ (\Re)
  2. ( ) (\Re)
  3. ζ ( s ) \zeta(s)
  4. s = - 1 s=-1

Abductive_logic_programming.html

  1. P , A , I C , \langle P,A,IC\rangle,
  2. P , A , 𝐼𝐶 \langle P,A,\mathit{IC}\rangle
  3. P P
  4. A A
  5. 𝐼𝐶 \mathit{IC}
  6. G = feed(lactose) G=\,\text{feed(lactose)}
  7. Δ 1 = { amount(lactose, hi), amount(glucose, low) } \Delta_{1}=\{\,\text{amount(lactose, hi), amount(glucose, low)}\}
  8. Δ 2 = { amount(lactose, medium), amount(glucose, medium) } \Delta_{2}=\{\,\text{amount(lactose, medium), amount(glucose, medium)}\}
  9. P , A , 𝐼𝐶 \langle P,A,\mathit{IC}\rangle
  10. G G
  11. Δ \Delta
  12. P Δ G P\cup\Delta\models G
  13. P Δ I C P\cup\Delta\models IC
  14. P Δ P\cup\Delta
  15. \models
  16. 𝐼𝐶 \mathit{IC}
  17. Δ \Delta
  18. P 𝐼𝐶 Δ P\cup\mathit{IC}\cup\Delta

ABS_methods.html

  1. m n \scriptstyle m\,\leq\,n

Abscisic-aldehyde_oxidase.html

  1. \rightleftharpoons

Absorbing_element.html

  1. z z
  2. z z^{\prime}
  3. z = z × z = z z=z\times z^{\prime}=z^{\prime}

Acetate_CoA-transferase.html

  1. \rightleftharpoons

Acetoacetyl-CoA_reductase.html

  1. \rightleftharpoons

Acetoin_racemase.html

  1. \rightleftharpoons

Acetolactate_decarboxylase.html

  1. \rightleftharpoons

Acetylacetone-cleaving_enzyme.html

  1. \rightleftharpoons

Acetylenedicarboxylate_decarboxylase.html

  1. \rightleftharpoons

Acetylindoxyl_oxidase.html

  1. \rightleftharpoons

Acetylpyruvate_hydrolase.html

  1. \rightleftharpoons

Acey_Deucey_(card_game).html

  1. n n
  2. 4 ( n - 1 ) = 4 ( 11 - n ) + 2 × 2 × 3 4(n-1)=4(11-n)+2\times 2\times 3

Acireductone_dioxygenase_(iron(II)-requiring).html

  1. \rightleftharpoons

Acireductone_dioxygenase_(Ni2+-requiring).html

  1. \rightleftharpoons

Aconitate_decarboxylase.html

  1. \rightleftharpoons

Aconitate_Delta-isomerase.html

  1. \rightleftharpoons

Acoustic_rheometer.html

  1. T i j = G S i j {T_{ij}=G\cdot S_{ij}}
  2. P = - K S {P=-K\cdot S}
  3. M = M + M ′′ = K + 4 3 G M=M^{\prime}+M^{\prime\prime}=K+\frac{4}{3}G
  4. M = ρ V 2 M^{\prime}=\rho\cdot V^{2}
  5. M ′′ = 2 ρ α V 3 ω M^{\prime\prime}=\frac{2\rho\alpha V^{3}}{\omega}

Activation_function.html

  1. ϕ ( v i ) = U ( v i ) \phi(v_{i})=U(v_{i})
  2. U U
  3. ϕ ( v i ) = μ v i \phi(v_{i})=\mu v_{i}
  4. μ \mu
  5. ϕ ( v i ) = U ( v i ) tanh ( v i ) \phi(v_{i})=U(v_{i})\tanh(v_{i})
  6. ϕ ( v i ) = tanh ( v i ) \phi(v_{i})=\tanh(v_{i})
  7. ϕ ( v i ) = ( 1 + exp ( - v i ) ) - 1 \phi(v_{i})=(1+\exp(-v_{i}))^{-1}
  8. ϕ ( v i ) = exp ( - v i - c i 2 2 σ 2 ) \,\phi(v_{i})=\exp\left(-\frac{\|v_{i}-c_{i}\|^{2}}{2\sigma^{2}}\right)
  9. ϕ ( v i ) = v i - c i 2 + a 2 \,\phi(v_{i})=\sqrt{\|v_{i}-c_{i}\|^{2}+a^{2}}
  10. ϕ ( v i ) = ( v i - c i 2 + a 2 ) - 1 / 2 \,\phi(v_{i})=(\|v_{i}-c_{i}\|^{2}+a^{2})^{-1/2}
  11. c i c_{i}
  12. a a
  13. σ \sigma
  14. x x
  15. K ( v i , x ) = ϕ ( v i ) K(v_{i},x)=\phi(v_{i})
  16. ϕ ( v i ) = tanh ( β 1 + β 0 j v i , j x j ) \,\phi(v_{i})=\tanh\left(\beta_{1}+\beta_{0}\sum_{j}v_{i,j}x_{j}\right)
  17. β 0 \beta_{0}
  18. β 1 \beta_{1}
  19. ϕ ( v i ) = ( 1 + j v i , j x j ) p \,\phi(v_{i})=\left(1+\sum_{j}v_{i,j}x_{j}\right)^{p}

Acyl-(acyl-carrier-protein)_desaturase.html

  1. \rightleftharpoons

Acyl-CoA_dehydrogenase_(NADP+).html

  1. \rightleftharpoons

Acyl-CoA_oxidase.html

  1. \rightleftharpoons

Acylglycerone-phosphate_reductase.html

  1. \rightleftharpoons

Acylpyruvate_hydrolase.html

  1. \rightleftharpoons

Adenosylmethionine_hydrolase.html

  1. \rightleftharpoons

Adenylyl-sulfate_reductase.html

  1. \rightleftharpoons

Adenylyl-sulfate_reductase_(glutathione).html

  1. \rightleftharpoons

Adenylyl-sulfate_reductase_(thioredoxin).html

  1. \rightleftharpoons

ADP-glyceromanno-heptose_6-epimerase.html

  1. \rightleftharpoons

Aggregate_Level_Simulation_Protocol.html

  1. ( T , T + ? T ] (T,T+?T]
  2. T + ? T T+?T
  3. ( T , T + ? T ] (T,T+?T]
  4. ( T , T + ? T ] (T,T+?T]

Air_gap.html

  1. N I NI

Alanine_dehydrogenase.html

  1. \rightleftharpoons

Alanine_racemase.html

  1. \rightleftharpoons

Alanopine_dehydrogenase.html

  1. \rightleftharpoons

Albendazole_monooxygenase.html

  1. \rightleftharpoons

Albrecht_Beutelspacher.html

  1. α \alpha

Alcohol_dehydrogenase_(acceptor).html

  1. \rightleftharpoons

Alcohol_dehydrogenase_(NAD(P)+).html

  1. \rightleftharpoons

Alcohol_oxidase.html

  1. \rightleftharpoons

Aldehyde_dehydrogenase_(FAD-independent).html

  1. \rightleftharpoons

Aldehyde_dehydrogenase_(NAD(P)+).html

  1. \rightleftharpoons

Aldehyde_dehydrogenase_(NAD+).html

  1. \rightleftharpoons

Aldehyde_dehydrogenase_(NADP+).html

  1. \rightleftharpoons

Aldehyde_dehydrogenase_(pyrroloquinoline-quinone).html

  1. \rightleftharpoons

Aldose-6-phosphate_reductase_(NADPH).html

  1. \rightleftharpoons

Aldose_1-dehydrogenase.html

  1. \rightleftharpoons

Aldose_1-epimerase.html

  1. \rightleftharpoons

Aleksandrov–Clark_measure.html

  1. H 2 ( 𝔻 , ) . H^{2}(\mathbb{D},\mathbb{C}).
  2. θ H 2 ( 𝔻 , ) , \theta H^{2}(\mathbb{D},\mathbb{C}),
  3. θ \theta
  4. K θ = ( θ H 2 ( 𝔻 , ) ) . K_{\theta}=\left(\theta H^{2}(\mathbb{D},\mathbb{C})\right)^{\perp}.
  5. S θ S_{\theta}
  6. K θ K_{\theta}
  7. S θ = P K θ S | K θ . S_{\theta}=P_{K_{\theta}}S|_{K_{\theta}}.
  8. S θ S_{\theta}
  9. U α ( f ) = S θ ( f ) + α f , θ z , U_{\alpha}(f)=S_{\theta}(f)+\alpha\left\langle f,\frac{\theta}{z}\right\rangle,
  10. σ α \sigma_{\alpha}
  11. α \alpha
  12. 𝕋 {}^{\mathbb{T}}
  13. θ \theta
  14. ϕ \phi
  15. 𝔻 {}^{\mathbb{D}}
  16. u α u_{\alpha}
  17. u α ( z ) = ( α + φ ( z ) α - φ ( z ) ) , u_{\alpha}(z)=\Re\left(\frac{\alpha+\varphi(z)}{\alpha-\varphi(z)}\right),
  18. α 𝕋 {}^{\alpha\in\mathbb{T}}
  19. μ α \mu_{\alpha}
  20. 𝕋 {}^{\mathbb{T}}
  21. φ \varphi

Aliphatic_aldoxime_dehydratase.html

  1. \rightleftharpoons

Alkan-1-ol_dehydrogenase_(acceptor).html

  1. \rightleftharpoons

Alkanal_monooxygenase_(FMN-linked).html

  1. \rightleftharpoons

Alkane_1-monooxygenase.html

  1. \rightleftharpoons

Alkanesulfonate_monooxygenase.html

  1. \rightleftharpoons

Alkene_monooxygenase.html

  1. \rightleftharpoons

Alkenylglycerophosphocholine_hydrolase.html

  1. \rightleftharpoons

Alkenylglycerophosphoethanolamine_hydrolase.html

  1. \rightleftharpoons

Alkylglycerol_monooxygenase.html

  1. \rightleftharpoons

Alkylhalidase.html

  1. \rightleftharpoons

Alkylmercury_lyase.html

  1. \rightleftharpoons

All-trans-retinol_13,14-reductase.html

  1. \rightleftharpoons

Allantoin_racemase.html

  1. \rightleftharpoons

Allene-oxide_cyclase.html

  1. \rightleftharpoons

Allyl-alcohol_dehydrogenase.html

  1. \rightleftharpoons

Almost_integer.html

  1. 1 2 1 30 ( 61421 - 23 5831385 ) \frac{1}{2}\sqrt{\frac{1}{30}(61421-23\sqrt{5831385})}
  2. ϕ = 1 + 5 2 1.618 \phi=\frac{1+\sqrt{5}}{2}\approx 1.618\,
  3. ϕ 17 = 3571 + 1597 5 2 3571.00028 \phi^{17}=\frac{3571+1597\sqrt{5}}{2}\approx 3571.00028\,
  4. ϕ 18 = 2889 + 1292 5 5777.999827 \phi^{18}=2889+1292\sqrt{5}\approx 5777.999827\,
  5. ϕ 19 = 9349 + 4181 5 2 9349.000107 \phi^{19}=\frac{9349+4181\sqrt{5}}{2}\approx 9349.000107\,
  6. e π 43 884736743.999777466 e^{\pi\sqrt{43}}\approx 884736743.999777466\,
  7. e π 67 147197952743.999998662454 e^{\pi\sqrt{67}}\approx 147197952743.999998662454\,
  8. e π 163 262537412640768743.99999999999925007 e^{\pi\sqrt{163}}\approx 262537412640768743.99999999999925007\,
  9. e π 43 = 12 3 ( 9 2 - 1 ) 3 + 744 - 2.225 × 10 - 4 e^{\pi\sqrt{43}}=12^{3}(9^{2}-1)^{3}+744-2.225\cdots\times 10^{-4}\,
  10. e π 67 = 12 3 ( 21 2 - 1 ) 3 + 744 - 1.337 × 10 - 6 e^{\pi\sqrt{67}}=12^{3}(21^{2}-1)^{3}+744-1.337\cdots\times 10^{-6}\,
  11. e π 163 = 12 3 ( 231 2 - 1 ) 3 + 744 - 7.499 × 10 - 13 e^{\pi\sqrt{163}}=12^{3}(231^{2}-1)^{3}+744-7.499\cdots\times 10^{-13}\,
  12. 21 = 3 × 7 , 231 = 3 × 7 × 11 , 744 = 24 × 31 21=3\times 7,231=3\times 7\times 11,744=24\times 31\,
  13. e π 163 e^{\pi\sqrt{163}}\,
  14. e π - π = 19.999099979189 e^{\pi}-\pi=19.999099979189\cdots\,
  15. e π e^{\pi}\,
  16. π + 20 \pi+20\,

Alpha-methylacyl-CoA_racemase.html

  1. \rightleftharpoons

Alpha-pinene-oxide_decyclase.html

  1. \rightleftharpoons

Alpha-santonin_1,2-reductase.html

  1. \rightleftharpoons

Alternating_step_generator.html

  1. O ( L 2 .2 2 L / 3 ) O(L^{2}.2^{2L/3})
  2. O ( 2 2 L / 3 ) O(2^{2L/3})
  3. L L

Amine_N-methyltransferase.html

  1. \rightleftharpoons

Amine_oxidase_(copper-containing).html

  1. \rightleftharpoons

Amine_sulfotransferase.html

  1. \rightleftharpoons

Amino-acid_racemase.html

  1. \rightleftharpoons

Aminobenzoate_decarboxylase.html

  1. \rightleftharpoons

Aminobutyraldehyde_dehydrogenase.html

  1. \rightleftharpoons

Aminocarboxymuconate-semialdehyde_decarboxylase.html

  1. \rightleftharpoons

Aminocyclopropanecarboxylate_oxidase.html

  1. \rightleftharpoons

Aminodeoxychorismate_lyase.html

  1. \rightleftharpoons

Aminomuconate-semialdehyde_dehydrogenase.html

  1. \rightleftharpoons

An_Exceptionally_Simple_Theory_of_Everything.html

  1. su ( 2 ) R \mathrm{su}(2)_{R}\,
  2. u ( 1 ) B - L \mathrm{u}(1)_{B-L}\,
  3. u ( 1 ) \mathrm{u}(1)\,
  4. s o ( 3 , 11 ) 64 so(3,11)\oplus 64

Analytic_semigroup.html

  1. Δ θ = { 0 } { t : | arg ( t ) | < θ } , \Delta_{\theta}=\{0\}\cup\{t\in\mathbb{C}:|\mathrm{arg}(t)|<\theta\},
  2. R λ ( A ) C | λ - ω | \|R_{\lambda}(A)\|\leq\frac{C}{|\lambda-\omega|}
  3. R λ ( A ) R_{\lambda}(A)
  4. { λ 𝐂 : | arg ( λ - ω ) | < π 2 + δ } \left\{\lambda\in\mathbf{C}:|\mathrm{arg}(\lambda-\omega)|<\frac{\pi}{2}+% \delta\right\}
  5. exp ( A t ) = 1 2 π i γ e λ t ( λ id - A ) - 1 d λ , \exp(At)=\frac{1}{2\pi i}\int_{\gamma}e^{\lambda t}(\lambda\mathrm{id}-A)^{-1}% \,\mathrm{d}\lambda,
  6. { λ 𝐂 : | arg ( λ - ω ) | θ } , \big\{\lambda\in\mathbf{C}:|\mathrm{arg}(\lambda-\omega)|\leq\theta\big\},

Androst-4-ene-3,17-dione_monooxygenase.html

  1. \rightleftharpoons

Anhydrotetracycline_monooxygenase.html

  1. \rightleftharpoons

ANOVA–simultaneous_component_analysis.html

  1. X = A + B + A B + E X=A+B+AB+E\,
  2. X = T P + E X=TP^{{}^{\prime}}+E\,
  3. A = T a P a + E a A=T_{a}P_{a}^{{}^{\prime}}+E_{a}\,
  4. B = T b P b + E b B=T_{b}P_{b}^{{}^{\prime}}+E_{b}\,
  5. A B = T a b P a b + E a b AB=T_{ab}P_{ab}^{{}^{\prime}}+E_{ab}\,
  6. E = T e P e + E e E=T_{e}P_{e}^{{}^{\prime}}+E_{e}\,
  7. X = A + B + A B + E X=A+B+AB+E\,
  8. X = T a P a + T b P b + T a b P a b + T e P e + E a + E b + E a b + E e + E X=T_{a}P_{a}^{{}^{\prime}}+T_{b}P_{b}^{{}^{\prime}}+T_{ab}P_{ab}^{{}^{\prime}}% +T_{e}P_{e}^{{}^{\prime}}+E_{a}+E_{b}+E_{ab}+E_{e}+E\,

Anthocyanidin_reductase.html

  1. \rightleftharpoons

Anthranilate_1,2-dioxygenase_(deaminating,_decarboxylating).html

  1. \rightleftharpoons

Anthranilate_3-monooxygenase.html

  1. \rightleftharpoons

Anthranilate_3-monooxygenase_(deaminating).html

  1. \rightleftharpoons

Anthranilate_N-methyltransferase.html

  1. \rightleftharpoons

Anthranilate_synthase.html

  1. \rightleftharpoons
  2. \rightleftharpoons

Anthraniloyl-CoA_monooxygenase.html

  1. \rightleftharpoons

Anti-symmetric_operator.html

  1. S 2 S^{2}
  2. S z S_{z}
  3. S 2 | s , m = s ( s + 1 ) 2 | s , m S^{2}|s,m\rangle=s(s+1)\hbar^{2}|s,m\rangle
  4. S z | s , m = m | s , m S_{z}|s,m\rangle=m\hbar|s,m\rangle
  5. [ S x , S y ] = i S z [S_{x},S_{y}]=i\hbar S_{z}
  6. [ S y , S z ] = i S x [S_{y},S_{z}]=i\hbar S_{x}
  7. [ S z , S x ] = i S y [S_{z},S_{x}]=i\hbar S_{y}
  8. S + S_{+}
  9. S - S_{-}
  10. S + = S x + i S y S_{+}=S_{x}+i\cdot S_{y}
  11. S - = S x - i S y S_{-}=S_{x}-i\cdot S_{y}
  12. S + | s , m = s ( s + 1 ) - m ( m + 1 ) | s , m + 1 S_{+}|s,m\rangle=\hbar\sqrt{s(s+1)-m(m+1)}|s,m+1\rangle
  13. S - | s , m = s ( s + 1 ) - m ( m - 1 ) | s , m - 1 S_{-}|s,m\rangle=\hbar\sqrt{s(s+1)-m(m-1)}|s,m-1\rangle
  14. S + S_{+}
  15. S + | + = 0 S_{+}|+\rangle=0
  16. S + | - = | + S_{+}|-\rangle=\hbar|+\rangle
  17. S - S_{-}
  18. S - | - = 0 S_{-}|-\rangle=0
  19. S - | + = | - S_{-}|+\rangle=\hbar|-\rangle
  20. [ S + ] = [ + | S + | + + | S + | - - | S + | + - | S + | - ] = [ 0 1 0 0 ] [S_{+}]=\begin{bmatrix}\langle+|S_{+}|+\rangle&\langle+|S_{+}|-\rangle\\ \langle-|S_{+}|+\rangle&\langle-|S_{+}|-\rangle\end{bmatrix}=\hbar\cdot\begin{% bmatrix}0&1\\ 0&0\end{bmatrix}
  21. [ S - ] = [ + | S - | + + | S - | - - | S - | + - | S - | - ] = [ 0 0 1 0 ] [S_{-}]=\begin{bmatrix}\langle+|S_{-}|+\rangle&\langle+|S_{-}|-\rangle\\ \langle-|S_{-}|+\rangle&\langle-|S_{-}|-\rangle\end{bmatrix}=\hbar\cdot\begin{% bmatrix}0&0\\ 1&0\end{bmatrix}
  22. S x S_{x}
  23. S y S_{y}
  24. [ S x ] = 2 [ 0 1 1 0 ] [S_{x}]=\frac{\hbar}{2}\cdot\begin{bmatrix}0&1\\ 1&0\end{bmatrix}
  25. [ S y ] = 2 [ 0 - i i 0 ] [S_{y}]=\frac{\hbar}{2}\cdot\begin{bmatrix}0&-i\\ i&0\end{bmatrix}
  26. Δ ψ A Δ ψ B 1 2 | [ A , B ] ψ | \Delta_{\psi}A\,\Delta_{\psi}B\geq\frac{1}{2}\left|\left\langle\left[{A},{B}% \right]\right\rangle_{\psi}\right|
  27. S x S_{x}
  28. S y S_{y}
  29. Δ ψ S x Δ ψ S y 1 2 | [ S x , S y ] ψ | = 1 2 ( i S z ) = 2 S z \Delta_{\psi}S_{x}\,\Delta_{\psi}S_{y}\geq\frac{1}{2}\left|\left\langle\left[{% S_{x}},{S_{y}}\right]\right\rangle_{\psi}\right|=\frac{1}{2}(i\hbar S_{z})=% \frac{\hbar}{2}S_{z}
  30. S 2 S^{2}
  31. S z S_{z}
  32. ε i j k = { + 1 if ( i , j , k , , ) is an even permutation of ( 1 , 2 , 3 , 4 , ) - 1 if ( i , j , k , , ) is an odd permutation of ( 1 , 2 , 3 , 4 , ) 0 if any two labels are the same \varepsilon_{ijk\ell\dots}=\left\{\begin{matrix}+1&\mbox{if }~{}(i,j,k,\ell,% \dots)\mbox{ is an even permutation of }~{}(1,2,3,4,\dots)\\ -1&\mbox{if }~{}(i,j,k,\ell,\dots)\mbox{ is an odd permutation of }~{}(1,2,3,4% ,\dots)\\ 0&\mbox{if any two labels are the same}\end{matrix}\right.
  33. [ S i , S j ] = i S k ε i j k [S_{i},S_{j}]=i\hbar S_{k}\varepsilon_{ijk}
  34. S 2 S^{2}
  35. S 2 = m = 1 n S m 2 S^{2}=\sum_{m=1}^{n}S_{m}^{2}
  36. S 2 | s , m s ( s + 1 ) 2 | s , m Align g t ; S^{2}|s,m>=s(s+1)\hbar^{2}|s,m&gt;
  37. [ a i , a j ] = [ a i , a j ] = 0 [a_{i},a_{j}]=[a^{\dagger}_{i},a^{\dagger}_{j}]=0
  38. [ a i , a i ] = f | g [a_{i},a^{\dagger}_{i}]=\langle f|g\rangle
  39. | ϕ 1 , | ϕ 2 , | ϕ 3 |\phi_{1}\rangle,|\phi_{2}\rangle,|\phi_{3}\rangle
  40. 1 3 [ | ϕ 1 | ϕ 2 | ϕ 2 + | ϕ 2 | ϕ 1 | ϕ 2 + | ϕ 2 | ϕ 2 | ϕ 1 ] . \frac{1}{\sqrt{3}}\left[|\phi_{1}\rangle|\phi_{2}\rangle|\phi_{2}\rangle+|\phi% _{2}\rangle|\phi_{1}\rangle|\phi_{2}\rangle+|\phi_{2}\rangle|\phi_{2}\rangle|% \phi_{1}\rangle\right].
  41. | 1 , 2 , 0 , 0 , 0 , , |1,2,0,0,0,\cdots\rangle,
  42. a 2 a_{2}
  43. a 2 a_{2}^{\dagger}
  44. a 2 | N 1 , N 2 , N 3 , = N 2 N 1 , ( N 2 - 1 ) , N 3 , , a_{2}|N_{1},N_{2},N_{3},\cdots\rangle=\sqrt{N_{2}}\mid N_{1},(N_{2}-1),N_{3},% \cdots\rangle,
  45. a 2 | N 1 , N 2 , N 3 , = N 2 + 1 N 1 , ( N 2 + 1 ) , N 3 , . a_{2}^{\dagger}|N_{1},N_{2},N_{3},\cdots\rangle=\sqrt{N_{2}+1}\mid N_{1},(N_{2% }+1),N_{3},\cdots\rangle.
  46. a i a_{i}
  47. a i a_{i}^{\dagger}
  48. S i + S_{i}^{+}
  49. S i - S_{i}^{-}
  50. a i a_{i}
  51. a i a_{i}^{\dagger}
  52. S i + S_{i}^{+}
  53. S i - S_{i}^{-}
  54. 1 2 \frac{1}{2}
  55. | 1 , i x , 0 , 0 , 0 , , |1,ix,0,0,0,\cdots\rangle,
  56. | 1 , - i x , 0 , 0 , 0 , , |1,-ix,0,0,0,\cdots\rangle,
  57. S i + S_{i}+
  58. S i - S_{i}-
  59. S + S_{+}
  60. S - S_{-}

Antony_Valentini.html

  1. ρ ( x , y , z , t ) = | ψ ( x , y , z , t ) | 2 \rho(x,y,z,t)=|\psi(x,y,z,t)|^{2}
  2. ρ ( x , y , z , t ) \rho(x,y,z,t)
  3. | ψ ( x , y , z , t ) | 2 |\psi(x,y,z,t)|^{2}
  4. ρ ( x , y , z , t ) \rho(x,y,z,t)
  5. | ψ ( x , y , z , t ) | 2 |\psi(x,y,z,t)|^{2}
  6. 1 / 2 1/2

Apigenin_4'-O-methyltransferase.html

  1. \rightleftharpoons

Apiose_1-reductase.html

  1. \rightleftharpoons

Apo-beta-carotenoid-14',13'-dioxygenase.html

  1. \rightleftharpoons

Appleton–Hartree_equation.html

  1. n 2 = ( c k ω ) 2 n^{2}=\left(\frac{ck}{\omega}\right)^{2}
  2. n 2 = 1 - X 1 - i Z - 1 2 Y 2 sin 2 θ 1 - X - i Z ± 1 1 - X - i Z ( 1 4 Y 4 sin 4 θ + Y 2 cos 2 θ ( 1 - X - i Z ) 2 ) 1 / 2 n^{2}=1-\frac{X}{1-iZ-\frac{\frac{1}{2}Y^{2}\sin^{2}\theta}{1-X-iZ}\pm\frac{1}% {1-X-iZ}\left(\frac{1}{4}Y^{4}\sin^{4}\theta+Y^{2}\cos^{2}\theta\left(1-X-iZ% \right)^{2}\right)^{1/2}}
  3. n 2 = 1 - X ( 1 - X ) 1 - X - 1 2 Y 2 sin 2 θ ± ( ( 1 2 Y 2 sin 2 θ ) 2 + ( 1 - X ) 2 Y 2 cos 2 θ ) 1 / 2 n^{2}=1-\frac{X\left(1-X\right)}{1-X-{\frac{1}{2}Y^{2}\sin^{2}\theta}\pm\left(% \left(\frac{1}{2}Y^{2}\sin^{2}\theta\right)^{2}+\left(1-X\right)^{2}Y^{2}\cos^% {2}\theta\right)^{1/2}}
  4. n n
  5. i i
  6. - 1 \sqrt{-1}
  7. X = ω 0 2 ω 2 X=\frac{\omega_{0}^{2}}{\omega^{2}}
  8. Y = ω H ω Y=\frac{\omega_{H}}{\omega}
  9. Z = ν ω Z=\frac{\nu}{\omega}
  10. ν \nu
  11. ω = 2 π f \omega=2\pi f
  12. f f
  13. ω 0 = 2 π f 0 = N e 2 ϵ 0 m \omega_{0}=2\pi f_{0}=\sqrt{\frac{Ne^{2}}{\epsilon_{0}m}}
  14. ω H = 2 π f H = B 0 | e | m \omega_{H}=2\pi f_{H}=\frac{B_{0}|e|}{m}
  15. ϵ 0 \epsilon_{0}
  16. B 0 B_{0}
  17. e e
  18. m m
  19. θ \theta
  20. ± \pm
  21. k B 0 k\perp B_{0}
  22. k B 0 k\parallel B_{0}
  23. k k
  24. ν \nu
  25. ω \omega
  26. ν ω \nu\ll\omega
  27. Z = ν ω 1 Z=\frac{\nu}{\omega}\ll 1
  28. Z Z
  29. n 2 = 1 - X 1 - 1 2 Y 2 sin 2 θ 1 - X ± 1 1 - X ( 1 4 Y 4 sin 4 θ + Y 2 cos 2 θ ( 1 - X ) 2 ) 1 / 2 n^{2}=1-\frac{X}{1-\frac{\frac{1}{2}Y^{2}\sin^{2}\theta}{1-X}\pm\frac{1}{1-X}% \left(\frac{1}{4}Y^{4}\sin^{4}\theta+Y^{2}\cos^{2}\theta\left(1-X\right)^{2}% \right)^{1/2}}
  30. θ 0 \theta\approx 0
  31. Y 4 sin 4 θ Y^{4}\sin^{4}\theta
  32. n 2 = 1 - X 1 - 1 2 Y 2 sin 2 θ 1 - X ± Y cos θ n^{2}=1-\frac{X}{1-\frac{\frac{1}{2}Y^{2}\sin^{2}\theta}{1-X}\pm Y\cos\theta}

Aquacobalamin_reductase.html

  1. \rightleftharpoons

Aquacobalamin_reductase_(NADPH).html

  1. \rightleftharpoons

Arabinose-5-phosphate_isomerase.html

  1. \rightleftharpoons

Arabinose_isomerase.html

  1. \rightleftharpoons

Arachidonate_12-lipoxygenase.html

  1. \rightleftharpoons

Arachidonate_8-lipoxygenase.html

  1. \rightleftharpoons

Arginine_2-monooxygenase.html

  1. \rightleftharpoons

Arginine_decarboxylase.html

  1. \rightleftharpoons

Arginine_racemase.html

  1. \rightleftharpoons

Arogenate_dehydrogenase.html

  1. \rightleftharpoons

Arogenate_dehydrogenase_(NAD(P)+).html

  1. \rightleftharpoons

Arogenate_dehydrogenase_(NADP+).html

  1. \rightleftharpoons

Aronszajn_tree.html

  1. 1 \aleph_{1}
  2. 0 \aleph_{0}
  3. 1 \aleph_{1}
  4. 2 \aleph_{2}
  5. 2 \aleph_{2}
  6. 2 \aleph_{2}
  7. n \aleph_{n}

Arrhenius_plot.html

  1. ln ( k ) \ln(k)
  2. 1 / T 1/T
  3. k = A e - E a / R T k=Ae^{-E_{a}/RT}
  4. k = A e - E a / k B T k=Ae^{-E_{a}/k_{B}T}
  5. R R
  6. k B k_{B}
  7. ln ( k ) = ln ( A ) - E a R ( 1 T ) \ln(k)=\ln(A)-\frac{E_{a}}{R}\left(\frac{1}{T}\right)
  8. k k
  9. A A
  10. E a E_{a}
  11. R R
  12. T T
  13. x = 1 / T = 0 x=1/T=0
  14. ln ( A ) \ln(A)
  15. - E a / R -E_{a}/R
  16. e - E a / R T e^{-E_{a}/RT}
  17. ln ( k ) = ln ( A ) - E a R ( 1 T ) \ln(k)=\ln(A)-\frac{E_{a}}{R}\left(\frac{1}{T}\right)
  18. ln ( k ) = 23.1 - 12 , 667 ( 1 / T ) \ln(k)=23.1-12,667(1/T)
  19. k = e 23.1 e - 12 , 667 / T k=e^{23.1}\cdot e^{-12,667/T}
  20. k = 1.08 × 10 10 e - 12 , 667 / T k=1.08\times 10^{10}\cdot e^{-12,667/T}
  21. e e

Arsenate_reductase_(azurin).html

  1. \rightleftharpoons

Arsenate_reductase_(donor).html

  1. \rightleftharpoons

Arsenate_reductase_(glutaredoxin).html

  1. \rightleftharpoons

Arthur_Thomas_Doodson.html

  1. β 1 = τ = ( θ M + π - s ) \beta_{1}=\tau=(\theta_{M}+\pi-s)
  2. β 2 = s = ( F + Ω ) \beta_{2}=s=(F+\Omega)
  3. β 3 = h = ( s - D ) \beta_{3}=h=(s-D)
  4. β 4 = p = ( s - l ) \beta_{4}=p=(s-l)
  5. β 5 = N = ( - Ω ) \beta_{5}=N^{\prime}=(-\Omega)
  6. β 6 = p l \beta_{6}=p_{l}
  7. p s = ( s - D - l ) p_{s}=(s-D-l^{\prime})
  8. l l
  9. l l^{\prime}
  10. F F
  11. D D
  12. l l
  13. l l^{\prime}
  14. F F
  15. D D
  16. T T
  17. N N
  18. 0
  19. h h
  20. 2 h 2h
  21. 3 h 3h
  22. ...
  23. ( N - 1 ) h = T (N-1)h=T
  24. N N
  25. N / 2 N/2
  26. 0
  27. T T
  28. T / 2 T/2
  29. T / 3 T/3
  30. A cos ( ω t + ϕ ) A\cos(\omega t+\phi)
  31. A A
  32. ω \omega
  33. ϕ \phi
  34. A [ 1 + A a cos ( W a t + P a ) ] A[1+A_{a}\cos(W_{a}t+P_{a})]
  35. A a A_{a}
  36. A A
  37. W a W_{a}
  38. P a P_{a}
  39. t = 0 t=0
  40. cos ( a ) cos ( b ) = [ cos ( a + b ) + cos ( a - b ) ] / 2 \cos(a)\cos(b)=[\cos(a+b)+\cos(a-b)]/2
  41. ω \omega
  42. ω + W a \omega+W_{a}
  43. ω - W a \omega-W_{a}
  44. f 1 f_{1}
  45. f 2 f_{2}
  46. f 3 f_{3}
  47. f 4 f_{4}
  48. f 5 f_{5}
  49. f 6 f_{6}
  50. ( f 2 + f 3 - 3. f 5 ) (f_{2}+f_{3}-3.f_{5})
  51. 0. f 1 + 1. f 2 + 1. f 3 + 0. f 4 - 3. f 5 + 0. f 6 0.f_{1}+1.f_{2}+1.f_{3}+0.f_{4}-3.f_{5}+0.f_{6}

Aryl-alcohol_dehydrogenase.html

  1. \rightleftharpoons

Aryl-alcohol_dehydrogenase_(NADP+).html

  1. \rightleftharpoons

Aryl-alcohol_oxidase.html

  1. \rightleftharpoons

Aryl-aldehyde_dehydrogenase.html

  1. \rightleftharpoons

Aryl-aldehyde_dehydrogenase_(NADP+).html

  1. \rightleftharpoons

Aryl-aldehyde_oxidase.html

  1. \rightleftharpoons

Aryl-sulfate_sulfotransferase.html

  1. \rightleftharpoons

Aryl_sulfotransferase.html

  1. \rightleftharpoons

Arylmalonate_decarboxylase.html

  1. \rightleftharpoons

Ascopyrone_tautomerase.html

  1. \rightleftharpoons

Ascorbate_2,3-dioxygenase.html

  1. \rightleftharpoons

Asparagusate_reductase.html

  1. \rightleftharpoons

Aspartate-semialdehyde_dehydrogenase.html

  1. \rightleftharpoons

Aspartate_1-decarboxylase.html

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Aspartate_4-decarboxylase.html

  1. \rightleftharpoons

Aspartate_ammonia-lyase.html

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Aspartate_dehydrogenase.html

  1. \rightleftharpoons

Aspartate_racemase.html

  1. \rightleftharpoons

Asymmetric_norm.html

  1. p ( x ) = { | x | , x 0 ; 2 | x | , x 0 ; p(x)=\begin{cases}|x|,&x\leq 0;\\ 2|x|,&x\geq 0;\end{cases}
  2. p ( x ) = inf { r > 0 : x r K } p(x)=\inf\left\{r>0:x\in rK\right\}\,

Automobile_drag_coefficient.html

  1. 1 2 × a i r d e n s i t y × D r a g A r e a × S p e e d 2 \frac{1}{2}\times airdensity\times DragArea\times Speed^{2}

Automorphisms_of_the_symmetric_and_alternating_groups.html

  1. Aut ( S n ) \operatorname{Aut}(S_{n})
  2. Out ( S n ) \operatorname{Out}(S_{n})
  3. n 2 , 6 n\neq 2,6
  4. S n S_{n}
  5. n = 2 n=2
  6. n = 6 n=6
  7. S 6 C 2 S_{6}\rtimes C_{2}
  8. C 2 C_{2}
  9. Aut ( A n ) \operatorname{Aut}(A_{n})
  10. Out ( A n ) \operatorname{Out}(A_{n})
  11. n 4 , n 6 n\geq 4,n\neq 6
  12. S n S_{n}
  13. C 2 C_{2}
  14. n = 1 , 2 n=1,2
  15. n = 3 n=3
  16. C 2 C_{2}
  17. C 2 C_{2}
  18. n = 6 n=6
  19. S 6 C 2 S_{6}\rtimes C_{2}
  20. V = C 2 × C 2 V=C_{2}\times C_{2}
  21. n 2 , 6 n\neq 2,6
  22. Aut ( S n ) = S n \operatorname{Aut}(S_{n})=S_{n}
  23. Out ( S n ) = 1 \operatorname{Out}(S_{n})=1
  24. S n S_{n}
  25. S n Aut ( S n ) S_{n}\to\operatorname{Aut}(S_{n})
  26. n 2 , 6 n\neq 2,6
  27. Out ( A n ) = S n / A n = C 2 \operatorname{Out}(A_{n})=S_{n}/A_{n}=C_{2}
  28. n 2 , 3 , 6 n\neq 2,3,6
  29. Aut ( A n ) = Aut ( S n ) = S n \operatorname{Aut}(A_{n})=\operatorname{Aut}(S_{n})=S_{n}
  30. S n Aut ( S n ) Aut ( A n ) S_{n}\to\operatorname{Aut}(S_{n})\to\operatorname{Aut}(A_{n})
  31. n = 1 , 2 n=1,2
  32. Aut ( S 1 ) = Out ( S 1 ) = Aut ( A 1 ) = Out ( A 1 ) = 1 \operatorname{Aut}(S_{1})=\operatorname{Out}(S_{1})=\operatorname{Aut}(A_{1})=% \operatorname{Out}(A_{1})=1
  33. Aut ( S 2 ) = Out ( S 2 ) = Aut ( A 2 ) = Out ( A 2 ) = 1 \operatorname{Aut}(S_{2})=\operatorname{Out}(S_{2})=\operatorname{Aut}(A_{2})=% \operatorname{Out}(A_{2})=1
  34. n = 3 n=3
  35. Aut ( A 3 ) = Out ( A 3 ) = S 3 / A 3 = C 2 \operatorname{Aut}(A_{3})=\operatorname{Out}(A_{3})=S_{3}/A_{3}=C_{2}
  36. n = 6 n=6
  37. Out ( S 6 ) = C 2 \operatorname{Out}(S_{6})=C_{2}
  38. Aut ( S 6 ) = S 6 C 2 \operatorname{Aut}(S_{6})=S_{6}\rtimes C_{2}
  39. n = 6 n=6
  40. Out ( A 6 ) = C 2 × C 2 \operatorname{Out}(A_{6})=C_{2}\times C_{2}
  41. Aut ( A 6 ) = Aut ( S 6 ) = S 6 C 2 . \operatorname{Aut}(A_{6})=\operatorname{Aut}(S_{6})=S_{6}\rtimes C_{2}.
  42. \mapsto

Azobenzene_reductase.html

  1. \rightleftharpoons
  2. \rightleftharpoons

Babuška–Lax–Milgram_theorem.html

  1. Λ u = f . \Lambda u=f.
  2. B ( u , v ) = f , v for all v V . B(u,v)=\langle f,v\rangle\mbox{ for all }~{}v\in V.
  3. | B ( u , u ) | c u 2 |B(u,u)|\geq c\|u\|^{2}
  4. { - Δ u ( x ) = f ( x ) , x Ω ; u ( x ) = 0 , x Ω ; \begin{cases}-\Delta u(x)=f(x),&x\in\Omega;\\ u(x)=0,&x\in\partial\Omega;\end{cases}
  5. B ( u , v ) = Ω u ( x ) v ( x ) d x . B(u,v)=\int_{\Omega}\nabla u(x)\cdot\nabla v(x)\,\mathrm{d}x.
  6. Ω u f ( x ) v ( x ) d x = Ω f ( x ) v ( x ) d x for all v H 0 1 ( Ω ) . \int_{\Omega}\nabla u_{f}(x)\cdot\nabla v(x)\,\mathrm{d}x=\int_{\Omega}f(x)v(x% )\,\mathrm{d}x\mbox{ for all }~{}v\in H_{0}^{1}(\Omega).
  7. sup v = 1 | B ( u , v ) | c u \sup_{\|v\|=1}|B(u,v)|\geq c\|u\|
  8. sup u = 1 | B ( u , v ) | > 0 \sup_{\|u\|=1}|B(u,v)|>0
  9. B ( u f , v ) = f , v for all v V . B(u_{f},v)=\langle f,v\rangle\mbox{ for all }~{}v\in V.
  10. u f 1 c f . \|u_{f}\|\leq\frac{1}{c}\|f\|.

Bachmann–Howard_ordinal.html

  1. ϕ ε Ω + 1 ( 0 ) \phi_{\varepsilon_{\Omega+1}}(0)

Banach–Stone_theorem.html

  1. 𝒪 X \mathcal{O}_{X}
  2. | g ( y ) | = 1 for all y Y |g(y)|=1\mbox{ for all }~{}y\in Y
  3. ( T f ) ( y ) = g ( y ) f ( φ ( y ) ) for all y Y , f C ( X ; 𝐑 ) . (Tf)(y)=g(y)f(\varphi(y))\mbox{ for all }~{}y\in Y,f\in C(X;\mathbf{R}).

Banded_waveguide_synthesis.html

  1. y t t = c 2 y x x y_{tt}=c^{2}y_{xx}
  2. c c
  3. c ( ω ) c(\omega)
  4. ω \omega
  5. y t t = k y x x x x y_{tt}=ky_{xxxx}
  6. k k

Base_locus.html

  1. [ D ] [D]
  2. X X
  3. Bl ( [ D ] ) := D eff [ D ] Supp D eff \textrm{Bl}\ ([D]):=\bigcap_{D\text{eff}\in[D]}\textrm{ Supp }\ D\text{eff}
  4. $\textrm{Supp}$
  5. D eff D\text{eff}
  6. [ D ] [D]
  7. $\textrm{Bl}$
  8. [ D ] [D]
  9. X X
  10. C C
  11. X X
  12. C C
  13. [ D ] [D]
  14. D ~ \tilde{D}
  15. C C
  16. [ D ] C 0 [D]\cdot C\geq 0
  17. [ D ] [D]
  18. X X
  19. L [ D ] L_{[D]}
  20. X X
  21. Bl ( [ D ] ) \textrm{Bl}\ ([D])
  22. L [ D ] L_{[D]}

Bayliss_effect.html

  1. M A P = C O * T P R MAP=CO*TPR

BCM_theory.html

  1. d m j ( t ) d t = ϕ ( 𝐜 ( t ) ) d j ( t ) - ϵ m j ( t ) , \,\frac{dm_{j}(t)}{dt}=\phi(\,\textbf{c}(t))d_{j}(t)-\epsilon m_{j}(t),
  2. m j m_{j}
  3. j j
  4. d j d_{j}
  5. 𝐜 \,\textbf{c}
  6. ϕ \phi
  7. θ M \theta_{M}
  8. ϵ \epsilon
  9. m j ˙ = c d j \dot{m_{j}}=cd_{j}
  10. c ( t ) = 𝐦 ( t ) 𝐝 ( t ) c(t)=\,\textbf{m}(t)\cdot\,\textbf{d}(t)
  11. 𝐜 ¯ ( t ) 𝐦 ( t ) d ¯ ( t ) \bar{\,\textbf{c}}(t)\approx\,\textbf{m}(t)\bar{d}(t)
  12. sgn ϕ ( c , c ¯ ) = sgn ( c - ( c ¯ c 0 ) p c ¯ ) for c > 0 , and \,\operatorname{sgn}\phi(c,\bar{c})=\operatorname{sgn}\left(c-\left(\frac{\bar% {c}}{c_{0}}\right)^{p}\bar{c}\right)~{}~{}\textrm{for}~{}c>0,~{}\textrm{and}
  13. ϕ ( 0 , c ¯ ) = 0 for all c ¯ , \,\phi(0,\bar{c})=0~{}~{}\textrm{for}~{}\textrm{all}~{}\bar{c},
  14. θ M ( c ¯ ) = ( c ¯ / c 0 ) p c ¯ \theta_{M}(\bar{c})=(\bar{c}/c_{0})^{p}\bar{c}
  15. p p
  16. c 0 c_{0}
  17. ϕ ( c , c ¯ ) = c ( c - θ M ) and θ M = c 2 = 1 τ - t c 2 ( t ) e - ( t - t ) / τ d t , \,\phi(c,\bar{c})=c(c-\theta_{M})~{}~{}~{}\textrm{and}~{}~{}~{}\theta_{M}=% \langle c^{2}\rangle=\frac{1}{\tau}\int_{-\infty}^{t}c^{2}(t^{\prime})e^{-(t-t% ^{\prime})/\tau}dt^{\prime},
  18. τ \tau
  19. c 0 c_{0}
  20. p p
  21. log ( m closed ( t ) m closed ( 0 ) ) - n 2 ¯ t , \log\left(\frac{m_{\rm closed}(t)}{m_{\rm closed}(0)}\right)\sim-\overline{n^{% 2}}t,
  22. n 2 ¯ \overline{n^{2}}
  23. t t

Behavioral_momentum.html

  1. log ( B x B o ) = - ( f r b ) \log{\left({Bx\over Bo}\right)}\ =\ -\left({f\over r^{b}}\right)
  2. log ( B x 1 / B o 1 ) log ( B x 2 / B o 2 ) = ( r 2 r 1 ) a {{\log(Bx_{1}/Bo_{1})}\over{\log(Bx_{2}/Bo_{2})}}\ =\ \left({r_{2}\over r_{1}}% \right)^{a}

Bell_Laboratories_Layered_Space-Time.html

  1. i \displaystyle i
  2. w k \displaystyle w_{k}

Bending_stiffness.html

  1. K K
  2. E E
  3. I I
  4. K = p w K=\frac{\mathrm{p}}{\mathrm{w}}
  5. p \mathrm{p}
  6. w \mathrm{w}
  7. M M
  8. κ \kappa
  9. M = E I κ = E I d 2 w d x 2 M=EI\kappa=EI\frac{\mathrm{d}^{2}w}{\mathrm{d}x^{2}}
  10. w w
  11. x x

Benesi–Hildebrand_method.html

  1. H + G H G H+G\rightleftharpoons HG
  2. A = A H G + A G + A H A=A^{HG}+A^{G}+A^{H}\,
  3. A = A H G + A G A=A^{HG}+A^{G}\,
  4. Δ A = A - A 0 {\Delta}A=A-A_{0}\,
  5. Δ A = ϵ H G [ H G ] b + ϵ G [ G ] b - ϵ G [ G ] 0 b {\Delta}A=\epsilon^{HG}[HG]b+\epsilon^{G}[G]b-\epsilon^{G}[G]_{0}b\,
  6. Δ A = Δ ϵ [ H G ] b {\Delta}A={\Delta}\epsilon[HG]b\,
  7. [ H G ] = [ H ] 0 K a [ G ] 1 + K a [ G ] [HG]=\frac{[H]_{0}K_{a}[G]}{1+K_{a}[G]}
  8. Δ A = b Δ ϵ [ H ] 0 K a [ G ] 0 1 + K a [ G ] 0 {\Delta}A=b{\Delta}\epsilon{\frac{[H]_{0}K_{a}[G]_{0}}{1+K_{a}[G]_{0}}}
  9. 1 Δ A = 1 b Δ ϵ [ G ] 0 [ H ] 0 K a + 1 b Δ ϵ [ H ] 0 \frac{1}{{\Delta}A}=\frac{1}{b{\Delta}\epsilon[G]_{0}[H]_{0}K_{a}}+\frac{1}{b{% \Delta}\epsilon[H]_{0}}
  10. K - 1 = A ϵ H G - [ H ] 0 - [ G ] 0 + C H C G A ϵ H G K^{-1}=\frac{A}{\epsilon_{HG}}-[H]_{0}-[G]_{0}+\frac{C_{H}C_{G}}{A}\epsilon_{HG}

Benzaldehyde_dehydrogenase_(NAD+).html

  1. \rightleftharpoons

Benzaldehyde_dehydrogenase_(NADP+).html

  1. \rightleftharpoons

Benzene_1,2-dioxygenase.html

  1. \rightleftharpoons

Benzoate_1,2-dioxygenase.html

  1. \rightleftharpoons

Benzoate_4-monooxygenase.html

  1. \rightleftharpoons

Benzoin_aldolase.html

  1. \rightleftharpoons

Benzoyl-CoA_3-monooxygenase.html

  1. \rightleftharpoons

Benzoyl-CoA_reductase.html

  1. \rightleftharpoons

Benzoylformate_decarboxylase.html

  1. \rightleftharpoons

Benzyl-2-methyl-hydroxybutyrate_dehydrogenase.html

  1. \rightleftharpoons

Benzylsuccinate_synthase.html

  1. \rightleftharpoons

Berbamunine_synthase.html

  1. \rightleftharpoons

Berberine_reductase.html

  1. \rightleftharpoons

Berezin_transform.html

  1. ( B f ) ( z ) = D ( 1 - | z | 2 ) 2 | 1 - z w ¯ | 4 f ( w ) dA ( w ) , (Bf)(z)=\int_{D}\frac{(1-|z|^{2})^{2}}{|1-z\bar{w}|^{4}}f(w)\,\mathrm{dA}(w),
  2. w ¯ \overline{w}
  3. d A dA

Berger–Kazdan_comparison_theorem.html

  1. vol ( M ) c m ( inj ( M ) ) π , \mathrm{vol}(M)\geq\frac{c_{m}(\mathrm{inj}(M))}{\pi},

Bessel's_correction.html

  1. 1 n \frac{1}{n}
  2. n n 1 n\frac{n}{− 1}
  3. 1 n 1 1\frac{n}{− 1}
  4. 1 n \frac{1}{n}
  5. n n 1 n\frac{n}{− 1}
  6. ( x 1 - x ¯ , , x n - x ¯ ) , (x_{1}-\overline{x},\,\dots,\,x_{n}-\overline{x}),
  7. x ¯ \overline{x}
  8. 2051 , 2053 , 2055 , 2050 , 2051 2051,\quad 2053,\quad 2055,\quad 2050,\quad 2051\,
  9. 1 5 ( 2051 + 2053 + 2055 + 2050 + 2051 ) = 2052 \frac{1}{5}\left(2051+2053+2055+2050+2051\right)=2052
  10. 1 5 [ ( 2051 - 2050 ) 2 + ( 2053 - 2050 ) 2 + ( 2055 - 2050 ) 2 + ( 2050 - 2050 ) 2 + ( 2051 - 2050 ) 2 ] \displaystyle\frac{1}{5}\left[(2051-2050)^{2}+(2053-2050)^{2}+(2055-2050)^{2}+% (2050-2050)^{2}+(2051-2050)^{2}\right]
  11. 1 5 [ ( 2051 - 2052 ) 2 + ( 2053 - 2052 ) 2 + ( 2055 - 2052 ) 2 + ( 2050 - 2052 ) 2 + ( 2051 - 2052 ) 2 ] \displaystyle\frac{1}{5}\left[(2051-2052)^{2}+(2053-2052)^{2}+(2055-2052)^{2}+% (2050-2052)^{2}+(2051-2052)^{2}\right]
  12. ( a + b ) 2 = a 2 + 2 a b + b 2 (a+b)^{2}=a^{2}+2ab+b^{2}\,
  13. a a
  14. b b
  15. [ 2053 - 2050 Deviation from the population mean ] 2 \displaystyle{[}\,\underbrace{2053-2050}_{\begin{smallmatrix}\,\text{Deviation% from}\\ \,\text{the population}\\ \,\text{mean}\end{smallmatrix}}\,]^{2}
  16. ( 2051 - 2052 ) 2 This is a 2 . \displaystyle\overbrace{(2051-2052)^{2}}^{\,\text{This is }a^{2}.}
  17. x ¯ \overline{x}\,
  18. x ¯ = 1 n i = 1 n x i . \overline{x}=\frac{1}{n}\sum_{i=1}^{n}x_{i}.
  19. s n 2 = 1 n i = 1 n ( x i - x ¯ ) 2 = i = 1 n ( x i 2 ) n - ( i = 1 n x i ) 2 n 2 s_{n}^{2}=\frac{1}{n}\sum_{i=1}^{n}\left(x_{i}-\overline{x}\right)^{2}=\frac{% \sum_{i=1}^{n}\left(x_{i}^{2}\right)}{n}-\frac{\left(\sum_{i=1}^{n}x_{i}\right% )^{2}}{n^{2}}
  20. s 2 = 1 n - 1 i = 1 n ( x i - x ¯ ) 2 = i = 1 n ( x i 2 ) n - 1 - ( i = 1 n x i ) 2 ( n - 1 ) n = ( n n - 1 ) s n 2 . s^{2}=\frac{1}{n-1}\sum_{i=1}^{n}\left(x_{i}-\overline{x}\right)^{2}=\frac{% \sum_{i=1}^{n}\left(x_{i}^{2}\right)}{n-1}-\frac{\left(\sum_{i=1}^{n}x_{i}% \right)^{2}}{(n-1)n}=\left(\frac{n}{n-1}\right)\,s_{n}^{2}.
  21. E [ x 2 ] = μ 2 + σ 2 E[x^{2}]=\mu^{2}+\sigma^{2}
  22. ( x 1 - x 2 ) 2 (x_{1}-x_{2})^{2}
  23. x 1 , x 2 x_{1},x_{2}
  24. E [ x 1 x 2 ] = E [ x 1 ] E [ x 2 ] E[x_{1}x_{2}]=E[x_{1}]E[x_{2}]
  25. E [ ( x 1 - x 2 ) 2 ] = E [ x 1 2 ] - E [ 2 x 1 x 2 ] + E [ x 2 2 ] = ( σ 2 + μ 2 ) - 2 μ 2 + ( σ 2 + μ 2 ) = 2 σ 2 E[(x_{1}-x_{2})^{2}]=E[x_{1}^{2}]-E[2x_{1}x_{2}]+E[x_{2}^{2}]=(\sigma^{2}+\mu^% {2})-2\mu^{2}+(\sigma^{2}+\mu^{2})=2\sigma^{2}
  26. x 1 , , x n x_{1},\ldots,x_{n}
  27. ( n - 1 ) / n (n-1)/n
  28. x u x_{u}
  29. x v x_{v}
  30. n / n 2 = 1 / n n/n^{2}=1/n
  31. 1 - 1 / n 1-1/n
  32. E [ ( x u - x v ) 2 ] E[(x_{u}-x_{v})^{2}]
  33. ( 1 - 1 / n ) (1-1/n)
  34. 1 / ( 1 - 1 / n ) = n / ( n - 1 ) , 1/(1-1/n)=n/(n-1),
  35. i = 1 n ( x i - x ¯ ) 2 = i = 1 n ( x i - 1 n j = 1 n x j ) 2 = i = 1 n x i 2 - n ( 1 n j = 1 n x j ) 2 = i = 1 n x i 2 - n x ¯ 2 \begin{aligned}\displaystyle\sum_{i=1}^{n}\left(x_{i}-\overline{x}\right)^{2}&% \displaystyle=\sum_{i=1}^{n}\left(x_{i}-\frac{1}{n}\sum_{j=1}^{n}x_{j}\right)^% {2}\\ &\displaystyle=\sum_{i=1}^{n}x_{i}^{2}-n\left(\frac{1}{n}\sum_{j=1}^{n}x_{j}% \right)^{2}\\ &\displaystyle=\sum_{i=1}^{n}x_{i}^{2}-n\overline{x}^{2}\end{aligned}
  36. E ( i = 1 n [ x i - μ - ( x ¯ - μ ) ] 2 ) = E ( i = 1 n ( x i - μ ) 2 - n ( x ¯ - μ ) 2 ) = i = 1 n E ( ( x i - μ ) 2 ) - n E ( ( x ¯ - μ ) 2 ) = i = 1 n Var ( x i ) - n Var ( x ¯ ) \begin{aligned}\displaystyle\operatorname{E}\left(\sum_{i=1}^{n}\left[x_{i}-% \mu-\left(\overline{x}-\mu\right)\right]^{2}\right)&\displaystyle=% \operatorname{E}\left(\sum_{i=1}^{n}(x_{i}-\mu)^{2}-n(\overline{x}-\mu)^{2}% \right)\\ &\displaystyle=\sum_{i=1}^{n}\operatorname{E}\left((x_{i}-\mu)^{2}\right)-n% \operatorname{E}\left((\overline{x}-\mu)^{2}\right)\\ &\displaystyle=\sum_{i=1}^{n}\operatorname{Var}\left(x_{i}\right)-n% \operatorname{Var}\left(\overline{x}\right)\end{aligned}
  37. E ( s 2 ) = E ( i = 1 n ( x i - x ¯ ) 2 n - 1 ) = 1 n - 1 E ( i = 1 n [ x i - μ - ( x ¯ - μ ) ] 2 ) = 1 n - 1 [ i = 1 n Var ( x i ) - n Var ( x ¯ ) ] \begin{aligned}\displaystyle\operatorname{E}(s^{2})&\displaystyle=% \operatorname{E}\left(\sum_{i=1}^{n}\frac{(x_{i}-\overline{x})^{2}}{n-1}\right% )\\ &\displaystyle=\frac{1}{n-1}\operatorname{E}\left(\sum_{i=1}^{n}\left[x_{i}-% \mu-\left(\overline{x}-\mu\right)\right]^{2}\right)\\ &\displaystyle=\frac{1}{n-1}\left[\sum_{i=1}^{n}\operatorname{Var}\left(x_{i}% \right)-n\operatorname{Var}\left(\overline{x}\right)\right]\end{aligned}
  38. Var ( x i ) = σ 2 \operatorname{Var}(x_{i})=\sigma^{2}
  39. Var ( x ¯ ) = σ 2 / n \operatorname{Var}(\overline{x})=\sigma^{2}/n
  40. E ( s 2 ) = 1 n - 1 [ i = 1 n σ 2 - n σ 2 / n ] = 1 n - 1 ( n σ 2 - σ 2 ) = σ 2 . \operatorname{E}(s^{2})=\frac{1}{n-1}\left[\sum_{i=1}^{n}\sigma^{2}-n\sigma^{2% }/n\right]=\frac{1}{n-1}(n\sigma^{2}-\sigma^{2})=\sigma^{2}.\,
  41. E [ σ 2 - s b i a s e d 2 ] = E [ 1 n i = 1 n ( x i - μ ) 2 - 1 n i = 1 n ( x i - x ¯ ) 2 ] = 1 n E [ i = 1 n ( ( x i 2 - 2 x i μ + μ 2 ) - ( x i 2 - 2 x i x ¯ + x ¯ 2 ) ) ] = E [ μ 2 - 2 x ¯ μ + x ¯ 2 ] = E [ ( x ¯ - μ ) 2 ] = Var ( x ¯ ) = σ 2 n \begin{aligned}\displaystyle E\left[\sigma^{2}-s_{biased}^{2}\right]&% \displaystyle=E\left[\frac{1}{n}\sum_{i=1}^{n}(x_{i}-\mu)^{2}-\frac{1}{n}\sum_% {i=1}^{n}(x_{i}-\overline{x})^{2}\right]\\ &\displaystyle=\frac{1}{n}E\left[\sum_{i=1}^{n}\left((x_{i}^{2}-2x_{i}\mu+\mu^% {2})-(x_{i}^{2}-2x_{i}\overline{x}+\overline{x}^{2})\right)\right]\\ &\displaystyle=E\left[\mu^{2}-2\overline{x}\mu+\overline{x}^{2}\right]\\ &\displaystyle=E\left[(\overline{x}-\mu)^{2}\right]\\ &\displaystyle=\,\text{Var}(\overline{x})\\ &\displaystyle=\frac{\sigma^{2}}{n}\end{aligned}
  42. E [ s biased 2 ] = σ 2 - σ 2 n = n - 1 n σ 2 \operatorname{E}\left[s^{2}_{\,\text{biased}}\right]=\sigma^{2}-\frac{\sigma^{% 2}}{n}=\frac{n-1}{n}\sigma^{2}
  43. s unbiased 2 = n n - 1 s biased 2 s_{\,\text{unbiased}}^{2}=\frac{n}{n-1}s_{\,\text{biased}}^{2}

Beta-alanopine_dehydrogenase.html

  1. \rightleftharpoons

Beta-alanyl-CoA_ammonia-lyase.html

  1. \rightleftharpoons

Beta-cyclopiazonate_dehydrogenase.html

  1. \rightleftharpoons

Beta-diketone_hydrolase.html

  1. \rightleftharpoons

Beta-lysine_5,6-aminomutase.html

  1. \rightleftharpoons

Beta-nitroacrylate_reductase.html

  1. \rightleftharpoons

Beta-phosphoglucomutase.html

  1. \rightleftharpoons

Betaine-aldehyde_dehydrogenase.html

  1. \rightleftharpoons

Betaine_reductase.html

  1. \rightleftharpoons

Beurling–Lax_theorem.html

  1. H 2 ( 𝔻 , ) H^{2}(\mathbb{D},\mathbb{C})
  2. θ H 2 ( 𝔻 , ) , \theta H^{2}(\mathbb{D},\mathbb{C}),
  3. θ \theta

Bhaskara's_lemma.html

  1. N x 2 + k = y 2 N ( m x + y k ) 2 + m 2 - N k = ( m y + N x k ) 2 \,Nx^{2}+k=y^{2}\implies\,N\left(\frac{mx+y}{k}\right)^{2}+\frac{m^{2}-N}{k}=% \left(\frac{my+Nx}{k}\right)^{2}
  2. m , x , y , N , m,\,x,\,y,\,N,
  3. k k
  4. m 2 - N m^{2}-N
  5. N 2 x 2 + 2 N m x y + N y 2 N^{2}x^{2}+2Nmxy+Ny^{2}
  6. k 2 k^{2}
  7. N x 2 + k = y 2 N m 2 x 2 - N 2 x 2 + k ( m 2 - N ) = m 2 y 2 - N y 2 \,Nx^{2}+k=y^{2}\implies Nm^{2}x^{2}-N^{2}x^{2}+k(m^{2}-N)=m^{2}y^{2}-Ny^{2}
  8. N m 2 x 2 + 2 N m x y + N y 2 + k ( m 2 - N ) = m 2 y 2 + 2 N m x y + N 2 x 2 \implies Nm^{2}x^{2}+2Nmxy+Ny^{2}+k(m^{2}-N)=m^{2}y^{2}+2Nmxy+N^{2}x^{2}
  9. N ( m x + y ) 2 + k ( m 2 - N ) = ( m y + N x ) 2 \implies N(mx+y)^{2}+k(m^{2}-N)=(my+Nx)^{2}
  10. N ( m x + y k ) 2 + m 2 - N k = ( m y + N x k ) 2 . \implies\,N\left(\frac{mx+y}{k}\right)^{2}+\frac{m^{2}-N}{k}=\left(\frac{my+Nx% }{k}\right)^{2}.
  11. k k
  12. m 2 - N m^{2}-N

Bicentric_polygon.html

  1. 1 R - x + 1 R + x = 1 r \frac{1}{R-x}+\frac{1}{R+x}=\frac{1}{r}
  2. R > r R>r
  3. 1 ( R - x ) 2 + 1 ( R + x ) 2 = 1 r 2 \frac{1}{(R-x)^{2}}+\frac{1}{(R+x)^{2}}=\frac{1}{r^{2}}
  4. n = 5 : r ( R - x ) = ( R + x ) ( R - r + x ) ( R - r - x ) + ( R + x ) 2 R ( R - r - x ) , n=5:\quad r(R-x)=(R+x)\sqrt{(R-r+x)(R-r-x)}+(R+x)\sqrt{2R(R-r-x)},
  5. n = 6 : 3 ( R 2 - x 2 ) 4 = 4 r 2 ( R 2 + x 2 ) ( R 2 - x 2 ) 2 + 16 r 4 x 2 R 2 , n=6:\quad 3(R^{2}-x^{2})^{4}=4r^{2}(R^{2}+x^{2})(R^{2}-x^{2})^{2}+16r^{4}x^{2}% R^{2},
  6. n = 8 : 16 p 4 q 4 ( p 2 - 1 ) ( q 2 - 1 ) = ( p 2 + q 2 - p 2 q 2 ) 4 , n=8:\quad 16p^{4}q^{4}(p^{2}-1)(q^{2}-1)=(p^{2}+q^{2}-p^{2}q^{2})^{4},
  7. p = R + x r p=\tfrac{R+x}{r}
  8. q = R - x r . q=\tfrac{R-x}{r}.
  9. R = a 2 sin π n = r cos π n . R=\frac{a}{2\sin\frac{\pi}{n}}=\frac{r}{\cos\frac{\pi}{n}}.
  10. n n\!\,
  11. R and a R\,\,\text{and}\,a\!\,
  12. r and a r\,\,\text{and}\,a\!\,
  13. r and R r\,\,\text{and}\,R\!\,
  14. R 3 = a R\sqrt{3}=a\!\,
  15. 2 r = a 3 3 2r=\frac{a}{3}\sqrt{3}\!\,
  16. 2 r = R 2r=R\!\,
  17. R 2 = a R\sqrt{2}=a\!\,
  18. r = a 2 r=\frac{a}{2}\!\,
  19. 2 r = R 2 2r=R\sqrt{2}\!\,
  20. R 5 - 5 2 = a R\sqrt{\frac{5-\sqrt{5}}{2}}=a\!\,
  21. r ( 5 - 1 ) = a 10 50 + 10 5 r\left(\sqrt{5}-1\right)=\frac{a}{10}\sqrt{50+10\sqrt{5}}\!\,
  22. r ( 5 - 1 ) = R r(\sqrt{5}-1)=R\!\,
  23. R = a R=a\!\,
  24. 2 r 3 3 = a \frac{2r}{3}\sqrt{3}=a\!\,
  25. 2 r 3 3 = R \frac{2r}{3}\sqrt{3}=R\!\,
  26. R 2 + 2 = a ( 2 + 1 ) R\sqrt{2+\sqrt{2}}=a\left(\sqrt{2}+1\right)\!\,
  27. r 4 - 2 2 = a 2 4 + 2 2 r\sqrt{4-2\sqrt{2}}=\frac{a}{2}\sqrt{4+2\sqrt{2}}\!\,
  28. 2 r ( 2 - 1 ) = R 2 - 2 2r\left(\sqrt{2}-1\right)=R\sqrt{2-\sqrt{2}}\!\,
  29. ( 5 - 1 ) R = 2 a (\sqrt{5}-1)R=2a\!\,
  30. 2 r 25 - 10 5 = 5 a 2r\sqrt{25-10\sqrt{5}}=5a\!\,
  31. 2 r 5 25 - 10 5 = R 2 ( 5 - 1 ) \frac{2r}{5}\sqrt{25-10\sqrt{5}}=\frac{R}{2}\left(\sqrt{5}-1\right)\!\,
  32. n n\!\,
  33. R / a R/a\!\,
  34. r / a r/a\!\,
  35. R / r R/r\!\,
  36. 3 3\,
  37. 0.577 0.577\,
  38. 0.289 0.289
  39. 2.000 2.000\,
  40. 4 4
  41. 0.707 0.707\,
  42. 0.500 0.500
  43. 1.414 1.414\,
  44. 5 5
  45. 0.851 0.851\,
  46. 0.688 0.688
  47. 1.236 1.236\,
  48. 6 6
  49. 1.000 1.000\,
  50. 0.866 0.866
  51. 1.155 1.155\,
  52. 8 8
  53. 1.307 1.307\,
  54. 1.207 1.207
  55. 1.082 1.082\,
  56. 10 10
  57. 1.618 1.618\,
  58. 1.539 1.539
  59. 1.051 1.051\,

Bicircular_matroid.html

  1. p B ( G ) ( λ ) := k = 0 n ( - 1 ) k f k ( λ - 1 ) n - k , p_{B(G)}(\lambda):=\sum_{k=0}^{n}(-1)^{k}f_{k}(\lambda-1)^{n-k},

Bilirubin_oxidase.html

  1. \rightleftharpoons

Biochanin-A_reductase.html

  1. \rightleftharpoons

Biological_exponential_growth.html

  1. d N / d t = ( b - d ) N dN/dt=(b-d)N

Biotin_synthase.html

  1. \rightleftharpoons

Biphenyl-2,3-diol_1,2-dioxygenase.html

  1. \rightleftharpoons

Biphenyl_2,3-dioxygenase.html

  1. \rightleftharpoons

Bipolar_transistor_biasing.html

  1. R B R_{\,\text{B}}
  2. V cc V_{\,\text{cc}}
  3. R C R_{\,\text{C}}
  4. V R b V_{\,\text{R}_{\,\text{b}}}
  5. R b R_{\,\text{b}}
  6. V R b = V cc - ( I c + I b ) R c Voltage drop across R c - V be Voltage at base . V_{\,\text{R}_{\,\text{b}}}=V_{\,\text{cc}}\,-\,\mathord{\overbrace{(I_{\,% \text{c}}+I_{\,\text{b}})R_{\,\text{c}}}^{\,\text{Voltage drop across }R_{\,% \text{c}}}}\,-\,\mathord{\overbrace{V_{\,\text{be}}}^{\,\text{Voltage at base}% }}.
  7. I c = β I b I_{\,\text{c}}=\beta I_{\,\text{b}}
  8. V R b = V cc - ( β I b I c + I b ) R c - V be = V cc - I b ( β + 1 ) R c - V be . V_{\,\text{R}_{\,\text{b}}}=V_{\,\text{cc}}-(\overbrace{\beta I_{\,\text{b}}}^% {I_{\,\text{c}}}+I_{\,\text{b}})R_{\,\text{c}}-V_{\,\text{be}}=V_{\,\text{cc}}% -I_{\,\text{b}}(\beta+1)R_{\,\text{c}}-V_{\,\text{be}}.
  9. I b = V R b / R b I_{\,\text{b}}=V_{\,\text{R}_{\,\text{b}}}/R_{\,\text{b}}
  10. I b R b V R b = V cc - I b ( β + 1 ) R c - V be . \overbrace{I_{\,\text{b}}R_{\,\text{b}}}^{V_{\,\text{R}_{\,\text{b}}}}=V_{\,% \text{cc}}-I_{\,\text{b}}(\beta+1)R_{\,\text{c}}-V_{\,\text{be}}.
  11. I b I_{\,\text{b}}
  12. I b = V cc - V be R b + ( β + 1 ) R c I_{\,\text{b}}=\frac{V_{\,\text{cc}}-V_{\,\text{be}}}{R_{\,\text{b}}+(\beta+1)% R_{\,\text{c}}}
  13. V be V_{\,\text{be}}
  14. I c I_{\,\text{c}}
  15. I c I_{\,\text{c}}
  16. R c R_{\,\text{c}}
  17. V R b V_{\,\text{R}_{\,\text{b}}}
  18. R b R_{\,\text{b}}
  19. I b I_{\,\text{b}}
  20. I c I_{\,\text{c}}
  21. V cc V_{\,\text{cc}}
  22. V cc V_{\,\text{cc}}
  23. R b R_{\,\text{b}}
  24. I c I_{\,\text{c}}
  25. β \beta
  26. I c = β I b = β ( V cc - V be ) R b + R c + β R c ( V cc - V be ) R c I_{\,\text{c}}=\beta I_{\,\text{b}}=\frac{\beta(V_{\,\text{cc}}-V_{\,\text{be}% })}{R_{\,\text{b}}+R_{\,\text{c}}+\beta R_{\,\text{c}}}\approx\frac{(V_{\,% \text{cc}}-V_{\,\text{be}})}{R_{\,\text{c}}}
  27. β R c R b . \beta R_{\,\text{c}}\gg R_{\,\text{b}}.
  28. β \beta
  29. R c R_{\,\text{c}}
  30. R b R_{\,\text{b}}
  31. R c R_{\,\text{c}}
  32. V cc V_{\,\text{cc}}
  33. R b R_{\,\text{b}}
  34. R b R_{\,\text{b}}
  35. V R b = V C C - I e R e - V b e V_{R_{b}}=V_{CC}-I_{e}R_{e}-V_{be}
  36. I b = V R b R b I_{b}=\frac{V_{R_{b}}}{R_{b}}
  37. I B = V C C - V b e R B + ( β + 1 ) R E I_{B}=\frac{V_{CC}-V_{be}}{R_{B}+(\beta+1)R_{E}}
  38. I C = β I B = β ( V C C - V b e ) R B + ( β + 1 ) R E ( V C C - V b e ) R E I_{C}=\beta I_{B}=\frac{\beta(V_{CC}-V_{be})}{R_{B}+(\beta+1)R_{E}}\approx% \frac{(V_{CC}-V_{be})}{R_{E}}
  39. ( β + 1 ) R E R B (\beta+1)R_{E}\gg R_{B}
  40. V B = V_{B}=
  41. R 2 R_{2}
  42. = V c c R 2 ( R 1 + R 2 ) - I B R 1 R 2 ( R 1 + R 2 ) =V_{cc}\frac{R_{2}}{(R_{1}+R_{2})}-I_{B}\frac{R_{1}R_{2}}{(R_{1}+R_{2})}
  43. V c c R 2 ( R 1 + R 2 ) \approx V_{cc}\frac{R_{2}}{(R_{1}+R_{2})}
  44. I B I 2 = V B / R 2 I_{B}<<I_{2}=V_{B}/R_{2}
  45. V B = V b e + I E R E V_{B}=V_{be}+I_{E}R_{E}
  46. I B = V C C 1 + R 1 / R 2 - V b e ( β + 1 ) R E + R 1 R 2 . I_{B}=\frac{\frac{V_{CC}}{1+R_{1}/R_{2}}-V_{be}}{(\beta+1)R_{E}+R_{1}\parallel R% _{2}}.
  47. I C = β I B = β V C C 1 + R 1 / R 2 - V b e ( β + 1 ) R E + R 1 R 2 V C C 1 + R 1 / R 2 - V b e R E , I_{C}=\beta I_{B}=\beta\frac{\frac{V_{CC}}{1+R_{1}/R_{2}}-V_{be}}{(\beta+1)R_{% E}+R_{1}\parallel R_{2}}\approx\frac{\frac{V_{CC}}{1+R_{1}/R_{2}}-V_{be}}{R_{E% }},
  48. ( β + 1 ) R E R 1 R 2 (\beta+1)R_{E}>>R_{1}\parallel R_{2}
  49. R c / R e R_{\,\text{c}}/R_{\,\text{e}}

Bis-gamma-glutamylcystine_reductase.html

  1. \rightleftharpoons

Bisymmetric_matrix.html

  1. [ a b c d e b f g h d c g i g c d h g f b e d c b a ] . \begin{bmatrix}a&b&c&d&e\\ b&f&g&h&d\\ c&g&i&g&c\\ d&h&g&f&b\\ e&d&c&b&a\end{bmatrix}.

Bleach.html

  1. \rightleftharpoons

Bloch_spectrum.html

  1. H = - d 2 d x 2 + U α , H=-\frac{d^{2}}{dx^{2}}+U_{\alpha},

Boat_rigging.html

  1. G = 2 ( O A - I B ) S G=\frac{2(OA-IB)}{S}
  2. G = ( O A - I B ) S G=\frac{(OA-IB)}{S}
  3. O A OA
  4. I B IB
  5. S S

Bochner_identity.html

  1. 1 2 Δ ( | u | 2 ) = | ( d u ) | 2 + Ric M u , u - Riem N ( u ) ( u , u ) u , u . \frac{1}{2}\Delta\big(|\nabla u|^{2}\big)=\big|\nabla(\mathrm{d}u)\big|^{2}+% \big\langle\mathrm{Ric}_{M}\nabla u,\nabla u\big\rangle-\big\langle\mathrm{% Riem}_{N}(u)(\nabla u,\nabla u)\nabla u,\nabla u\big\rangle.

Bornyl_diphosphate_synthase.html

  1. \rightleftharpoons

Bramble–Hilbert_lemma.html

  1. u \textstyle u
  2. m - 1 \textstyle m-1
  3. u \textstyle u
  4. m \textstyle m
  5. u \textstyle u
  6. L p \textstyle L^{p}
  7. n \textstyle\mathbb{R}^{n}
  8. u \textstyle u
  9. u \textstyle u
  10. u \textstyle u
  11. u \textstyle u
  12. m - 1 \textstyle m-1
  13. u \textstyle u
  14. m \textstyle m
  15. u \textstyle u
  16. m \textstyle m
  17. ( a , b ) \textstyle\left(a,b\right)
  18. inf v P m - 1 u ( k ) - v ( k ) L p ( a , b ) C ( m ) ( b - a ) m - k u ( m ) L p ( a , b ) , \inf_{v\in P_{m-1}}\bigl\|u^{\left(k\right)}-v^{\left(k\right)}\bigr\|_{L^{p}% \left(a,b\right)}\leq C\left(m\right)\left(b-a\right)^{m-k}\bigl\|u^{\left(m% \right)}\bigr\|_{L^{p}\left(a,b\right)},
  19. P m - 1 \textstyle P_{m-1}
  20. m - 1 \textstyle m-1
  21. p = \textstyle p=\infty
  22. m = 2 \textstyle m=2
  23. k = 0 \textstyle k=0
  24. u \textstyle u
  25. v \textstyle v
  26. x ( a , b ) \textstyle x\in\left(a,b\right)
  27. | u ( x ) - v ( x ) | C ( b - a ) 2 sup ( a , b ) | u ′′ | . \left|u\left(x\right)-v\left(x\right)\right|\leq C\left(b-a\right)^{2}\sup_{% \left(a,b\right)}\left|u^{\prime\prime}\right|.
  28. v \textstyle v
  29. u \textstyle u
  30. Ω \textstyle\Omega
  31. n \textstyle\mathbb{R}^{n}
  32. n 1 \textstyle n\geq 1
  33. Ω \textstyle\partial\Omega
  34. d \textstyle d
  35. W p k ( Ω ) \textstyle W_{p}^{k}(\Omega)
  36. u \textstyle u
  37. Ω \textstyle\Omega
  38. D α u \textstyle D^{\alpha}u
  39. | α | \textstyle\left|\alpha\right|
  40. k \textstyle k
  41. L p ( Ω ) \textstyle L^{p}(\Omega)
  42. α = ( α 1 , α 2 , , α n ) \textstyle\alpha=\left(\alpha_{1},\alpha_{2},\ldots,\alpha_{n}\right)
  43. | α | = \textstyle\left|\alpha\right|=
  44. α 1 + α 2 + + α n \textstyle\alpha_{1}+\alpha_{2}+\cdots+\alpha_{n}
  45. D α \textstyle D^{\alpha}
  46. α 1 \textstyle\alpha_{1}
  47. x 1 \textstyle x_{1}
  48. α 2 \textstyle\alpha_{2}
  49. x 2 \textstyle x_{2}
  50. W p m ( Ω ) \textstyle W_{p}^{m}(\Omega)
  51. L p \textstyle L^{p}
  52. | u | W p m ( Ω ) = ( | α | = m D α u L p ( Ω ) p ) 1 / p if 1 p < \left|u\right|_{W_{p}^{m}(\Omega)}=\left(\sum_{\left|\alpha\right|=m}\left\|D^% {\alpha}u\right\|_{L^{p}(\Omega)}^{p}\right)^{1/p}\,\text{ if }1\leq p<\infty
  53. | u | W m ( Ω ) = max | α | = m D α u L ( Ω ) \left|u\right|_{W_{\infty}^{m}(\Omega)}=\max_{\left|\alpha\right|=m}\left\|D^{% \alpha}u\right\|_{L^{\infty}(\Omega)}
  54. P k \textstyle P_{k}
  55. k \textstyle k
  56. n \textstyle\mathbb{R}^{n}
  57. D α v = 0 \textstyle D^{\alpha}v=0
  58. v P m - 1 \textstyle v\in P_{m-1}
  59. | α | = m \textstyle\left|\alpha\right|=m
  60. | u + v | W p m ( Ω ) \textstyle\left|u+v\right|_{W_{p}^{m}(\Omega)}
  61. v P k - 1 \textstyle v\in P_{k-1}
  62. Ω \textstyle\Omega
  63. C = C ( m , Ω ) \textstyle C=C\left(m,\Omega\right)
  64. p \textstyle p
  65. u \textstyle u
  66. u W p m ( Ω ) \textstyle u\in W_{p}^{m}(\Omega)
  67. v P m - 1 \textstyle v\in P_{m-1}
  68. k = 0 , , m , \textstyle k=0,\ldots,m,
  69. | u - v | W p k ( Ω ) C d m - k | u | W p m ( Ω ) . \left|u-v\right|_{W_{p}^{k}(\Omega)}\leq Cd^{m-k}\left|u\right|_{W_{p}^{m}(% \Omega)}.
  70. Ω \textstyle\Omega
  71. { O i } \textstyle\left\{O_{i}\right\}
  72. Ω \textstyle\partial\Omega
  73. { C i } \textstyle\{C_{i}\}
  74. x + C i \textstyle x+C_{i}
  75. Ω \textstyle\Omega
  76. x \textstyle x
  77. Ω O i \textstyle\in\Omega\cap O_{i}
  78. W p m ( Ω ) / P m - 1 \textstyle W_{p}^{m}(\Omega)/P_{m-1}
  79. W p m ( Ω ) \textstyle W_{p}^{m}(\Omega)
  80. W p m ( Ω ) \textstyle W_{p}^{m}(\Omega)
  81. d \textstyle d
  82. Ω \textstyle\Omega
  83. Ω \textstyle\Omega
  84. B \textstyle B
  85. x Ω \textstyle x\in\Omega
  86. { x } B \textstyle\left\{x\right\}\cup B
  87. Ω \textstyle\Omega
  88. ρ max \textstyle\rho_{\max}
  89. γ = d / ρ max \textstyle\gamma=d/\rho_{\max}
  90. Ω \textstyle\Omega
  91. C = C ( m , n , γ ) \textstyle C=C\left(m,n,\gamma\right)
  92. Ω \textstyle\Omega
  93. γ \textstyle\gamma
  94. n \textstyle n
  95. v v
  96. v = Q m u v=Q^{m}u
  97. Q m u \textstyle Q^{m}u
  98. Q m u = B T y m u ( x ) ψ ( y ) d x , Q^{m}u=\int_{B}T_{y}^{m}u\left(x\right)\psi\left(y\right)\,dx,
  99. T y m u ( x ) = k = 0 m - 1 | α | = k 1 α ! D α u ( y ) ( x - y ) α T_{y}^{m}u\left(x\right)=\sum\limits_{k=0}^{m-1}\sum\limits_{\left|\alpha% \right|=k}\frac{1}{\alpha!}D^{\alpha}u\left(y\right)\left(x-y\right)^{\alpha}
  100. m - 1 \textstyle m-1
  101. u \textstyle u
  102. y \textstyle y
  103. x \textstyle x
  104. ψ 0 \textstyle\psi\geq 0
  105. B \textstyle B
  106. B ψ d x = 1. \int_{B}\psi\,dx=1.
  107. ψ \textstyle\psi
  108. Ω \textstyle\Omega
  109. \textstyle\ell
  110. W p m ( Ω ) \textstyle W_{p}^{m}(\Omega)
  111. W p m ( Ω ) \textstyle\left\|\ell\right\|_{W_{p}^{m}(\Omega)^{{}^{\prime}}}
  112. ( v ) = 0 \textstyle\ell\left(v\right)=0
  113. v P m - 1 \textstyle v\in P_{m-1}
  114. C = C ( Ω ) \textstyle C=C\left(\Omega\right)
  115. | ( u ) | C W p m ( Ω ) | u | W p m ( Ω ) . \left|\ell\left(u\right)\right|\leq C\left\|\ell\right\|_{W_{p}^{m}(\Omega)^{{% }^{\prime}}}\left|u\right|_{W_{p}^{m}(\Omega)}.

Branched-chain-2-oxoacid_decarboxylase.html

  1. \rightleftharpoons

Breather_surface.html

  1. x = - u + 2 ( 1 - a 2 ) cosh ( a u ) sinh ( a u ) a ( ( 1 - a 2 ) cosh 2 ( a u ) + a 2 sin 2 ( 1 - a 2 v ) ) y = 2 1 - a 2 cosh ( a u ) ( - 1 - a 2 cos ( v ) cos ( 1 - a 2 v ) - sin ( v ) sin ( 1 - a 2 v ) ) a ( ( 1 - a 2 ) cosh 2 ( a u ) + a 2 sin 2 ( 1 - a 2 v ) ) z = 2 1 - a 2 cosh ( a u ) ( - 1 - a 2 sin ( v ) cos ( 1 - a 2 v ) + cos ( v ) sin ( 1 - a 2 v ) ) a ( ( 1 - a 2 ) cosh 2 ( a u ) + a 2 sin 2 ( 1 - a 2 v ) ) \begin{aligned}\displaystyle x&\displaystyle{}=-u+\frac{2\left(1-a^{2}\right)% \cosh(au)\sinh(au)}{a\left(\left(1-a^{2}\right)\cosh^{2}(au)+a^{2}\,\sin^{2}% \left(\sqrt{1-a^{2}}v\right)\right)}\\ \\ \displaystyle y&\displaystyle{}=\frac{2\sqrt{1-a^{2}}\cosh(au)\left(-\sqrt{1-a% ^{2}}\cos(v)\cos\left(\sqrt{1-a^{2}}v\right)-\sin(v)\sin\left(\sqrt{1-a^{2}}v% \right)\right)}{a\left(\left(1-a^{2}\right)\cosh^{2}(au)+a^{2}\,\sin^{2}\left(% \sqrt{1-a^{2}}v\right)\right)}\\ \\ \displaystyle z&\displaystyle{}=\frac{2\sqrt{1-a^{2}}\cosh(au)\left(-\sqrt{1-a% ^{2}}\sin(v)\cos\left(\sqrt{1-a^{2}}v\right)+\cos(v)\sin\left(\sqrt{1-a^{2}}v% \right)\right)}{a\left(\left(1-a^{2}\right)\cosh^{2}(au)+a^{2}\,\sin^{2}\left(% \sqrt{1-a^{2}}v\right)\right)}\end{aligned}

Bubble_point.html

  1. i = 1 N c y i = i = 1 N c K i x i = 1 \sum_{i=1}^{N_{c}}y_{i}=\sum_{i=1}^{N_{c}}K_{i}x_{i}=1
  2. K i y i e x i e K_{i}\equiv\frac{y_{ie}}{x_{ie}}
  3. ( y i e ) \big(y_{ie}\big)
  4. ( x i e ) \big(x_{ie}\big)
  5. K i = P i P K_{i}=\frac{P^{\prime}_{i}}{P}

Buffon's_noodle.html

  1. P = 2 L / π D P=2L/\pi D
  2. E ( X 1 + + X n ) = E ( X 1 ) + + E ( X n ) . E(X_{1}+\cdots+X_{n})=E(X_{1})+\cdots+E(X_{n}).

Bullough–Dodd_model.html

  1. = 1 2 ( μ ϕ ) 2 - m 0 2 6 g 2 ( 2 e g ϕ + e - 2 g ϕ ) \mathcal{L}=\frac{1}{2}(\partial_{\mu}\phi)^{2}-\frac{m_{0}^{2}}{6g^{2}}(2e^{g% \phi}+e^{-2g\phi})
  2. m 0 m_{0}\,
  3. g g\,
  4. ϕ \phi\,

Bundle_adjustment.html

  1. n n
  2. m m
  3. 𝐱 i j \mathbf{x}_{ij}
  4. i i
  5. j j
  6. v i j \displaystyle v_{ij}
  7. i i
  8. j j
  9. j j
  10. 𝐚 j \mathbf{a}_{j}
  11. i i
  12. 𝐛 i \mathbf{b}_{i}
  13. min 𝐚 j , 𝐛 i i = 1 n j = 1 m v i j d ( 𝐐 ( 𝐚 j , 𝐛 i ) , 𝐱 i j ) 2 , \min_{\mathbf{a}_{j},\,\mathbf{b}_{i}}\displaystyle\sum_{i=1}^{n}\;% \displaystyle\sum_{j=1}^{m}\;v_{ij}\,d(\mathbf{Q}(\mathbf{a}_{j},\,\mathbf{b}_% {i}),\;\mathbf{x}_{ij})^{2},
  14. 𝐐 ( 𝐚 j , 𝐛 i ) \mathbf{Q}(\mathbf{a}_{j},\,\mathbf{b}_{i})
  15. i i
  16. j j
  17. d ( 𝐱 , 𝐲 ) d(\mathbf{x},\,\mathbf{y})
  18. 𝐱 \mathbf{x}
  19. 𝐲 \mathbf{y}

Butanal_dehydrogenase.html

  1. \rightleftharpoons

Butyrate—acetoacetate_CoA-transferase.html

  1. \rightleftharpoons

Butyryl-CoA_dehydrogenase.html

  1. \rightleftharpoons

C-ROT_gate.html

  1. π / 2 \pi/2

Caffeate_3,4-dioxygenase.html

  1. \rightleftharpoons

Caffeate_O-methyltransferase.html

  1. \rightleftharpoons

Caffeoyl-CoA_O-methyltransferase.html

  1. \rightleftharpoons

Calculation_of_glass_properties.html

  1. Glass Property = b 0 + i = 1 n b i C i \mbox{Glass Property}~{}=b_{0}+\sum_{i=1}^{n}b_{i}C_{i}
  2. Glass Property = b 0 + i = 1 n ( b i C i + k = i n b i k C i C k ) \mbox{Glass Property}~{}=b_{0}+\sum_{i=1}^{n}\left(b_{i}C_{i}+\sum_{k=i}^{n}b_% {ik}C_{i}C_{k}\right)

Call_volume_(telecommunications).html

  1. y = m x + b , y=mx+b,
  2. C = 0.02 P 1 P 2 d 2 , C=\frac{0.02P_{1}P_{2}}{d^{2}},

Calmodulin-lysine_N-methyltransferase.html

  1. \rightleftharpoons

Caloric_polynomial.html

  1. P t = 2 P x 2 . \frac{\partial P}{\partial t}=\frac{\partial^{2}P}{\partial x^{2}}.
  2. P ( λ x , λ 2 t ) = λ m P ( x , t ) for λ > 0. P(\lambda x,\lambda^{2}t)=\lambda^{m}P(x,t)\,\text{ for }\lambda>0.\,
  3. P m ( x , t ) = = 0 m / 2 m ! ! ( m - 2 ) ! x m - 2 t . P_{m}(x,t)=\sum_{\ell=0}^{\lfloor m/2\rfloor}\frac{m!}{\ell!(m-2\ell)!}x^{m-2% \ell}t^{\ell}.

Cameron–Erdős_conjecture.html

  1. | N | = { 1 , , N } |N|=\{1,\ldots,N\}
  2. O ( 2 N / 2 ) . O\left({2^{N/2}}\right).
  3. N / 2 \lceil N/2\rceil
  4. 2 N / 2 2^{N/2}

Camphor_1,2-monooxygenase.html

  1. \rightleftharpoons

Camphor_5-monooxygenase.html

  1. \rightleftharpoons

Capillary_surface.html

  1. S S
  2. ( σ i j - σ ¯ i j ) 𝐧 ^ = - γ 𝐧 ^ ( S 𝐧 ^ ) + S γ ; S γ = γ - 𝐧 ^ ( 𝐧 ^ γ ) (\sigma_{ij}-\bar{\sigma}_{ij})\mathbf{\hat{n}}=-\gamma\mathbf{\hat{n}}(\nabla% _{\!S}\cdot\mathbf{\hat{n}})+\nabla_{\!S}\gamma\qquad;\quad\nabla_{\!S}\gamma=% \nabla\gamma-\mathbf{\hat{n}}(\mathbf{\hat{n}}\cdot\nabla\gamma)
  3. 𝐧 ^ \scriptstyle\mathbf{\hat{n}}
  4. σ i j \scriptstyle\sigma_{ij}
  5. γ \scriptstyle\gamma
  6. S \scriptstyle\nabla_{S}
  7. - S 𝐧 ^ \scriptstyle-\nabla_{\!S}\cdot\mathbf{\hat{n}}
  8. S S
  9. ( ( σ i j - σ ¯ i j ) 𝐧 ^ ) 𝐧 ^ = - γ S 𝐧 ^ ((\sigma_{ij}-\bar{\sigma}_{ij})\mathbf{\hat{n}})\cdot\mathbf{\hat{n}}=-\gamma% \nabla_{\!S}\cdot\mathbf{\hat{n}}
  10. ( ( σ i j - σ ¯ i j ) 𝐧 ^ ) 𝐭 ^ 𝟏 = S γ 𝐭 ^ 𝟏 ((\sigma_{ij}-\bar{\sigma}_{ij})\mathbf{\hat{n}})\cdot\mathbf{\hat{t}_{1}}=% \nabla_{\!S}\gamma\cdot\mathbf{\hat{t}_{1}}
  11. ( ( σ i j - σ ¯ i j ) 𝐧 ^ ) 𝐭 ^ 𝟐 = S γ 𝐭 ^ 𝟐 ((\sigma_{ij}-\bar{\sigma}_{ij})\mathbf{\hat{n}})\cdot\mathbf{\hat{t}_{2}}=% \nabla_{\!S}\gamma\cdot\mathbf{\hat{t}_{2}}
  12. σ i j = - ( p 0 0 0 p 0 0 0 p ) + μ ( 2 u x u y + v x u z + w x v x + u y 2 v y v z + w y w x + u z w y + v z 2 w z ) = - p I + μ ( 𝐯 + ( 𝐯 ) T ) \begin{aligned}\displaystyle\sigma_{ij}&\displaystyle=-\begin{pmatrix}p&0&0\\ 0&p&0\\ 0&0&p\end{pmatrix}+\mu\begin{pmatrix}2\frac{\partial u}{\partial x}&\frac{% \partial u}{\partial y}+\frac{\partial v}{\partial x}&\frac{\partial u}{% \partial z}+\frac{\partial w}{\partial x}\\ \frac{\partial v}{\partial x}+\frac{\partial u}{\partial y}&2\frac{\partial v}% {\partial y}&\frac{\partial v}{\partial z}+\frac{\partial w}{\partial y}\\ \frac{\partial w}{\partial x}+\frac{\partial u}{\partial z}&\frac{\partial w}{% \partial y}+\frac{\partial v}{\partial z}&2\frac{\partial w}{\partial z}\end{% pmatrix}\\ &\displaystyle=-pI+\mu(\nabla\mathbf{v}+(\nabla\mathbf{v})^{T})\end{aligned}
  13. p p
  14. 𝐯 \scriptstyle\mathbf{v}
  15. μ \mu
  16. σ i j = - p I \scriptstyle\sigma_{ij}=-pI
  17. p ¯ - p = γ 𝐧 ^ \bar{p}-p=\gamma\nabla\cdot\mathbf{\hat{n}}
  18. 0 = γ 𝐭 ^ 0=\nabla\gamma\cdot\mathbf{\hat{t}}
  19. 0 = - p + ρ 𝐠 0=-\nabla p+\rho\mathbf{g}
  20. z z
  21. d p d z = ρ g p = ρ g z + p 0 \frac{dp}{dz}=\rho g\quad\Rightarrow\quad p=\rho gz+p_{0}
  22. p 0 p_{0}
  23. z = 0 z=0
  24. ρ ¯ g z + p ¯ 0 - ( ρ g z + p 0 ) = γ 𝐧 ^ Δ ρ g z + Δ p = γ 𝐧 ^ \bar{\rho}gz+\bar{p}_{0}-(\rho gz+p_{0})=\gamma\nabla\cdot\mathbf{\hat{n}}% \quad\Rightarrow\quad\Delta\rho gz+\Delta p=\gamma\nabla\cdot\mathbf{\hat{n}}
  25. Δ p \Delta p
  26. Δ ρ \Delta\rho
  27. z z
  28. z z
  29. z z
  30. z z
  31. Δ p = 0 \Delta p=0
  32. κ z + λ = 𝐧 ^ \kappa z+\lambda=\nabla\cdot\mathbf{\hat{n}}
  33. z z
  34. κ \kappa
  35. λ \lambda
  36. λ \lambda
  37. E S = γ S A S E_{S}=\gamma_{S}A_{S}\,
  38. A A
  39. E = γ S A S = γ L G A L G + γ S G A S G + γ S L A S L E=\sum\gamma_{S}A_{S}=\gamma_{LG}A_{LG}+\gamma_{SG}A_{SG}+\gamma_{SL}A_{SL}\,
  40. L G LG
  41. S G SG
  42. S L SL
  43. γ L G \gamma_{LG}
  44. A S G + A S L A_{SG}+A_{SL}
  45. E = γ S L ( A S L + A S G ) + γ L G A L G + γ L G A S G cos ( θ ) E=\gamma_{SL}(A_{SL}+A_{SG})+\gamma_{LG}A_{LG}+\gamma_{LG}A_{SG}\cos(\theta)\,
  46. Δ E γ L G = Δ A L G + Δ A S G cos ( θ ) = Δ A L G - Δ A S L cos ( θ ) \frac{\Delta E}{\gamma_{LG}}=\Delta A_{LG}+\Delta A_{SG}\cos(\theta)=\Delta A_% {LG}-\Delta A_{SL}\cos(\theta)\,
  47. θ \theta
  48. 0 \displaystyle 0
  49. S S
  50. 𝐧 ^ 𝐯 ^ = cos ( θ ) \mathbf{\hat{n}}\cdot\mathbf{\hat{v}}=\cos(\theta)\,
  51. θ \theta
  52. S \scriptstyle\partial S
  53. v ^ \scriptstyle\hat{v}
  54. n ^ \scriptstyle\hat{n}
  55. S S
  56. n ^ \scriptstyle\hat{n}

Carbamoyl-serine_ammonia-lyase.html

  1. \rightleftharpoons

Carbon-monoxide_dehydrogenase_(cytochrome_b-561).html

  1. \rightleftharpoons

Carbon-monoxide_dehydrogenase_(ferredoxin).html

  1. \rightleftharpoons

Carbon_monoxide_dehydrogenase.html

  1. \rightleftharpoons

Carbonyl_reductase_(NADPH).html

  1. \rightleftharpoons

Carboxy-cis,cis-muconate_cyclase.html

  1. \rightleftharpoons

Carboxylate_reductase.html

  1. \rightleftharpoons

Cardinal_function.html

  1. add ( I ) = min { | 𝒜 | : 𝒜 I 𝒜 I } {\rm add}(I)=\min\{|{\mathcal{A}}|:{\mathcal{A}}\subseteq I\wedge\bigcup{% \mathcal{A}}\notin I\big\}
  2. 0 \aleph_{0}
  3. 1 \aleph_{1}
  4. cov ( I ) = min { | 𝒜 | : 𝒜 I 𝒜 = X } {\rm cov}(I)=\min\{|{\mathcal{A}}|:{\mathcal{A}}\subseteq I\wedge\bigcup{% \mathcal{A}}=X\big\}
  5. non ( I ) = min { | A | : A X A I } {\rm non}(I)=\min\{|A|:A\subseteq X\ \wedge\ A\notin I\big\}
  6. unif ( I ) {\rm unif}(I)
  7. cof ( I ) = min { | | : I ( A I ) ( B ) ( A B ) } . {\rm cof}(I)=\min\{|{\mathcal{B}}|:{\mathcal{B}}\subseteq I\wedge(\forall A\in I% )(\exists B\in{\mathcal{B}})(A\subseteq B)\big\}.
  8. I I
  9. ( , ) ({\mathbb{P}},\sqsubseteq)
  10. 𝔟 ( ) {\mathfrak{b}}({\mathbb{P}})
  11. 𝔡 ( ) {\mathfrak{d}}({\mathbb{P}})
  12. 𝔟 ( ) = min { | Y | : Y ( x ) ( y Y ) ( y x ) } {\mathfrak{b}}({\mathbb{P}})=\min\big\{|Y|:Y\subseteq{\mathbb{P}}\ \wedge\ (% \forall x\in{\mathbb{P}})(\exists y\in Y)(y\not\sqsubseteq x)\big\}
  13. 𝔡 ( ) = min { | Y | : Y ( x ) ( y Y ) ( x y ) } {\mathfrak{d}}({\mathbb{P}})=\min\big\{|Y|:Y\subseteq{\mathbb{P}}\ \wedge\ (% \forall x\in{\mathbb{P}})(\exists y\in Y)(x\sqsubseteq y)\big\}
  14. p p κ ( λ ) pp_{\kappa}(\lambda)
  15. + 0 \;\;+\;\aleph_{0}
  16. 0 \aleph_{0}
  17. π \pi
  18. π \pi
  19. χ ( X ) = sup { χ ( x , X ) : x X } . \chi(X)=\sup\;\{\chi(x,X):x\in X\}.
  20. χ ( X ) = 0 \chi(X)=\aleph_{0}
  21. d ( X ) = 0 \rm{d}(X)=\aleph_{0}
  22. L ( X ) = 0 \rm{L}(X)=\aleph_{0}
  23. c ( X ) = sup { | 𝒰 | : 𝒰 {\rm c}(X)=\sup\{|{\mathcal{U}}|:{\mathcal{U}}
  24. X } X\}
  25. s ( X ) = hc ( X ) = sup { c ( Y ) : Y X } s(X)={\rm hc}(X)=\sup\{{\rm c}(Y):Y\subseteq X\}
  26. s ( X ) = sup { | Y | : Y X s(X)=\sup\{|Y|:Y\subseteq X
  27. } \}
  28. x X x\in X
  29. α \alpha
  30. x cl X ( Y ) x\in{\rm cl}_{X}(Y)
  31. α \alpha
  32. x cl X ( Z ) x\in{\rm cl}_{X}(Z)
  33. t ( x , X ) = sup { min { | Z | : Z Y x cl X ( Z ) } : Y X x cl X ( Y ) } . t(x,X)=\sup\big\{\min\{|Z|:Z\subseteq Y\ \wedge\ x\in{\rm cl}_{X}(Z)\}:Y% \subseteq X\ \wedge\ x\in{\rm cl}_{X}(Y)\big\}.
  34. t ( X ) = sup { t ( x , X ) : x X } t(X)=\sup\{t(x,X):x\in X\}
  35. 0 \aleph_{0}
  36. t + ( X ) t^{+}(X)
  37. α \alpha
  38. Y X Y\subseteq X
  39. x cl X ( Y ) x\in{\rm cl}_{X}(Y)
  40. α \alpha
  41. x cl X ( Z ) x\in{\rm cl}_{X}(Z)
  42. χ \chi
  43. c ( 𝔹 ) c({\mathbb{B}})
  44. 𝔹 {\mathbb{B}}
  45. 𝔹 {\mathbb{B}}
  46. length ( 𝔹 ) {\rm length}({\mathbb{B}})
  47. 𝔹 {\mathbb{B}}
  48. length ( 𝔹 ) = sup { | A | : A 𝔹 {\rm length}({\mathbb{B}})=\sup\big\{|A|:A\subseteq{\mathbb{B}}
  49. } \big\}
  50. depth ( 𝔹 ) {\rm depth}({\mathbb{B}})
  51. 𝔹 {\mathbb{B}}
  52. depth ( 𝔹 ) = sup { | A | : A 𝔹 {\rm depth}({\mathbb{B}})=\sup\big\{|A|:A\subseteq{\mathbb{B}}
  53. } \big\}
  54. Inc ( 𝔹 ) {\rm Inc}({\mathbb{B}})
  55. 𝔹 {\mathbb{B}}
  56. Inc ( 𝔹 ) = sup { | A | : A 𝔹 {\rm Inc}({\mathbb{B}})=\sup\big\{|A|:A\subseteq{\mathbb{B}}
  57. ( a , b A ) ( a b ¬ ( a b b a ) ) } \big(\forall a,b\in A\big)\big(a\neq b\ \Rightarrow\neg(a\leq b\ \vee\ b\leq a% )\big)\big\}
  58. π ( 𝔹 ) \pi({\mathbb{B}})
  59. 𝔹 {\mathbb{B}}
  60. π ( 𝔹 ) = min { | A | : A 𝔹 { 0 } \pi({\mathbb{B}})=\min\big\{|A|:A\subseteq{\mathbb{B}}\setminus\{0\}
  61. ( b B { 0 } ) ( a A ) ( a b ) } \big(\forall b\in B\setminus\{0\}\big)\big(\exists a\in A\big)\big(a\leq b\big% )\big\}
  62. rank ( M ) {\rm rank}(M)

Carnitine_3-dehydrogenase.html

  1. \rightleftharpoons

Carnitine_decarboxylase.html

  1. \rightleftharpoons

Carnosine_N-methyltransferase.html

  1. \rightleftharpoons

Carotene_7,8-desaturase.html

  1. \rightleftharpoons

Carr_index.html

  1. C = 100 V B - V T V B C=100\frac{V_{B}-V_{T}}{V_{B}}
  2. V B V_{B}
  3. V T V_{T}
  4. C = 100 × ( 1 - ρ B ρ T ) C=100\times(1-\frac{\rho_{B}}{\rho_{T}})
  5. ρ B \rho_{B}
  6. ρ T \rho_{T}
  7. H = ρ T / ρ B H=\rho_{T}/\rho_{B}

Carveol_dehydrogenase.html

  1. \rightleftharpoons

CAT(k)_space.html

  1. 𝐂𝐀𝐓 ( 𝐤 ) \mathbf{\operatorname{\,\textbf{CAT}}(k)}
  2. k k
  3. CAT ( k ) \operatorname{CAT}(k)
  4. k k
  5. CAT ( k ) \operatorname{CAT}(k)
  6. k k
  7. k = 0 k=0
  8. CAT ( 0 ) \operatorname{CAT}(0)
  9. k \mathfrak{R}_{k}
  10. CAT ( k ) \operatorname{CAT}(k)
  11. k k
  12. M k M_{k}
  13. k k
  14. D k D_{k}
  15. M k M_{k}
  16. + +\infty
  17. k 0 k\leq 0
  18. π k \frac{\pi}{\sqrt{k}}
  19. k > 0 k>0
  20. ( X , d ) (X,d)
  21. x , y X x,y\in X
  22. γ : [ a , b ] X , γ ( a ) = x , γ ( b ) = y \gamma\,:\,[a,b]\to X,\ \gamma(a)=x,\ \gamma(b)=y
  23. L ( γ ) = sup { i = 1 r d ( γ ( t i - 1 ) , γ ( t i ) ) | a = t 0 < t 1 < < t r = b , r } L(\gamma)=\sup\left\{\left.\sum_{i=1}^{r}d\big(\gamma(t_{i-1}),\gamma(t_{i})% \big)\right|a=t_{0}<t_{1}<\cdots<t_{r}=b,r\in\mathbb{N}\right\}
  24. d ( x , y ) d(x,y)
  25. Δ \Delta
  26. X X
  27. Δ \Delta
  28. 𝐂𝐀𝐓 ( 𝐤 ) \mathbf{\operatorname{\,\textbf{CAT}}(k)}
  29. Δ \Delta^{\prime}
  30. M k M_{k}
  31. Δ \Delta
  32. Δ \Delta
  33. Δ \Delta^{\prime}
  34. ( X , d ) (X,d)
  35. 𝐂𝐀𝐓 ( 𝐤 ) \mathbf{\operatorname{\,\textbf{CAT}}(k)}
  36. Δ \Delta
  37. X X
  38. 2 D k 2D_{k}
  39. CAT ( k ) \operatorname{CAT}(k)
  40. ( X , d ) (X,\,d)
  41. k \leq k
  42. X X
  43. CAT ( k ) \operatorname{CAT}(k)
  44. 0 \leq 0
  45. CAT ( k ) \operatorname{CAT}(k)
  46. ( X , d ) (X,d)
  47. CAT ( ) \operatorname{CAT}(\ell)
  48. > k \ell>k
  49. ( X , d ) (X,d)
  50. CAT ( ) \operatorname{CAT}(\ell)
  51. > k \ell>k
  52. CAT ( k ) \operatorname{CAT}(k)
  53. n n
  54. 𝐄 n \mathbf{E}^{n}
  55. CAT ( 0 ) \operatorname{CAT}(0)
  56. CAT ( 0 ) \operatorname{CAT}(0)
  57. CAT ( k ) \operatorname{CAT}(k)
  58. k k
  59. n n
  60. 𝐇 n \mathbf{H}^{n}
  61. CAT ( - 1 ) \operatorname{CAT}(-1)
  62. CAT ( 0 ) \operatorname{CAT}(0)
  63. n n
  64. 𝐒 n \mathbf{S}^{n}
  65. CAT ( 1 ) \operatorname{CAT}(1)
  66. M k M_{k}
  67. CAT ( k ) \operatorname{CAT}(k)
  68. r r
  69. 1 r 2 \frac{1}{r^{2}}
  70. CAT ( 1 r 2 ) \operatorname{CAT}(\frac{1}{r^{2}})
  71. π r \pi r
  72. 2 r 2r
  73. Π = 𝐄 2 \ { 𝟎 } \Pi=\mathbf{E}^{2}\backslash\{\mathbf{0}\}
  74. CAT ( 0 ) \operatorname{CAT}(0)
  75. ( 0 , 1 ) (0,1)
  76. ( 0 , - 1 ) (0,-1)
  77. > Π >\Pi
  78. Π \Pi
  79. CAT ( 0 ) \operatorname{CAT}(0)
  80. Π \Pi
  81. 0 \leq 0
  82. X X
  83. 𝐄 3 \mathbf{E}^{3}
  84. X = 𝐄 3 { ( x , y , z ) | x > 0 , y > 0 and z > 0 } X=\mathbf{E}^{3}\setminus\{(x,y,z)|x>0,y>0\,\text{ and }z>0\}
  85. CAT ( k ) \operatorname{CAT}(k)
  86. k k
  87. CAT ( 0 ) \operatorname{CAT}(0)
  88. CAT ( 0 ) \operatorname{CAT}(0)
  89. t d ( σ 1 ( t ) , σ 2 ( t ) ) t\mapsto d\big(\sigma_{1}(t),\sigma_{2}(t)\big)
  90. CAT ( k ) \operatorname{CAT}(k)
  91. ( X , d ) (X,d)
  92. CAT ( k ) \operatorname{CAT}(k)
  93. x , y X x,y\in X
  94. d ( x , y ) < D k d(x,y)<D_{k}
  95. k > 0 k>0
  96. x x
  97. y y
  98. X X
  99. D k D_{k}
  100. d d
  101. X X
  102. 1 2 D k \frac{1}{2}D_{k}
  103. d d
  104. X X
  105. D k D_{k}
  106. λ < D k \lambda<D_{k}
  107. ϵ > 0 \epsilon>0
  108. δ = δ ( k , λ , ϵ ) > 0 \delta=\delta(k,\lambda,\epsilon)>0
  109. m m
  110. x x
  111. y y
  112. d ( x , y ) λ d(x,y)\leq\lambda
  113. max { d ( x , m ) , d ( y , m ) } 1 2 d ( x , y ) + δ , \max\big\{d(x,m^{\prime}),d(y,m^{\prime})\big\}\leq\frac{1}{2}d(x,y)+\delta,
  114. d ( m , m ) < ϵ d(m,m^{\prime})<\epsilon
  115. k 0 k\leq 0
  116. CAT ( k ) \operatorname{CAT}(k)
  117. n n
  118. 𝐒 n \mathbf{S}^{n}
  119. CAT ( k ) \operatorname{CAT}(k)
  120. k > 0 k>0
  121. n n
  122. CAT ( k ) \operatorname{CAT}(k)
  123. n n
  124. CD [ n , ( n - 1 ) k ] \operatorname{CD}[n,(n-1)k]

Catechol_oxidase_(dimerizing).html

  1. \rightleftharpoons

Category_algebra.html

  1. a i f i \sum a_{i}f_{i}
  2. a i f i b j g j = a i b j f i g j \sum a_{i}f_{i}\sum b_{j}g_{j}=\sum a_{i}b_{j}f_{i}g_{j}
  3. f i g j = 0 f_{i}g_{j}=0
  4. a , b R C a,b\in RC
  5. ( a * b ) ( h ) := f g = h a ( f ) b ( g ) . (a*b)(h):=\sum_{fg=h}a(f)b(g).
  6. a * b R C a*b\in RC
  7. f i Hom ( C ) a i f i , \sum_{f_{i}\in\mathrm{Hom}(C)}a_{i}f_{i},
  8. a i a_{i}

Cauchy–Hadamard_theorem.html

  1. f ( z ) = n = 0 c n ( z - a ) n f(z)=\sum_{n=0}^{\infty}c_{n}(z-a)^{n}
  2. a , c n . a,c_{n}\in\mathbb{C}.
  3. 1 R = lim sup n ( | c n | 1 / n ) \frac{1}{R}=\limsup_{n\to\infty}\big(|c_{n}|^{1/n}\big)
  4. a = 0 a=0
  5. c n z n \sum c_{n}z^{n}
  6. | z | < R |z|<R
  7. | z | > R |z|>R
  8. | z | < R |z|<R
  9. t = 1 / R t=1/R
  10. ϵ > 0 \epsilon>0
  11. n n
  12. | c n | n t + ϵ \sqrt[n]{|c_{n}|}\geq t+\epsilon
  13. | c n | ( t + ϵ ) n |c_{n}|\leq(t+\epsilon)^{n}
  14. c n c_{n}
  15. c n z n \sum c_{n}z^{n}
  16. | z | < 1 / ( t + ϵ ) |z|<1/(t+\epsilon)
  17. ϵ > 0 \epsilon>0
  18. | c n | ( t - ϵ ) n |c_{n}|\geq(t-\epsilon)^{n}
  19. c n c_{n}
  20. | z | = 1 / ( t - ϵ ) > R |z|=1/(t-\epsilon)>R
  21. α \alpha
  22. | α | = α 1 + + α n |\alpha|=\alpha_{1}+\ldots+\alpha_{n}
  23. f ( x ) f(x)
  24. ρ \rho
  25. lim | α | | c α | ρ α | α | = 1 \lim_{|\alpha|\to\infty}\sqrt[|\alpha|]{|c_{\alpha}|\rho^{\alpha}}=1
  26. α 0 c α ( z - a ) α := α 1 0 , , α n 0 c α 1 , , α n ( z 1 - a 1 ) α 1 ( z n - a n ) α n \sum_{\alpha\geq 0}c_{\alpha}(z-a)^{\alpha}:=\sum_{\alpha_{1}\geq 0,\ldots,% \alpha_{n}\geq 0}c_{\alpha_{1},\ldots,\alpha_{n}}(z_{1}-a_{1})^{\alpha_{1}}% \ldots(z_{n}-a_{n})^{\alpha_{n}}

Causal_structure.html

  1. ( M , g ) \,(M,g)
  2. g g
  3. M M
  4. X X
  5. g ( X , X ) > 0 \,g(X,X)>0
  6. g ( X , X ) = 0 \,g(X,X)=0
  7. g ( X , X ) < 0 \,g(X,X)<0
  8. ( + , - , - , - , ) (+,-,-,-,\cdots)
  9. M M
  10. X X
  11. Y Y
  12. X X
  13. Y Y
  14. X Y X\sim Y
  15. g ( X , Y ) > 0 \,g(X,Y)>0
  16. M M
  17. μ : Σ M \mu:\Sigma\to M
  18. Σ \Sigma
  19. \mathbb{R}
  20. μ \mu
  21. C C^{\infty}
  22. M M
  23. Σ \Sigma
  24. M M
  25. M M
  26. Σ \Sigma
  27. M M
  28. x x
  29. y y
  30. M M
  31. x x
  32. y y
  33. x y \,x\ll y
  34. x x
  35. y y
  36. x x
  37. y y
  38. x < y x<y
  39. x x
  40. y y
  41. x x
  42. y y
  43. x y x\prec y
  44. x y x\leq y
  45. x x
  46. y y
  47. x = y x=y
  48. x x
  49. y y
  50. x y x\to y
  51. x y x\nearrow y
  52. x y x\prec y
  53. x ≪̸ y x\not\ll y
  54. x y x\ll y
  55. y z y\ll z
  56. x z x\ll z
  57. x y \,x\prec y
  58. y z \,y\prec z
  59. x z \,x\prec z
  60. x y x\ll y
  61. x y x\prec y
  62. x y x\ll y
  63. y z y\prec z
  64. x z x\ll z
  65. x y x\prec y
  66. y z y\ll z
  67. x z x\ll z
  68. x x
  69. M M
  70. x x
  71. I + ( x ) \,I^{+}(x)
  72. y y
  73. M M
  74. x x
  75. y y
  76. I + ( x ) = { y M | x y } \,I^{+}(x)=\{y\in M|x\ll y\}
  77. x x
  78. I - ( x ) \,I^{-}(x)
  79. y y
  80. M M
  81. y y
  82. x x
  83. I - ( x ) = { y M | y x } \,I^{-}(x)=\{y\in M|y\ll x\}
  84. x x
  85. J + ( x ) \,J^{+}(x)
  86. y y
  87. M M
  88. x x
  89. y y
  90. J + ( x ) = { y M | x y } \,J^{+}(x)=\{y\in M|x\prec y\}
  91. x x
  92. J - ( x ) \,J^{-}(x)
  93. y y
  94. M M
  95. y y
  96. x x
  97. J - ( x ) = { y M | y x } \,J^{-}(x)=\{y\in M|y\prec x\}
  98. I + ( x ) \,I^{+}(x)
  99. x x
  100. x x
  101. J - ( x ) \,J^{-}(x)
  102. I + ( x ) \,I^{+}(x)
  103. x x
  104. J + ( x ) \,J^{+}(x)
  105. x x
  106. I + ( x ) , I - ( x ) , J + ( x ) , J - ( x ) \,I^{+}(x),I^{-}(x),J^{+}(x),J^{-}(x)
  107. x x
  108. M M
  109. M M
  110. S S
  111. M M
  112. I ± ( S ) = x S I ± ( x ) I^{\pm}(S)=\bigcup_{x\in S}I^{\pm}(x)
  113. J ± ( S ) = x S J ± ( x ) J^{\pm}(S)=\bigcup_{x\in S}J^{\pm}(x)
  114. S , T S,T
  115. M M
  116. S S
  117. T T
  118. I + ( S ; T ) I^{+}(S;T)
  119. S S
  120. T T
  121. I + ( S ) T I^{+}(S)\cap T
  122. T T
  123. S S
  124. T T
  125. S S
  126. T T
  127. J + ( S ; T ) J^{+}(S;T)
  128. S S
  129. T T
  130. J + ( S ) T J^{+}(S)\cap T
  131. T T
  132. S S
  133. T T
  134. I - ( x ) I^{-}(x)
  135. S S
  136. D + ( S ) D^{+}(S)
  137. x x
  138. x x
  139. S S
  140. S M S\subset M
  141. q , r S q,r\in S
  142. r I + ( q ) r\in I^{+}(q)
  143. S S
  144. I + ( S ) I^{+}(S)
  145. M M
  146. γ \gamma
  147. J + ( γ ) J - ( γ ) J^{+}(\gamma)\cap J^{-}(\gamma)
  148. γ \gamma
  149. γ \gamma
  150. γ \gamma
  151. x x
  152. I - ( y ) \,I^{-}(y)
  153. y y
  154. I + ( x ) \,I^{+}(x)
  155. x y I - ( x ) I - ( y ) x\prec y\implies I^{-}(x)\subset I^{-}(y)
  156. x y I + ( y ) I + ( x ) x\prec y\implies I^{+}(y)\subset I^{+}(x)
  157. I + [ S ] = I + [ I + [ S ] ] J + [ S ] = J + [ J + [ S ] ] I^{+}[S]=I^{+}[I^{+}[S]]\subset J^{+}[S]=J^{+}[J^{+}[S]]
  158. I - [ S ] = I - [ I - [ S ] ] J - [ S ] = J - [ J - [ S ] ] I^{-}[S]=I^{-}[I^{-}[S]]\subset J^{-}[S]=J^{-}[J^{-}[S]]
  159. I ± ( x ) I^{\pm}(x)
  160. x x
  161. M M
  162. I ± [ S ] I^{\pm}[S]
  163. S M S\subset M
  164. I ± [ S ] = I ± [ S ¯ ] I^{\pm}[S]=I^{\pm}[\overline{S}]
  165. S M S\subset M
  166. S ¯ \overline{S}
  167. S S
  168. J ± [ S ] I ± [ S ] ¯ J^{\pm}[S]\subset\overline{I^{\pm}[S]}
  169. g \,g
  170. g ^ \hat{g}
  171. g ^ = Ω 2 g \hat{g}=\Omega^{2}g
  172. Ω \Omega
  173. g \,g
  174. g ^ . \hat{g}.
  175. X X
  176. g \,g
  177. g ( X , X ) > 0 \,g(X,X)>0
  178. g ^ ( X , X ) = Ω 2 g ( X , X ) > 0 \hat{g}(X,X)=\Omega^{2}g(X,X)>0
  179. X X
  180. g ^ \hat{g}

CCWAPSS.html

  1. S c o r e = 10 - R i s k s + ( E x c e l l e n t s / R i s k s ) Score=10-\sum Risks+(\sum Excellents/\sum Risks)

CDP-4-dehydro-6-deoxyglucose_reductase.html

  1. \rightleftharpoons

CDP-paratose_2-epimerase.html

  1. \rightleftharpoons

CEILIDH.html

  1. q q
  2. n n
  3. T n T_{n}
  4. Φ n ( q ) \Phi_{n}(q)
  5. l l
  6. Φ n \Phi_{n}
  7. n t h n^{th}
  8. m = ϕ ( n ) m=\phi(n)
  9. ϕ \phi
  10. ρ : T n ( 𝔽 q ) 𝔽 q m \rho:T_{n}(\mathbb{F}_{q})\rightarrow{\mathbb{F}_{q}}^{m}
  11. ψ \psi
  12. α T n \alpha\in T_{n}
  13. l l
  14. g = ρ ( α ) ) g=\rho(\alpha))
  15. a ( mod Φ n ( q ) ) a\ \;\;(\mathop{{\rm mod}}\Phi_{n}(q))
  16. P A = ρ ( ψ ( g ) a ) 𝔽 q m P_{A}=\rho(\psi(g)^{a})\in\mathbb{F}_{q}^{m}
  17. b ( mod Φ n ( q ) ) b\ \;\;(\mathop{{\rm mod}}\Phi_{n}(q))
  18. P B = ρ ( ψ ( g ) b ) 𝔽 q m P_{B}=\rho(\psi(g)^{b})\in\mathbb{F}_{q}^{m}
  19. ρ ( ψ ( P B ) ) a ) 𝔽 q m \rho(\psi(P_{B}))^{a})\in\mathbb{F}_{q}^{m}
  20. ρ ( ψ ( P A ) ) b ) 𝔽 q m \rho(\psi(P_{A}))^{b})\in\mathbb{F}_{q}^{m}
  21. ψ ϕ \psi\circ\phi
  22. ρ ( ψ ( P B ) ) a ) = ρ ( ψ ( P A ) ) b ) = ρ ( ψ ( g ) a b ) \rho(\psi(P_{B}))^{a})=\rho(\psi(P_{A}))^{b})=\rho(\psi(g)^{ab})
  23. a ( mod Φ n ( q ) ) a\ \;\;(\mathop{{\rm mod}}\Phi_{n}(q))
  24. P A = ρ ( ψ ( g ) a ) 𝔽 q m P_{A}=\rho(\psi(g)^{a})\in\mathbb{F}_{q}^{m}
  25. M M
  26. 𝔽 q m \mathbb{F}_{q}^{m}
  27. k k
  28. 1 k l - 1 1\leq k\leq l-1
  29. γ = ρ ( ψ ( g ) k ) 𝔽 q m \gamma=\rho(\psi(g)^{k})\in\mathbb{F}_{q}^{m}
  30. δ = ρ ( ψ ( M ) ψ ( P A ) k ) 𝔽 q m \delta=\rho(\psi(M)\psi(P_{A})^{k})\in\mathbb{F}_{q}^{m}
  31. ( γ , δ ) (\gamma,\delta)
  32. M = ρ ( ψ ( δ ) ψ ( γ ) - a ) M=\rho(\psi(\delta)\psi(\gamma)^{-a})
  33. G G
  34. G G
  35. ( c 1 , c 2 ) (c_{1},c_{2})
  36. m m
  37. ( c 1 , 2 c 2 ) (c_{1},2c_{2})
  38. 2 m 2m

Cellobiose_dehydrogenase_(acceptor).html

  1. \rightleftharpoons

Cellobiose_epimerase.html

  1. \rightleftharpoons

Certain_safety_factor.html

  1. Certain safety factor = LD 1 ED 99 \mbox{Certain safety factor}~{}=\frac{\mathrm{LD}_{1}}{\mathrm{ED}_{99}}

Chalcone_isomerase.html

  1. \rightleftharpoons

Chaos_computing.html

  1. x n + 1 = r x n ( 1 - x n ) \qquad x_{n+1}=rx_{n}(1-x_{n})
  2. x x
  3. r r
  4. x x
  5. n n
  6. x x
  7. x x

Chapman–Robbins_bound.html

  1. E { δ ( X ) } = g ( θ ) for all θ . E\{\delta(X)\}=g(\theta)\,\text{ for all }\theta.\,
  2. Var ( δ ( X ) ) sup Δ [ g ( θ + Δ ) - g ( θ ) ] 2 E θ [ p ( X ; θ + Δ ) p ( X ; θ ) - 1 ] 2 . \mathrm{Var}(\delta(X))\geq\sup_{\Delta}\frac{\left[g(\theta+\Delta)-g(\theta)% \right]^{2}}{E_{\theta}\left[\tfrac{p(X;\theta+\Delta)}{p(X;\theta)}-1\right]^% {2}}.
  3. χ 2 \chi^{2}
  4. p ( ; θ + Δ ) p(\cdot;\theta+\Delta)
  5. p ( ; θ ) p(\cdot;\theta)

Chebyshev_linkage.html

  1. L 1 : L 2 : L 3 = 2 : 2.5 : 1 = 4 : 5 : 2. L_{1}:L_{2}:L_{3}=2:2.5:1=4:5:2.\,
  2. L 4 = L 3 + L 2 2 - L 1 2 . L_{4}=L_{3}+\sqrt{L_{2}^{2}-L_{1}^{2}}.\,
  3. L 4 = L 2 . L_{4}=L_{2}.\,
  4. x A = L 2 cos ( φ 1 ) x_{A}=L_{2}\cos(\varphi_{1})\,
  5. y A = L 2 sin ( φ 1 ) y_{A}=L_{2}\sin(\varphi_{1})\,
  6. x B = L 1 - L 4 cos ( φ 2 ) x_{B}=L_{1}-L_{4}\cos(\varphi_{2})\,
  7. y B = L 4 sin ( φ 2 ) y_{B}=L_{4}\sin(\varphi_{2})\,
  8. φ 2 = arcsin [ L 2 sin ( φ 1 ) A O 2 ¯ ] - arccos ( L 4 2 + A O 2 ¯ 2 - L 3 2 2 L 4 A O 2 ¯ ) \varphi_{2}=\arcsin\left[\frac{L_{2}\,\sin(\varphi_{1})}{\overline{AO_{2}}}% \right]-\arccos\left(\frac{L_{4}^{2}+\overline{AO_{2}}^{2}-L_{3}^{2}}{2\,L_{4}% \,\overline{AO_{2}}}\right)\,
  9. x P = x A + x B 2 x_{P}=\frac{x_{A}+x_{B}}{2}\,
  10. y P = y A + y B 2 y_{P}=\frac{y_{A}+y_{B}}{2}\,
  11. φ min = arccos ( 4 5 ) 36.8699 . \varphi_{\,\text{min}}=\arccos\left(\frac{4}{5}\right)\approx 36.8699^{\circ}.\,
  12. φ max = arccos ( - 1 5 ) 101.537 . \varphi_{\,\text{max}}=\arccos\left(\frac{-1}{5}\right)\approx 101.537^{\circ}.\,

Chirikov_criterion.html

  1. K S 2 = ( Δ ω r / Δ d ) 2 Align g t ; 1. K\approx S^{2}=(\Delta\omega_{r}/\Delta_{d})^{2}&gt;1.
  2. K K
  3. S = Δ ω r / Δ d S=\Delta\omega_{r}/\Delta_{d}
  4. Δ ω r \Delta\omega_{r}
  5. Δ d \Delta_{d}

Chlorate_reductase.html

  1. \rightleftharpoons

Chlordecone_reductase.html

  1. \rightleftharpoons

Chloridazon-catechol_dioxygenase.html

  1. \rightleftharpoons

Chloromuconate_cycloisomerase.html

  1. \rightleftharpoons

Chlorophenol_O-methyltransferase.html

  1. \rightleftharpoons

Cholest-5-ene-3beta,7alpha-diol_3beta-dehydrogenase.html

  1. \rightleftharpoons

Cholestanetetraol_26-dehydrogenase.html

  1. \rightleftharpoons

Cholestanetriol_26-monooxygenase.html

  1. \rightleftharpoons

Cholestenol_Delta-isomerase.html

  1. \rightleftharpoons

Cholestenone_5alpha-reductase.html

  1. \rightleftharpoons

Cholesterol_24-hydroxylase.html

  1. \rightleftharpoons

Cholesterol_25-hydroxylase.html

  1. \rightleftharpoons

Cholesterol_7alpha-monooxygenase.html

  1. \rightleftharpoons

Cholesterol_oxidase.html

  1. \rightleftharpoons

Choline_dehydrogenase.html

  1. \rightleftharpoons

Choline_monooxygenase.html

  1. \rightleftharpoons

Choline_oxidase.html

  1. \rightleftharpoons

Choline_sulfotransferase.html

  1. \rightleftharpoons

Chondroitin-glucuronate_5-epimerase.html

  1. \rightleftharpoons

Chondroitin_4-sulfotransferase.html

  1. \rightleftharpoons

Chondroitin_6-sulfotransferase.html

  1. \rightleftharpoons

Chorismate_lyase.html

  1. \rightleftharpoons

Chow–Liu_tree.html

  1. P ( X 1 , X 2 , , X n ) P(X_{1},X_{2},\ldots,X_{n})
  2. P ( X 1 , X 2 , X 3 , X 4 , X 5 , X 6 ) P(X_{1},X_{2},X_{3},X_{4},X_{5},X_{6})
  3. P ( X 1 , X 2 , X 3 , X 4 , X 5 , X 6 ) = P ( X 6 | X 5 ) P ( X 5 | X 2 ) P ( X 4 | X 2 ) P ( X 3 | X 2 ) P ( X 2 | X 1 ) P ( X 1 ) P^{\prime}(X_{1},X_{2},X_{3},X_{4},X_{5},X_{6})=P(X_{6}|X_{5})P(X_{5}|X_{2})P(% X_{4}|X_{2})P(X_{3}|X_{2})P(X_{2}|X_{1})P(X_{1})
  4. P P^{\prime}
  5. P P
  6. D ( P P ) = - I ( X i ; X j ( i ) ) + H ( X i ) - H ( X 1 , X 2 , , X n ) D(P\parallel P^{\prime})=-\sum I(X_{i};X_{j(i)})+\sum H(X_{i})-H(X_{1},X_{2},% \ldots,X_{n})
  7. I ( X i ; X j ( i ) ) I(X_{i};X_{j(i)})
  8. X i X_{i}
  9. X j ( i ) X_{j(i)}
  10. H ( X 1 , X 2 , , X n ) H(X_{1},X_{2},\ldots,X_{n})
  11. { X 1 , X 2 , , X n } \{X_{1},X_{2},\ldots,X_{n}\}
  12. H ( X i ) \sum H(X_{i})
  13. H ( X 1 , X 2 , , X n ) H(X_{1},X_{2},\ldots,X_{n})
  14. I ( X i ; X j ( i ) ) \sum I(X_{i};X_{j(i)})

Churchill–Bernstein_equation.html

  1. Nu ¯ D = 0.3 + 0.62 Re D 1 / 2 Pr 1 / 3 [ 1 + ( 0.4 / Pr ) 2 / 3 ] 1 / 4 [ 1 + ( Re D 282000 ) 5 / 8 ] 4 / 5 Pr Re D 0.2 \overline{\mathrm{Nu}}_{D}\ =0.3+\frac{0.62\mathrm{Re}_{D}^{1/2}\Pr^{1/3}}{% \left[1+(0.4/\Pr)^{2/3}\,\right]^{1/4}\,}\bigg[1+\bigg(\frac{\mathrm{Re}_{D}}{% 282000}\bigg)^{5/8}\bigg]^{4/5}\quad\Pr\mathrm{Re}_{D}\geq 0.2
  2. Nu ¯ D \overline{\mathrm{Nu}}_{D}
  3. Re D \mathrm{Re}_{D}\,\!
  4. Pr \Pr
  5. Sh D = 0.3 + 0.62 Re D 1 / 2 Sc 1 / 3 [ 1 + ( 0.4 / Sc ) 2 / 3 ] 1 / 4 [ 1 + ( Re D 282000 ) 5 / 8 ] 4 / 5 Sc Re D 0.2 \mathrm{Sh}_{D}=0.3+\frac{0.62\mathrm{Re}_{D}^{1/2}\mathrm{Sc}^{1/3}}{\left[1+% (0.4/\mathrm{Sc})^{2/3}\,\right]^{1/4}\,}\bigg[1+\bigg(\frac{\mathrm{Re}_{D}}{% 282000}\bigg)^{5/8}\bigg]^{4/5}\quad\mathrm{Sc}\,\mathrm{Re}_{D}\geq 0.2
  6. Sh D \mathrm{Sh}_{D}
  7. Sc \mathrm{Sc}

Cinnamoyl-CoA:phenyllactate_CoA-transferase.html

  1. \rightleftharpoons

Cinnamoyl-CoA_reductase.html

  1. \rightleftharpoons

Cinnamyl-alcohol_dehydrogenase.html

  1. \rightleftharpoons

Circuit_minimization_for_Boolean_functions.html

  1. Σ 2 P \Sigma_{2}^{P}
  2. ( A B ¯ ) ( A ¯ B ) (A\wedge\bar{B})\vee(\bar{A}\wedge B)
  3. A B A\neq B
  4. ( A B ¯ ) ( A ¯ B ) A B (A\wedge\bar{B})\vee(\bar{A}\wedge B)\iff A\neq B

Cis-1,2-dihydro-1,2-dihydroxynaphthalene_dehydrogenase.html

  1. \rightleftharpoons

Cis-1,2-dihydrobenzene-1,2-diol_dehydrogenase.html

  1. \rightleftharpoons

Cis-1,2-dihydroxy-4-methylcyclohexa-3,5-diene-1-carboxylate_dehydrogenase.html

  1. \rightleftharpoons

Cis-2,3-dihydrobiphenyl-2,3-diol_dehydrogenase.html

  1. \rightleftharpoons

Cis-2-enoyl-CoA_reductase_(NADPH).html

  1. \rightleftharpoons

Cis-3,4-dihydrophenanthrene-3,4-diol_dehydrogenase.html

  1. \rightleftharpoons

Cis-dihydroethylcatechol_dehydrogenase.html

  1. \rightleftharpoons

Citramalate_CoA-transferase.html

  1. \rightleftharpoons

Citramalate_lyase.html

  1. \rightleftharpoons

Citramalyl-CoA_lyase.html

  1. \rightleftharpoons

Citrate_(pro-3S)-lyase.html

  1. \rightleftharpoons

Citrate_CoA-transferase.html

  1. \rightleftharpoons

Citryl-CoA_lyase.html

  1. \rightleftharpoons

Clarkson's_inequalities.html

  1. 1 p + 1 q = 1 , \frac{1}{p}+\frac{1}{q}=1,
  2. x x p . x\mapsto x^{p}.\,

Classification_of_manifolds.html

  1. Diff Top \mbox{Diff}~{}\to\mbox{Top}~{}
  2. Diff Top \mbox{Diff}~{}\to\mbox{Top}~{}
  3. n 0 n\geq 0
  4. M O * ( M ) MO_{*}(M)
  5. [ 0 , 1 ] [0,1]
  6. S 1 S^{1}
  7. ( 0 , 1 ) (0,1)
  8. [ 0 , 1 ) [0,1)
  9. n 4 n\geq 4
  10. n 3 n\geq 3
  11. 2 + 2 < 5 2+2<5

Cluster_state.html

  1. K G ( a ) | G = ( - 1 ) k a | G K_{G}^{(a)}{\left|G\right\rangle}=(-1)^{k_{a}}{\left|G\right\rangle}
  2. K G ( a ) = σ x ( a ) b N ( a ) σ z ( b ) . K_{G}^{(a)}=\sigma_{x}^{(a)}\bigotimes_{b\in\mathrm{N}(a)}\sigma_{z}^{(b)}.
  3. N ( a ) N(a)
  4. a a

CMB_cold_spot.html

  1. z 1 z\simeq 1

CMP-N-acetylneuraminate_monooxygenase.html

  1. \rightleftharpoons

CoA-disulfide_reductase.html

  1. \rightleftharpoons

CoA-glutathione_reductase.html

  1. \rightleftharpoons

Cob(II)alamin_reductase.html

  1. \rightleftharpoons

Cob(II)yrinic_acid_a,c-diamide_reductase.html

  1. \rightleftharpoons

Cobalt-factor_II_C20-methyltransferase.html

  1. \rightleftharpoons

CoB—CoM_heterodisulfide_reductase.html

  1. \rightleftharpoons

Codeinone_reductase_(NADPH).html

  1. \rightleftharpoons

Codex_Boernerianus.html

  1. 𝔓 \mathfrak{P}

Coenzyme-B_sulfoethylthiotransferase.html

  1. \rightleftharpoons

Coenzyme_F420_hydrogenase.html

  1. \rightleftharpoons

Columbamine_O-methyltransferase.html

  1. \rightleftharpoons

Columbamine_oxidase.html

  1. \rightleftharpoons

Complementary_monopoly.html

  1. D = D m a x ( P m a x - P ) D=D_{max}\cdot(P_{max}-P)
  2. P = P m a x 2 P=\frac{P_{max}}{2}
  3. R = D P = D m a x ( P m a x - P m a x 2 ) P m a x 2 = D m a x P m a x 2 4 R={D}\cdot{P}={D_{max}\cdot(P_{max}-\frac{P_{max}}{2})}\cdot\frac{P_{max}}{2}=% {D_{max}\cdot\frac{P_{max}^{2}}{4}}
  4. P = P m a x 3 P=\frac{P_{max}}{3}
  5. P = 2 P m a x 3 P=\frac{2\cdot P_{max}}{3}
  6. R = D P = D m a x ( P m a x - 2 P m a x 3 ) 2 P m a x 3 = D m a x 2 P m a x 2 9 R={D}\cdot{P}={D_{max}\cdot(P_{max}-\frac{2\cdot P_{max}}{3})}\cdot\frac{2% \cdot P_{max}}{3}={D_{max}\cdot\frac{2\cdot P_{max}^{2}}{9}}

Computers_and_Intractability.html

  1. H H

Computron_tube.html

  1. S = ( A * B ) + C + D S=(A*B)+C+D

Conditional_short_circuit_current.html

  1. I = 1 t 1 - t 0 t 0 t 1 i 2 ( t ) d t I=\sqrt{\frac{1}{t_{1}-t_{0}}\int_{t_{0}}^{t_{1}}i^{2}(t)dt}

Cone_(formal_languages).html

  1. 𝒮 \mathcal{S}
  2. L 𝒮 L\in\mathcal{S}
  3. Σ \Sigma
  4. h h
  5. Σ \Sigma^{\ast}
  6. Δ \Delta^{\ast}
  7. h ( L ) h(L)
  8. 𝒮 \mathcal{S}
  9. h h
  10. Δ \Delta^{\ast}
  11. Σ \Sigma^{\ast}
  12. h - 1 ( L ) h^{-1}(L)
  13. 𝒮 \mathcal{S}
  14. R R
  15. Σ \Sigma
  16. L R L\cap R
  17. 𝒮 \mathcal{S}
  18. λ \lambda
  19. T T
  20. L L
  21. T ( L ) T(L)
  22. T T
  23. T T
  24. T ( L ) = g ( h - 1 ( L ) R ) T(L)=g(h^{-1}(L)\cap R)
  25. g , h g,h
  26. R R
  27. T T
  28. { a , b } \{a,b\}
  29. b b

Coniferyl-alcohol_dehydrogenase.html

  1. \rightleftharpoons

Coniferyl-aldehyde_dehydrogenase.html

  1. \rightleftharpoons

Conjunctive_query.html

  1. \wedge
  2. \exists
  3. \lor
  4. ¬ \neg
  5. \forall
  6. ( x 1 , , x k ) . x k + 1 , x m . A 1 A r (x_{1},\ldots,x_{k}).\exists x_{k+1},\ldots x_{m}.A_{1}\wedge\ldots\wedge A_{r}
  7. x 1 , , x k x_{1},\ldots,x_{k}
  8. x k + 1 , , x m x_{k+1},\ldots,x_{m}
  9. A 1 , , A r A_{1},\ldots,A_{r}
  10. x 1 . x 2 . R ( x 2 ) x_{1}.\exists x_{2}.R(x_{2})
  11. R S R\subseteq S
  12. R , S R,S
  13. R R
  14. S S
  15. Q Q
  16. I I
  17. Q ( I ) Q(I)
  18. Q 1 Q_{1}
  19. Q 2 Q_{2}
  20. I I
  21. Q 1 ( I ) Q 2 ( I ) Q_{1}(I)\subseteq Q_{2}(I)
  22. { x , y } \{x,y\}
  23. R ( x , y ) R(x,y)
  24. R ( y , x ) R(y,x)

Consumption_smoothing.html

  1. E t E_{t}
  2. t t
  3. δ = 1 / β - 1 \delta=1/\beta-1
  4. r t = R t - 1 δ r_{t}=R_{t}-1\geq\delta
  5. t t
  6. u u
  7. c t c_{t}
  8. t t
  9. y t = w t y_{t}=w_{t}
  10. t t
  11. A t A_{t}
  12. t t
  13. E 0 t = 0 β t [ u ( c t ) ] E_{0}\sum_{t=0}^{\infty}\beta^{t}\left[u(c_{t})\right]
  14. A t + 1 = R t + 1 ( A t + y t - c t ) A_{t+1}=R_{t+1}(A_{t}+y_{t}-c_{t})
  15. β E t R t + 1 u ( c t + 1 ) u ( c t ) = 1 \beta E_{t}R_{t+1}\frac{u^{\prime}(c_{t+1})}{u^{\prime}(c_{t})}=1
  16. R t + 1 = R = β - 1 R_{t+1}=R=\beta^{-1}
  17. E t u ( c t + 1 ) = u ( c t ) E_{t}u^{\prime}(c_{t+1})=u^{\prime}(c_{t})
  18. E t [ c t + 1 ] = c t E_{t}[c_{t+1}]=c_{t}
  19. c t = [ r 1 + r ] [ E t i = 0 ( 1 1 + r ) i y t + i + A t ] c_{t}=\left[\frac{r}{1+r}\right]\left[E_{t}\sum_{i=0}^{\infty}\left(\frac{1}{1% +r}\right)^{i}y_{t+i}+A_{t}\right]
  20. β E t R t + 1 u ( c t + 1 ) u ( c t ) = 1 \beta E_{t}R_{t+1}\frac{u^{\prime}(c_{t+1})}{u^{\prime}(c_{t})}=1
  21. c t + 1 = c t c_{t+1}=c_{t}
  22. i = 0 b t [ u 0 + u 1 c 1 - u 2 2 c t 2 ] , \sum_{i=0}^{\infty}b^{t}\left[u_{0}+u_{1}c_{1}-\frac{u_{2}}{2}c_{t}^{2}\right],
  23. A t = R [ A t + y t - c t ] A_{t}=R[A_{t}+y_{t}-c_{t}]
  24. y t y_{t}
  25. E t y t E_{t}y_{t}
  26. c c
  27. A A
  28. y y
  29. R R
  30. E E
  31. t t
  32. c t = ( 1 - R - 2 b - 1 ) A t - u 1 u 2 ( R - 1 b - 1 L - 1 ) 1 - R + ( 1 - R - 2 b - 1 ) 1 - L - 1 R - 1 E t y t c_{t}=(1-R^{-2}b^{-1})A_{t}-\frac{u_{1}}{u_{2}}\frac{(R^{-1}b^{-1}L^{-1})}{1-R% }+\frac{(1-R^{-2}b^{-1})}{1-L^{-1}R^{-1}}E_{t}y_{t}
  33. L L
  34. c t + 1 , c t + 2 , , c t + n c_{t+1},c_{t+2},...,c_{t+n}
  35. c t + 1 = ( 1 - R - 2 b - 1 ) A t + 1 - u 1 u 2 ( R - 1 b - 1 L - 1 ) 1 - R + ( 1 - R - 2 b - 1 ) 1 - L - 1 R - 1 E t + 1 y t + 1 c_{t+1}=(1-R^{-2}b^{-1})A_{t+1}-\frac{u_{1}}{u_{2}}\frac{(R^{-1}b^{-1}L^{-1})}% {1-R}+\frac{(1-R^{-2}b^{-1})}{1-L^{-1}R^{-1}}E_{t+1}y_{t+1}
  36. c t + 2 = ( 1 - R - 2 b - 1 ) A t + 2 - u 1 u 2 ( R - 1 b - 1 L - 1 ) 1 - R + ( 1 - R - 2 b - 1 ) 1 - L - 1 R - 1 E t + 2 y t + 2 c_{t+2}=(1-R^{-2}b^{-1})A_{t+2}-\frac{u_{1}}{u_{2}}\frac{(R^{-1}b^{-1}L^{-1})}% {1-R}+\frac{(1-R^{-2}b^{-1})}{1-L^{-1}R^{-1}}E_{t+2}y_{t+2}
  37. c t + n = ( 1 - R - 2 b - 1 ) A t + 1 - u 1 u 2 ( R - 1 b - 1 L - 1 ) 1 - R + ( 1 - R - 2 b - 1 ) 1 - L - 1 R - 1 E t + n y t + n c_{t+n}=(1-R^{-2}b^{-1})A_{t+1}-\frac{u_{1}}{u_{2}}\frac{(R^{-1}b^{-1}L^{-1})}% {1-R}+\frac{(1-R^{-2}b^{-1})}{1-L^{-1}R^{-1}}E_{t+n}y_{t+n}
  38. R b = 1 Rb=1
  39. c t + n = ( 1 - R - 1 ) [ A t + n + E t + n y t + n 1 - L - 1 R - 1 ] c_{t+n}=(1-R^{-1})\left[A_{t+n}+\frac{E_{t+n}y_{t+n}}{1-L^{-1}R^{-1}}\right]
  40. 1 1 - R L \frac{1}{1-RL}
  41. 1 1 - R L = - ( R L ) - 1 1 - ( R L ) - 1 = - 1 R L - 1 - ( 1 R ) 2 L - 2 - ( 1 R ) 3 L - 3 - \frac{1}{1-RL}=\frac{-(RL)^{-1}}{1-(RL)^{-1}}=-\frac{1}{R}L^{-1}-\left(\frac{1% }{R}\right)^{2}L^{-2}-\left(\frac{1}{R}\right)^{3}L^{-3}-...
  42. L - n y t = y t + n L^{-n}y_{t}=y_{t+n}
  43. ( R L ) - 1 1 - ( R L ) - 1 y t = 1 R L - 1 y t + ( 1 R ) 2 L - 2 y t + ( 1 R ) 3 L - 3 y t + = j = 1 ( 1 R ) j y t + j \frac{(RL)^{-1}}{1-(RL)^{-1}}y_{t}=\frac{1}{R}L^{-1}y_{t}+\left(\frac{1}{R}% \right)^{2}L^{-2}y_{t}+\left(\frac{1}{R}\right)^{3}L^{-3}y_{t}+...=\sum_{j=1}^% {\infty}\left(\frac{1}{R}\right)^{j}y_{t+j}
  44. E t + n y t + n 1 - L - 1 R - 1 = j = n ( 1 R ) j - n E t + n y t + j \frac{E_{t+n}y_{t+n}}{1-L^{-1}R^{-1}}=\sum_{j=n}^{\infty}\left(\frac{1}{R}% \right)^{j-n}E_{t+n}y_{t+j}
  45. c t + n = ( 1 - R - 1 ) [ A t + n + j = n ( 1 R ) j - n E t + n y t + j ] c_{t+n}=(1-R^{-1})\left[A_{t+n}+\sum_{j=n}^{\infty}\left(\frac{1}{R}\right)^{j% -n}E_{t+n}y_{t+j}\right]
  46. c t + 1 = ( 1 - R - 1 ) [ A t + 1 + j = 1 ( 1 R ) j - 1 E t + 1 y t + j ] c_{t+1}=(1-R^{-1})\left[A_{t+1}+\sum_{j=1}^{\infty}\left(\frac{1}{R}\right)^{j% -1}E_{t+1}y_{t+j}\right]
  47. c t + 1 = ( 1 - R - 1 ) [ A t + 1 + j = 0 ( 1 R ) j E t + 1 y t + j + 1 ] c_{t+1}=(1-R^{-1})\left[A_{t+1}+\sum_{j=0}^{\infty}\left(\frac{1}{R}\right)^{j% }E_{t+1}y_{t+j+1}\right]
  48. c t + 1 - c t = ( 1 - R - 1 ) [ A t + 1 - A t + j = 0 ( 1 R ) j E t + 1 y t + j + 1 - j = 0 ( 1 R ) j E t y t + j ] = ( 1 - R - 1 ) j = 0 ( 1 R ) j ( E t + 1 - E t ) y t + j + 1 c_{t+1}-c_{t}=(1-R^{-1})\left[A_{t+1}-A_{t}+\sum_{j=0}^{\infty}\left(\frac{1}{% R}\right)^{j}E_{t+1}y_{t+j+1}-\sum_{j=0}^{\infty}\left(\frac{1}{R}\right)^{j}E% _{t}y_{t+j}\right]=(1-R^{-1})\sum_{j=0}^{\infty}\left(\frac{1}{R}\right)^{j}(E% _{t+1}-E_{t})y_{t+j+1}
  49. ( E t + 1 - E t ) y t + j + 1 (E_{t+1}-E_{t})y_{t+j+1}
  50. E t c t + 1 = c t E_{t}c_{t+1}=c_{t}
  51. A t + 1 - A t = 0 A_{t+1}-A_{t}=0
  52. ( 1 R ) j - n E t + n y t + j \left(\frac{1}{R}\right)^{j-n}E_{t+n}{y_{t+j}}
  53. Y Y
  54. c t = A t + n Y c_{t}=A_{t}+nY
  55. t + 1 t+1
  56. c t + 1 = A t + 1 + ( n - 1 ) Y c_{t+1}=A_{t+1}+(n-1)Y
  57. c t + 1 - c t = - Y c_{t+1}-c_{t}=-Y
  58. c t + 1 c_{t+1}
  59. c t + 1 - c t = ( 1 - R - 1 ) [ A t + 1 - A t + j = 1 ( 1 R ) j - 1 E t + 1 y t + j - j = 0 ( 1 R ) j E t y t + j ] c_{t+1}-c_{t}=(1-R^{-1})\left[A_{t+1}-A_{t}+\sum_{j=1}^{\infty}\left(\frac{1}{% R}\right)^{j-1}E_{t+1}y_{t+j}-\sum_{j=0}^{\infty}\left(\frac{1}{R}\right)^{j}E% _{t}y_{t+j}\right]
  60. j = 0 ( 1 R ) j E t y t + j = E t y t + j = 1 ( 1 R ) j E t y t + j = y t + j = 1 ( 1 R ) j E t y t + j \sum_{j=0}^{\infty}\left(\frac{1}{R}\right)^{j}E_{t}y_{t+j}=E_{t}y_{t}+\sum_{j% =1}^{\infty}\left(\frac{1}{R}\right)^{j}E_{t}y_{t+j}=y_{t}+\sum_{j=1}^{\infty}% \left(\frac{1}{R}\right)^{j}E_{t}y_{t+j}
  61. j = 1 ( 1 R ) j - 1 E t + 1 y t + j - j = 1 ( 1 R ) j E t y t + j = 0 \sum_{j=1}^{\infty}\left(\frac{1}{R}\right)^{j-1}E_{t+1}y_{t+j}-\sum_{j=1}^{% \infty}\left(\frac{1}{R}\right)^{j}E_{t}y_{t+j}=0
  62. y m t = ( 1 - 1 R ) A t + y t y_{mt}=\left(1-\frac{1}{R}\right)A_{t}+y_{t}
  63. c t + 1 - c t = y m t + 1 - y t + 1 - y m t + y t - ( R - 1 ) R y t c_{t+1}-c_{t}=y_{mt+1}-y_{t+1}-y_{mt}+y_{t}-\frac{(R-1)}{R}y_{t}
  64. ( y m t + 1 - c t + 1 ) - ( y m t - c t ) = ( y t + 1 - y t R ) (y_{mt+1}-c_{t+1})-(y_{mt}-c_{t})=\left(y_{t+1}-\frac{y_{t}}{R}\right)

Contraction_principle_(large_deviations_theory).html

  1. J ( y ) := inf { I ( x ) | x X and T ( x ) = y } , J(y):=\inf\big\{I(x)\big|x\in X\mbox{ and }~{}T(x)=y\big\},

Cooling_flow.html

  1. M ˙ = 2 5 L μ m k T , \dot{M}=\frac{2}{5}\frac{L\mu m}{kT},

Coomber's_relationship.html

  1. p i = ( E V ) T p_{i}=\left(\frac{\partial E}{\partial V}\right)_{T}\,
  2. p i = n I b ( T ) N 2 α 2 V n + 1 p_{i}=n\cdot{I}\cdot{b(T)}\frac{N^{2}\alpha^{2}}{V^{n+1}}\,
  3. N N\,
  4. I I\,
  5. b ( T ) b(T)\,
  6. α \alpha\,
  7. V V\,
  8. n = 1 n=1\,

Copalyl_diphosphate_synthase.html

  1. \rightleftharpoons

Coproporphyrinogen_dehydrogenase.html

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Corticosteroid_side-chain-isomerase.html

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Corticosterone_18-monooxygenase.html

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Cortisol_sulfotransferase.html

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Cortisone_alpha-reductase.html

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Corydaline_synthase.html

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Cramér's_theorem.html

  1. ( k = 1 n X k n ) n \left(\frac{\sum_{k=1}^{n}X_{k}}{n}\right)_{n\in\mathbb{N}}

Crop_coefficient.html

  1. P E T = K c * R E T PET=K_{c}*RET
  2. E T e s t i m a t e = K w * K s 1 * K s 2 * K c * E T o ET_{estimate}=K_{w}*K_{s_{1}}*K_{s_{2}}*K_{c}*ET_{o}

Cucurbitacin_Delta23-reductase.html

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Cut_locus_(Riemannian_manifold).html

  1. p p
  2. p p
  3. p p
  4. ( M , g ) (M,g)
  5. T p M T_{p}M
  6. v v
  7. T p M T_{p}M
  8. γ ( t ) = exp p ( t v ) \gamma(t)=\exp_{p}(tv)
  9. t t
  10. [ 0 , 1 ] [0,1]
  11. exp p \exp_{p}
  12. p p
  13. p p
  14. v v
  15. T p M T_{p}M
  16. γ ( t ) = exp p ( t v ) \gamma(t)=\exp_{p}(tv)
  17. t [ 0 , 1 ] t\in[0,1]
  18. t [ 0 , 1 + ϵ ) t\in[0,1+\epsilon)
  19. ϵ > 0 \epsilon>0
  20. p p
  21. M M
  22. p p
  23. p p
  24. p p
  25. M M
  26. p p
  27. q q
  28. p p
  29. M M
  30. p p
  31. q q
  32. p p
  33. q q
  34. p p
  35. p p

Cyanocobalamin_reductase_(cyanide-eliminating).html

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Cyclamate_sulfohydrolase.html

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Cycloartenol_24-C-methyltransferase.html

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Cycloartenol_synthase.html

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Cycloeucalenol_cycloisomerase.html

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Cyclohexane-1,2-diol_dehydrogenase.html

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Cyclohexane-1,3-dione_hydrolase.html

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Cyclohexanol_dehydrogenase.html

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Cyclohexanone_dehydrogenase.html

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Cyclohexylamine_oxidase.html

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Cyclopentanol_dehydrogenase.html

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Cyclopentanone_monooxygenase.html

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Cyclopropane-fatty-acyl-phospholipid_synthase.html

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Cypridina-luciferin_2-monooxygenase.html

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Cystathionine_beta-lyase.html

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Cysteamine_dioxygenase.html

  1. \rightleftharpoons

Cysteine-S-conjugate_beta-lyase.html

  1. \rightleftharpoons

Cysteine_desulfurase.html

  1. \rightleftharpoons

Cysteine_lyase.html

  1. \rightleftharpoons

Cystine_reductase.html

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Cytidylate_cyclase.html

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Cytochrome-c3_hydrogenase.html

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Cytokinin_dehydrogenase.html

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D-2-hydroxy-acid_dehydrogenase.html

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D-alanine_2-hydroxymethyltransferase.html

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D-arabinitol_2-dehydrogenase.html

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D-arabinitol_4-dehydrogenase.html

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D-arabinono-1,4-lactone_oxidase.html

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D-arabinose_1-dehydrogenase.html

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D-arabinose_1-dehydrogenase_(NAD(P)+).html

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D-aspartate_oxidase.html

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D-cysteine_desulfhydrase.html

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D-dopachrome_decarboxylase.html

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D-glutamate(D-aspartate)_oxidase.html

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D-glutamate_oxidase.html

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D-iditol_2-dehydrogenase.html

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D-lactate_dehydrogenase_(cytochrome).html

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D-lactate_dehydrogenase_(cytochrome_c-553).html

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D-lysine_5,6-aminomutase.html

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D-lysopine_dehydrogenase.html

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D-lyxose_ketol-isomerase.html

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D-malate_dehydrogenase_(decarboxylating).html

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D-mannitol_oxidase.html

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D-nopaline_dehydrogenase.html

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D-octopine_dehydrogenase.html

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D-ornithine_4,5-aminomutase.html

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D-pinitol_dehydrogenase.html

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D-proline_reductase_(dithiol).html

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D-serine_ammonia-lyase.html

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D-sorbitol_dehydrogenase_(acceptor).html

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D-threo-aldose_1-dehydrogenase.html

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D-xylose_1-dehydrogenase.html

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D-xylose_1-dehydrogenase_(NADP+).html

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D-xylulose_reductase.html

  1. \rightleftharpoons

Darcy_friction_factor_formulae.html

  1. f = 64 Re f=\frac{64}{\mathrm{Re}}
  2. f f
  3. Re \mathrm{Re}
  4. 1 f = - 2 log 10 ( ε 3.7 D h + 2.51 Re f ) \frac{1}{\sqrt{f}}=-2\log_{10}\left(\frac{\varepsilon}{3.7D_{\mathrm{h}}}+% \frac{2.51}{\mathrm{Re}\sqrt{f}}\right)
  5. 1 f = - 2 log 10 ( ε 14.8 R h + 2.51 Re f ) \frac{1}{\sqrt{f}}=-2\log_{10}\left(\frac{\varepsilon}{14.8R_{\mathrm{h}}}+% \frac{2.51}{\mathrm{Re}\sqrt{f}}\right)
  6. f f
  7. ε \varepsilon
  8. D h D_{\mathrm{h}}
  9. D h D_{\mathrm{h}}
  10. R h R_{\mathrm{h}}
  11. R h R_{\mathrm{h}}
  12. Re \mathrm{Re}
  13. f f
  14. f f
  15. f f
  16. 1 f = 1.7384 - 2 log 10 ( 2 ε D h + 18.574 Re f ) \frac{1}{\sqrt{f}}=1.7384\ldots-2\log_{10}\left(\frac{2\varepsilon}{D_{\mathrm% {h}}}+\frac{18.574}{\mathrm{Re}\sqrt{f}}\right)
  17. 1 f = 1.1364 + 2 log 10 ( D h / ε ) - 2 log 10 ( 1 + 9.287 Re ( ε / D h ) f ) \frac{1}{\sqrt{f}}=1.1364\ldots+2\log_{10}(D_{\mathrm{h}}/\varepsilon)-2\log_{% 10}\left(1+\frac{9.287}{\mathrm{Re}(\varepsilon/D_{\mathrm{h}})\sqrt{f}}\right)
  18. 1 f = 1.1364 - 2 log 10 ( ε D h + 9.287 Re f ) \frac{1}{\sqrt{f}}=1.1364\ldots-2\log_{10}\left(\frac{\varepsilon}{D_{\mathrm{% h}}}+\frac{9.287}{\mathrm{Re}\sqrt{f}}\right)
  19. 1 f = - 2 log 10 ( ε 12 R h + 2.51 Re f ) . \frac{1}{\sqrt{f}}=-2\log_{10}\left(\frac{\varepsilon}{12R_{\mathrm{h}}}+\frac% {2.51}{\mathrm{Re}\sqrt{f}}\right).
  20. 1 f = - 1.8 log 10 [ ( ε / D 3.7 ) 1.11 + 6.9 Re ] \frac{1}{\sqrt{f}}=-1.8\log_{10}\left[\left(\frac{\varepsilon/D}{3.7}\right)^{% 1.11}+\frac{6.9}{\mathrm{Re}}\right]
  21. f f
  22. ε / D \varepsilon/D
  23. Re \mathrm{Re}
  24. f = 0.25 [ log 10 ( ε 3.7 D + 5.74 Re 0.9 ) ] - 2 f=0.25\left[\log_{10}\left(\frac{\varepsilon}{3.7D}+\frac{5.74}{\mathrm{Re}^{0% .9}}\right)\right]^{-2}
  25. A = - 2 log 10 ( ε 3.7 D + 12 Re ) A=-2\log_{10}\left({\varepsilon\over 3.7D}+{12\over\mbox{Re}~{}}\right)
  26. B = - 2 log 10 ( ε 3.7 D + 2.51 A Re ) B=-2\log_{10}\left({\varepsilon\over 3.7D}+{2.51A\over\mbox{Re}~{}}\right)
  27. C = - 2 log 10 ( ε 3.7 D + 2.51 B Re ) C=-2\log_{10}\left({\varepsilon\over 3.7D}+{2.51B\over\mbox{Re}~{}}\right)
  28. 1 f = ( A - ( B - A ) 2 C - 2 B + A ) \frac{1}{\sqrt{f}}=\left(A-\frac{(B-A)^{2}}{C-2B+A}\right)
  29. a = 2 ln ( 10 ) a={2\over\ln(10)}
  30. b = ε / D 3.7 b={\varepsilon/D\over 3.7}
  31. d = ln ( 10 ) R e 5.02 d={\ln(10)Re\over 5.02}
  32. s = b d + ln ( d ) s={bd+\ln(d)}
  33. q = s s / ( s + 1 ) q={{s}^{s/(s+1)}}
  34. g = b d + ln d q g={bd+\ln{d\over q}}
  35. z = ln q g z={\ln{q\over g}}
  36. D L A = z g g + 1 D_{LA}=z{{g\over{g+1}}}
  37. D C F A = D L A ( 1 + z / 2 ( g + 1 ) 2 + ( z / 3 ) ( 2 g - 1 ) ) D_{CFA}=D_{LA}\left(1+\frac{z/2}{(g+1)^{2}+(z/3)(2g-1)}\right)
  38. 1 f = a [ ln ( d q ) + D C F A ] \frac{1}{\sqrt{f}}={a\left[\ln\left(\frac{d}{q}\right)+D_{CFA}\right]}
  39. S = l n R e 1.816 ln 1.1 Re ln ( 1 + 1.1 Re ) S=ln\frac{Re}{\mathrm{1.816ln\frac{1.1Re}{\mathrm{ln(1+1.1Re)}}}}
  40. 1 f = - 2 log 10 ( ε / D 3.71 + 2.18 S Re ) \frac{1}{\sqrt{f}}=-2\log_{10}\left({\varepsilon/D\over 3.71}+{2.18S\over\mbox% {Re}~{}}\right)
  41. f = .316 Re - 1 4 f=.316\mathrm{Re}^{-{1\over 4}}
  42. f = 0.316 Re - 1 4 + 0.0075 D 2 R c f=0.316\mathrm{Re}^{-{1\over 4}}+0.0075\sqrt{\frac{D}{2R_{c}}}
  43. R c = R [ 1 + ( H 2 π R ) 2 ] R_{c}=R\left[1+\left(\frac{H}{2\pi R}\right)^{2}\right]
  44. log ( x ) \log(x)
  45. λ = .0055 ( 1 + ( 2 × 10 4 ε D + 10 6 R e ) 1 3 ) \lambda=.0055(1+(2\times 10^{4}\cdot\frac{\varepsilon}{D}+\frac{10^{6}}{Re})^{% \frac{1}{3}})
  46. λ = .094 ( ε D ) 0.225 + 0.53 ( ε D ) + 88 ( ε D ) 0.44 R e - Ψ \lambda=.094(\frac{\varepsilon}{D})^{0.225}+0.53(\frac{\varepsilon}{D})+88(% \frac{\varepsilon}{D})^{0.44}\cdot{Re}^{-{\Psi}}
  47. Ψ = 1.62 ( ε D ) 0.134 \Psi=1.62(\frac{\varepsilon}{D})^{0.134}
  48. 1 λ = - 2 log ( ε 3.715 D + 15 R e ) \frac{1}{\sqrt{\lambda}}=-2\log(\frac{\varepsilon}{3.715D}+\frac{15}{Re})
  49. 1 λ = - 2 log ( ε 3.7 D + 5.74 R e 0.9 ) \frac{1}{\sqrt{\lambda}}=-2\log(\frac{\varepsilon}{3.7D}+\frac{5.74}{Re^{0.9}})
  50. 1 λ = - 2 log ( ( ε 3.71 D ) + ( 7 R e ) 0.9 ) \frac{1}{\sqrt{\lambda}}=-2\log((\frac{\varepsilon}{3.71D})+(\frac{7}{Re})^{0.% 9})
  51. 1 λ = - 2 log ( ( ε 3.715 D ) + ( 6.943 R e ) 0.9 ) ) \frac{1}{\sqrt{\lambda}}=-2\log((\frac{\varepsilon}{3.715D})+(\frac{6.943}{Re}% )^{0.9}))
  52. λ = 8 [ ( 8 R e ) 12 + 1 ( Θ 1 + Θ 2 ) 1.5 ) ] 1 12 \lambda=8[(\frac{8}{Re})^{12}+\frac{1}{(\Theta_{1}+\Theta_{2})^{1.5}})]^{\frac% {1}{12}}
  53. Θ 1 = [ - 2.457 ln [ ( 7 R e ) 0.9 + 0.27 ε D ] ] 16 \Theta_{1}=[-2.457\ln[(\frac{7}{Re})^{0.9}+0.27\frac{\varepsilon}{D}]]^{16}
  54. Θ 2 = ( 37530 R e ) 16 \Theta_{2}=(\frac{37530}{Re})^{16}
  55. 1 λ = - 2 log [ ε 3.7065 D - 5.0452 R e log ( 1 2.8257 ( ε D ) 1.1098 + 5.8506 R e 0.8981 ) ] \frac{1}{\sqrt{\lambda}}=-2\log[\frac{\varepsilon}{3.7065D}-\frac{5.0452}{Re}% \log(\frac{1}{2.8257}(\frac{\varepsilon}{D})^{1.1098}+\frac{5.8506}{Re^{0.8981% }})]
  56. 1 λ = 1.8 log [ R e 0.135 R e ( ε D ) + 6.5 ] \frac{1}{\sqrt{\lambda}}=1.8\log[\frac{Re}{0.135Re(\frac{\varepsilon}{D})+6.5}]
  57. 1 λ = - 2 log ( ε 3.7 D + 5.158 l o g ( R e 7 ) R e ( 1 + R e 0.52 29 ( ε D ) 0.7 ) ) \frac{1}{\sqrt{\lambda}}=-2\log\left(\frac{\varepsilon}{3.7D}+\frac{5.158log(% \frac{Re}{7})}{Re\left(1+\frac{Re^{0.52}}{29}(\frac{\varepsilon}{D})^{0.7}% \right)}\right)
  58. 1 λ = - 2 log [ ε 3.7 D - 5.02 R e log ( ε 3.7 D - 5.02 R e log ( ε 3.7 D + 13 R e ) ) ] \frac{1}{\sqrt{\lambda}}=-2\log[\frac{\varepsilon}{3.7D}-\frac{5.02}{Re}\log(% \frac{\varepsilon}{3.7D}-\frac{5.02}{Re}\log(\frac{\varepsilon}{3.7D}+\frac{13% }{Re}))]
  59. 1 λ = - 2 log [ ε 3.7 D - 5.02 R e log ( ε 3.7 D + 13 R e ) ] \frac{1}{\sqrt{\lambda}}=-2\log[\frac{\varepsilon}{3.7D}-\frac{5.02}{Re}\log(% \frac{\varepsilon}{3.7D}+\frac{13}{Re})]
  60. 1 λ = - 1.8 log [ ( ε 3.7 D ) 1.11 + 6.9 R e ] \frac{1}{\sqrt{\lambda}}=-1.8\log\left[\left(\frac{\varepsilon}{3.7D}\right)^{% 1.11}+\frac{6.9}{Re}\right]
  61. λ = [ Ψ 1 - ( Ψ 2 - Ψ 1 ) 2 Ψ 3 - 2 Ψ 2 + Ψ 1 ] - 2 \lambda=[\Psi_{1}-\frac{(\Psi_{2}-\Psi_{1})^{2}}{\Psi_{3}-2\Psi_{2}+\Psi_{1}}]% ^{-2}
  62. λ = [ 4.781 - ( Ψ 1 - 4.781 ) 2 Ψ 2 - 2 Ψ 1 + 4.781 ] - 2 \lambda=[4.781-\frac{(\Psi_{1}-4.781)^{2}}{\Psi_{2}-2\Psi_{1}+4.781}]^{-2}
  63. Ψ 1 = - 2 log ( ε 3.7 D + 12 R e ) \Psi_{1}=-2\log(\frac{\varepsilon}{3.7D}+\frac{12}{Re})
  64. Ψ 2 = - 2 log ( ε 3.7 D + 2.51 Ψ 1 R e ) \Psi_{2}=-2\log(\frac{\varepsilon}{3.7D}+\frac{2.51\Psi_{1}}{Re})
  65. Ψ 3 = - 2 log ( ε 3.7 D + 2.51 Ψ 2 R e ) \Psi_{3}=-2\log(\frac{\varepsilon}{3.7D}+\frac{2.51\Psi_{2}}{Re})
  66. 1 λ = - 2 log ( ε 3.7 D + 95 R e 0.983 - 96.82 R e ) \frac{1}{\sqrt{\lambda}}=-2\log(\frac{\varepsilon}{3.7D}+\frac{95}{Re^{0.983}}% -\frac{96.82}{Re})
  67. 1 λ = - 2 log { ε 3.7065 D - 5.0272 R e log [ ε 3.827 D - 4.657 R e log ( ( ε 7.7918 D ) 0.9924 + ( 5.3326 208.815 + R e ) 0.9345 ) ] } \frac{1}{\sqrt{\lambda}}=-2\log\{\frac{\varepsilon}{3.7065D}-\frac{5.0272}{Re}% \log[\frac{\varepsilon}{3.827D}-\frac{4.657}{Re}\log((\frac{\varepsilon}{7.791% 8D})^{0.9924}+(\frac{5.3326}{208.815+Re})^{0.9345})]\}
  68. 1 λ = 0.8686 ln [ 0.4587 R e ( S - 0.31 ) S ( S + 1 ) ] \frac{1}{\sqrt{\lambda}}=0.8686\ln[\frac{0.4587Re}{(S-0.31)^{\frac{S}{(S+1)}}}]
  69. S = 0.124 R e ε D + ln ( 0.4587 R e ) S=0.124Re\frac{\varepsilon}{D}+\ln(0.4587Re)
  70. 1 λ = 0.8686 ln [ 0.4587 R e ( S - 0.31 ) S ( S + 0.9633 ) ] \frac{1}{\sqrt{\lambda}}=0.8686\ln[\frac{0.4587Re}{(S-0.31)^{\frac{S}{(S+0.963% 3)}}}]
  71. S = 0.124 R e ε D + ln ( 0.4587 R e ) S=0.124Re\frac{\varepsilon}{D}+\ln(0.4587Re)
  72. 1 λ = α - [ α + 2 log ( B R e ) 1 + 2.18 B ] \frac{1}{\sqrt{\lambda}}=\alpha-[\frac{\alpha+2\log(\frac{B}{Re})}{1+\frac{2.1% 8}{B}}]
  73. α = ( 0.744 ln ( R e ) ) - 1.41 ( 1 + 1.32 ε D ) \alpha=\frac{(0.744\ln(Re))-1.41}{(1+1.32\sqrt{\frac{\varepsilon}{D}})}
  74. B = ε 3.7 D R e + 2.51 α B=\frac{\varepsilon}{3.7D}Re+2.51\alpha
  75. λ = 6.4 ( ln ( R e ) - ln ( 1 + .01 R e ε D ( 1 + 10 ε D ) ) ) 2.4 \lambda=\frac{6.4}{(\ln(Re)-\ln(1+.01Re\frac{\varepsilon}{D}(1+10\sqrt{\frac{% \varepsilon}{D}})))^{2.4}}
  76. λ = 0.2479 - 0.0000947 ( 7 - log R e ) 4 ( log ( ε 3.615 D + 7.366 R e 0.9142 ) ) 2 \lambda=\frac{0.2479-0.0000947(7-\log Re)^{4}}{(\log(\frac{\varepsilon}{3.615D% }+\frac{7.366}{Re^{0.9142}}))^{2}}

David_X._Li.html

  1. C ρ ( u , v ) = Φ ρ ( Φ - 1 ( u ) , Φ - 1 ( v ) ) C_{\rho}(u,v)=\Phi_{\rho}\left(\Phi^{-1}(u),\Phi^{-1}(v)\right)

Dawson–Gärtner_theorem.html

  1. X = lim j J Y j = { y = ( y j ) j J Y = j J Y j | i < j y i = p i j ( y j ) } . X=\underleftarrow{\lim}_{j\in J}Y_{j}=\left\{\left.y=(y_{j})_{j\in J}\in Y=% \prod_{j\in J}Y_{j}\right|i<j\implies y_{i}=p_{ij}(y_{j})\right\}.
  2. I ( x ) = sup j J I j ( p j ( x ) ) . I(x)=\sup_{j\in J}I_{j}(p_{j}(x)).

DDT-dehydrochlorinase.html

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Deacetoxycephalosporin-C_hydroxylase.html

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Deacetoxycephalosporin-C_synthase.html

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Deacetylipecoside_synthase.html

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Deacetylisoipecoside_synthase.html

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Decision_Linear_assumption.html

  1. ( f , g , f x , g y ) (f,\,g,\,f^{x},\,g^{y})
  2. f , g f,\,g
  3. x , y x,\,y
  4. ( h , h x + y ) (h,\,h^{x+y})
  5. h h
  6. ( h , h ) (h,\,h^{\prime})
  7. h , h h,\,h^{\prime}

Deep_Storm.html

  1. a 3 + b 3 = c 3 a^{3}+b^{3}=c^{3}
  2. x = 0 0 x=0^{0}

Dehydro-L-gulonate_decarboxylase.html

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Dehydrogluconate_dehydrogenase.html

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Delta1-piperideine-2-carboxylate_reductase.html

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Delta12-fatty_acid_dehydrogenase.html

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Delta14-sterol_reductase.html

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Delta24(241)-sterol_reductase.html

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Delta24-sterol_reductase.html

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Demethylmacrocin_O-methyltransferase.html

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Demethylsterigmatocystin_6-O-methyltransferase.html

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Demographic_gravitation.html

  1. F = N 1 N 2 d 2 F=\frac{N_{1}\cdot N_{2}}{d^{2}}
  2. E = N 1 N 2 d E=\frac{N_{1}\cdot N_{2}}{d}
  3. P N 1 = N 2 d PN_{1}=\frac{N_{2}}{d}
  4. P = N d P=\frac{N}{d}
  5. Gradient = N m 2 \,\text{Gradient}=\frac{N}{m^{2}}
  6. N 1 d 2 = N 2 d 2 \frac{N_{1}}{d^{2}}=\frac{N_{2}}{d^{2}}

Densely_defined_operator.html

  1. ( D u ) ( x ) = u ( x ) (\mathrm{D}u)(x)=u^{\prime}(x)\,
  2. u n ( x ) = e - n x u_{n}(x)=e^{-nx}\,
  3. D u n u n = n . \frac{\|\mathrm{D}u_{n}\|_{\infty}}{\|u_{n}\|_{\infty}}=n.

Deoxycytidylate_5-hydroxymethyltransferase.html

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Deoxycytidylate_C-methyltransferase.html

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Deoxyhypusine_monooxygenase.html

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Deoxyribodipyrimidine_photo-lyase.html

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Deoxyribose-phosphate_aldolase.html

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Deoxysarpagine_hydroxylase.html

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Desacetoxyvindoline_4-hydroxylase.html

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Desorption_electrospray_ionization.html

  1. A ( a q ) - + S ( s ) A ( a q ) + S ( s ) - ( 1 ) A^{-}_{(aq)}+S_{(s)}\to A_{(aq)}+S^{-}_{(s)}\,\qquad(1)
  2. A ( g ) - + S ( s ) A ( g ) + S ( s ) - ( 2 ) A^{-}_{(g)}+S_{(s)}\to A_{(g)}+S^{-}_{(s)}\,\qquad(2)
  3. A ( g ) - + S ( g ) A ( g ) + S ( g ) - ( 3 ) A^{-}_{(g)}+S_{(g)}\to A_{(g)}+S^{-}_{(g)}\,\qquad(3)

Desulfoglucosinolate_sulfotransferase.html

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Diaminobutyrate_decarboxylase.html

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Diaminopimelate_decarboxylase.html

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Diaminopimelate_dehydrogenase.html

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Diaminopimelate_epimerase.html

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Diaminopropionate_ammonia-lyase.html

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Dibenzothiophene_dihydrodiol_dehydrogenase.html

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Dichloromuconate_cycloisomerase.html

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Dielectric_resonator_antenna.html

  1. λ 0 ϵ r \frac{\lambda_{0}}{\sqrt{\epsilon_{r}}}
  2. λ 0 \lambda_{0}
  3. ϵ r \epsilon_{r}
  4. ϵ r \epsilon_{r}
  5. ϵ r 10 - 100 \epsilon_{r}\approx 10-100

Diethyl_2-methyl-3-oxosuccinate_reductase.html

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Diferric-transferrin_reductase.html

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Differential_capacitance.html

  1. C = d σ d Ψ C=\frac{d\sigma}{d\Psi}

Differential_inclusion.html

  1. d x d t ( t ) F ( t , x ( t ) ) , \frac{dx}{dt}(t)\in F(t,x(t)),
  2. d \scriptstyle{\mathbb{R}}^{d}
  3. d x d t ( t ) F ( t , x ( t ) ) , x ( t 0 ) = x 0 \frac{dx}{dt}(t)\in F(t,x(t)),\quad x(t_{0})=x_{0}
  4. x ( t ) \scriptstyle\|x(t)\|\,\to\,\infty
  5. t t * \scriptstyle t\,\to\,t^{*}
  6. t * \scriptstyle t^{*}
  7. F ( t , x ) F(t,x)
  8. ( x 1 - x 2 ) T ( F ( t , x 1 ) - F ( t , x 2 ) ) C x 1 - x 2 2 (x_{1}-x_{2})^{T}(F(t,x_{1})-F(t,x_{2}))\leq C\|x_{1}-x_{2}\|^{2}
  9. d x d t ( t ) F ( t , x ( t ) ) , x ( t 0 ) = x 0 \frac{dx}{dt}(t)\in F(t,x(t)),\quad x(t_{0})=x_{0}
  10. d x d t ( t ) \frac{dx}{dt}(t)
  11. x ( t ) x(t)
  12. x ( t ) x(t)

Differential_nonlinearity.html

  1. DNL(i) = V out ( i + 1 ) - V out ( i ) ideal LSB step width - 1 \,\text{DNL(i)}={{V\text{out}(i+1)-V\text{out}(i)}\over\,\text{ideal LSB step % width}}-1

Differentiation_of_integrals.html

  1. lim r 0 1 μ ( B r ( x ) ) B r ( x ) f ( y ) d μ ( y ) = f ( x ) \lim_{r\to 0}\frac{1}{\mu\big(B_{r}(x)\big)}\int_{B_{r}(x)}f(y)\,\mathrm{d}\mu% (y)=f(x)
  2. lim r 0 1 λ n ( B r ( x ) ) B r ( x ) f ( y ) d λ n ( y ) = f ( x ) \lim_{r\to 0}\frac{1}{\lambda^{n}\big(B_{r}(x)\big)}\int_{B_{r}(x)}f(y)\,% \mathrm{d}\lambda^{n}(y)=f(x)
  3. lim r 0 1 μ ( B r ( x ) ) B r ( x ) f ( y ) d μ ( y ) = f ( x ) \lim_{r\to 0}\frac{1}{\mu\big(B_{r}(x)\big)}\int_{B_{r}(x)}f(y)\,\mathrm{d}\mu% (y)=f(x)
  4. lim r 0 γ ( M B r ( x ) ) γ ( B r ( x ) ) = 1. \lim_{r\to 0}\frac{\gamma\big(M\cap B_{r}(x)\big)}{\gamma\big(B_{r}(x)\big)}=1.
  5. lim r 0 inf { 1 γ ( B s ( x ) ) B s ( x ) f ( y ) d γ ( y ) | x H , 0 < s < r } = + . \lim_{r\to 0}\inf\left\{\left.\frac{1}{\gamma\big(B_{s}(x)\big)}\int_{B_{s}(x)% }f(y)\,\mathrm{d}\gamma(y)\right|x\in H,0<s<r\right\}=+\infty.
  6. S x , y = H x , z y , z d γ ( z ) , \langle Sx,y\rangle=\int_{H}\langle x,z\rangle\langle y,z\rangle\,\mathrm{d}% \gamma(z),
  7. S x = i 𝐍 σ i 2 x , e i e i . Sx=\sum_{i\in\mathbf{N}}\sigma_{i}^{2}\langle x,e_{i}\rangle e_{i}.
  8. σ i + 1 2 q σ i 2 , \sigma_{i+1}^{2}\leq q\sigma_{i}^{2},
  9. 1 μ ( B r ( x ) ) B r ( x ) f ( y ) d μ ( y ) r 0 𝛾 f ( x ) , \frac{1}{\mu\big(B_{r}(x)\big)}\int_{B_{r}(x)}f(y)\,\mathrm{d}\mu(y)% \xrightarrow[r\to 0]{\gamma}f(x),
  10. σ i + 1 2 σ i 2 i α \sigma_{i+1}^{2}\leq\frac{\sigma_{i}^{2}}{i^{\alpha}}
  11. 1 μ ( B r ( x ) ) B r ( x ) f ( y ) d μ ( y ) r 0 f ( x ) , \frac{1}{\mu\big(B_{r}(x)\big)}\int_{B_{r}(x)}f(y)\,\mathrm{d}\mu(y)% \xrightarrow[r\to 0]{}f(x),
  12. lim r 0 1 γ ( B r ( x ) ) B r ( x ) f ( y ) d γ ( y ) = f ( x ) \lim_{r\to 0}\frac{1}{\gamma\big(B_{r}(x)\big)}\int_{B_{r}(x)}f(y)\,\mathrm{d}% \gamma(y)=f(x)

Differentiation_of_trigonometric_functions.html

  1. sin ( x ) \sin(x)
  2. cos ( x ) \cos(x)
  3. cos ( x ) \cos(x)
  4. - sin ( x ) -\sin(x)
  5. tan ( x ) \tan(x)
  6. sec 2 ( x ) \sec^{2}(x)
  7. cot ( x ) \cot(x)
  8. - csc 2 ( x ) -\csc^{2}(x)
  9. sec ( x ) \sec(x)
  10. sec ( x ) tan ( x ) \sec(x)\tan(x)
  11. csc ( x ) \csc(x)
  12. - csc ( x ) cot ( x ) -\csc(x)\cot(x)
  13. arcsin ( x ) \arcsin(x)
  14. 1 1 - x 2 \frac{1}{\sqrt{1-x^{2}}}
  15. arccos ( x ) \arccos(x)
  16. - 1 1 - x 2 \frac{-1}{\sqrt{1-x^{2}}}
  17. arctan ( x ) \arctan(x)
  18. 1 x 2 + 1 \frac{1}{x^{2}+1}
  19. ( sin ( x ) ) = cos ( x ) \left(\sin(x)\right)^{\prime}=\cos(x)
  20. ( cos ( x ) ) = - sin ( x ) \left(\cos(x)\right)^{\prime}=-\sin(x)
  21. ( tan ( x ) ) = ( sin ( x ) cos ( x ) ) = cos 2 ( x ) + sin 2 ( x ) cos 2 ( x ) = 1 cos 2 ( x ) = sec 2 ( x ) = 1 + tan 2 ( x ) \left(\tan(x)\right)^{\prime}=\left(\frac{\sin(x)}{\cos(x)}\right)^{\prime}=% \frac{\cos^{2}(x)+\sin^{2}(x)}{\cos^{2}(x)}=\frac{1}{\cos^{2}(x)}=\sec^{2}(x)=% 1+\tan^{2}(x)
  22. ( cot ( x ) ) = ( cos ( x ) sin ( x ) ) = - sin 2 ( x ) - cos 2 ( x ) sin 2 ( x ) = - ( 1 + cot 2 ( x ) ) = - csc 2 ( x ) \left(\cot(x)\right)^{\prime}=\left(\frac{\cos(x)}{\sin(x)}\right)^{\prime}=% \frac{-\sin^{2}(x)-\cos^{2}(x)}{\sin^{2}(x)}=-(1+\cot^{2}(x))=-\csc^{2}(x)
  23. ( sec ( x ) ) = ( 1 cos ( x ) ) = sin ( x ) cos 2 ( x ) = 1 cos ( x ) . sin ( x ) cos ( x ) = sec ( x ) tan ( x ) \left(\sec(x)\right)^{\prime}=\left(\frac{1}{\cos(x)}\right)^{\prime}=\frac{% \sin(x)}{\cos^{2}(x)}=\frac{1}{\cos(x)}.\frac{\sin(x)}{\cos(x)}=\sec(x)\tan(x)
  24. ( csc ( x ) ) = ( 1 sin ( x ) ) = - cos ( x ) sin 2 ( x ) = - 1 sin ( x ) . cos ( x ) sin ( x ) = - csc ( x ) cot ( x ) \left(\csc(x)\right)^{\prime}=\left(\frac{1}{\sin(x)}\right)^{\prime}=-\frac{% \cos(x)}{\sin^{2}(x)}=-\frac{1}{\sin(x)}.\frac{\cos(x)}{\sin(x)}=-\csc(x)\cot(x)
  25. ( arcsin ( x ) ) = 1 1 - x 2 \left(\arcsin(x)\right)^{\prime}=\frac{1}{\sqrt{1-x^{2}}}
  26. ( arccos ( x ) ) = - 1 1 - x 2 \left(\arccos(x)\right)^{\prime}=\frac{-1}{\sqrt{1-x^{2}}}
  27. ( arctan ( x ) ) = 1 x 2 + 1 \left(\arctan(x)\right)^{\prime}=\frac{1}{x^{2}+1}
  28. Area ( R 1 ) < Area ( R 2 ) < Area ( R 3 ) . \,\text{Area}(R_{1})<\,\text{Area}(R_{2})<\,\text{Area}(R_{3})\,.
  29. 1 2 × || O A || × || O B || × sin θ = 1 2 r 2 sin θ . \frac{1}{2}\times||OA||\times||OB||\times\sin\theta=\frac{1}{2}r^{2}\sin\theta\,.
  30. 1 2 r 2 θ \frac{1}{2}r^{2}\theta
  31. 1 2 × || O A || × || A C || = 1 2 × r × r tan θ = 1 2 r 2 tan θ . \frac{1}{2}\times||OA||\times||AC||=\frac{1}{2}\times r\times r\tan\theta=% \frac{1}{2}r^{2}\tan\theta\,.
  32. Area ( R 1 ) < Area ( R 2 ) < Area ( R 3 ) 1 2 r 2 sin θ < 1 2 r 2 θ < 1 2 r 2 tan θ . \,\text{Area}(R_{1})<\,\text{Area}(R_{2})<\,\text{Area}(R_{3})\iff\frac{1}{2}r% ^{2}\sin\theta<\frac{1}{2}r^{2}\theta<\frac{1}{2}r^{2}\tan\theta\,.
  33. 1 < θ sin θ < 1 cos θ 1 > sin θ θ > cos θ . 1<\frac{\theta}{\sin\theta}<\frac{1}{\cos\theta}\implies 1>\frac{\sin\theta}{% \theta}>\cos\theta\,.
  34. lim θ 0 - sin θ θ = lim θ 0 + sin ( - θ ) - θ = lim θ 0 + - sin θ - θ = lim θ 0 + sin θ θ = 1 . \lim_{\theta\to 0^{-}}\frac{\sin\theta}{\theta}=\lim_{\theta\to 0^{+}}\frac{% \sin(-\theta)}{-\theta}=\lim_{\theta\to 0^{+}}\frac{-\sin\theta}{-\theta}=\lim% _{\theta\to 0^{+}}\frac{\sin\theta}{\theta}=1\,.
  35. lim θ 0 ( cos θ - 1 θ ) = lim θ 0 [ ( cos θ - 1 θ ) ( cos θ + 1 cos θ + 1 ) ] = lim θ 0 ( cos 2 θ - 1 θ ( cos θ + 1 ) ) . \lim_{\theta\to 0}\left(\frac{\cos\theta-1}{\theta}\right)=\lim_{\theta\to 0}% \left[\left(\frac{\cos\theta-1}{\theta}\right)\left(\frac{\cos\theta+1}{\cos% \theta+1}\right)\right]=\lim_{\theta\to 0}\left(\frac{\cos^{2}\theta-1}{\theta% (\cos\theta+1)}\right).
  36. lim θ 0 ( cos θ - 1 θ ) = lim θ 0 ( - sin 2 θ θ ( cos θ + 1 ) ) = lim θ 0 ( - sin θ θ ) × lim θ 0 ( sin θ cos θ + 1 ) = ( - 1 ) × 0 2 = 0 . \lim_{\theta\to 0}\left(\frac{\cos\theta-1}{\theta}\right)=\lim_{\theta\to 0}% \left(\frac{-\sin^{2}\theta}{\theta(\cos\theta+1)}\right)=\lim_{\theta\to 0}% \left(\frac{-\sin\theta}{\theta}\right)\times\lim_{\theta\to 0}\left(\frac{% \sin\theta}{\cos\theta+1}\right)=(-1)\times\frac{0}{2}=0\,.
  37. lim θ 0 - tan θ θ = lim θ 0 + tan θ θ = lim θ 0 tan θ θ = lim θ 0 sin θ θ × lim θ 0 1 cos θ = 1 × 1 = 1 . \lim_{\theta\to 0^{-}}\frac{\tan\theta}{\theta}=\lim_{\theta\to 0^{+}}\frac{% \tan\theta}{\theta}=\lim_{\theta\to 0}\frac{\tan\theta}{\theta}=\lim_{\theta% \to 0}\frac{\sin\theta}{\theta}\times\lim_{\theta\to 0}\frac{1}{\cos\theta}=1% \times 1=1\,.
  38. d d θ sin θ = lim δ 0 ( sin ( θ + δ ) - sin θ δ ) . \frac{\operatorname{d}}{\operatorname{d}\!\theta}\,\sin\theta=\lim_{\delta\to 0% }\left(\frac{\sin(\theta+\delta)-\sin\theta}{\delta}\right).
  39. d d θ sin θ = lim δ 0 ( sin θ cos δ + sin δ cos θ - sin θ δ ) = lim δ 0 [ ( sin δ δ cos θ ) + ( cos δ - 1 δ sin θ ) ] . \frac{\operatorname{d}}{\operatorname{d}\!\theta}\,\sin\theta=\lim_{\delta\to 0% }\left(\frac{\sin\theta\cos\delta+\sin\delta\cos\theta-\sin\theta}{\delta}% \right)=\lim_{\delta\to 0}\left[\left(\frac{\sin\delta}{\delta}\cos\theta% \right)+\left(\frac{\cos\delta-1}{\delta}\sin\theta\right)\right].
  40. d d θ sin θ = ( 1 × cos θ ) + ( 0 × sin θ ) = cos θ . \frac{\operatorname{d}}{\operatorname{d}\!\theta}\,\sin\theta=(1\times\cos% \theta)+(0\times\sin\theta)=\cos\theta\,.
  41. d d θ cos θ = lim δ 0 ( cos ( θ + δ ) - cos θ δ ) . \frac{\operatorname{d}}{\operatorname{d}\!\theta}\,\cos\theta=\lim_{\delta\to 0% }\left(\frac{\cos(\theta+\delta)-\cos\theta}{\delta}\right).
  42. d d θ cos θ = lim δ 0 ( cos θ cos δ - sin θ sin δ - cos θ δ ) = lim δ 0 [ ( cos δ - 1 δ cos θ ) - ( sin δ δ sin θ ) ] . \frac{\operatorname{d}}{\operatorname{d}\!\theta}\,\cos\theta=\lim_{\delta\to 0% }\left(\frac{\cos\theta\cos\delta-\sin\theta\sin\delta-\cos\theta}{\delta}% \right)=\lim_{\delta\to 0}\left[\left(\frac{\cos\delta-1}{\delta}\cos\theta% \right)-\left(\frac{\sin\delta}{\delta}\sin\theta\right)\right].
  43. d d θ cos θ = ( 0 × cos θ ) - ( 1 × sin θ ) = - sin θ . \frac{\operatorname{d}}{\operatorname{d}\!\theta}\,\cos\theta=(0\times\cos% \theta)-(1\times\sin\theta)=-\sin\theta\,.
  44. cos θ = sin ( θ + π 2 ) \cos\theta=\sin\left(\theta+\frac{\pi}{2}\right)
  45. d d θ sin θ = cos θ \frac{\operatorname{d}}{\operatorname{d}\!\theta}\sin\theta=\cos\theta
  46. d d θ cos θ = d d θ sin ( θ + π 2 ) \frac{\operatorname{d}}{\operatorname{d}\!\theta}\cos\theta=\frac{% \operatorname{d}}{\operatorname{d}\!\theta}\sin\left(\theta+\frac{\pi}{2}\right)
  47. Let f ( x ) = sin x , g ( x ) = θ + π 2 \mbox{Let}~{}\ f\!\left(x\right)=\sin x,\ g\!\left(x\right)=\theta+\frac{\pi}{2}
  48. d d θ f ( g ( x ) ) = f ( g ( x ) ) g ( x ) = cos ( θ + π 2 ) ( 1 + 0 ) = cos ( θ + π 2 ) \frac{\operatorname{d}}{\operatorname{d}\!\theta}f\!\left(g\!\left(x\right)% \right)=f^{\prime}\!\left(g\!\left(x\right)\right)\cdot g^{\prime}\!\left(x% \right)=\cos\left(\theta+\frac{\pi}{2}\right)\cdot(1+0)=\cos\left(\theta+\frac% {\pi}{2}\right)
  49. cos ( θ + π 2 ) = sin ( ( θ + π 2 ) + π 2 ) = sin ( θ + π ) \cos\left(\theta+\frac{\pi}{2}\right)=\sin\left(\left(\theta+\frac{\pi}{2}% \right)+\frac{\pi}{2}\right)=\sin\left(\theta+\pi\right)
  50. sin ( θ + π ) = - sin θ \sin\left(\theta+\pi\right)=-\sin\theta
  51. d d θ cos θ = - sin θ \frac{\operatorname{d}}{\operatorname{d}\!\theta}\cos\theta=-\sin\theta
  52. d d θ tan θ = lim δ 0 ( tan ( θ + δ ) - tan θ δ ) . \frac{\operatorname{d}}{\operatorname{d}\!\theta}\,\tan\theta=\lim_{\delta\to 0% }\left(\frac{\tan(\theta+\delta)-\tan\theta}{\delta}\right).
  53. d d θ tan θ = lim δ 0 [ tan θ + tan δ 1 - tan θ tan δ - tan θ δ ] = lim δ 0 [ tan θ + tan δ - tan θ + tan 2 θ tan δ δ ( 1 - tan θ tan δ ) ] . \frac{\operatorname{d}}{\operatorname{d}\!\theta}\,\tan\theta=\lim_{\delta\to 0% }\left[\frac{\frac{\tan\theta+\tan\delta}{1-\tan\theta\tan\delta}-\tan\theta}{% \delta}\right]=\lim_{\delta\to 0}\left[\frac{\tan\theta+\tan\delta-\tan\theta+% \tan^{2}\theta\tan\delta}{\delta\left(1-\tan\theta\tan\delta\right)}\right].
  54. d d θ tan θ = lim δ 0 tan δ δ × lim δ 0 ( 1 + tan 2 θ 1 - tan θ tan δ ) . \frac{\operatorname{d}}{\operatorname{d}\!\theta}\,\tan\theta=\lim_{\delta\to 0% }\frac{\tan\delta}{\delta}\times\lim_{\delta\to 0}\left(\frac{1+\tan^{2}\theta% }{1-\tan\theta\tan\delta}\right).
  55. d d θ tan θ = 1 × 1 + tan 2 θ 1 - 0 = 1 + tan 2 θ . \frac{\operatorname{d}}{\operatorname{d}\!\theta}\,\tan\theta=1\times\frac{1+% \tan^{2}\theta}{1-0}=1+\tan^{2}\theta.
  56. d d θ tan θ = 1 + sin 2 θ cos 2 θ = cos 2 θ + sin 2 θ cos 2 θ = 1 cos 2 θ = sec 2 θ . \frac{\operatorname{d}}{\operatorname{d}\!\theta}\,\tan\theta=1+\frac{\sin^{2}% \theta}{\cos^{2}\theta}=\frac{\cos^{2}\theta+\sin^{2}\theta}{\cos^{2}\theta}=% \frac{1}{\cos^{2}\theta}=\sec^{2}\theta\,.
  57. d d θ tan θ = d d θ sin θ cos θ = ( sin θ ) cos θ - sin θ ( cos θ ) cos 2 θ = cos 2 θ + sin 2 θ cos 2 θ \frac{\operatorname{d}}{\operatorname{d}\!\theta}\tan\theta=\frac{% \operatorname{d}}{\operatorname{d}\!\theta}\frac{\sin\theta}{\cos\theta}=\frac% {\left(\sin\theta\right)^{\prime}\cdot\cos\theta-\sin\theta\cdot\left(\cos% \theta\right)^{\prime}}{\cos^{2}\theta}=\frac{\cos^{2}\theta+\sin^{2}\theta}{% \cos^{2}\theta}
  58. 1 cos 2 θ = sec 2 θ \frac{1}{\cos^{2}\theta}=\sec^{2}\theta
  59. d d θ tan θ = sec 2 θ \frac{\operatorname{d}}{\operatorname{d}\!\theta}\tan\theta=\sec^{2}\theta
  60. y = arcsin x y=\arcsin x\,\!
  61. - π 2 y π 2 -\frac{\pi}{2}\leq y\leq\frac{\pi}{2}
  62. sin y = x \sin y=x\,\!
  63. d d x sin y = d d x x {d\over dx}\sin y={d\over dx}x
  64. d y d x cos y = 1 {dy\over dx}\cos y=1\,\!
  65. cos y = 1 - sin 2 y \cos y=\sqrt{1-\sin^{2}y}
  66. d y d x 1 - sin 2 y = 1 {dy\over dx}\sqrt{1-\sin^{2}y}=1
  67. x = sin y x=\sin y
  68. d y d x 1 - x 2 = 1 {dy\over dx}\sqrt{1-x^{2}}=1
  69. d y d x = 1 1 - x 2 {dy\over dx}=\frac{1}{\sqrt{1-x^{2}}}
  70. y = arccos x y=\arccos x\,\!
  71. 0 y π 0\leq y\leq\pi
  72. cos y = x \cos y=x\,\!
  73. d d x cos y = d d x x {d\over dx}\cos y={d\over dx}x
  74. - d y d x sin y = 1 -{dy\over dx}\sin y=1
  75. sin y = 1 - cos 2 y \sin y=\sqrt{1-\cos^{2}y}\,\!
  76. - d y d x 1 - cos 2 y = 1 -{dy\over dx}\sqrt{1-\cos^{2}y}=1
  77. x = cos y x=\cos y\,\!
  78. - d y d x 1 - x 2 = 1 -{dy\over dx}\sqrt{1-x^{2}}=1
  79. d y d x = - 1 1 - x 2 {dy\over dx}=-\frac{1}{\sqrt{1-x^{2}}}
  80. y = arctan x y=\arctan x\,\!
  81. - π 2 < y < π 2 -\frac{\pi}{2}<y<\frac{\pi}{2}
  82. tan y = x \tan y=x\,\!
  83. d d x tan y = d d x x {d\over dx}\tan y={d\over dx}x
  84. d d x tan y = d d x sin y cos y = d y d x cos 2 y + sin 2 y d y d x cos 2 y = d y d x ( 1 + tan 2 y ) {d\over dx}\tan y={d\over dx}\frac{\sin y}{\cos y}=\frac{{dy\over dx}\cos^{2}y% +\sin^{2}y{dy\over dx}}{\cos^{2}y}={dy\over dx}\left(1+\tan^{2}y\right)
  85. d d x x = 1 {d\over dx}x=1
  86. d y d x ( 1 + tan 2 y ) = 1 {dy\over dx}(1+\tan^{2}y)=1
  87. x = tan y x=\tan y\,\!
  88. d y d x ( 1 + x 2 ) = 1 {dy\over dx}(1+x^{2})=1
  89. d y d x = 1 1 + x 2 {dy\over dx}=\frac{1}{1+x^{2}}
  90. y = \arccot x y=\arccot x\,\!
  91. 0 < y < π 0<y<\pi
  92. cot y = x \cot y=x\,\!
  93. d d x cot y = d d x x {d\over dx}\cot y={d\over dx}x
  94. d y d x - csc 2 y = 1 {dy\over dx}-\csc^{2}y=1
  95. 1 + cot 2 y = csc 2 y 1+\cot^{2}y=\csc^{2}y\,\!
  96. d y d x - ( 1 + cot 2 y ) = 1 {dy\over dx}-(1+\cot^{2}y)=1
  97. x = cot y x=\cot y\,\!
  98. d y d x - ( 1 + x 2 ) = 1 {dy\over dx}-(1+x^{2})=1
  99. d y d x = - 1 1 + x 2 {dy\over dx}=-\frac{1}{1+x^{2}}

Digital_delay_line.html

  1. z - 1 \mathrm{z}^{-1}
  2. N N
  3. z - N \mathrm{z}^{-N}

Digital_differential_analyzer_(graphics_algorithm).html

  1. m = y e n d - y s t a r t x e n d - x s t a r t m=\frac{y_{end}-y_{start}}{x_{end}-x_{start}}
  2. y k + 1 = y k + m y_{k+1}=y_{k}+m
  3. x k + 1 = x k + 1 m x_{k+1}=x_{k}+\frac{1}{m}
  4. x s t a r t < x e n d x_{start}<x_{end}

Dihydrobunolol_dehydrogenase.html

  1. \rightleftharpoons

Dihydrochelirubine_12-monooxygenase.html

  1. \rightleftharpoons

Dihydrokaempferol_4-reductase.html

  1. \rightleftharpoons

Dihydroneopterin_aldolase.html

  1. \rightleftharpoons

Dihydropyrimidine_dehydrogenase_(NADP+).html

  1. \rightleftharpoons

Dihydrosanguinarine_10-monooxygenase.html

  1. \rightleftharpoons

Dihydrouracil_dehydrogenase_(NAD+).html

  1. \rightleftharpoons

Dihydrouracil_oxidase.html

  1. \rightleftharpoons

Dihydroxyfumarate_decarboxylase.html

  1. \rightleftharpoons

Dihydroxyphenylalanine_ammonia-lyase.html

  1. \rightleftharpoons

Diiodophenylpyruvate_reductase.html

  1. \rightleftharpoons

Dimethylamine_dehydrogenase.html

  1. \rightleftharpoons

Dimethylaniline-N-oxide_aldolase.html

  1. \rightleftharpoons

Dimethylglycine_dehydrogenase.html

  1. \rightleftharpoons

Dimethylglycine_oxidase.html

  1. \rightleftharpoons

Dimethylhistidine_N-methyltransferase.html

  1. \rightleftharpoons

Dimethylmalate_dehydrogenase.html

  1. \rightleftharpoons

Dimethylpropiothetin_dethiomethylase.html

  1. \rightleftharpoons

Diophantus_II.VIII.html

  1. x 2 x^{2}
  2. 16 - x 2 16-x^{2}
  3. 4 x 2 + 16 - 16 x 4x^{2}+16-16x
  4. 16 - x 2 16-x^{2}
  5. x 2 + 16 x x^{2}+16x
  6. 5 x 2 = 16 x 5x^{2}=16x
  7. x = 16 / 5 x=16/5
  8. ( t x - a ) 2 = a 2 - x 2 \displaystyle(tx-a)^{2}=a^{2}-x^{2}
  9. x 2 = ( 2 a t t 2 + 1 ) 2 x^{2}=\left(\tfrac{2at}{t^{2}+1}\right)^{2}
  10. ( t x - a ) 2 = ( a ( t 2 - 1 ) t 2 + 1 ) 2 (tx-a)^{2}=\left(\tfrac{a(t^{2}-1)}{t^{2}+1}\right)^{2}
  11. a 2 a^{2}
  12. [ a ; 2 a t t 2 + 1 ; a ( t 2 - 1 ) t 2 + 1 ] \left[a;\frac{2at}{t^{2}+1};\frac{a(t^{2}-1)}{t^{2}+1}\right]
  13. [ a ; 2 a t t 2 + 1 ; a ( t 2 - 1 ) t 2 + 1 ] = [ 20 5 ; 16 5 ; 12 5 ] = 4 5 [ 5 ; 4 ; 3 ] . \left[a;\frac{2at}{t^{2}+1};\frac{a(t^{2}-1)}{t^{2}+1}\right]=\left[\frac{20}{% 5};\frac{16}{5};\frac{12}{5}\right]=\frac{4}{5}\left[5;4;3\right].
  14. [ t 2 + 1 2 ; t ; t 2 - 1 2 ] [\tfrac{t^{2}+1}{2};t;\tfrac{t^{2}-1}{2}]
  15. t 2 + 1 2 a \quad\tfrac{t^{2}+1}{2a}
  16. [ 1 ; 2 t t 2 + 1 ; t 2 - 1 t 2 + 1 ] . \left[1;\frac{2t}{t^{2}+1};\frac{t^{2}-1}{t^{2}+1}\right].
  17. ( 1 , sin θ , cos θ ) , (1,\sin\theta,\cos\theta),
  18. N 2 + ( 2 N - 4 ) 2 = 16 \displaystyle N^{2}+(2N-4)^{2}=16