Returned 97 matches (100 formulae, 88 docs)
    Lookup 112557.000 ms, Re-ranking 35132.194 ms
    Found 153173708 tuple postings, 15155960 formulae, 4965759 documents
[ formulas ] [ documents ] [ documents-by-formula ]

0.1826
-32.0000
9.0000
p1(x,ξ)=-i2gjkxj(x)(ξk-Ak(x))-i2gjk(x)Akxj(x).

0.1582
-37.0000
8.0000
Gv(ψ)(z1,z2)=-1δ8(z1-z2)+14(ψ(z1)D¯2δ8(z1-z2))+O(Ψ¯)

0.1582
-58.0000
9.0000
F(x1,x2)=x1(f(x1-x2)f(x3-x1))+x2(f(x2-x3)f(x1-x2))+x3(f(x3-x1)f(x2-x3)),

0.1535
-41.0000
6.0000
ft(x)=ut(x)vt(x),ut(x)t=2ut(x)x2,vt(x)t=-2vt(x)x2.

0.1527
-32.0000
7.0000
μ±u1±x2=x1f±(x1):=μ±x1(ψ±(x1)u0±x1),

0.1440
-25.0000
5.0000
(x)=-12g2(Aja(x))2+12g2(Bja(x))2,

0.1440
-35.0000
5.0000
t(z1-z)=0η(z1,η1)-0η(z,η)+V~η(z1,η1),

0.1440
-36.0000
4.0000
X2=f3(z2)z3,X1=g1(z1)z1+z2+g3(z1,z2)z3,

0.1440
-52.0000
6.0000
(f(z1)-f(z2))μod(z1,z2)=(f(z1)+c)g(z1)+(f(z2)+c)g(z2)-12Q(f(z1))-12Q(f(z2)),

0.1388
-40.0000
4.0000
Ui(x,y)=k=1nχik(y)uixk(x)+γi(y)(u1(x)-u2(x))+u~i(x), i=1,2

0.1386
-34.0000
4.0000
+x[12Z0(ux)(tux)2-12Z1(ux)(ux)2-U2(ux)+iϵux2],

0.1345
-34.0000
6.0000
+c(g,h)b(z)a(z1)wz1(z0-1(z-z1z0)(g,h)δ(z-z1-z0))

0.1325
-21.0000
5.0000
gt(x)=ut(x)vt(x)x-ut(x)xvt(x),

0.1297
-28.0000
6.0000
12t(u0(x+t)+u0(x-t))+12(u1(x+t)-u1(x-t))

0.1244
-30.0000
3.0000
12Z0(n)(ux)(tux)2-12Z1(n)(ux)(ux)2-U2(n)(ux)

0.1244
-33.0000
6.0000
g(1)(x)f(1)xi(x)f(2)g(2)=g(1)(x)f(1)xi(x)g(2)f(2)

0.1244
-38.0000
6.0000
e(x)=r(x)(u1x1(x)u2x2(x)-u1x2(x)u2x1(x))+h,

0.1244
-49.0000
6.0000
(α=(2,1),i=1,j=2):-13u2x1(x)R1212x2(x)+g11(x)4u1x12x22(x)+

0.1244
-53.0000
5.0000
LD(f)g(x)=(-1)d-1j=1dzˇjxˇjxj[ajj(xj)dg(z)z1zd(zˇj,xj)]dzˇj

0.1198
-35.0000
8.0000
=(x)2-kx(s-1)x-xkx(s-1)+kx(s-1)kx(s-1)

0.1198
-36.0000
6.0000
z1XR-a(z1)b(z)wz1(z0-1(z1-zz0)(g,h)δ(z1-zz0))

0.1198
-39.0000
4.0000
(f(z1)-f(z2))μev(z1,z2)=g(z1)+g(z2)-12Q(f(z1))-12Q(f(z2)),

0.1198
-41.0000
6.0000
K=(Dxvx+vxDx+12(Dzuxy+uxyDz)-12(Dyuxz+uxzDy)-uxxuxx0)

0.1185
-29.0000
3.0000
+μ2z2(k0(𝐫+𝐦,z2)[z1-1(z2)2δ(z2z1)])

0.1185
-35.0000
5.0000
r+1ujxα+(i)(x)gjj(x)+r+1uixα+(j)(x)gii(x)=0,

0.1153
-34.0000
5.0000
tu(t,x)=-122x2Ψ1(u(t,x))-12xΨ2(u(t,x))

0.1153
-39.0000
6.0000
z(f1(z)f2(z))=f1(z)zf2(z)+(-1)𝔞(f1)f1f2z,

0.1153
-45.0000
7.0000
(nμod(z1,z2)+g(z2)-g(z1)+12b2(f(z1)-f(z2)))(ϕ(z1)ψ(z2)-ψ(z1)ϕ(z2))

0.1153
-51.0000
5.0000
iX0(n)(ux)t-X1(n)(ux)+U1(n)(ux)+12Y0(n)(ux)(tux)2+12Y1(n)(ux)(ux)2,

0.1153
-65.0000
8.0000
D^t=-D^z1V1-D^z2V2-(z1v1+z2v2+v3)+k(g1(D^f1+g1-D^V1)+g2(D^f2+g2-D^V2))

0.1121
-47.0000
8.0000
ut1=-ux,ut2=-uux+(-1v),ut3=-12u2ux+u(-1v)+-1(uxx(-2v)),.

0.1121
-51.0000
7.0000
D^t=-D^z1(f1+ΓHSg1)-D^z2(f2+ΓHSg2)-(z1v1+z2v2+v3)+k(1-D^ΓHS).

0.1102
-18.0000
4.0000
g(u0(0))=u0+x(0)-u0-x(0),

0.1102
-29.0000
4.0000
ui(x)=0    gii(x)uixj(x)+gjj(x)ujxi(x)=0,

0.1102
-29.0000
3.0000
N2G2c(z1,z2)=2z1z2Log[u(z1)-u(z2)z1-z2]
N2G2c(z1,z2)=2z1z2Log(u(z1)-u(z2)z1-z2)

0.1102
-37.0000
4.0000
-14π2𝒞1t𝒞2tf(z1)f(z2)2z1z2𝒢n(z1,z2)dz1dz2,

0.1102
-40.0000
6.0000
2f(x1)2x12+2x12h(x1,x2,t)=22f(x1)x12(1-f(x2))

0.1102
-41.0000
5.0000
{ut=12σ22ux12+μux2,u(0,x)=f(x1)+g(x2).

0.1102
-42.0000
3.0000
Q=p12+u2(x)p2+u3(x)p3-12(w1(y)u2′′(x)+v1(z)u3′′(x)+u1(x)),

0.1102
-45.0000
5.0000
vx(x,0)=(a(u-1)x+b(u-1)t)x=-(b(u-1)xt+c(u-1)tt)=-bux-cut=f(x).

0.1102
-49.0000
4.0000
(φ,u¯δδδ)=-φt-(A(x)(φ+u¯δδδ))x+(B(x)(φx+u¯xδδδ)x-u¯δδδ˙

0.1102
-51.0000
4.0000
(α=(2,1),i=j=2):-13u2x1(x)R1212x1(x)+2g11(x)4u2x12x22(x)=0,

0.1088
-40.0000
5.0000
(fg)x(y)=fx(y)gx(y)+ϵi,j=1dαxij(y)fx(y)yigx(y)yj+

0.1051
-21.0000
6.0000
F(z1,z2)=12(F(z1)+F(z2)-(z12-z22)2)

0.1051
-35.0000
7.0000
Φ1(z0, z1)=ez01z1(z1g1(z1)+g1(0)-g1(0))=ez0g1(z1).

0.1051
-53.0000
6.0000
u1+-u1-=g(x1):=-ϕ(x1)(u0+x2-u0-x2)=-ϕ(x1)u0+x2(1-μ+μ-), on ζ0,formulae-sequencesuperscriptsubscriptu1superscriptsubscriptu1gsubscriptx1assignϕsubscriptx1superscriptsubscriptu0subscriptx2superscriptsubscriptu0subscriptx2ϕsubscriptx1superscriptsubscriptu0subscriptx21subscriptμsubscriptμon ζ0superscriptζ0\zeta^{0}u_{1}^{+}-u_{1}^{-}=g(x_{1}):=-\phi(x_{1})\left(\frac{\partial u_{0}^{+}}{% \partial x_{2}}-\frac{\partial u_{0}^{-}}{\partial x_{2}}\right)=-\phi(x_{1})% \frac{\partial u_{0}^{+}}{\partial x_{2}}\left(1-\frac{\mu_{+}}{\mu_{-}}\right% ),\quad\text{on $\zeta^{0}$},

0.1045
-22.0000
5.0000
gt(x)=-ft(x)x,ht(x)=2ft(x)x2

0.1045
-36.0000
4.0000
w2(z1,z2)=1x(z1)x(z2)1(z1-z2)2-1(x(z1)-x(z2))2

0.1045
-40.0000
4.0000
xk0(x)+g0(λx)k0(x)2(-1-1x2g0(λx)k0(x))τxk0(x)(λ2-1),

0.1045
-42.0000
4.0000
Nf(z1,z2)=ln(f(0)z1-z2(1(f(0)-f(z2-1))-1(f(0)-f(z1-1)))),

0.1045
-48.0000
6.0000
uut=-x[αup+2(p+2)+β(uu2x-12ux2)+γ(uu4x-uxu3x+12u2x2)].

0.1045
-48.0000
3.0000
j=1𝑛Ω[aj(x,u0x)-fj(x)]g(x)xjdx-Ωc(x,f(x)-u0(x))g(x)dx=0
j=1𝑛Ω[aj(x,u0x)-fj(x)]g(x)xjdx-Ωc(x,f(x)-u0(x))g(x)dx0.

0.1008
-34.0000
5.0000
-162Vx2+12(V(x))2+43v3f02(x)+4vf02(x)V(x),

0.1008
-35.0000
5.0000
ω(z^)-ω(z^)=1g(x-1)xh(z-1)-1g(x-1)xh(z-1)+

0.1008
-44.0000
3.0000
i=1dxi(Ai(x)Tl(un)(x))=fn(x)+i=1dxi(Ai(x)(Tl(un)(x)-un(x))),

0.1008
-53.0000
6.0000
12(1-x12)2Vx1x12-(n+1+12)Vx1x1=e-(n+12)tte(n+12)tVx1,

0.0964
-37.0000
5.0000
c32=-ux3(Xuxx)-12Xuxxuxxx-12x2(Xuxx)ux

0.0960
-27.0000
4.0000
+g(ux)-g(vx)ux-vxf(u)+f(v)2(ux-vx)

0.0960
-44.0000
3.0000
X1(z,v(z))vz1(z)+X2(z,v(z))vz2(z)=X3(z,v(z)), z=(z1,z2),

0.0960
-51.0000
6.0000
L(f,n)g(x)=12(g(x+f(x)+1n)+g(x+f(x)-1n))-g(x)-f(x)g(x)1n+f(x)2

0.0960
-57.0000
4.0000
H(x,λ)=(a1(x)+i=1kλifix1(x),,an(x)+i=1kλifixn(x), f1(x),,fk(x)).  

0.0935
-32.0000
6.0000
c21=ux2(Xux)-12Xuxuxx+12x(Xux)ux

0.0904
-28.0000
3.0000
-V(u1)u1-W(u2-u1)u1+Asin(ωt)+ξ1(t),
-V(u2)u2-W(u2-u1)u2+Asin(ωt)+ξ2(t),

0.0904
-31.0000
4.0000
+μ2(z2)2(k0(𝐫+𝐦,z2)[z1-1z2δ(z2z1)])

0.0904
-32.0000
3.0000
X1=g1(z1)z1+g2(z1)z2+g3(z1,z2)z3,

0.0904
-37.0000
4.0000
G(z1,z2)=G(z1-z2)=-1(z1-z2)2+κ241sinh2κ(z1-z2)2

0.0904
-41.0000
5.0000
+(xig(z))Cij=2mf(z)γj+g(z)xi(j=2mf(z)γj)+ρFi(t)

0.0904
-41.0000
4.0000
ρ(1|2)(z1,z2)=(z2z2+12)ρ(1|1)(z1)-ρ(1|1)(z2)z1-z2

0.0904
-42.0000
3.0000
S(g)|g(ξ,x)=Exp(ξω(x))=-16ξ-2(x3FxF-32(x2FxF)2)+

0.0904
-43.0000
3.0000
u(x,t)=14πtSt(x)(v0(x)+1tu0(x)+u0(x)nx(x))dS(x),

0.0904
-45.0000
3.0000
e(z1-z)x1e(z2-z)x2Singx1,x2(Y-(Y-(u,x1-x2)v,x2+z)ezw)

0.0904
-47.0000
3.0000
vt=12(vux-uvx)-Ak-1[vxAk(u)+uxAk(v)+12vAk(ux)+12uAk(vx)],

0.0901
-28.0000
7.0000
ut-utxx=-32x(u2)-12x(ux2)+12x3(u2)

0.0901
-52.0000
4.0000
{u(x1),v(x2)}=x1((uv)(x1))x1-1δ(x1x2)+(uv+vu)(x1)x1x1-1δ(x1x2).

0.0862
-25.0000
5.0000
-12(1+ϵ(z12-z22))z1-ϵz1z2z2,

0.0862
-33.0000
4.0000
H=L1=1f1(x1)+f2(x2)(x12+x22+v1(x1)+v2(x2),

0.0862
-38.0000
4.0000
R1k(t,x)-12((ukvk-uxkvxk)x-(ukvxk-uxkvk))mk-buxk

0.0862
-56.0000
3.0000
uxt=12{ux(x),H-2}2=-12(ux)2-uuxx-12ρ2ρt=12{ρ(x),H-2}2=-(uρ)x

0.0817
-39.0000
4.0000
Fλ(λ,t)=(xL(t,u(t)+λv(t),ut(t)+λvt(t)),v(t))

0.0777
-26.0000
4.0000
ΔReu1(z)=(ddJcz1)y(z)(ux(z),Jux(z)).

0.0763
-27.0000
4.0000
-ϵz1z2z1-12(1-ϵ(z12-z22))z2,

0.0763
-29.0000
4.0000
S(z1,z)=(z-1z)2(z1-1z1)(z-z1)(z-1z1)

0.0763
-32.0000
4.0000
V1(1)=V1+ηx(1)ux+ηy(1)uy+ηt(1)ut,

0.0763
-34.0000
3.0000
(u1,v1,w1)=(p(zf1(x)+xg1(x))x,x,zf1(x)+xg1(x))

0.0763
-44.0000
3.0000
e(z1-z2)x0e(z1-z0)x1e(z2-z0)x2(Y(v,x2)Y(u,x1)w)

0.0763
-44.0000
3.0000
e(z1-z2)x0e(z1-z0)x1e(z2-z0)x2(Y(u,x1)Y(v,x2)w)

0.0763
-44.0000
2.0000
e(z1-z2)x0e(z1-z0)x1e(z2-z0)x2(Y(Y(u,x0)v,x2)w)

0.0763
-47.0000
3.0000
(α=(3,0),i=1,j=2):g22(x)4u2x14(x)+g11(x)4u1x13x2(x)=0,

0.0763
-56.0000
3.0000
(12u2,1n+2α(t)un+2+β(t)(uuxx-12ux2)+σ(t)(uuxxxx-uxuxxx+12uxx2)).

0.0748
-35.0000
6.0000
-[x1(δ(ux1)ux1x1)+x2(δ(ux2)ux1x2)+γΔux1]=-utx1

0.0672
-25.0000
3.0000
2v1x2=u¨1(gx)2+u˙1(2gx2)

0.0672
-44.0000
3.0000
12[Λσ,(u1+u2)]xv+12[Λσ,v]x(u1+u2)+u2Λσxv+vΛσxu1.

0.0622
-36.0000
3.0000
-12x2(σ(x2)-σ(x1)x2-x1)+R2(x1;x2)M(x1)

0.0622
-38.0000
3.0000
=-12t(2v12+2x12)-α2t(2u12+2y12)

0.0622
-46.0000
3.0000
-ψb+1(y(z1);a)ψc+1(y(P(z1));a)lny(z1)-lny(P(z1))x1z1x1,

0.0525
-41.0000
3.0000
1φ=-x2(x1)2+(x2)2, 2φ=x1(x1)2+(x2)2-2πθ(x1)δ(x2),

0.0480
-29.0000
2.0000
t(ux)=x(ut)-x(ux)=cx(ut)+dt(ut),