wpmath0000007_15

Zubov's_method.html

  1. { x : v ( x ) < 1 } \{x:\,v(x)<1\}
  2. v ( x ) v(x)
  3. x = f ( x ) , t \R x^{\prime}=f(x),t\in\R
  4. \R n \R^{n}
  5. f ( 0 ) = 0 f(0)=0
  6. A A
  7. v , h v,h
  8. v ( 0 ) = h ( 0 ) = 0 v(0)=h(0)=0
  9. 0 < v ( x ) < 1 0<v(x)<1
  10. x A { 0 } x\in A\setminus\{0\}
  11. h > 0 h>0
  12. \R n { 0 } \R^{n}\setminus\{0\}
  13. γ 2 > 0 \gamma_{2}>0
  14. γ 1 > 0 , α 1 > 0 \gamma_{1}>0,\alpha_{1}>0
  15. v ( x ) > γ 1 , h ( x ) > α 1 v(x)>\gamma_{1},h(x)>\alpha_{1}
  16. || x || > γ 2 ||x||>\gamma_{2}
  17. v ( x n ) 1 v(x_{n})\rightarrow 1
  18. x n A x_{n}\rightarrow\partial A
  19. || x n || ||x_{n}||\rightarrow\infty
  20. v ( x ) f ( x ) = - h ( x ) ( 1 - v ( x ) ) 1 + || f ( x ) || 2 \nabla v(x)\cdot f(x)=-h(x)(1-v(x))\sqrt{1+||f(x)||^{2}}
  21. v ( 0 ) = 0 v(0)=0

Ø_(disambiguation).html

  1. \varnothing

Σ-finite_measure.html

  1. m m
  2. ( m n ) n : m = n m n (m_{n})_{n}:m=\sum_{n\in\mathbb{N}}m_{n}
  3. \mathbb{N}
  4. H = n V n H=\bigcup_{n\in\mathbb{N}}V^{n}
  5. \infty
  6. \R \scriptstyle\R
  7. A \R \scriptstyle A\subset\R
  8. μ ( A ) = \scriptstyle\mu(A)=\infty
  9. A \R \scriptstyle A\subset\R
  10. μ ( A ) = \scriptstyle\mu(A)=\infty
  11. n = 1 w n = 1. \sum_{n=1}^{\infty}w_{n}=1.
  12. ν ( A ) = n = 1 w n μ ( A V n ) μ ( V n ) \nu(A)=\sum_{n=1}^{\infty}w_{n}\frac{\mu(A\cap V_{n})}{\mu(V_{n})}

Ω-consistent_theory.html

  1. x c = x \exists x\,c=x
  2. w [ B ( 0 , w ) x ( B ( x , w ) B ( x + 1 , w ) ) x B ( x , w ) ] . \forall w\,[B(0,w)\land\forall x\,(B(x,w)\to B(x+1,w))\to\forall x\,B(x,w)].
  3. w [ B ( 0 , w ) x ( B ( x , w ) B ( x + 1 , w ) ) B ( n , w ) ] \forall w\,[B(0,w)\land\forall x\,(B(x,w)\to B(x+1,w))\to B(n,w)]
  4. x ¬ P ( x ) \exists x\,\neg P(x)
  5. P ( 0 ) , P ( 1 ) , P ( 2 ) , P(0),P(1),P(2),\ldots
  6. x ( N ( x ) P ( x ) ) \forall x\,(N(x)\to P(x))
  7. x P ( x ) \forall x\,P(x)
  8. T + RFN T + Th Π 2 0 ( ) T+\mathrm{RFN}_{T}+\mathrm{Th}_{\Pi^{0}_{2}}(\mathbb{N})
  9. Th Π 2 0 ( ) \mathrm{Th}_{\Pi^{0}_{2}}(\mathbb{N})
  10. RFN T \mathrm{RFN}_{T}
  11. x ( Prov T ( φ ( x ˙ ) ) φ ( x ) ) \forall x\,(\mathrm{Prov}_{T}(\ulcorner\varphi(\dot{x})\urcorner)\to\varphi(x))
  12. φ \varphi
  13. Σ 2 0 \Sigma^{0}_{2}

∂.html

  1. \partial
  2. z x \frac{\partial z}{\partial x}
  3. ( x , y , z ) ( u , v , w ) \frac{\partial(x,y,z)}{\partial(u,v,w)}