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searching for Z/X 544 found (2107 total)

alternate case: z/X

Kriging (5,267 words) [view diff] no match in snippet view article find links to article

Z ( x 1 ) , Z ( x 2 ) ) = C ( Z ( x i ) , Z ( x i + h ) ) = C ( h ) {\displaystyle C(Z(x_{1}),Z(x_{2}))=C(Z(x_{i}),Z(x_{i}+\mathbf {h} ))=C(h)} γ ( Z
Associative property (3,115 words) [view diff] no match in snippet view article find links to article
+ z = x + ( y + z ) = x + y + z ( x y ) z = x ( y z ) = x y z     } for all  x , y , z ∈ R . {\displaystyle \left.{\begin{matrix}(x+y)+z=x+(y+z)=x+y+z\quad
Standard score (1,650 words) [view diff] no match in snippet view article find links to article
student A is z = x − μ σ = 1800 − 1500 300 = 1 {\displaystyle z={x-\mu \over \sigma }={1800-1500 \over 300}=1} The z-score for student B is z = x − μ σ = 24
Geostatistics (1,704 words) [view diff] no match in snippet view article find links to article
N-dimensional joint distribution function F ( z , x ) = Prob ⁡ { Z ( x 1 ) ⩽ z 1 , Z ( x 2 ) ⩽ z 2 , . . . , Z ( x N ) ⩽ z N } . {\displaystyle F(\mathbf {z}
Boolean algebra (structure) (3,278 words) [view diff] no match in snippet view article
following laws: Commutativity: x + y = y + x. Associativity: (x + y) + z = x + (y + z). Huntington equation: n(n(x) + y) + n(n(x) + n(y)) = x. Herbert
Z-transform (3,482 words) [view diff] no match in snippet view article find links to article
{d} v} Initial value theorem: If x[n] is causal, then x [ 0 ] = lim z → ∞ X ( z ) . {\displaystyle x[0]=\lim _{z\to \infty }X(z).} Final value theorem:
Lie algebra (6,851 words) [view diff] no match in snippet view article find links to article
Bilinearity: [ x + y , z ] = [ x , z ] + [ y , z ] , [ z , x + y ] = [ z , x ] + [ z , y ] {\displaystyle [x+y,z]=[x,z]+[y,z],\quad [z,x+y]=[z,x]+[z,y]} for all
Commutator (2,300 words) [view diff] no match in snippet view article find links to article
[ [ x , y ] , z x ] ⋅ [ [ z , x ] , y z ] ⋅ [ [ y , z ] , x y ] = 1. {\displaystyle \left[\left[x,y\right],z^{x}\right]\cdot \left[[z,x],y^{z}\right]\cdot
Paraboloid (2,242 words) [view diff] no match in snippet view article find links to article
paraboloids z = x 2 + y 2 b 2 ,   b > 0 , {\displaystyle z=x^{2}+{\frac {y^{2}}{b^{2}}},\ b>0,} and the pencil of hyperbolic paraboloids z = x 2 − y 2 b
Peano axioms (5,744 words) [view diff] no match in snippet view article find links to article
discrete ordered semiring. ∀ x , y , z   ( ( x + y ) + z = x + ( y + z ) ) {\displaystyle \forall x,y,z\ ((x+y)+z=x+(y+z))} , i.e., addition is associative
Split-complex number (3,725 words) [view diff] no match in snippet view article find links to article
real number components x and y, and is written z = x + y j, where j2 = 1. The conjugate of z is z∗ = x − y j. Since j2 = 1, the product of a number z
Partial derivative (4,159 words) [view diff] no match in snippet view article find links to article
z {\displaystyle z} with respect to x {\displaystyle x} is denoted as ∂ zx . {\displaystyle {\tfrac {\partial z}{\partial x}}.} Since a partial derivative
Bitwise operation (3,751 words) [view diff] no match in snippet view article find links to article
~y ~(x & y) = ~x | ~y x | (y & z) = (x | y) & (x | z) x & (y | z) = (x & y) | (x & z) x & (y ^ z) = (x & y) ^ (x & z) x + y = (x ^ y) + ((x & y) << 1)
Mutual information (8,026 words) [view diff] no match in snippet view article find links to article
∑ z ∈ Z ∑ y ∈ Y ∑ x ∈ X p Z ( z ) p X , Y | Z ( x , y | z ) log ⁡ [ p X , Y | Z ( x , y | z ) p X | Z ( x | z ) p Y | Z ( y | z ) ] , {\displaystyle \operatorname
Euler angles (5,081 words) [view diff] no match in snippet view article find links to article
in two groups: Proper Euler angles (z-x-z, x-y-x, y-z-y, z-y-z, x-z-x, y-x-y) Tait–Bryan angles (x-y-z, y-z-x, z-x-y, x-z-y, z-y-x, y-x-z). Tait–Bryan
Integral domain (3,186 words) [view diff] no match in snippet view article find links to article
Z [ x ] {\displaystyle \mathbb {Z} [x]} . By the Chinese remainder theorem, there is an isomorphism Z [ x ] / ( x 2 − n ) ≅ Z [ x ] / ( x − m ) × Z [
Minimal surface (2,382 words) [view diff] no match in snippet view article find links to article
expanding Lagrange's equation to ( 1 + z x 2 ) z y y − 2 z x z y z x y + ( 1 + z y 2 ) z x x = 0 {\displaystyle \left(1+z_{x}^{2}\right)z_{yy}-2z_{x}z_{y}z_
Camber (aerodynamics) (712 words) [view diff] no match in snippet view article
follows: Z upper ( x ) = Z ( x ) + 1 2 T ( x ) {\displaystyle Z_{\text{upper}}(x)=Z(x)+{\frac {1}{2}}T(x)} Z lower ( x ) = Z ( x ) − 1 2 T ( x ) {\displaystyle
Cartesian closed category (2,512 words) [view diff] no match in snippet view article find links to article
→ Y gives morphisms p Z : X Z → Y Z , {\displaystyle p^{Z}:X^{Z}\to Y^{Z},} Z p : Z Y → Z X , {\displaystyle Z^{p}:Z^{Y}\to Z^{X},} corresponding to the
Linear elasticity (5,781 words) [view diff] no match in snippet view article find links to article
{\displaystyle \epsilon _{z}={\frac {\partial u_{z}}{\partial z}}\,\!} γ z x = ∂ u zx + ∂ u x ∂ z {\displaystyle \gamma _{zx}={\frac {\partial u_{z}}{\partial
Vertex operator algebra (7,440 words) [view diff] no match in snippet view article find links to article
u , v , w ; z , x ) ∈ V [ [ z , x ] ] [ z − 1 , x − 1 , ( zx ) − 1 ] {\displaystyle X(u,v,w;z,x)\in V[[z,x]]\left[z^{-1},x^{-1},(z-x)^{-1}\right]}
Poisson's ratio (4,618 words) [view diff] no match in snippet view article find links to article
expressed in matrix form as [ ϵ x x ϵ y y ϵ z z 2 ϵ y z 2 ϵ z x 2 ϵ x y ] = [ 1 E x − ν y x E y − ν z x E z 0 0 0 − ν x y E x 1 E y − ν z y E z 0 0 0 − ν x z
Periodic function (1,540 words) [view diff] no match in snippet view article find links to article
quotient space: R / Z = { x + Z : x ∈ R } = { { y : y ∈ R ∧ y − x ∈ Z } : x ∈ R } {\displaystyle {\mathbb {R} /\mathbb {Z} }=\{x+\mathbb {Z} :x\in \mathbb {R}
Wigner semicircle distribution (3,658 words) [view diff] no match in snippet view article find links to article
spherical (parametric) distribution f X , Y , Z ( x , y , z ) = 3 4 π , x 2 + y 2 + z 2 ≤ 1 , {\displaystyle f_{X,Y,Z}(x,y,z)={\frac {3}{4\pi }},\qquad \qquad
Jacobi identity (965 words) [view diff] no match in snippet view article find links to article
, Z } , X ] + [ { Z , X } , Y ] = 0 , [ { X , Y } , Z ] + { [ Z , Y ] , X } + { [ Z , X ] , Y } = 0. {\displaystyle [\{X,Y\},Z]+[\{Y,Z\},X]+[\{Z,X\},Y]=0
Distributive property (2,699 words) [view diff] no match in snippet view article find links to article
+ z ) = ( x ∗ y ) + ( x ∗ z ) , {\displaystyle x*(y+z)=(x*y)+(x*z),} is right-distributive over + if, given any elements x, y, and z of S, ( y + z ) ∗
Inner product space (5,935 words) [view diff] no match in snippet view article find links to article
linearity in the first and second argument: ⟨ x + y , z ⟩ = ⟨ x , z ⟩ + ⟨ y , z ⟩ , ⟨ x , y + z ⟩ = ⟨ x , y ⟩ + ⟨ x , z ⟩ {\displaystyle {\begin{aligned}\langle
Berlekamp–Rabin algorithm (1,981 words) [view diff] no match in snippet view article find links to article
polynomial f z ( x ) = f ( x − z ) = ( x − λ 1 − z ) ( x − λ 2 − z ) ⋯ ( x − λ n − z ) {\textstyle f_{z}(x)=f(x-z)=(x-\lambda _{1}-z)(x-\lambda _{2}-z)\cdots
Levi-Civita connection (2,841 words) [view diff] no match in snippet view article find links to article
then find: X ( g ( Y , Z ) ) + Y ( g ( Z , X ) ) − Z ( g ( Y , X ) ) = g ( ∇ X Y + ∇ Y X , Z ) + g ( ∇ X Z − ∇ Z X , Y ) + g ( ∇ Y Z − ∇ Z Y , X ) . {\displaystyle
Infinitesimal strain theory (6,542 words) [view diff] no match in snippet view article find links to article
x y ε x z ε y x ε y y ε y z ε z x ε z y ε z z ] = [ ∂ u x ∂ x 1 2 ( ∂ u x ∂ y + ∂ u y ∂ x ) 1 2 ( ∂ u x ∂ z + ∂ u zx ) 1 2 ( ∂ u y ∂ x + ∂ u x ∂ y
Saddle point (938 words) [view diff] no match in snippet view article find links to article
saddle point. For example, the Hessian matrix of the function z = x 2 − y 2 {\displaystyle z=x^{2}-y^{2}} at the stationary point ( x , y , z ) = ( 0 , 0
Instrumental variables estimation (6,315 words) [view diff] no match in snippet view article find links to article
{\displaystyle Z'e=0} in the true model: β ^ I V = ( ZX ) − 1 Z ′ y = ( ZX ) − 1 ZX β + ( ZX ) − 1 Z ′ e → β {\displaystyle {\widehat {\beta }}_{\mathrm
Exact differential (2,149 words) [view diff] no match in snippet view article find links to article
such that d Q ≡ ( ∂ Q ∂ x ) y , z d x + ( ∂ Q ∂ y ) x , z d y + ( ∂ Q ∂ z ) x , y d z , {\displaystyle dQ\equiv \left({\frac {\partial Q}{\partial x}}\right)_{y
Short integer solution problem (2,995 words) [view diff] no match in snippet view article find links to article
polynomial ring R = Z [ x ] / ( x n − 1 ) {\displaystyle R=\mathbb {Z} [x]/(x^{n}-1)} are cyclic: consider the quotient polynomial ring R = Z [ x ] / ( x n −
Stabilizer code (2,850 words) [view diff] no match in snippet view article find links to article
g 1 = X Z Z X I g 2 = I X Z Z X g 3 = X I X Z Z g 4 = Z X I X Z {\displaystyle {\begin{array}{ccccccc}g_{1}&=&X&Z&Z&X&I\\g_{2}&=&I&X&Z&Z&X
Surface integral (2,204 words) [view diff] no match in snippet view article find links to article
{d} x\,\mathrm {d} y} where r = ( x , y , z ) = ( x , y , f ( x , y ) ) {\displaystyle \mathbf {r} =(x,y,z)=(x,y,f(x,y))} . So that ∂ r ∂ x = ( 1 , 0 ,
Covariance function (561 words) [view diff] no match in snippet view article find links to article
cov ⁡ ( Z ( x ) , Z ( y ) ) = E [ { Z ( x ) − E [ Z ( x ) ] } ⋅ { Z ( y ) − E [ Z ( y ) ] } ] . {\displaystyle C(x,y):=\operatorname {cov} (Z(x),Z(y))=\mathbb
Convolution theorem (2,449 words) [view diff] no match in snippet view article find links to article
( zx ) d x . {\displaystyle h(z)=\int _{\mathbb {R} ^{n}}f(x)g(z-x)\,dx.} Also ∬ | f ( x ) g ( zx ) | d z d x = ∫ ( | f ( x ) | ∫ | g ( zx )
Voigt notation (1,386 words) [view diff] no match in snippet view article find links to article
matrix notation) is given as σ = [ σ x x σ x y σ x z σ y x σ y y σ y z σ z x σ z y σ z z ] . {\displaystyle {\boldsymbol {\sigma }}=\left[{\begin{matrix}\sigma
Complex plane (4,570 words) [view diff] no match in snippet view article find links to article
can be separated into its real (x) and imaginary (y) parts: z = x + i y {\displaystyle z=x+iy} for example: z = 4 + 5i, where x and y are real numbers
Expectation–maximization algorithm (7,119 words) [view diff] no match in snippet view article find links to article
get: log ⁡ p ( X ∣ θ ) = ∑ Z p ( ZX , θ ( t ) ) log ⁡ p ( X , Z ∣ θ ) − ∑ Z p ( ZX , θ ( t ) ) log ⁡ p ( ZX , θ ) = Q ( θ ∣ θ ( t ) ) + H ( θ
Beta decay (6,760 words) [view diff] no match in snippet view article find links to article
{\displaystyle m\left({\ce {^{\mathit {A}}_{\mathit {Z}}X}}\right)c^{2}=m_{N}\left({\ce {^{\mathit {A}}_{\mathit {Z}}X}}\right)c^{2}+Zm_{e}c^{2}-\sum _{i=1}^{Z}B_{i}}
Mandelbulb (2,061 words) [view diff] no match in snippet view article find links to article
y → y 5 − 10 y 3 ( z 2 + A x z + x 2 ) + 5 y ( z 4 + B z 3 x + C z 2 x 2 + B z x 3 + x 4 ) + D y 2 z x ( z + x ) + y 0 {\displaystyle y\rightarrow
Ecological fallacy (2,742 words) [view diff] no match in snippet view article find links to article
Z = z , X = 1 ] > E [ Y ∣ Z = z , X = 0 ]   for all  z ,  while  E [ Y ∣ X = 1 ] < E [ Y ∣ X = 0 ] {\displaystyle E[Y\mid Z=z,X=1]>E[Y\mid Z=z,X=0]\ {\text{for
Dense order (645 words) [view diff] no match in snippet view article find links to article
integers Z [ x ] {\displaystyle \mathbb {Z} [x]} is a densely ordered set. Proof — For the element x ∈ Z [ x ] {\displaystyle x\in \mathbb {Z} [x]} , due
Power set (1,921 words) [view diff] no match in snippet view article find links to article
null set) {x} {y} {z} {x, y} {x, z} {y, z} {x, y, z} and hence the power set of S is {{}, {x}, {y}, {z}, {x, y}, {x, z}, {y, z}, {x, y, z}}. If S is a
Quasigroup (3,426 words) [view diff] no match in snippet view article find links to article
y, z: x ∗ (y ∗ (x ∗ z)) = ((x ∗ y) ∗ x) ∗ z, z ∗ (x ∗ (y ∗ x)) = ((zx) ∗ y) ∗ x, (x ∗ y) ∗ (zx) = x ∗ ((y ∗ z) ∗ x), or (x ∗ y) ∗ (zx) = (x
Complex number (13,771 words) [view diff] no match in snippet view article find links to article
absolute value (or modulus or magnitude) of a complex number z = x + yi is r = | z | = x 2 + y 2 . {\displaystyle r=|z|={\sqrt {x^{2}+y^{2}}}.} If z is
Cauchy–Riemann equations (4,441 words) [view diff] no match in snippet view article find links to article
respectively of a complex-valued function of a single complex variable z = x + iy, f(x + iy) = u(x,y) + iv(x,y). Suppose that u and v are real-differentiable
Z-test (1,741 words) [view diff] no match in snippet view article find links to article
hypothesis H1: μ≠μ0 , it is two-tailed. Third, calculate the standard score : Z = ( X ¯ − μ 0 ) s {\displaystyle Z={\frac {({\bar {X}}-\mu _{0})}{s}}} , which
Euler's formula (3,387 words) [view diff] no match in snippet view article find links to article
complex number z = x + iy, and its complex conjugate, z = x − iy, can be written as z = x + i y = | z | ( cos ⁡ φ + i sin ⁡ φ ) = r e i φ , z ¯ = x − i y = |
Product (category theory) (1,521 words) [view diff] no match in snippet view article
isomorphisms X × ( Y × Z ) ≃ ( X × Y ) × ZX × Y × Z , {\displaystyle X\times (Y\times Z)\simeq (X\times Y)\times Z\simeq X\times Y\times Z,} X × 1 ≃ 1 × X ≃
Monomorphism (1,336 words) [view diff] no match in snippet view article find links to article
an arrow f : X → Y such that for all objects Z and all morphisms g1, g2: ZX, f ∘ g 1 = f ∘ g 2 ⟹ g 1 = g 2 . {\displaystyle f\circ g_{1}=f\circ g_{2}\implies
Dirichlet problem (1,964 words) [view diff] no match in snippet view article find links to article
G ( z , x ) = − 1 2 π log ⁡ | zx | + γ ( z , x ) {\displaystyle G(z,x)=-{\frac {1}{2\pi }}\log \vert z-x\vert +\gamma (z,x)} where γ ( z , x ) {\displaystyle
Bending moment (3,104 words) [view diff] no match in snippet view article find links to article
compute the cross products, we have M = | e x e y e z x A − x 0 0 0 − F 0 | + | e x e y e zx 0 0 0 R 0 0 | = F ( x − x A ) e z − R 0 x e z = − F x
Boolean algebra (9,451 words) [view diff] no match in snippet view article find links to article
is a self-dual operation. For example, if f(x, y, z) = (x∧y) ∨ (y∧z) ∨ (zx), then f(f(x, y, z), x, t) is a self-dual operation of four arguments x,y
Shifted log-logistic distribution (801 words) [view diff] no match in snippet view article find links to article
+1)}}{\sigma \left(1+(1+\xi z)^{-1/\xi }\right)^{2}}}} where z = ( x − μ ) / σ {\displaystyle z=(x-\mu )/\sigma \,} CDF ( 1 + ( 1 + ξ z ) − 1 / ξ ) − 1 {\displaystyle
Lie superalgebra (2,296 words) [view diff] no match in snippet view article find links to article
x | | z | [ x , [ y , z ] ] + ( − 1 ) | y | | x | [ y , [ z , x ] ] + ( − 1 ) | z | | y | [ z , [ x , y ] ] = 0 , {\displaystyle (-1)^{|x||z|}[x,[y,z]]+(-1)^{|y||x|}[y
Ellipsoid method (1,522 words) [view diff] no match in snippet view article find links to article
  ( zx 0 ) T P ( 0 ) − 1 ( zx 0 ) ⩽ 1 } {\displaystyle {\mathcal {E}}^{(0)}=\left\{z\in \mathbb {R} ^{n}\ :\ (z-x_{0})^{T}P_{(0)}^{-1}(z-x_{0})\leqslant
Zermelo–Fraenkel set theory (5,673 words) [view diff] no match in snippet view article find links to article
{\displaystyle x\equiv 0{\pmod {2}}} : { x ∈ Z : x ≡ 0 ( mod 2 ) } . {\displaystyle \{x\in \mathbb {Z} :x\equiv 0{\pmod {2}}\}.} In general, the subset
Join and meet (1,116 words) [view diff] no match in snippet view article find links to article
by a; and if x ≤ y and y ≤ z, then x ≤ z, since then x ∧ z = (x ∧ y) ∧ z = x ∧ (y ∧ z) = x ∧ y = x by b. Note that both meets and joins equally satisfy
Distributive lattice (2,011 words) [view diff] no match in snippet view article find links to article
following additional identity holds for all x, y, and z in L: x ∧ (y ∨ z) = (x ∧ y) ∨ (x ∧ z). Viewing lattices as partially ordered sets, this says that
Pushout (category theory) (1,776 words) [view diff] no match in snippet view article
amalgamated sum) is the colimit of a diagram consisting of two morphisms f : ZX and g : Z → Y with a common domain. The pushout consists of an object P
Cartesian coordinate system (5,696 words) [view diff] no match in snippet view article find links to article
octants. The octants are: | (+x,+y,+z) | (-x,+y,+z) | (+x,+y,-z) | (-x,+y,-z) | (+x,-y,+z) | (-x,-y,+z) | (+x,-y,-z) | (-x,-y,-z) | The coordinates are usually
Identity (mathematics) (1,356 words) [view diff] no match in snippet view article
identity set {   ∀x,y,z. x*(y*z)=(x*y)*z   ,   ∀x. x*1=x   ,   ∀x. 1*x=x   }, or, in short notation, as {   x*(y*z)=(x*y)*z   ,   x*1=x   ,   1*x=x   }
Conditional independence (2,861 words) [view diff] no match in snippet view article find links to article
. Formally: where F X , Y ∣ Z = z ( x , y ) = Pr ( X ≤ x , Y ≤ y ∣ Z = z ) {\displaystyle F_{X,Y\,\mid \,Z\,=\,z}(x,y)=\Pr(X\leq x,Y\leq y\mid Z=z)}
Trilinear coordinates (2,505 words) [view diff] no match in snippet view article find links to article
y' : z' is y z ( x ′ − y ′ − z ′ ) + z x ( y ′ − z ′ − x ′ ) + x y ( z ′ − x ′ − y ′ ) = 0. {\displaystyle yz(x'-y'-z')+zx(y'-z'-x')+xy(z'-x'-y')=0.} Every
Experimental uncertainty analysis (15,176 words) [view diff] no match in snippet view article find links to article
σ z 2 ≈ ( ∂ zx 1 ) ( ∂ zx 1 ) σ 11 + ( ∂ zx 2 ) ( ∂ zx 2 ) σ 22 + ( ∂ zx 1 ) ( ∂ zx 2 ) σ 12 + ( ∂ zx 2 ) ( ∂ zx 1 ) σ 21 {\displaystyle
Simon (cipher) (1,781 words) [view diff] no match in snippet view article
z x {\displaystyle z_{x}} . The z x {\displaystyle z_{x}} bit operates on the lowest bit of the key word once per round. The constant sequence, z x {\displaystyle
Composition ring (910 words) [view diff] no match in snippet view article find links to article
and assign ∘ : Z [ x ] × Z [ x ] → Z [ x ] {\displaystyle \circ :{\mathbb {Z} }[x]\times {\mathbb {Z} }[x]\rightarrow {\mathbb {Z} }[x]} , accordingly
Principal ideal domain (1,409 words) [view diff] no match in snippet view article find links to article
example ( 2 , X ) ⊆ Z [ X ] {\displaystyle (2,X)\subseteq \mathbb {Z} [X]} of modules over Z [ X ] {\displaystyle \mathbb {Z} [X]} shows. In a principal
Cohomology (6,529 words) [view diff] no match in snippet view article find links to article
subscheme ZX {\displaystyle Z\subset X} there is a Cartesian square E ⟶ B l Z ( X ) ↓ ↓ ZX {\displaystyle {\begin{matrix}E&\longrightarrow &Bl_{Z}(X)\\\downarrow
Exponential distribution (5,853 words) [view diff] no match in snippet view article find links to article
probability density of Z = X 1 + X 2 {\displaystyle Z=X_{1}+X_{2}} is given by f Z ( z ) = ∫ − ∞ ∞ f X 1 ( x 1 ) f X 2 ( zx 1 ) d x 1 = ∫ 0 z λ 1 e
Semivariance (321 words) [view diff] no match in snippet view article find links to article
) ∑ i = 1 n ( h ) [ z ( x i + h ) − z ( x i ) ] 2 {\displaystyle \gamma (h)={\dfrac {1}{2n(h)}}\sum _{i=1}^{n(h)}[z(x_{i}+h)-z(x_{i})]^{2}} where z is
Absolute value (3,701 words) [view diff] no match in snippet view article find links to article
computed using the Pythagorean theorem: for any complex number z = x + i y , {\displaystyle z=x+iy,} where x and y are real numbers, the absolute value or
Absolute difference (269 words) [view diff] no match in snippet view article find links to article
only if   x = y. |x − y| = |y − x|     (symmetry or commutativity). |x − z| ≤ |x − y| + |y − z|     (triangle inequality); in the case of the absolute difference
Inequality of arithmetic and geometric means (6,880 words) [view diff] no match in snippet view article find links to article
function f ( x , y , z ) = x y + y z + z x 3 {\displaystyle f(x,y,z)={\frac {x}{y}}+{\sqrt {\frac {y}{z}}}+{\sqrt[{3}]{\frac {z}{x}}}} for all positive
Hash function (6,961 words) [view diff] no match in snippet view article find links to article
{\displaystyle m} th degree polynomial Z ( x ) = x m + ζ m − 1 x m − 1 + . . . + ζ 0 {\displaystyle \mathrm {Z} (x)=x^{m}+\zeta _{m-1}x^{m-1}+...+\zeta
Castorocauda (1,926 words) [view diff] no match in snippet view article find links to article
with an annual temperature of below 15 °C (59 °F). Haldanodon Ji, Q.; Luo, Z.-X.; Yuan, C.-X.; Tabrum, A. R. (2006). "A swimming mammaliaform from the Middle
Conditional mutual information (2,364 words) [view diff] no match in snippet view article find links to article
= H ( Z | X ) + H ( X ) + H ( Z | Y ) + H ( Y ) − H ( Z | X , Y ) − H ( X , Y ) − H ( Z ) = I ( X ; Y ) + H ( Z | X ) + H ( Z | Y ) − H ( Z | X , Y )
Surface roughness (2,418 words) [view diff] no match in snippet view article find links to article
r | z ( x ) | d x {\displaystyle Ra={\frac {1}{l_{r}}}\int _{0}^{l_{r}}\left|z(x)\right|dx} Rq, Rms Root mean squared R q = 1 l r ∫ 0 l r z ( x ) 2 d
Algebra of random variables (3,530 words) [view diff] no match in snippet view article find links to article
possible: Addition: Z = X + Y = Y + X {\displaystyle Z=X+Y=Y+X} Subtraction: Z = X − Y = − Y + X {\displaystyle Z=X-Y=-Y+X} Multiplication: Z = X Y = Y X {\displaystyle
Maximal ideal (1,482 words) [view diff] no match in snippet view article find links to article
maximal ideal in ring Z [ x ] {\displaystyle \mathbb {Z} [x]} . Generally, the maximal ideals of Z [ x ] {\displaystyle \mathbb {Z} [x]} are of the form (
Product distribution (7,902 words) [view diff] no match in snippet view article find links to article
the distribution of the random variable Z that is formed as the product Z = X Y {\displaystyle Z=XY} is a product distribution. The product is one type
Superstring theory (2,875 words) [view diff] no match in snippet view article find links to article
Heterotic ∂ z X μ − i θ L ¯ Γ μ ∂ z θ L {\displaystyle \partial _{z}X^{\mu }-i{\overline {\theta _{L}}}\Gamma ^{\mu }\partial _{z}\theta _{L}} IIA ∂ z X μ − i
Sublinear function (1,301 words) [view diff] no match in snippet view article find links to article
z = { x ∈ X : p(x) < 1  } so that V = z + { x ∈ X : p(x) < 1  }. But z + { x ∈ X : p(x) < 1 } = { z + x : x ∈ X, p(x) < 1 } = { z + x : x ∈ X, p((z +
Universal algebra (2,964 words) [view diff] no match in snippet view article find links to article
Associativity (as in the previous section): x ∗ (y ∗ z)  =  (x ∗ y) ∗ z;   formally: ∀x,y,z. x∗(y∗z)=(x∗y)∗z. Identity element: There exists an element e
Multicomplex number (439 words) [view diff] no match in snippet view article find links to article
imaginary number. Then C n + 1 = { z = x + y i n + 1 : x , y ∈ C n } {\displaystyle {\text{C}}_{n+1}=\lbrace z=x+yi_{n+1}:x,y\in {\text{C}}_{n}\rbrace
Euler diagram (3,475 words) [view diff] no match in snippet view article find links to article
+ xyz' = x'y' + yz'). P → Q , P ⊢ Q i.e.: ( ~(y & z) & (x → y) ) → ( ~ (x & z) ) , ( ~(y & z) & (x → y) ) ⊢ ( ~ (x & z) ) i.e.: IF "No Ys are Zs" and
ISO 31-11 (117 words) [view diff] no match in snippet view article find links to article
vector and its differential Name of coordinate system Remarks x, y, z [ x y z ] = [ x y z ] ; {\displaystyle [xyz]=[xyz];} [ d x d y d z ] ; {\displaystyle
Monkey saddle (393 words) [view diff] no match in snippet view article find links to article
the monkey saddle is the surface defined by the equation z = x 3 − 3 x y 2 , {\displaystyle z=x^{3}-3xy^{2},\,} or in cylindrical coordinates z = ρ 3 cos
Malcev algebra (324 words) [view diff] no match in snippet view article find links to article
Malcev identity ( x y ) ( x z ) = ( ( x y ) z ) x + ( ( y z ) x ) x + ( ( z x ) x ) y . {\displaystyle (xy)(xz)=((xy)z)x+((yz)x)x+((zx)x)y.} They were
Probability-generating function (1,612 words) [view diff] no match in snippet view article find links to article
defined as G ( z ) = E ⁡ ( z X ) = ∑ x = 0 ∞ p ( x ) z x , {\displaystyle G(z)=\operatorname {E} (z^{X})=\sum _{x=0}^{\infty }p(x)z^{x},} where p is the probability
First-order logic (12,687 words) [view diff] no match in snippet view article find links to article
∀ z ( zx ⇔ z ∈ y ) ⇒ ∀ z ( x ∈ z ⇔ y ∈ z ) ] {\displaystyle \forall x\forall y[\forall z(z\in x\Leftrightarrow z\in y)\Rightarrow \forall z(x\in z\Leftrightarrow
Sum of normally distributed random variables (3,340 words) [view diff] no match in snippet view article find links to article
σ Y 2 ) {\displaystyle Y\sim N(\mu _{Y},\sigma _{Y}^{2})} Z = X + Y , {\displaystyle Z=X+Y,} then Z ∼ N ( μ X + μ Y , σ X 2 + σ Y 2 ) . {\displaystyle
Tangent (3,656 words) [view diff] no match in snippet view article find links to article
equation of the tangent line is ∂ g ∂ x ( X , Y , Z ) ⋅ x + ∂ g ∂ y ( X , Y , Z ) ⋅ y + ∂ g ∂ z ( X , Y , Z ) ⋅ z = 0. {\displaystyle {\frac {\partial
Borealestes (546 words) [view diff] no match in snippet view article find links to article
119–125. doi:10.1144/gsjgs.128.2.0119. Panciroli, E., Benson, R.B. and Luo, Z.X., 2019. The mandible and dentition of Borealestes serendipitus (Docodonta)
Positive-definite kernel (4,297 words) [view diff] no match in snippet view article find links to article
random variable Z ( x i ) {\displaystyle Z(x_{i})} . The goal is to get information about the function E [ Z ( x i ) ] {\displaystyle E[Z(x_{i})]} which
Rotation matrix (14,370 words) [view diff] no match in snippet view article find links to article
y − Q z z Q y x + Q x y Q z x + Q x z Q y z − Q z y Q y x + Q x y Q y y − Q x x − Q z z Q z y + Q y z Q z x − Q x z Q z x + Q x z Q z y + Q y z Q z z
Axiom of adjunction (256 words) [view diff] no match in snippet view article find links to article
given by "adjoining" the set y to the set x. ∀ x ∀ y ∃ w ∀ z [ z ∈ w ↔ ( zx ∨ z = y ) ] . {\displaystyle \forall x\,\forall y\,\exists w\,\forall z\
Moufang loop (1,669 words) [view diff] no match in snippet view article find links to article
z ( y ) = L z x z ( y ) {\displaystyle L_{z}L_{x}L_{z}(y)=L_{zxz}(y)} R z R y R z ( x ) = R z y z ( x ) {\displaystyle R_{z}R_{y}R_{z}(x)=R_{zyz}(x)}
Tak (function) (497 words) [view diff] no match in snippet view article
( y − 1 , z , x ) , τ ( z − 1 , x , y ) ) if  y < x z otherwise {\displaystyle \tau (x,y,z)={\begin{cases}\tau (\tau (x-1,y,z),\tau (y-1,z,x),\tau (z-1
(803 words) [view diff] no match in snippet view article find links to article
This symbol can be used variously to denote a partial derivative such as ∂ zx {\displaystyle {\tfrac {\partial z}{\partial x}}} (read as "the partial
Polynomial ring (8,025 words) [view diff] no match in snippet view article find links to article
K[X_{1},\ldots ,X_{n}]} and Z [ X 1 , … , X n ] {\displaystyle \mathbb {Z} [X_{1},\ldots ,X_{n}]} are regular rings, gl dim ⁡ Z [ X 1 , … , X n ] = n + 1
Triple product rule (1,482 words) [view diff] no match in snippet view article find links to article
the implicit function theorem and is given by ( ∂ x ∂ y ) z ( ∂ y ∂ z ) x ( ∂ zx ) y = − 1. {\displaystyle \left({\frac {\partial x}{\partial
Adequate equivalence relation (573 words) [view diff] no match in snippet view article find links to article
divisors. All cycles modulo rational equivalence form the Chow ring. Let Z*(X) := Z[X] be the free abelian group on the algebraic cycles of X. Then an adequate
Consensus theorem (704 words) [view diff] no match in snippet view article find links to article
x y ∨ x ¯ z ∨ ( x ∨ x ¯ ) y z = x y ∨ x ¯ zx y zx ¯ y z = ( x y ∨ x y z ) ∨ ( x ¯ zx ¯ y z ) = x y ( 1 ∨ z ) ∨ x ¯ z ( 1 ∨ y ) = x y ∨ x ¯ z
Davenport chained rotations (2,791 words) [view diff] no match in snippet view article find links to article
Generalized Euler rotations (z-x-z, x-y-x, y-z-y, z-y-z, x-z-x, y-x-y) Generalized Tait–Bryan rotations (x-y-z, y-z-x, z-x-y, x-z-y, z-y-x, y-x-z). Most
Roman surface (2,776 words) [view diff] no match in snippet view article find links to article
to these points the transformation T defined by T ( x , y , z ) = ( y z , z x , x y ) = ( U , V , W ) , {\displaystyle T(x,y,z)=(yz,zx,xy)=(U,V,W),\,}
Conjunctive normal form (2,218 words) [view diff] no match in snippet view article find links to article
v e s ( z , x ) ] {\displaystyle \forall x[\exists y\mathrm {Animal} (y)\land \lnot \mathrm {Loves} (x,y)]\lor [\exists z\mathrm {Loves} (z,x)]} . Skolemize
Equality (mathematics) (1,700 words) [view diff] no match in snippet view article
set. Logic axiom: x = y ⇒ ∀z, (zx ⇔ z ∈ y) Logic axiom: x = y ⇒ ∀z, (x ∈ z ⇔ y ∈ z) Set theory axiom: (∀z, (zx ⇔ z ∈ y)) ⇒ x = y Incorporating
Median algebra (582 words) [view diff] no match in snippet view article find links to article
y\rangle =y} ⟨ x , y , z ⟩ = ⟨ z , x , y ⟩ {\displaystyle \langle x,y,z\rangle =\langle z,x,y\rangle } ⟨ x , y , z ⟩ = ⟨ x , z , y ⟩ {\displaystyle \langle
Division polynomials (1,177 words) [view diff] no match in snippet view article find links to article
division polynomials is a sequence of polynomials in Z [ x , y , A , B ] {\displaystyle \mathbb {Z} [x,y,A,B]} with x , y , A , B {\displaystyle x,y,A,B}
6-sphere coordinates (315 words) [view diff] no match in snippet view article find links to article
z 2 , w = z x 2 + y 2 + z 2 . {\displaystyle u={\frac {x}{x^{2}+y^{2}+z^{2}}},\quad v={\frac {y}{x^{2}+y^{2}+z^{2}}},\quad w={\frac {z}{x^{2}+y^{2}+z^{2}}}
Abelian sandpile model (4,531 words) [view diff] no match in snippet view article find links to article
z ( x , y ) − 4 , {\displaystyle z(x,y)\rightarrow z(x,y)-4,} z ( x ± 1 , y ) → z ( x ± 1 , y ) + 1 , {\displaystyle z(x\pm 1,y)\rightarrow z(x\pm
Von Neumann–Bernays–Gödel set theory (13,024 words) [view diff] no match in snippet view article find links to article
permutation ( y , z , x ) ↦ ( x , y , z ) {\displaystyle (y,z,x)\mapsto (x,y,z)} to the 3‑tuples of A {\displaystyle A} . ∀ A ∃ B ∀ x ∀ y ∀ z [ ( x , y , z )
Bernoulli differential equation (895 words) [view diff] no match in snippet view article find links to article
linear differential equation z ′ ( x ) = ( 1 − α ) P ( x ) z ( x ) + ( 1 − α ) Q ( x ) . {\displaystyle z'(x)=(1-\alpha )P(x)z(x)+(1-\alpha )Q(x).} Then we
Voigt profile (2,096 words) [view diff] no match in snippet view article find links to article
where Re[w(z)] is the real part of the Faddeeva function evaluated for z = x + i γ σ 2 . {\displaystyle z={\frac {x+i\gamma }{\sigma {\sqrt {2}}}}.}
List of first-order theories (5,265 words) [view diff] no match in snippet view article find links to article
properties include: ∀ x ∀ y ∀ z x ∨ ( y ∧ z ) = ( x ∨ y ) ∧ ( x ∨ z ) {\displaystyle \forall x\forall y\forall z\;x\vee (y\wedge z)=(x\vee y)\wedge (x\vee z)}
Harmonic conjugate (1,080 words) [view diff] no match in snippet view article find links to article
function f ( z ) {\displaystyle f(z)} of the complex variable z := x + i y ∈ Ω . {\displaystyle z:=x+iy\in \Omega .} That is, v {\displaystyle v} is conjugate
Comb filter (1,633 words) [view diff] no match in snippet view article find links to article
transfer function as: H ( z ) = Y ( z ) X ( z ) = 1 + α z − K = z K + α z K {\displaystyle H(z)={\frac {Y(z)}{X(z)}}=1+\alpha z^{-K}={\frac {z^{K}+\alpha
Seven-dimensional cross product (4,796 words) [view diff] no match in snippet view article find links to article
{y} )} Malcev identity: ( x × y ) × ( x × z ) = ( ( x × y ) × z ) × x + ( ( y × z ) × x ) × x + ( ( z × x ) × x ) × y {\displaystyle (\mathbf {x} \times
F4 (mathematics) (945 words) [view diff] no match in snippet view article
{X}}+2Y{\overline {Y}}+2Z{\overline {Z}}} C 3 = x y zx X X ¯ − y Y Y ¯ − z Z Z ¯ + X Y Z + X Y Z ¯ {\displaystyle C_{3}=xyz-xX{\overline {X}}-yY{\overline
Factorization (7,628 words) [view diff] no match in snippet view article find links to article
+ z 2 + 2 ( x y + y z + x z ) = ( x + y + z ) 2 x 3 + y 3 + z 3 − 3 x y z = ( x + y + z ) ( x 2 + y 2 + z 2 − x y − x z − y z ) x 3 + y 3 + z 3 + 3 x
Umbral calculus (1,492 words) [view diff] no match in snippet view article find links to article
z+x)^{n}\right)\end{aligned}}} This enables one to replace occurrences of B n ( x ) {\displaystyle B_{n}(x)} by L ( ( z + x ) n ) {\displaystyle L((z+x)^{n})}
Algebra over a field (3,352 words) [view diff] no match in snippet view article find links to article
a and b of K: Right distributivity: (x + y) · z = x · z + y · z Left distributivity: z · (x + y) = z · x + z · y Compatibility with scalars: (ax) · (by)
Hyperconnected space (1,486 words) [view diff] no match in snippet view article find links to article
example, the schemes Spec ( Z [ x , y , z ] x 4 + y 3 + z 2 ) {\displaystyle {\text{Spec}}\left({\frac {\mathbb {Z} [x,y,z]}{x^{4}+y^{3}+z^{2}}}\right)}
Beta rectangular distribution (851 words) [view diff] no match in snippet view article find links to article
{(1-\theta )(x-a)}{b-a}}\quad \quad \mathrm {for} \ a\leq x\leq b,} where z = x − a b − a {\displaystyle z={\dfrac {x-a}{b-a}}} and I z ( α , β ) {\displaystyle
Duality (order theory) (448 words) [view diff] no match in snippet view article
lattices for which ∀x,y,z: x ∧ (y ∨ z) = (x ∧ y) ∨ (x ∧ z) holds are exactly those for which the dual statement ∀x,y,z: x ∨ (y ∧ z) = (x ∨ y) ∧ (x ∨ z) holds
Independence (probability theory) (4,162 words) [view diff] no match in snippet view article
{\displaystyle Z} if f X Y | Z ( x , y | z ) = f X | Z ( x | z ) ⋅ f Y | Z ( y | z ) {\displaystyle f_{XY|Z}(x,y|z)=f_{X|Z}(x|z)\cdot f_{Y|Z}(y|z)} for all
Cohn's irreducibility criterion (577 words) [view diff] no match in snippet view article find links to article
sufficient condition for a polynomial to be irreducible in Z [ x ] {\displaystyle \mathbb {Z} [x]} —that is, for it to be unfactorable into the product of
Torsion tensor (3,298 words) [view diff] no match in snippet view article find links to article
X , Y ) Z + R ( Y , Z ) X + R ( Z , X ) Y . {\displaystyle {\mathfrak {S}}\left(R\left(X,Y\right)Z\right):=R(X,Y)Z+R(Y,Z)X+R(Z,X)Y.} Then the following
Power associativity (690 words) [view diff] no match in snippet view article find links to article
{\displaystyle [x^{2},x,x]=0} , where [ x , y , z ] := ( x y ) zx ( y z ) {\displaystyle [x,y,z]:=(xy)z-x(yz)} is the associator (Albert 1948). Over an
Spatial variability (464 words) [view diff] no match in snippet view article find links to article
us suppose, that the Rev' z(x) is perfectly known at any point x within the field under study. Then the uncertainty about z(x) is reduced to zero, whereas
Bernoulli process (4,153 words) [view diff] no match in snippet view article find links to article
there is a sequence of integers Z x = { n ∈ Z : X n ( x ) = 1 } {\displaystyle \mathbb {Z} ^{x}=\{n\in \mathbb {Z} :X_{n}(x)=1\}\,} called the Bernoulli
Composition of relations (2,137 words) [view diff] no match in snippet view article find links to article
"is a brother of" ( xBy ) and "is a parent of" ( yPz ). U = B P ≡ x B y P zx U z . {\displaystyle U=BP\quad \equiv \quad xByPz\iff xUz.} Beginning with
Algebra of communicating processes (1,752 words) [view diff] no match in snippet view article find links to article
z = x + ( y + z ) x + x = x ( x + y ) ⋅ z = ( x ⋅ z ) + ( y ⋅ z ) ( x ⋅ y ) ⋅ z = x ⋅ ( y ⋅ z ) {\displaystyle {\begin{matrix}x+y&=&y+x\\(x+y)+z&=&x
Decipherment of rongorongo (8,165 words) [view diff] no match in snippet view article find links to article
Y Z X.76 Y Z A A | X.76 Y Z | X.76 Y Z | X.76 Y Z X.76 Y Z X.76 Y Z | X.76 Y Z X.76(?) Y Z X.76 Y Z | X.76 Y Z | X.76 Y Z X.76 Y Z X.76 Y Z Z | X.76
Algebraic variety (3,430 words) [view diff] no match in snippet view article find links to article
It may be defined by the equations y − x 2 = 0 zx 3 = 0 {\displaystyle {\begin{aligned}y-x^{2}&=0\\z-x^{3}&=0\end{aligned}}} The irreducibility of this
Affine connection (7,493 words) [view diff] no match in snippet view article find links to article
Z x ) = ⟨ ( d Y ) x ( Z x ) , x ( γ ′ ( t ) ) ⟩ + ⟨ Y x , Z x ⟩ = 0 . {\displaystyle \mathrm {d} f_{x}(Z_{x})={\bigl \langle }(\mathrm {d} Y)_{x}(Z_{x})
Variational Bayesian methods (10,850 words) [view diff] no match in snippet view article find links to article
approximation, using Q ( Z ) ≈ P ( ZX ) {\displaystyle Q(\mathbf {Z} )\approx P(\mathbf {Z} \mid \mathbf {X} )} . Given that P ( ZX ) = P ( X , Z ) P ( X )
Lommel function (396 words) [view diff] no match in snippet view article find links to article
0 z x μ J ν ( x ) d x − J ν ( z ) ∫ 0 z x μ Y ν ( x ) d x ] , {\displaystyle s_{\mu ,\nu }(z)={\frac {\pi }{2}}\left[Y_{\nu }(z)\!\int _{0}^{z}\!\!x^{\mu
Abuse of notation (1,254 words) [view diff] no match in snippet view article find links to article
{\displaystyle z\in G} , the identity ( ( x , y ) , z ) = ( x , ( y , z ) ) {\displaystyle ((x,y),z)=(x,(y,z))} would imply that ( x , y ) = x {\displaystyle
Local zeta-function (1,391 words) [view diff] no match in snippet view article find links to article
infinite product formula for Z ( X , t ) {\displaystyle Z(X,t)} is Z ( X , t ) = ∏   ( 1 − t deg ⁡ ( x ) ) − 1 . {\displaystyle Z(X,t)=\prod \ (1-t^{\deg(x)})^{-1}
Quasi-interior point (264 words) [view diff] no match in snippet view article find links to article
positive cone C of X if x ≥ 0 and if the order interval [0, x] := { zX : 0 ≤ z and zx } is a total subset of X (i.e. if the linear span of [0, x] is
Relevance logic (3,418 words) [view diff] no match in snippet view article find links to article
{\displaystyle x\cdot x=x} ( x ⋅ y ) ⋅ z = x ⋅ ( y ⋅ z ) {\displaystyle (x\cdot y)\cdot z=x\cdot (y\cdot z)} x ⋅ y = y ⋅ x {\displaystyle x\cdot y=y\cdot
Metric (mathematics) (3,338 words) [view diff] no match in snippet view article
[0,\infty )} is the set of non-negative real numbers and for all x , y , zX {\displaystyle x,y,z\in X} , the following three axioms are satisfied: These
Joukowsky transform (1,700 words) [view diff] no match in snippet view article find links to article
+ 1 ζ , {\displaystyle z=\zeta +{\frac {1}{\zeta }},} where z = x + i y {\displaystyle z=x+iy} is a complex variable in the new space and ζ = χ + i η {\displaystyle
Three subgroups lemma (462 words) [view diff] no match in snippet view article find links to article
{\displaystyle [X,Y,Z]=1} and [ Y , Z , X ] = 1 {\displaystyle [Y,Z,X]=1} Then [ Z , X , Y ] = 1 {\displaystyle [Z,X,Y]=1} . More generally, if N ◃ G {\displaystyle
Isotropy (1,417 words) [view diff] no match in snippet view article find links to article
0} . Whatever algebraic form holds for f ( x , y , z ) = x 2 + y 2 + z 2 {\displaystyle f(x,y,z)=x^{2}+y^{2}+z^{2}} when r ≠ 0 {\displaystyle r\neq 0}
Entanglement-assisted stabilizer formalism (4,144 words) [view diff] no match in snippet view article find links to article
Π 4 {\displaystyle \Pi ^{4}} : Z X Z I Z Z I Z X Y X I X X I X {\displaystyle {\begin{array}{cccc}Z&X&Z&I\\Z&Z&I&Z\\X&Y&X&I\\X&X&I&X\end{array}}} The
Ratio distribution (10,361 words) [view diff] no match in snippet view article find links to article
the distribution of the random variable Z that is formed as the ratio Z = X/Y is a ratio distribution. An example is the Cauchy distribution (also called
Decoding methods (2,167 words) [view diff] no match in snippet view article find links to article
F 2 n {\displaystyle e\in \mathbb {F} _{2}^{n}} occurs. Then z = x + e {\displaystyle z=x+e} is received. Ordinary minimum distance decoding would lookup
Scheme (mathematics) (4,463 words) [view diff] no match in snippet view article
Z [ x , y ] {\displaystyle f\in \mathbb {Z} [x,y]} then the affine scheme X = Spec ( Z [ x , y ] / ( f ) ) {\displaystyle X={\text{Spec}}(\mathbb {Z}
Prime ideal (2,590 words) [view diff] no match in snippet view article find links to article
− 1 is a prime ideal (see elliptic curve). In the ring Z [ X ] {\displaystyle \mathbb {Z} [X]} of all polynomials with integer coefficients, the ideal
List of common coordinate transformations (2,086 words) [view diff] no match in snippet view article find links to article
z ′ − zx ′ ) 2 + ( y ″ x ′ − x ″ y ′ ) 2 ( x ′ 2 + y ′ 2 + z ′ 2 ) 3 2 τ = x ‴ ( y ′ z ″ − y ″ z ′ ) + y ‴ ( x ″ z ′ − x ′ z ″ ) + z ‴ ( x ′ y ″ −
Wang Zhuxi (369 words) [view diff] no match in snippet view article find links to article
Wang Z.X; Peking University Press 2005 ISBN 7-301-08495-1 Statistical Physics, Wang Z. X., Peking University Press Special Functions, Wang Z. X., Guo
Convex preferences (1,130 words) [view diff] no match in snippet view article find links to article
called convex if for any x , y , zX {\displaystyle x,y,z\in X} where y ⪰ x {\displaystyle y\succeq x} and zx {\displaystyle z\succeq x} , and for
Loop space (587 words) [view diff] no match in snippet view article find links to article
Eckmann–Hilton duality. The basic observation is that [ Σ Z , X ] ≊ [ Z , Ω X ] {\displaystyle [\Sigma Z,X]\approxeq [Z,\Omega X]} where [ A , B ] {\displaystyle
Homotopy theory (1,266 words) [view diff] no match in snippet view article find links to article
given (1) a map ZX {\displaystyle Z\to X} and (2) a homotopy g t : Z → B {\displaystyle g_{t}:Z\to B} , there exists a homotopy h t : ZX {\displaystyle
Baker–Campbell–Hausdorff formula (5,377 words) [view diff] no match in snippet view article find links to article
terms of this series are: Z = X + Y + 1 2 [ X , Y ] + 1 12 [ X , [ X , Y ] ] − 1 12 [ Y , [ X , Y ] ] + ⋯ , {\displaystyle Z=X+Y+{\frac {1}{2}}[X,Y]+{\frac
Hyperstructure (293 words) [view diff] no match in snippet view article find links to article
associative hyperoperation, i.e. x ⋆ ( y ⋆ z ) = ( x ⋆ y ) ⋆ z ,   ∀ x , y , z ∈ H . {\displaystyle x\star (y\star z)=(x\star y)\star z,\ \forall x,y,z\in H
Durand–Kerner method (2,758 words) [view diff] no match in snippet view article find links to article
prescribed zeros, g z → ( X ) = X n + g n − 1 ( z → ) X n − 1 + ⋯ + g 0 ( z → ) . {\displaystyle g_{\vec {z}}(X)=X^{n}+g_{n-1}({\vec {z}})X^{n-1}+\cdots +g_{0}({\vec
Granny knot (mathematics) (404 words) [view diff] no match in snippet view article
of the granny knot is given by the presentation ⟨ x , y , zx y x = y x y , x z x = z x z ⟩ . {\displaystyle \langle x,y,z\mid xyx=yxy,xzx=zxz\rangle
EPR paradox (4,992 words) [view diff] no match in snippet view article find links to article
emitted by the source might be "(+z, −x) to Alice and (−z, +x) to Bob", the next pair "(−z, −x) to Alice and (+z, +x) to Bob", and so forth. Therefore
Pumping lemma for regular languages (2,316 words) [view diff] no match in snippet view article find links to article
portion y {\displaystyle y} must not be empty, such that the words x z , x y z , x y y z , x y y y z , . . . {\displaystyle xz,xyz,xyyz,xyyyz,...} constructed
Parity (physics) (4,555 words) [view diff] no match in snippet view article
sign of all three spatial coordinates (a point reflection): P : ( x y z ) ↦ ( − x − y − z ) . {\displaystyle \mathbf {P} :{\begin{pmatrix}x\\y\\z\end{pmatrix}}\mapsto
Free lattice (1,144 words) [view diff] no match in snippet view article find links to article
The table shows an example computation to show that the words x∧z and x∧z∧(x∨y) denote the same value in every bounded lattice. The case of lattices that
Peano existence theorem (559 words) [view diff] no match in snippet view article find links to article
R {\displaystyle \mathbb {R} } , such that z ′ ( x ) = f ( x , z ( x ) ) {\displaystyle z'(x)=f\left(x,z(x)\right)} for all x ∈ I {\displaystyle x\in
Coproduct (1,830 words) [view diff] no match in snippet view article find links to article
isomorphisms X ⊕ ( Y ⊕ Z ) ≅ ( X ⊕ Y ) ⊕ ZX ⊕ Y ⊕ Z {\displaystyle X\oplus (Y\oplus Z)\cong (X\oplus Y)\oplus Z\cong X\oplus Y\oplus Z} X ⊕ 0 ≅ 0 ⊕ X ≅ X
Hyperbolic metric space (3,125 words) [view diff] no match in snippet view article find links to article
points y , zX {\displaystyle y,z\in X} with respect to a third one x ∈ X {\displaystyle x\in X} is defined by the formula: ( y , z ) x = 1 2 ( d (
Algebraic curve (7,911 words) [view diff] no match in snippet view article find links to article
derivative at infinity p ∞ ′ ( x , y ) = h p z ′ ( x , y , 1 ) . {\displaystyle p'_{\infty }(x,y)={^{h}p'_{z}(x,y,1)}.} For example, the equation of the tangent
Del (3,016 words) [view diff] no match in snippet view article find links to article
{e}}_{z}\}} , del is written as ∇ = e → x ∂ ∂ x + e → y ∂ ∂ y + e → z ∂ ∂ z = ( ∂ ∂ x , ∂ ∂ y , ∂ ∂ z ) {\displaystyle \nabla ={\vec {e}}_{x}{\partial \over
Eomaia (1,232 words) [view diff] no match in snippet view article find links to article
Evolution of mammals Juramaia (160 million years ago) Sinodelphys Ji, Q.; Luo, Z-X.; Yuan, C-X.; Wible, J.R.; Zhang, J-P. & Georgi, J.A. (April 2002). "The
Rational mapping (1,467 words) [view diff] no match in snippet view article find links to article
example, the Cubic surface given by the vanishing locus Z ( x 3 + y 3 + z 3 + w 3 ) {\displaystyle Z(x^{3}+y^{3}+z^{3}+w^{3})} has a rational map to P 2 {\displaystyle
Cylinder set (1,154 words) [view diff] no match in snippet view article find links to article
these letters is denoted by S Z = { x = ( … , x − 1 , x 0 , x 1 , … ) : x k ∈ S ∀ k ∈ Z } . {\displaystyle S^{\mathbb {Z} }=\{x=(\ldots ,x_{-1},x_{0},x_{1}
Tensor product of algebras (924 words) [view diff] no match in snippet view article find links to article
coefficients. For example, Z [ x , y ] / ( x 3 + 5 x 2 + x − 1 ) ⊗ Z Z / 5 ≅ Z / 5 [ x , y ] / ( x 3 + x − 1 ) {\displaystyle \mathbb {Z} [x,y]/(x^{3}+5x^{2}+x-1)\otimes
Triangulated category (5,759 words) [view diff] no match in snippet view article find links to article
{\displaystyle u\colon X\to Y} , v : Y → Z {\displaystyle v\colon Y\to Z} and w : ZX [ 1 ] {\displaystyle w\colon Z\to X[1]} . Triangles are generally written
Lagrange's theorem (number theory) (468 words) [view diff] no match in snippet view article
states that if p is a prime number and f ( x ) ∈ Z [ x ] {\displaystyle \textstyle f(x)\in \mathbb {Z} [x]} is a polynomial with integer coefficients, then
General recursive function (2,401 words) [view diff] no match in snippet view article find links to article
g(x_{1},\ldots ,x_{k})\,} and k+2 -ary function h ( y , z , x 1 , … , x k ) {\displaystyle h(y,z,x_{1},\ldots ,x_{k})\,} :      ρ ( g , h ) = d e f f where
Del in cylindrical and spherical coordinates (2,593 words) [view diff] no match in snippet view article find links to article
}}}\end{aligned}}} Spherical r ^ = x x ^ + y y ^ + z z ^ x 2 + y 2 + z 2 θ ^ = ( x x ^ + y y ^ ) z − ( x 2 + y 2 ) z ^ x 2 + y 2 + z 2 x 2 + y 2 φ ^ = − y x ^ + x
Rotation formalisms in three dimensions (12,596 words) [view diff] no match in snippet view article find links to article
z + x y cos ⁡ θ + y y y z − w x x z − w y w x + y z cos ⁡ θ + z z ] {\displaystyle {\begin{bmatrix}\cos \theta +x_{x}&x_{y}+w_{z}&w_{y}+x_{z}\\w_{z}+x_{y}&\cos
Zero element (995 words) [view diff] no match in snippet view article find links to article
→ {\displaystyle {\vec {0}}} . The zero function or zero map defined by z(x) = 0, under pointwise addition (f + g)(x) = f(x) + g(x) The empty set under
Ideal lattice (5,823 words) [view diff] no match in snippet view article find links to article
lattices corresponding to ideals in rings of the form Z [ x ] / ⟨ f ⟩ {\displaystyle \mathbb {Z} [x]/\langle f\rangle } for some irreducible polynomial
Pseudoconvexity (560 words) [view diff] no match in snippet view article find links to article
{\displaystyle G} such that the set { z ∈ G ∣ φ ( z ) < x } {\displaystyle \{z\in G\mid \varphi (z)<x\}} is a relatively compact subset of G {\displaystyle
3D projection (4,342 words) [view diff] no match in snippet view article find links to article
z x ) − s y z d y = s x ( c y z + s y ( s z y + c z x ) ) + c x ( c z y − s z x ) d z = c x ( c y z + s y ( s z y + c z x ) ) − s x ( c z y − s z x )
Function of several real variables (7,376 words) [view diff] no match in snippet view article find links to article
{\displaystyle z:\mathbb {R} ^{2}\rightarrow \mathbb {R} } z ( x , y ) = a x + b y {\displaystyle z(x,y)=ax+by} where a and b are real non-zero constants. Using
Zonal spherical harmonics (744 words) [view diff] no match in snippet view article find links to article
degree ℓ. The general zonal spherical harmonic of degree ℓ is denoted by Z x ( ℓ ) ( y ) {\displaystyle Z_{\mathbf {x} }^{(\ell )}(\mathbf {y} )} , where
Maxwell relations (1,122 words) [view diff] no match in snippet view article find links to article
second derivatives), that is, that ∂ ∂ y ( ∂ zx ) y = ∂ ∂ x ( ∂ z ∂ y ) x = ∂ 2 z ∂ y ∂ x = ∂ 2 zx ∂ y {\displaystyle {\frac {\partial }{\partial
Schur's inequality (625 words) [view diff] no match in snippet view article find links to article
) + y t ( y − z ) ( y − x ) + z t ( zx ) ( z − y ) ≥ 0 {\displaystyle x^{t}(x-y)(x-z)+y^{t}(y-z)(y-x)+z^{t}(z-x)(z-y)\geq 0} with equality if and only
Expected value of sample information (1,404 words) [view diff] no match in snippet view article find links to article
Z_{i}=X} , p ( z | x ) = ∏ p ( z i | x ) {\displaystyle p(z|x)=\prod p(z_{i}|x)} and ∫ z p ( z | x ) d z = x {\displaystyle \int zp(z|x)dz=x} , which is
Indecomposable distribution (881 words) [view diff] no match in snippet view article find links to article
non-constant independent random variables: Z ≠ X + Y. If it can be so expressed, it is decomposable: Z = X + Y. If, further, it can be expressed as the
Heron's formula (2,651 words) [view diff] no match in snippet view article find links to article
(a+b-c+d)\,(a+b+c-d)}}{192\,u\,v\,w}}} where a = x Y Z b = y Z X c = z X Y d = x y z X = ( w − U + v ) ( U + v + w ) x = ( U − v + w ) ( v − w + U )
Graded Lie algebra (1,493 words) [view diff] no match in snippet view article find links to article
− 1 ) i j [ y , [ z , x ] ] + ( − 1 ) j k [ z , [ x , y ] ] = 0 {\displaystyle (-1)^{ik}[x,[y,z]]+(-1)^{ij}[y,[z,x]]+(-1)^{jk}[z,[x,y]]=0} . (If k has
Stereographic projection (4,784 words) [view diff] no match in snippet view article find links to article
and its inverse are given by the formulas ( X , Y ) = ( x 1 − z , y 1 − z ) , ( x , y , z ) = ( 2 X 1 + X 2 + Y 2 , 2 Y 1 + X 2 + Y 2 , − 1 + X 2 + Y 2
Minimal axioms for Boolean algebra (783 words) [view diff] no match in snippet view article find links to article
and the assumption of associativity, ( x ∨ y ) ∨ z = x ∨ ( y ∨ z ) {\displaystyle (x\lor y)\lor z=x\lor (y\lor z)} . Herbert Robbins conjectured that
Armstrong's axioms (956 words) [view diff] no match in snippet view article find links to article
The following property is a special case of augmentation when Z = X {\displaystyle Z=X} . If X → Y {\displaystyle X\to Y} , then X → X Y {\displaystyle
Armstrong's axioms (956 words) [view diff] no match in snippet view article find links to article
The following property is a special case of augmentation when Z = X {\displaystyle Z=X} . If X → Y {\displaystyle X\to Y} , then X → X Y {\displaystyle
Frobenius theorem (real division algebras) (1,229 words) [view diff] no match in snippet view article
( z ; x ) = x 2 − 2 Re ⁡ ( z ) x + | z | 2 = ( x − z ) ( x − z ¯ ) ∈ R [ x ] . {\displaystyle Q(z;x)=x^{2}-2\operatorname {Re} (z)x+|z|^{2}=(x-z)(x-{\overline
Superfunction (2,656 words) [view diff] no match in snippet view article find links to article
defined by the expression S ( z ; x ) = f ( f ( … f ( x ) … ) ) ⏟ z  evaluations of the function  f . {\displaystyle S(z;x)=\underbrace {f{\Big (}f{\big
Zhao Zhongxian (619 words) [view diff] no match in snippet view article find links to article
Situ Comosites Cu-Nb; Z. X. Zhao, C. G. Cui, S. Q. Gou, D. K. Finnemore and J. D. Verhoeven; Chinese Physics 5 (1985); 776. Zhao, Z.X.; Chen, L.Q.; Huang
Hooke's law (8,754 words) [view diff] no match in snippet view article find links to article
written as[page needed] [ ε x x ε y y ε z z 2 ε y z 2 ε z x 2 ε x y ] = [ 1 E x − ν y x E y − ν z x E z 0 0 0 − ν x y E x 1 E y − ν z y E z 0 0 0 − ν x z
Formal power series (9,213 words) [view diff] no match in snippet view article find links to article
series. Consider the ring of formal power series: Z [ [ X ] ] [ [ Y ] ] {\displaystyle \mathbb {Z} [[X]][[Y]]} ; then the topology of above construction
Electrical resistivity and conductivity (7,335 words) [view diff] no match in snippet view article find links to article
relation is given by: [ E x E y E z ] = [ ρ x x ρ x y ρ x z ρ y x ρ y y ρ y z ρ z x ρ z y ρ z z ] [ J x J y J z ] {\displaystyle {\begin{bmatrix}E_{x}\\E_{y
Inequality (mathematics) (3,279 words) [view diff] no match in snippet view article
{\displaystyle x^{x^{x}}\geq x.} If x, y, z > 0, then ( x + y ) z + ( x + z ) y + ( y + z ) x > 2. {\displaystyle \left(x+y\right)^{z}+\left(x+z\right)^{
Stable curve (1,073 words) [view diff] no match in snippet view article find links to article
zx ( x − z ) ( x − t z ) ) ↓ Spec ⁡ ( Q [ t ] ) {\displaystyle {\begin{matrix}\operatorname {Proj} \left({\frac {\mathbb {Q} [t][x,y,z]}{(y^{2}z-x
Deep Image Prior (786 words) [view diff] no match in snippet view article find links to article
minimizer θ ∗ = a r g m i n θ E ( f θ ( z ) ; x 0 ) {\displaystyle \theta ^{*}=argmin_{\theta }E(f_{\theta }(z);x_{0})} and the result of the optimization
Torsion of a curve (620 words) [view diff] no match in snippet view article find links to article
y ′ z ″ − y ″ z ′ ) + y ‴ ( x ″ z ′ − x ′ z ″ ) + z ‴ ( x ′ y ″ − x ″ y ′ ) ( y ′ z ″ − y ″ z ′ ) 2 + ( x ″ z ′ − x ′ z ″ ) 2 + ( x ′ y ″ − x ″ y ′ )
NTRUEncrypt (3,852 words) [view diff] no match in snippet view article find links to article
on objects in a truncated polynomial ring   R = Z [ X ] / ( X N − 1 ) {\displaystyle \ R=\mathbb {Z} [X]/(X^{N}-1)} with convolution multiplication and
Non-Euclidean geometry (5,825 words) [view diff] no match in snippet view article find links to article
numbers z = x + y ε where ε2 ∈ { –1, 0, 1}. The Euclidean plane corresponds to the case ε2 = −1 since the modulus of z is given by z z ∗ = ( x + y ϵ )
Bouc–Wen model of hysteresis (3,423 words) [view diff] no match in snippet view article find links to article
K [ z x z y ] {\displaystyle {\begin{bmatrix}q_{x}\\q_{y}\end{bmatrix}}=aK{\begin{bmatrix}u_{x}\\u_{y}\end{bmatrix}}+(1-a)K{\begin{bmatrix}z_{x}\\z_{y}\end{bmatrix}}}
Square knot (mathematics) (429 words) [view diff] no match in snippet view article
of the square knot is given by the presentation ⟨ x , y , zx y x = y x y , x z x = z x z ⟩ . {\displaystyle \langle x,y,z\mid xyx=yxy,xzx=zxz\rangle
Zygiella x-notata (2,182 words) [view diff] no match in snippet view article find links to article
family Araneidae. They are solitary spiders, residing in daily-spun orb webs. Z. x-notata are a member of the genus Zygiella, the orb-weaving spiders. The adult
Whitehead's point-free geometry (1,660 words) [view diff] no match in snippet view article find links to article
G4. ∃ z [ x ≤ z ∧ y ≤ z ] . {\displaystyle \exists z[x\leq z\land y\leq z].} Proper Part densely orders the domain. WP5. G5. x < y → ∃ z [ x < z < y
Quartic function (6,966 words) [view diff] no match in snippet view article find links to article
z + , x 2 = − z + , x 3 = + z − , x 4 = − z − . {\displaystyle {\begin{aligned}x_{1}&=+{\sqrt {z_{+}}},\\x_{2}&=-{\sqrt {z_{+}}},\\x_{3}&=+{\sqrt {z_{-}}}
Theria (583 words) [view diff] no match in snippet view article find links to article
Level. Columbia University Press, New York, 631 pp. ISBN 0-231-11013-8 Luo, Z.-X., Z. Kielan-Jaworowska, and R. L. Cifelli. 2002. In quest for a phylogeny
Dual norm (1,918 words) [view diff] no match in snippet view article find links to article
}x|\;|\;\|x\|\leq 1\}.} From the definition of dual norm we have the inequality zx = ‖ x ‖ ( zx ‖ x ‖ ) ≤ ‖ x ‖ ‖ z ‖ ∗ {\displaystyle z^{\intercal }x=\|x\|\left(z^{\intercal
Complex conjugate (1,776 words) [view diff] no match in snippet view article find links to article
identity map and complex conjugation. Once a complex number z = x + y i {\displaystyle z=x+yi} or z = r e i θ {\displaystyle z=re^{i\theta }} is given
Peres metric (155 words) [view diff] no match in snippet view article find links to article
d τ 2 = d t 2 − 2 f ( t + z , x , y ) ( d t + d z ) 2 − d x 2 − d y 2 − d z 2 {\displaystyle {d\tau }^{2}=dt^{2}-2f(t+z,x,y)(dt+dz)^{2}-dx^{2}-dy^{2}-dz^{2}}
Closed immersion (658 words) [view diff] no match in snippet view article find links to article
algebraic geometry, a closed immersion of schemes is a morphism of schemes f : ZX {\displaystyle f:Z\to X} that identifies Z as a closed subset of X such
Sandwich theory (6,775 words) [view diff] no match in snippet view article find links to article
core is given by σ z x c o r e = C 55 c o r e   ε z x c o r e = C 55 c o r e 2   γ z x c o r e = 2 h + f 4 h   C 55 c o r e   γ z x b e a m {\displaystyle
Incircle and excircles of a triangle (5,563 words) [view diff] no match in snippet view article find links to article
has the radius r = x y z x + y + z {\displaystyle r={\sqrt {\frac {xyz}{x+y+z}}}} and the area of the triangle is Δ = x y z ( x + y + z ) . {\displaystyle
Similarity learning (1,441 words) [view diff] no match in snippet view article find links to article
W that parametrizes the similarity function f W ( x , z ) = x T W z {\displaystyle f_{W}(x,z)=x^{T}Wz} . When data is abundant, a common approach is to
Stress functions (960 words) [view diff] no match in snippet view article find links to article
                σ x y = − ∂ 2 Φ x y ∂ z ∂ z − ∂ 2 Φ z zx ∂ y + ∂ 2 Φ y zx ∂ z + ∂ 2 Φ z x ∂ y ∂ z {\displaystyle \sigma _{xy}=-{\frac {\partial
Timoshenko-Ehrenfest beam theory (3,442 words) [view diff] no match in snippet view article find links to article
( x , y , z ) = 0   ;     u z ( x , y ) = w ( x ) {\displaystyle u_{x}(x,y,z)=-z~\varphi (x)~;~~u_{y}(x,y,z)=0~;~~u_{z}(x,y)=w(x)} where ( x , y , z )
Cauchy momentum equation (5,274 words) [view diff] no match in snippet view article find links to article
y x + ∂ σ y x ∂ y d y ) d x d z − σ y x d x d z + ( σ z x + ∂ σ z x ∂ z d z ) d x d y − σ z x d x d y {\displaystyle F_{p}^{x}=(\sigma _{xx}+{\frac {\partial
Glossary of Lie groups and Lie algebras (3,068 words) [view diff] no match in snippet view article find links to article
(alternating) [ [ x , y ] , z ] + [ [ y , z ] , x ] + [ [ z , x ] , y ] = 0 {\displaystyle [[x,y],z]+[[y,z],x]+[[z,x],y]=0} (Jacobi identity) 4.  Lie group–Lie
Conditioning (probability) (6,863 words) [view diff] no match in snippet view article
|Z|, E ( E ( | Z | | X ) ) = ∫ − ∞ + ∞ E ( | Z | | X = x ) f X ( x ) d x = E ( | Z | ) , {\displaystyle \mathbb {E} (\mathbb {E} (|Z||X))=\int _{-\infty
Curl (mathematics) (4,228 words) [view diff] no match in snippet view article
z ) ı ^ + ( ∂ F x ∂ z − ∂ F zx ) ȷ ^ + ( ∂ F y ∂ x − ∂ F x ∂ y ) k ^ = [ ∂ F z ∂ y − ∂ F y ∂ z ∂ F x ∂ z − ∂ F zx ∂ F y ∂ x − ∂ F x ∂ y ] {\displaystyle
Inversive geometry (4,130 words) [view diff] no match in snippet view article find links to article
interpreted as a complex number z = x + i y , {\displaystyle z=x+iy,} with complex conjugate z ¯ = x − i y , {\displaystyle {\bar {z}}=x-iy,} then the reciprocal
Fresnel diffraction (2,351 words) [view diff] no match in snippet view article find links to article
expressed as E ( x , y , z ) = e i k z i λ z e i π λ z ( x 2 + y 2 ) F { E ( x ′ , y ′ , 0 ) e i π λ z ( x ′ 2 + y ′ 2 ) } | p = x λ z ,   q = y λ z = H (
Motivic zeta function (814 words) [view diff] no match in snippet view article find links to article
{\displaystyle X} is the formal power series Z ( X , t ) = ∑ n = 0 ∞ [ X ( n ) ] t n {\displaystyle Z(X,t)=\sum _{n=0}^{\infty }[X^{(n)}]t^{n}} Here X
Code coverage (2,404 words) [view diff] no match in snippet view article find links to article
including z = x;. Tests calling foo(1,1) and foo(0,1) will satisfy branch coverage because, in the first case, both if conditions are met and z = x; is executed
Simplicial presheaf (803 words) [view diff] no match in snippet view article find links to article
simplicial presheaves, then the induced map Z f : Z X → Z Y {\displaystyle \mathbb {Z} f:\mathbb {Z} X\to \mathbb {Z} Y} is also a local weak equivalence
Minkowski addition (2,173 words) [view diff] no match in snippet view article find links to article
= sup x ∈ R n 1 A ( x ) 1 B ( zx ) , {\displaystyle 1_{A\,+\,B}(z)=\sup _{x\,\in \,\mathbb {R} ^{n}}1_{A}(x)1_{B}(z-x),} it can be seen that 1 A + e
Alternative algebra (985 words) [view diff] no match in snippet view article find links to article
associator is a trilinear map given by [ x , y , z ] = ( x y ) zx ( y z ) {\displaystyle [x,y,z]=(xy)z-x(yz)} . By definition, a multilinear map is alternating
Associator (489 words) [view diff] no match in snippet view article find links to article
]:R\times R\times R\to R} given by [ x , y , z ] = ( x y ) zx ( y z ) . {\displaystyle [x,y,z]=(xy)z-x(yz).} Just as the commutator [ x , y ] = x y
Construction of the real numbers (3,563 words) [view diff] no match in snippet view article find links to article
field. In other words, For all x, y, and z in R, x + (y + z) = (x + y) + z and x × (y × z) = (x × y) × z. (associativity of addition and multiplication)
Morse–Kelley set theory (3,120 words) [view diff] no match in snippet view article find links to article
Mx)].} Pairing: For any sets x and y, there exists a set z = { x , y } {\displaystyle z=\{x,y\}} whose members are exactly x and y. ∀ x ∀ y [ ( M x ∧
Starred transform (839 words) [view diff] no match in snippet view article find links to article
[citation needed] X ( z ) = X ∗ ( s ) | e s T = z {\displaystyle {\bigg .}X(z)=X^{*}(s){\bigg |}_{\displaystyle e^{sT}=z}}   X ( z ) = X ∗ ( s ) | s = ln ⁡
Lorentz group (7,015 words) [view diff] no match in snippet view article find links to article
matrix in the form X = [ t + z x − i y x + i y t − z ] = t 1 1 + x σ x + y σ y + z σ z , {\displaystyle X={\begin{bmatrix}t+z&x-iy\\x+iy&t-z\end{bmatrix}}=t1\
Multiplication (4,751 words) [view diff] no match in snippet view article find links to article
with respect to order of operations: ( x ⋅ y ) ⋅ z = x ⋅ ( y ⋅ z ) {\displaystyle (x\cdot y)\cdot z=x\cdot (y\cdot z)} Distributive property Holds with
Half-normal distribution (917 words) [view diff] no match in snippet view article find links to article
{x^{2}}{2\sigma ^{2}}}\right)\,dx} Using the change-of-variables z = x / ( 2 σ ) {\displaystyle z=x/({\sqrt {2}}\sigma )} , the CDF can be written as F Y ( y
Exact sequence (3,271 words) [view diff] no match in snippet view article find links to article
constraint, we have − ∂ x ∫ F x d z + ∂ x C 1 → ( x , y ) − ∂ y ∫ F y d z = F z − ∫ ( ∂ x F x + ∂ y F y ) d z + ∂ x C 1 → ( x , y ) = F z {\displaystyle
Representation ring (826 words) [view diff] no match in snippet view article find links to article
isomorphic to Z[X,Y]/(X2 − Y − 1, XY − 2Y,Y2 − 3Y). The continuous representation ring R(S1) for the circle group is isomorphic to Z[X, X −1]. The ring
Lie coalgebra (1,031 words) [view diff] no match in snippet view article find links to article
= 1 3 d 2 α ( x ∧ y ∧ z + y ∧ zx + zx ∧ y ) = 1 3 ( d α ( [ x , y ] ∧ z ) + d α ( [ y , z ] ∧ x ) + d α ( [ z , x ] ∧ y ) ) , {\displaystyle
Cohen–Daubechies–Feauveau wavelet (1,536 words) [view diff] no match in snippet view article find links to article
of the lifting are x − 1 ( z ) = z , x 0 ( z ) = 1 , x 1 ( z ) = x − 1 ( z ) + a 0 ⋅ x 0 ( z ) , x m + 1 ( z ) = x m − 1 ( z ) + a m ⋅ ( ( 2 ⋅ m + 1
Evidence lower bound (585 words) [view diff] no match in snippet view article find links to article
\mathbf {Z} } is optimized as an approximation to the true posterior P ( Z | X ) {\displaystyle P(\mathbf {Z} |\mathbf {X} )} , given observed data X {\displaystyle
Principal homogeneous space (1,687 words) [view diff] no match in snippet view article find links to article
group it is associated with. If we denote x / y ⋅ z := x ⋅ ( y ∖ z ) {\displaystyle x/y\cdot z\,:=\,x\cdot (y\backslash z)} the result of this ternary
Lie coalgebra (1,031 words) [view diff] no match in snippet view article find links to article
= 1 3 d 2 α ( x ∧ y ∧ z + y ∧ zx + zx ∧ y ) = 1 3 ( d α ( [ x , y ] ∧ z ) + d α ( [ y , z ] ∧ x ) + d α ( [ z , x ] ∧ y ) ) , {\displaystyle
Pulse-density modulation (1,357 words) [view diff] no match in snippet view article find links to article
modulator's operation is represented by Y ( z ) = X ( z ) + E ( z ) ( 1 − z − 1 ) {\displaystyle Y(z)=X(z)+E(z)\left(1-z^{-1}\right)} where E ( z ) {\displaystyle
Generalizations of the derivative (3,654 words) [view diff] no match in snippet view article find links to article
the interval. Since the line L ( z ) = f ′ ( x ) ( zx ) + f ( x ) {\displaystyle L(z)=f'(x)(z-x)+f(x)} is tangent to the original function at the point
Combustion (6,320 words) [view diff] no match in snippet view article find links to article
{z}}O2->{\mathit {x}}CO2{}+{\frac {\mathit {y}}{2}}H2O}}} where z = x + y 4 {\displaystyle z=x+{\frac {y}{4}}} . For example, the stoichiometric burning of
Method of characteristics (3,047 words) [view diff] no match in snippet view article find links to article
known, and consider the surface graph z = z(x,y) in R3. A normal vector to this surface is given by ( ∂ zx ( x , y ) , ∂ z ∂ y ( x , y ) , − 1 ) . {\displaystyle
Dark Matter Particle Explorer (1,062 words) [view diff] no match in snippet view article find links to article
De Mitri, I.; Di Santo, M.; Dong, J. N.; Dong, T. K.; Dong, Y. F.; Dong, Z. X.; Donvito, G.; Droz, D.; Duan, K. K.; Duan, J. L.; Duranti, M.; D'Urso, D
Cauchy stress tensor (8,249 words) [view diff] no match in snippet view article find links to article
] ≡ [ σ x x σ x y σ x z σ y x σ y y σ y z σ z x σ z y σ z z ] ≡ [ σ x τ x y τ x z τ y x σ y τ y z τ z x τ z y σ z ] {\displaystyle {\boldsymbol {\sigma
Divergence (4,298 words) [view diff] no match in snippet view article find links to article
r(\mathbf {x} )} , θ ( x ) {\displaystyle \theta (\mathbf {x} )} , and z ( x ) {\displaystyle z(\mathbf {x} )} , which assign the corresponding global
Laha language (576 words) [view diff] no match in snippet view article find links to article
(Alveolo-) palatal Velar Glottal Stop/ Affricate voiceless p t tʃ k ʔ aspirated pʰ tʰ kʰ voiced b d Fricative f s ʑ x h Nasal m n ɲ ŋ Approximant w l
Lambda calculus (10,729 words) [view diff] no match in snippet view article find links to article
only the following rules: producing expressions such as: (λx.λy.(λz.(λx.z x) (λy.z y)) (x y)). Parentheses can be dropped if the expression is unambiguous
Matrix mechanics (10,411 words) [view diff] no match in snippet view article find links to article
commutation rule, [ L z , X + i Y ] = ( X + i Y ) {\displaystyle [L_{z},X+iY]=(X+iY)\,} , [ L z , X − i Y ] = − ( X − i Y ) {\displaystyle [L_{z},X-iY]=-(X-iY)\
Coherent sheaf (6,256 words) [view diff] exact match in snippet view article find links to article
locally Noetherian scheme X {\displaystyle X} , the sheaf I Z / X {\displaystyle {\mathcal {I}}_{Z/X}} of all regular functions vanishing on Z {\displaystyle
Notation for differentiation (4,701 words) [view diff] no match in snippet view article find links to article
− ∂ A y ∂ z , ∂ A x ∂ z − ∂ A zx , ∂ A y ∂ x − ∂ A x ∂ y ) = ( ∂ A z ∂ y − ∂ A y ∂ z ) i + ( ∂ A x ∂ z − ∂ A zx ) j + ( ∂ A y ∂ x − ∂ A x ∂ y )
Surface (mathematics) (3,087 words) [view diff] no match in snippet view article
vector [ ∂ f ∂ x ( x 0 , y 0 , z 0 ) , ∂ f ∂ y ( x 0 , y 0 , z 0 ) , ∂ f ∂ z ( x 0 , y 0 , z 0 ) ] . {\displaystyle \left[{\frac {\partial f}{\partial x}}(x_{0}
Lie bracket of vector fields (1,666 words) [view diff] no match in snippet view article find links to article
identity, [ X , [ Y , Z ] ] + [ Z , [ X , Y ] ] + [ Y , [ Z , X ] ] = 0. {\displaystyle [X,[Y,Z]]+[Z,[X,Y]]+[Y,[Z,X]]=0.} An immediate consequence of
Abstract m-space (383 words) [view diff] no match in snippet view article find links to article
addition there exists some u ≥ 0 in X such that the interval [−u, u] := { zX : −u ≤ z and z ≤ u } is equal to the unit ball of X; such an element u is
Ricci curvature (6,635 words) [view diff] no match in snippet view article find links to article
fields X, Y, and Z, and returns the vector field R ( X , Y ) Z = ∇ X ∇ Y Z − ∇ Y ∇ X Z − ∇ [ X , Y ] Z {\displaystyle R(X,Y)Z=\nabla _{X}\nabla _{Y}Z-\nabla
Deformation (physics) (5,121 words) [view diff] no match in snippet view article
and xz-planes, we have γ y z = γ z y = ∂ u y ∂ z + ∂ u z ∂ y , γ z x = γ x z = ∂ u zx + ∂ u x ∂ z {\displaystyle \gamma _{yz}=\gamma _{zy}={\frac {\partial
Triangle inequality (4,201 words) [view diff] no match in snippet view article find links to article
no side being greater than z, then the triangle inequality states that zx + y , {\displaystyle z\leq x+y,} with equality only in the degenerate case
Chirality (mathematics) (873 words) [view diff] no match in snippet view article
such that F {\displaystyle F} is invariant under the mapping ( x , y , z ) ↦ ( x , y , − z ) {\displaystyle (x,y,z)\mapsto (x,y,-z)} , when P {\displaystyle
ELEMENTARY (1,083 words) [view diff] no match in snippet view article find links to article
) {\displaystyle xy(z+1)} has 1 floor, ( x + y ) y z + x + z x + 1 {\displaystyle (x+y)^{yz+x}+z^{x+1}} has 2 floors, 2 2 x {\displaystyle 2^{2^{x}}} has
Rejection sampling (4,291 words) [view diff] no match in snippet view article find links to article
the likelihood ratio is Z ( x ) = f ( x ) g θ ( x ) = f ( x ) e θ x − ψ ( θ ) f ( x ) = e − θ x + ψ ( θ ) {\displaystyle Z(x)={\frac {f(x)}{g_{\theta
Lambda calculus definition (4,922 words) [view diff] no match in snippet view article find links to article
Y)[x:=y]=X[x:=y]\,Y[x:=y]} z = x → ( z ) [ x := y ] = y {\displaystyle z=x\to (z)[x:=y]=y} zx → ( z ) [ x := y ] = z {\displaystyle z\neq x\to (z)[x:=y]=z} Note that
Inverse trigonometric functions (7,056 words) [view diff] no match in snippet view article find links to article
− 1 d z = π + ∫ x − 1 1 z z 2 − 1 d z , x ≥ 1 arccsc ⁡ ( x ) = ∫ x ∞ 1 z z 2 − 1 d z = ∫ − ∞ x 1 z z 2 − 1 d z , x ≥ 1 {\displaystyle {\begin{aligned}\arcsin(x)&{}=\int
Convolution of probability distributions (1,099 words) [view diff] no match in snippet view article find links to article
distributions The general formula for the distribution of the sum Z = X + Y {\displaystyle Z=X+Y} of two independent integer-valued (and hence discrete) random
Satisfiability (1,213 words) [view diff] no match in snippet view article find links to article
y)\rightarrow \exists zR(y,z))} ∀ x y z ( R ( y , x ) ∧ R ( z , x ) → x = z ) ) {\displaystyle \forall xyz(R(y,x)\wedge R(z,x)\rightarrow x=z))} The resulting
List of mathematic operators (120 words) [view diff] no match in snippet view article find links to article
{\displaystyle y=y(t)} F [ x , y , z ] = ∫ a t z ‴ ( x ′ y ″ − y ′ x ″ ) + z ″ ( x ‴ y ′ − x ′ y ‴ ) + z ′ ( x ″ y ‴ − x ‴ y ″ ) 3 {\displaystyle F[x,y,z]=\int
Binary response model with continuous endogenous explanatory variables (909 words) [view diff] no match in snippet view article find links to article
estimated by conditional Maximum Likelihood Method. Because P(y, zx) = P (y│z, x) P (z| x) where P (y│x, z) is given by [ ϕ ( x 1 ( β − ρ θ 1 ) − x 2 ρ
General set theory (1,165 words) [view diff] no match in snippet view article find links to article
x and y are the same set if they have the same members. ∀ x ∀ y [ ∀ z [ zx ↔ z ∈ y ] → x = y ] . {\displaystyle \forall x\forall y[\forall z[z\in x\leftrightarrow
Fundamental theorem of Riemannian geometry (1,266 words) [view diff] no match in snippet view article find links to article
following conditions: for any vector fields X, Y, Z we have ∂ X ⟨ Y , Z ⟩ = ⟨ ∇ X Y , Z ⟩ + ⟨ Y , ∇ X Z ⟩ , {\displaystyle \partial _{X}\langle Y,Z\rangle
Anyonic Lie algebra (291 words) [view diff] no match in snippet view article find links to article
(Y)+\varepsilon (X^{i}))}} [ X , [ Y , Z ] ] = [ [ X i , Y ] , [ X i , Z ] ] e 2 π i n ε ( Y ) ε ( X i ) {\displaystyle [X,[Y,Z]]=[[X_{i},Y],[X^{i},Z]]e^{{\frac {2\pi
Eutheria (727 words) [view diff] no match in snippet view article find links to article
University, San Diego, California, USA. PDF file from sdsu.edu Ji, Q.; Luo, Z-X.; Yuan, C-X.; Wible, J.R.; Zhang, J-P. & Georgi, J.A. (April 2002). "The
Mereotopology (2,085 words) [view diff] no match in snippet view article find links to article
Cyx.} (symmetric) Now posit the binary relation E, defined as: E x y ↔ [ C z x → C z y ] . {\displaystyle Exy\leftrightarrow [Czx\rightarrow Czy].} Exy
Comparison of programming languages (list comprehension) (1,251 words) [view diff] no match in snippet view article
{ for (x in 0..20) for (y in x..20) for (z in y..20) if (x*x + y*y == z*z) [x,y,z] }; // type of triples is Iterable<Integer[3]> An infinite lazy sequence:
Null vector (359 words) [view diff] no match in snippet view article find links to article
A null cone where q ( x , y , z ) = x 2 + y 2 − z 2 . {\displaystyle q(x,y,z)=x^{2}+y^{2}-z^{2}.}
Normal distribution (20,335 words) [view diff] no match in snippet view article find links to article
σ 2 {\displaystyle \sigma ^{2}} , then the distribution Z = ( X − μ ) / σ {\displaystyle Z=(X-\mu )/\sigma } will have a standard normal distribution
Complex analysis (2,103 words) [view diff] no match in snippet view article find links to article
into real and imaginary parts: z = x + i y  and  f ( z ) = f ( x + i y ) = u ( x , y ) + i v ( x , y ) , {\displaystyle z=x+iy\quad {\text{ and }}\quad f(z)=f(x+iy)=u(x
Gated recurrent unit (1,121 words) [view diff] no match in snippet view article find links to article
t=0} , the output vector is h 0 = 0 {\displaystyle h_{0}=0} . z t = σ g ( W z x t + U z h t − 1 + b z ) r t = σ g ( W r x t + U r h t − 1 + b r ) h ^ t =
Motor variable (2,618 words) [view diff] no match in snippet view article find links to article
( z ) + j   v ( z ) ,   z = x + j y ,   x , y ∈ R , j 2 = + 1 , u ( z ) , v ( z ) ∈ R . {\displaystyle f(z)=u(z)+j\ v(z),\ z=x+jy,\ x,y\in R,\quad j^{2}=+1
Adjoint representation (3,458 words) [view diff] no match in snippet view article find links to article
identity [ x , [ y , z ] ] + [ y , [ z , x ] ] + [ z , [ x , y ] ] = 0 {\displaystyle [x,[y,z]]+[y,[z,x]]+[z,[x,y]]=0} takes the form ( [ ad x , ad y
Path ordering (term rewriting) (690 words) [view diff] no match in snippet view article
for "multiplying out" mathematical expressions could contain a rule x*(y+z) → (x*y) + (x*z). In order to prove termination, a reduction ordering (>) must
Middle Jurassic (514 words) [view diff] no match in snippet view article find links to article
2015.06.047. PMID 26190074. Kielan-Jaworowska, Z., Cifelli, R.L., and Luo, Z.-X. 2004. Mammals from the age of dinosaurs: origins evolution and structure
Logarithmic mean (1,366 words) [view diff] no match in snippet view article find links to article
{\displaystyle n=2} this leads to L MV ( x , y , z ) = ( x − y ) ( y − z ) ( zx ) 2 ( ( y − z ) ln ⁡ ( x ) + ( zx ) ln ⁡ ( y ) + ( x − y ) ln ⁡ ( z ) ) {\displaystyle
Time-scale calculus (1,755 words) [view diff] no match in snippet view article find links to article
modified Z-transform: Z ′ { x [ z ] } = Z { x [ z + 1 ] } z + 1 {\displaystyle {\mathcal {Z}}'\{x[z]\}={\frac {{\mathcal {Z}}\{x[z+1]\}}{z+1}}} Partial
Coimage (224 words) [view diff] no match in snippet view article find links to article
Y} with f = f c ∘ c {\displaystyle f=f_{c}\circ c} , for any epimorphism z : X → Z {\displaystyle z:X\rightarrow Z} for which there is a map f z : Z →
Discriminative model (2,197 words) [view diff] no match in snippet view article find links to article
y | x ; w ) = 1 Z ( x ; w ) exp ⁡ ( w T ϕ ( x , y ) ) {\displaystyle P(y|x;w)={\frac {1}{Z(x;w)}}\exp(w^{T}\phi (x,y))} , with Z ( x ; w ) = ∑ y exp ⁡
Tarski's axioms (3,098 words) [view diff] no match in snippet view article find links to article
y ≡ y x . {\displaystyle xy\equiv yx\,.} Identity of Congruence x y ≡ z zx = y . {\displaystyle xy\equiv zz\rightarrow x=y.} Transitivity of Congruence
Omitted-variable bias (1,268 words) [view diff] no match in snippet view article find links to article
correlated with an independent variable specified in the regression (i.e., cov(z,x) must not equal zero). Suppose we omit z from the regression, and suppose
Routh's theorem (1,049 words) [view diff] no match in snippet view article find links to article
{\displaystyle ABC} times ( x y z − 1 ) 2 ( x y + y + 1 ) ( y z + z + 1 ) ( z x + x + 1 ) . {\displaystyle {\frac {(xyz-1)^{2}}{(xy+y+1)(yz+z+1)(zx+x+1)}}
Potential flow (4,266 words) [view diff] no match in snippet view article find links to article
− 2 M x M y ∂ 2 Φ ∂ x ∂ y − 2 M y M z ∂ 2 Φ ∂ y ∂ z − 2 M z M x ∂ 2 Φ ∂ zx = 0 , {\displaystyle \left(1-M_{x}^{2}\right){\frac {\partial ^{2}\Phi }{\partial
Tribosphenida (617 words) [view diff] no match in snippet view article find links to article
University Press. pp. 9–10. ISBN 978-0-231-11012-9. Retrieved 16 March 2015. Luo, Z.-X.; Cifelli, R.L.; Kielan-Jaworowska, Z. (2001). "Dual origins of tribosphenic
Statistical learning theory (1,440 words) [view diff] no match in snippet view article find links to article
some unknown probability distribution over the product space Z = X × Y {\displaystyle Z=X\times Y} , i.e. there exists some unknown p ( z ) = p ( x →
Poincaré metric (1,919 words) [view diff] no match in snippet view article find links to article
under the action of SL(2,R). That is, if we write z ′ = x ′ + i y ′ = a z + b c z + d {\displaystyle z'=x'+iy'={\frac {az+b}{cz+d}}} for a d − b c = 1 {\displaystyle
Lehmer's conjecture (1,675 words) [view diff] no match in snippet view article find links to article
every polynomial with integer coefficients P ( x ) ∈ Z [ x ] {\displaystyle P(x)\in \mathbb {Z} [x]} satisfies one of the following properties: The Mahler
Kronecker delta (3,569 words) [view diff] no match in snippet view article find links to article
i ∮ | z | = 1 ⁡ z x − n − 1 d z = 1 2 π ∫ 0 2 π e i ( x − n ) φ d φ {\displaystyle \delta _{x,n}={\frac {1}{2\pi i}}\oint _{|z|=1}z^{x-n-1}\,dz={\frac
Differential graded Lie algebra (736 words) [view diff] no match in snippet view article find links to article
x | | z | [ x , [ y , z ] ] + ( − 1 ) | y | | x | [ y , [ z , x ] ] + ( − 1 ) | z | | y | [ z , [ x , y ] ] = 0 , {\displaystyle (-1)^{|x||z|}[x,[y,z]]+(-1)^{|y||x|}[y
Siegel upper half-space (345 words) [view diff] no match in snippet view article find links to article
the Siegel upper half-space in terms of its real and imaginary parts as Z = X + iY, all metrics with isometry group Sp(2g, C) are proportional to d s
Pivotal quantity (1,128 words) [view diff] no match in snippet view article find links to article
variance σ 2 {\displaystyle \sigma ^{2}} , and an observation x, the z-score: z = x − μ σ , {\displaystyle z={\frac {x-\mu }{\sigma }},} has distribution N
Substitution (logic) (1,384 words) [view diff] no match in snippet view article
example for non-commuting substitutions is { x ↦ y } { y ↦ z } = { x ↦ z, y ↦ z }, but { y ↦ z} { x ↦ y} = { x ↦ y, y ↦ z }. Substitution property in Equality
Bernoulli polynomials of the second kind (1,895 words) [view diff] no match in snippet view article find links to article
generating function: z ( 1 + z ) x ln ⁡ ( 1 + z ) = ∑ n = 0 ∞ z n ψ n ( x ) , | z | < 1. {\displaystyle {\frac {z(1+z)^{x}}{\ln(1+z)}}=\sum _{n=0}^{\infty
Covariance operator (343 words) [view diff] no match in snippet view article find links to article
z ( x ) z ( y ) d P ( z ) = E ( z ( x ) z ( y ) ) {\displaystyle \mathrm {Cov} (x,y)=\int z(x)z(y)\,\mathrm {d} \mathbf {P} (z)=E(z(x)z(y))} where z(x)
Mereology (6,684 words) [view diff] no match in snippet view article find links to article
there exists an object z such that Pzx and Pzy both hold. O x y ↔ ∃ z [ P z x ∧ P z y ] . {\displaystyle Oxy\leftrightarrow \exists z[Pzx\land Pzy].} 3
Additive white Gaussian noise (2,996 words) [view diff] no match in snippet view article find links to article
= h ( Y ) − h ( X + Z | X ) = h ( Y ) − h ( Z | X ) {\displaystyle {\begin{aligned}I(X;Y)=h(Y)-h(Y|X)&=h(Y)-h(X+Z|X)&=h(Y)-h(Z|X)\end{aligned}}\,\!} But
Obfuscation (software) (2,955 words) [view diff] no match in snippet view article
=*c++); (y=x/8%8,z=(x&199)-4 S 1 S 1 S 186 S 2 S 2 S 3 S 0,r=(y>5)*2+y,z=(x& 207)-1 S 2 S 6 S 2 S 182 S 4)?D(0)D(1)D(2)D(3)D(4)D(5)D(6)D(7)(z=x-2 C C C C C
Riesz function (1,774 words) [view diff] no match in snippet view article find links to article
connection with the Riemann hypothesis, by means of the power series R i e s z ( x ) = − ∑ k = 1 ∞ ( − x ) k ( k − 1 ) ! ζ ( 2 k ) = x ∑ n = 1 ∞ μ ( n ) n
Hadamard space (653 words) [view diff] no match in snippet view article find links to article
m ) 2 + d ( x , y ) 2 4 ≤ d ( z , x ) 2 + d ( z , y ) 2 2 . {\displaystyle d(z,m)^{2}+{d(x,y)^{2} \over 4}\leq {d(z,x)^{2}+d(z,y)^{2} \over 2}.} The
Logarithmic spiral (1,666 words) [view diff] no match in snippet view article find links to article
y=ae^{k\varphi }\sin \varphi .} In the complex plane ( z = x + i y , e i φ = cos ⁡ φ + i sin ⁡ φ ) {\displaystyle (z=x+iy,\,e^{i\varphi }=\cos \varphi +i\sin \varphi
Shuotherium (662 words) [view diff] no match in snippet view article find links to article
Australian Mammalogy 54:127-142 Kielan−Jaworowska, Z.; Cifelli, R.L.; Luo, Z.−X. (2002). "Dentition and relationships of the Jurassic mammal Shuotherium"
Order bound dual (394 words) [view diff] no match in snippet view article find links to article
and y + z = |x| } inf(f, g)(|x|) = inf { f(y) + g(z) : y ≥ 0, z ≥ 0, and y + z = |x| } |f|(|x|) = sup { f(y - z) : y ≥ 0, z ≥ 0, and y + z = |x| } |f(x)|
Cone (2,144 words) [view diff] no match in snippet view article find links to article
z\geq 0,z\leq h\},} where F ( x , y , z ) = ( x 2 + y 2 ) ( cos ⁡ θ ) 2 − z 2 ( sin ⁡ θ ) 2 . {\displaystyle F(x,y,z)=(x^{2}+y^{2})(\cos \theta )^{2}-z^{2}(\sin
Semigroup with three elements (488 words) [view diff] no match in snippet view article find links to article
 x   y   z   x    x    y    z   y    y    z    x   z    z    x    y 
Heap (mathematics) (1,372 words) [view diff] no match in snippet view article
{\displaystyle x,y,z} are integers, we can set [ x , y , z ] = x − y + z {\displaystyle [x,y,z]=x-y+z} to produce a heap. We can then choose any integer
Trechnotheria (413 words) [view diff] no match in snippet view article find links to article
pattersoni Fox 1980 †Tirotherium aptum Montellano-Ballesteros & Fox 2015 Luo, Z.−X., Kielan−Jaworowska, Z., and Cifelli, R.L. (2002). "In quest for a phylogeny
Monotonicity criterion (1,933 words) [view diff] no match in snippet view article find links to article
of monotonicity. E.g., harming candidate x by changing some ballots from z > x > y to x > y > z isn't a violation of the monotonicity criterion. The monotonicity
Subjective logic (2,463 words) [view diff] no match in snippet view article find links to article
conditional opinions ω Z | X Y {\displaystyle \omega _{Z|XY}} in order to apply the deduction operator and derive the marginal opinion ω ZX Y {\displaystyle
Pixel connectivity (662 words) [view diff] no match in snippet view article find links to article
{\displaystyle \textstyle (x\pm 1,y\pm 1,z)} , ( x ± 1 , y ∓ 1 , z ) {\displaystyle \textstyle (x\pm 1,y\mp 1,z)} , ( x ± 1 , y , z ± 1 ) {\displaystyle \textstyle
Poisson superalgebra (196 words) [view diff] no match in snippet view article find links to article
{\displaystyle [x,\cdot ]:A\to A} is a superderivation of A: [ x , y z ] = [ x , y ] z + ( − 1 ) | x | | y | y [ x , z ] . {\displaystyle [x,yz]=[x
Contact mechanics (11,010 words) [view diff] no match in snippet view article find links to article
boundary conditions: σ x z ( x , 0 ) = 0   ;     σ z ( x , z ) = − P δ ( x , z ) {\displaystyle \sigma _{xz}(x,0)=0~;~~\sigma _{z}(x,z)=-P\delta (x,z)} where
Bismut connection (574 words) [view diff] no match in snippet view article find links to article
anti-symmetrization as T ( Z , X , Y ) + cyc~in~ X , Y , Z = T ( Z , X , Y ) + S ( Z , X , Y ) {\displaystyle T(Z,X,Y)+{\textrm {cyc~in~}}X,Y,Z=T(Z,X,Y)+S(Z,X,Y)} , with
Distributivity (order theory) (829 words) [view diff] no match in snippet view article
expressed by requiring that the identity x ∧ ( y ∨ z ) = ( x ∧ y ) ∨ ( x ∧ z ) {\displaystyle x\wedge (y\vee z)=(x\wedge y)\vee (x\wedge z)} hold for all elements
Segre class (2,325 words) [view diff] exact match in snippet view article find links to article
then, since C Z / X = N Z / X {\displaystyle C_{Z/X}=N_{Z/X}} is the normal bundle and N Z / X = ⨁ i = 1 n N D i / X | Z {\displaystyle N_{Z/X}=\bigoplus
Currying (4,485 words) [view diff] no match in snippet view article find links to article
{\displaystyle Y} is locally compact Hausdorff, then curry : Z X × Y → ( Z Y ) X {\displaystyle {\text{curry}}:Z^{X\times Y}\to (Z^{Y})^{X}} is a homeomorphism. This
Brun sieve (674 words) [view diff] no match in snippet view article find links to article
constants. Then S ( A , P , z ) = X ⋅ W ( z ) ⋅ ( 1 + O ( ( log ⁡ z ) − b log ⁡ b ) ) + O ( z b log ⁡ log ⁡ z ) {\displaystyle S(A,P,z)=X\cdot W(z)\cdot \left({1+O\left((\log
Gromov product (776 words) [view diff] no match in snippet view article find links to article
a metric space and let x, y, z ∈ X. Then the Gromov product of y and z at x, denoted (y, z)x, is defined by ( y , z ) x = 1 2 ( d ( x , y ) + d ( x ,
Blancmange curve (3,092 words) [view diff] no match in snippet view article find links to article
triangle wave, defined by s ( x ) = min n ∈ Z | x − n | {\displaystyle s(x)=\min _{n\in {\mathbf {Z} }}|x-n|} , that is, s ( x ) {\displaystyle s(x)}
Polynomial greatest common divisor (8,204 words) [view diff] no match in snippet view article find links to article
univariate polynomial ring Z[X], the Euclidean division (over Q) of A by B provides a quotient and a remainder which may not belong to Z[X]. For, if one applies
Hoare logic (3,614 words) [view diff] no match in snippet view article find links to article
≥ 0 ∧ 10 − x = z ] x := x + 1 [ x ≤ 10 ∧ 10 − x ≥ 0 ∧ 10 − x < z ] {\displaystyle [x\leq 10\wedge x<10\wedge 10-x\geq 0\wedge 10-x=z]x:=x+1[x\leq 10\wedge
Geographic information system (9,498 words) [view diff] case mismatch in snippet view article find links to article
east-west and north-south direction. These two tangents give two components, ∂z/∂x and ∂z/∂y, which then be used to determine the overall direction of slope
Volume integral (476 words) [view diff] no match in snippet view article find links to article
of the cube. For example for density function: { f : R 3 → R ( x , y , z ) ⟼ x + y + z {\displaystyle {\begin{cases}f:\mathbb {R} ^{3}\to \mathbb {R}
2 × 2 real matrices (2,039 words) [view diff] no match in snippet view article find links to article
Projecting z alternately onto these subspaces of R4 yields z = x I + n , x = a + d 2 , n = zx I . {\displaystyle z=xI+n,\quad x={\frac {a+d}{2}},\quad
Generalized inverse Gaussian distribution (1,149 words) [view diff] no match in snippet view article find links to article
the posterior for z {\displaystyle z} , given the data is also GIG: P ( zX , a , b , p , α , β ) = GIG ( z ∣ a + T β 2 , b + S , p − T 2 ) {\displaystyle
London equations (1,222 words) [view diff] no match in snippet view article find links to article
solution inside the superconductor may be shown to be B z ( x ) = B 0 e − x / λ s . {\displaystyle B_{z}(x)=B_{0}e^{-x/\lambda _{s}}.\,} From here the physical
Algebraic surface (1,002 words) [view diff] no match in snippet view article find links to article
theorem D ( S ) × D ( S ) → Z : ( X , Y ) ↦ X ⋅ Y {\displaystyle {\mathcal {D}}(S)\times {\mathcal {D}}(S)\rightarrow \mathbb {Z} :(X,Y)\mapsto X\cdot Y} is
Wess–Zumino–Witten model (3,634 words) [view diff] no match in snippet view article find links to article
{z}})} , where we have identified z = x + i y {\displaystyle z=x+iy} and z ¯ = x − i y {\displaystyle {\bar {z}}=x-iy} in terms of the Euclidean space
Matrix exponential (9,105 words) [view diff] no match in snippet view article find links to article
the Baker–Campbell–Hausdorff formula: Z = X + Y + 1 2 [ X , Y ] + 1 12 [ X , [ X , Y ] ] + ⋯ {\displaystyle Z=X+Y+{\frac {1}{2}}[X,Y]+{\frac {1}{12}}[X
Parallel transport (1,767 words) [view diff] no match in snippet view article find links to article
respect to the metric: ZX , Y ⟩ = ⟨ ∇ Z X , Y ⟩ + ⟨ X , ∇ Z Y ⟩ . {\displaystyle Z\langle X,Y\rangle =\langle \nabla _{Z}X,Y\rangle +\langle X,\nabla
Akivis algebra (380 words) [view diff] no match in snippet view article find links to article
identity: [ [ x , y ] , z ] + [ [ y , z ] , x ] + [ [ z , x ] , y ] = [ x , y , z ] + [ y , z , x ] + [ z , x , y ] − [ x , z , y ] − [ y , x , z ] − [ z , y
Matrix exponential (9,105 words) [view diff] no match in snippet view article find links to article
the Baker–Campbell–Hausdorff formula: Z = X + Y + 1 2 [ X , Y ] + 1 12 [ X , [ X , Y ] ] + ⋯ {\displaystyle Z=X+Y+{\frac {1}{2}}[X,Y]+{\frac {1}{12}}[X
Stokes' theorem (4,188 words) [view diff] no match in snippet view article find links to article
F_{x}dx+F_{y}dy+F_{z}dz} ∇ × ( F x F y F z ) ⋅ d S = ( ∂ y F z − ∂ z F y ∂ z F x − ∂ x F zx F y − ∂ y F x ) ⋅ d S → {\displaystyle \nabla \times
De Bruijn index (1,220 words) [view diff] no match in snippet view article find links to article
de Bruijn indices, is λ λ λ 3 1 (2 1). The term λz. (λy. y (λx. x)) (λx. z x) is λ (λ 1 (λ 1)) (λ 2 1). See the following illustration, where the binders
Rotation (mathematics) (3,099 words) [view diff] no match in snippet view article
point (x, y) in the plane is represented by the complex number z = x + i y {\displaystyle z=x+iy} This can be rotated through an angle θ by multiplying it
Generalized chi-squared distribution (1,633 words) [view diff] no match in snippet view article find links to article
) T A ( z + a ) + c T z = ( x + b ) T D ( x + b ) + d T x + e , {\displaystyle X=(z+a)^{\mathrm {T} }A(z+a)+c^{\mathrm {T} }z=(x+b)^{\mathrm {T} }D(x+b)+d^{\mathrm
Fishburn–Shepp inequality (212 words) [view diff] no match in snippet view article find links to article
x < y. In the language of conditional probability, P ( x < z ) < P ( x < zx < y ) . {\displaystyle P(x<z)<P(x<z\mid x<y).} The proof uses the Ahlswede–Daykin
Riemann–Lebesgue lemma (1,079 words) [view diff] no match in snippet view article find links to article
Fourier transform of ƒ satisfies f ^ ( z ) ≡ ∫ R d f ( x ) exp ⁡ ( − i zx ) d x → 0  as  | z | → ∞ . {\displaystyle {\hat {f}}(z)\equiv \int _{\mathbb
Mathematical analysis (3,317 words) [view diff] no match in snippet view article find links to article
(triangle inequality). By taking the third property and letting z = x {\displaystyle z=x} , it can be shown that d ( x , y ) ≥ 0 {\displaystyle d(x,y)\geq
Early Cretaceous (1,177 words) [view diff] no match in snippet view article find links to article
1093/sysbio/syt110. PMID 24449041. Retrieved 28 July 2019.CS1 maint: ref=harv (link) Luo, Z. X.; Ji, Q.; Wible, J. R.; Yuan, C. X. (2003). "An Early Cretaceous tribosphenic
Universal property (3,232 words) [view diff] no match in snippet view article find links to article
D} and morphisms f : ZX {\displaystyle f:Z\to X} and g : Z → Y {\displaystyle g:Z\to Y} there exists a unique morphism h : ZX × Y {\displaystyle h:Z\to
Gamma function (11,705 words) [view diff] no match in snippet view article find links to article
is Γ ( z , x ) = x z e − x ∑ n = 0 ∞ L n ( z ) ( x ) n + 1 , {\displaystyle \Gamma (z,x)=x^{z}e^{-x}\sum _{n=0}^{\infty }{\frac {L_{n}^{(z)}(x)}{n+1}}
Pairwise error probability (762 words) [view diff] no match in snippet view article find links to article
X + Z ) − X ^ | | 2 < | | ( X + Z ) − X | | 2 ) = P ( | | ( X − X ^ ) + Z | | 2 < | | Z | | 2 ) = P ( | | X − X ^ | | 2 + | | Z | | 2 + 2 ( Z , X − X
Stretch rule (412 words) [view diff] no match in snippet view article find links to article
since we are dealing with stretching over the z-axis only: I z = ∫ 0 L d zx , y d x d y ρ ( x , y , z ) r 2 {\displaystyle I_{z}=\int _{0}^{L}dz\int
Digital filter (3,560 words) [view diff] no match in snippet view article find links to article
8 z − 2 = Y ( z ) X ( z ) {\displaystyle H(z)={\frac {1+2z^{-1}+z^{-2}}{1+{\frac {1}{4}}z^{-1}-{\frac {3}{8}}z^{-2}}}={\frac {Y(z)}{X(z)}}} The coefficients
Columbia (supercontinent) (1,692 words) [view diff] no match in snippet view article
176G. doi:10.1016/j.jog.2010.01.017. Nordsvan, A. R.; Collins, W. J.; Li, Z. X.; Spencer, C. J.; Pourteau, A.; Withnall, I. W.; Betts, P. G.; Volante, S
Majority function (739 words) [view diff] no match in snippet view article find links to article
following equations. ⟨x, y, y⟩ = y ⟨x, y, z⟩ = ⟨z, x, y⟩ ⟨x, y, z⟩ = ⟨x, z, y⟩ ⟨⟨x, w, y⟩, w, z⟩ = ⟨x, w, ⟨y, w, z⟩⟩ An abstract system satisfying these
Fokker periodicity block (1,919 words) [view diff] no match in snippet view article find links to article
ϕ C ( x , y , z ) := ( x 0 , y 0 , z 0 ) + ( x , y , z ) ( u x u y u z v x v y v z w x w y w z ) {\displaystyle \phi _{C}(x,y,z):=(x_{0},y_{0},z_{0})+(x
Eutriconodonta (2,851 words) [view diff] no match in snippet view article find links to article
S2CID 205245235.CS1 maint: multiple names: authors list (link) Chen M., Luo Z.-X., Wilson G. P. (2017). "The postcranial skeleton of Yanoconodon allini from
Rothe–Hagen identity (242 words) [view diff] no match in snippet view article find links to article
denominators vanish: ∑ k = 0 n x x + k z ( x + k z k ) y y + ( n − k ) z ( y + ( n − k ) z n − k ) = x + y x + y + n z ( x + y + n z n ) . {\displaystyle \sum
Hilbert projection theorem (821 words) [view diff] no match in snippet view article find links to article
zx , a ⟩ = 0 {\displaystyle \langle z-x,a\rangle =0} for all a ∈ M {\displaystyle a\in M} . ‖ x − a ‖ 2 = ‖ zx ‖ 2 + ‖ a − z ‖ 2 + 2 ⟨ zx ,
Polynomial lemniscate (477 words) [view diff] no match in snippet view article find links to article
z ) p ¯ ( z ¯ ) {\displaystyle p(z){\bar {p}}({\bar {z}})} in terms of z = x + iy. When p is a polynomial of degree 1 then the resulting curve is simply
Wiener amalgam space (248 words) [view diff] no match in snippet view article find links to article
supported function, such that ∑ x ∈ Z d g ( zx ) = 1 {\displaystyle \sum _{x\in \mathbb {Z^{d}} }g(z-x)=1} , for all z ∈ R d {\displaystyle z\in \mathbb
Rössler attractor (3,403 words) [view diff] no match in snippet view article find links to article
+ a y d z d t = b + z ( x − c ) {\displaystyle {\begin{cases}{\frac {dx}{dt}}=-y-z\\{\frac {dy}{dt}}=x+ay\\{\frac {dz}{dt}}=b+z(x-c)\end{cases}}} Rössler
Finger tree (1,994 words) [view diff] no match in snippet view article find links to article
  ( E m p t y )   z   = z r e d u c e r   ( ≺ )   ( S i n g l e   x )   z = x   ≺   z r e d u c e r   ( ≺ )   ( D e e p   p r   m   s f )   z = p r  
Generalized structure tensor (1,939 words) [view diff] no match in snippet view article find links to article
{\begin{array}{c}\xi (x,y)=\Re g(z)\\\eta (x,y)=\Im g(z)\\\end{array}}} where z = x + i y {\displaystyle z=x+iy} . Examples of analytic functions include g ( z ) = log ⁡
Arithmetic zeta function (1,567 words) [view diff] no match in snippet view article find links to article
trace formula that ζ X ( s ) = Z ( X , q − s ) {\displaystyle \zeta _{X}(s)=Z(X,q^{-s})} where Z ( X , t ) {\displaystyle Z(X,t)} is a rational function (i
Oxypnictide (1,235 words) [view diff] no match in snippet view article find links to article
A.; Yang, J.; Lu, W.; Yi, W.; Che, G. C.; Dong, X. L.; Sun, L. L.; Zhao, Z. X. (2008). "Samarium based SmFeAsO1−xFx". Materials Research Innovations. 12
Quartic equation (5,872 words) [view diff] no match in snippet view article find links to article
and thus is a biquadratic equation, which is easy to solve: let z = x 2 {\displaystyle z=x^{2}} , so our equation turns to a 0 z 2 + a 2 z + a 4 = 0 {\displaystyle
Algebraic integer (996 words) [view diff] no match in snippet view article find links to article
monic polynomial f(x) ∈ [x] such that f(α) = 0. α ∈ K is an algebraic integer if the minimal monic polynomial of α over ℚ is in [x]. α ∈ K is an algebraic
DBAR problem (188 words) [view diff] no match in snippet view article find links to article
where g ( z ) {\displaystyle g(z)} is assumed to be known and z = x + i y {\displaystyle z=x+iy} is a complex number in a domain R ⊆ C {\displaystyle R\subseteq
Glossary of algebraic geometry (11,276 words) [view diff] no match in snippet view article find links to article
isomorphism classes of varieties with the relation: [ X ] = [ Z ] + [ X − Z ] {\displaystyle [X]=[Z]+[X-Z]} where Z is a closed subvariety of a variety X and
Sine (5,128 words) [view diff] no match in snippet view article find links to article
( z x ) {\displaystyle \cos(zx)} can be decomposed as cos ⁡ ( z x ) = z sin ⁡ ( π z ) π ∑ n = − ∞ ∞ ( − 1 ) n e i n x z 2 − n 2 , z ∈ C ∖ { Z } , x
Prenex normal form (1,756 words) [view diff] no match in snippet view article find links to article
)\rightarrow \rho )} ∀ z ( ( ∃ x ( ϕ ∨ ψ ) ) → ρ ) {\displaystyle \forall z((\exists x(\phi \lor \psi ))\rightarrow \rho )} , ∀ z ( ∀ x ( ( ϕ ∨ ψ ) → ρ ) )
Tapering (mathematics) (372 words) [view diff] no match in snippet view article
T(z) = 1/(a + bt) were applied to the cube's equation such that ƒ(t) = (T(z)x(t), T(z)y(t), T(z)z(t)), for some real constants a and b. 3D projection Shirley
Eruwa language (134 words) [view diff] no match in snippet view article find links to article
Alveolar Palatal Velar Labio-velar Glottal Plosive p  b [m] t  d k  ɡ k͡p  ɡ͡b   Fricative f  v s  z x  ɣ   h Approximant   l [n]         ʋ ɹ j   w  
Central limit theorem (8,644 words) [view diff] no match in snippet view article find links to article
{\bar {X}}} is the sample mean, the limiting form of the distribution of Z = ( X ¯ n − μ σ / √ n ) {\textstyle Z=\left({\frac {{\bar {X}}_{n}-\mu }{\sigma
Tight binding (6,789 words) [view diff] no match in snippet view article find links to article
}-m(1+l^{2}-m^{2})V_{pd\pi }} E z , x 2 − y 2 = 3 2 n ( l 2 − m 2 ) V p d σ − n ( l 2 − m 2 ) V p d π {\displaystyle E_{z,x^{2}-y^{2}}={\frac {\sqrt
Hilbert's irreducibility theorem (732 words) [view diff] no match in snippet view article find links to article
Z [ x ] {\displaystyle g(x)\in \mathbb {Z} [x]} is a perfect square for all large integer values of x, then g(x) is the square of a polynomial in Z [
Exceptional divisor (306 words) [view diff] no match in snippet view article find links to article
{\displaystyle X} and Y {\displaystyle Y} ). A codimension-1 subvariety ZX {\displaystyle Z\subset X} is said to be exceptional if f ( Z ) {\displaystyle
Residuated Boolean algebra (1,157 words) [view diff] case mismatch in snippet view article find links to article
permits an alternative expression of the three inequalities y ≤ x\z   ⇔   x•y ≤ z   ⇔   x ≤ z/y in the axiomatization of the two residuals in terms of disjointness
Pickover stalk (732 words) [view diff] no match in snippet view article find links to article
multiplication function for complex numbers z += c; x = z.x; y = z.y; float distanceToX = abs(z.x + transformationVector.x); //Checks the distance to the
Snapper (video game) (599 words) [view diff] no match in snippet view article
Snapper started the BBC Micro tradition of controlling arcade games using the Z, X, : and / keys for horizontal and vertical motion, since on most BBC models
All-pairs testing (954 words) [view diff] no match in snippet view article find links to article
form of p x y ( X , Y ) , p y z ( Y , Z ) , p z x ( Z , X ) {\displaystyle p_{xy}(X,Y),p_{yz}(Y,Z),p_{zx}(Z,X)} where comma denotes any combination. If the
Earnshaw's theorem (3,178 words) [view diff] no match in snippet view article find links to article
} The Laplacian will be ∇ 2 U = − ∂ 2 ( M x B x + M y B y + M z B z ) ∂ x 2 − ∂ 2 ( M x B x + M y B y + M z B z ) ∂ y 2 − ∂ 2 ( M x B x + M y B y
Quasi-Frobenius Lie algebra (314 words) [view diff] no match in snippet view article find links to article
Y ] , Z ) + β ( [ Z , X ] , Y ) + β ( [ Y , Z ] , X ) = 0 {\displaystyle \beta \left(\left[X,Y\right],Z\right)+\beta \left(\left[Z,X\right],Y\right)+\beta
Glennie's identity (229 words) [view diff] no match in snippet view article find links to article
triple product {X,Y,Z} = X•(Y•Z) − Y•(ZX) + Z•(X•Y) then Glennie's identity G8 holds in the form: 2{ {Z,{X,Y,X},Z}, Y, ZX} − {Z, {X, {Y, X•Z, Y}, X},
Edo language (358 words) [view diff] no match in snippet view article find links to article
[pm bm] t  d [tn dn] k  ɡ [kŋ ɡŋ] k͡p  ɡ͡b [k͡pŋ͡m ɡ͡bŋ͡m] Fricative f  v s  z x  ɣ h Close approximant ɹ̝̊  ɹ̝ Open approximant ʋ [ʋ̃] l  ɹ [n  ɾ̃] j [ɲ]
Tritheledon (85 words) [view diff] no match in snippet view article find links to article
were probably insectivores, and nocturnal animals. Paleontology portal Luo, Z-X, Z Kielan-Jaworowska & RL Cifelli (2002), In quest for a phylogeny of Mesozoic
Demonic composition (191 words) [view diff] no match in snippet view article find links to article
composition R ;← S is defined by { ( x , z )   |   x ( S ∘ R ) z ∧ ∀ y ∈ Y   ( y S zx R y ) } . {\displaystyle \{(x,z)\ |\ x\,(S\circ R)\,z\wedge \forall y\in
Herbrandization (591 words) [view diff] no match in snippet view article find links to article
{\displaystyle z} with a function symbol f z ( x ) {\displaystyle f_{z}(x)} : F H = ∃ x [ R ( c y , x ) ∧ ¬ S ( x , f z ( x ) ) ] . {\displaystyle F^{H}=\exists
Tritheledon (85 words) [view diff] no match in snippet view article find links to article
were probably insectivores, and nocturnal animals. Paleontology portal Luo, Z-X, Z Kielan-Jaworowska & RL Cifelli (2002), In quest for a phylogeny of Mesozoic
Subring (819 words) [view diff] no match in snippet view article find links to article
the field of real numbers and also a subring of the ring of polynomials Z[X]. Not to be confused with a ring-theoretic analog of a group extension. For
Factorization of polynomials (3,444 words) [view diff] no match in snippet view article find links to article
integers) is essentially the same problem. The content of a polynomial p ∈ Z[X], denoted "cont(p)", is, up to its sign, the greatest common divisor of its
AVL tree (4,504 words) [view diff] no match in snippet view article find links to article
right_child(X) = t23; 5 if (t23 != null) 6 parent(t23) = X; 7 left_child(Z) = X; 8 parent(X) = Z; 9 // 1st case, BalanceFactor(Z) == 0, only happens with
Lenstra elliptic-curve factorization (4,492 words) [view diff] no match in snippet view article find links to article
(a set of points with some structure on it) E ( Z / n Z ) = { ( x : y : z ) ∈ P 2   |   y 2 z = x 3 + a x z 2 + b z 3 } {\displaystyle E(\mathbb {Z} /n\mathbb
Order topology (functional analysis) (1,084 words) [view diff] no match in snippet view article
bounded, where an order interval in X is a set of the form [a, b] := { zX : a ≤ z and z ≤ b } where a and b belong to X. The order topology is an
Exponential function (5,073 words) [view diff] no match in snippet view article find links to article
complex exponential function based on this relationship. If z = x + i y {\displaystyle z=x+iy} , where x {\displaystyle x} and y {\displaystyle y} are
Sectional curvature (2,727 words) [view diff] no match in snippet view article find links to article
d ( z , m ) 2 ≥ 1 2 d ( z , x ) 2 + 1 2 d ( z , y ) 2 − 1 4 d ( x , y ) 2 {\displaystyle d(z,m)^{2}\geq {\tfrac {1}{2}}d(z,x)^{2}+{\tfrac {1}{2}}d(z,y)^{2}-{\tfrac
Interaction information (2,986 words) [view diff] no match in snippet view article find links to article
( Y ; Z ) − I ( Y ; Z | X ) {\displaystyle {\begin{matrix}I(X;Y;Z)&=&I(X;Y)-I(X;Y|Z)\\\ &=&I(X;Z)-I(X;Z|Y)\\\ &=&I(Y;Z)-I(Y;Z|X)\end{matrix}}} where
Latimer–MacDuffee theorem (259 words) [view diff] no match in snippet view article find links to article
{\displaystyle f} and the ideal classes in the order Z [ x ] / ( f ( x ) ) . {\displaystyle \mathbb {Z} [x]/(f(x)).} where ideals are considered equivalent
Veronese surface (925 words) [view diff] no match in snippet view article find links to article
:\mathbb {P} ^{2}\to \mathbb {P} ^{5}} given by ν : [ x : y : z ] ↦ [ x 2 : y 2 : z 2 : y z : x z : x y ] {\displaystyle \nu :[x:y:z]\mapsto [x^{2}:y^{2}:z^{2}:yz:xz:xy]}
MV-algebra (1,647 words) [view diff] no match in snippet view article find links to article
the following identities: ( x ⊕ y ) ⊕ z = x ⊕ ( y ⊕ z ) , {\displaystyle (x\oplus y)\oplus z=x\oplus (y\oplus z),} x ⊕ 0 = x , {\displaystyle x\oplus 0=x
Normalized compression distance (1,961 words) [view diff] no match in snippet view article find links to article
Z ( x , y ) = Z ( x y ) − min { Z ( x ) , Z ( y ) } max { Z ( x ) , Z ( y ) } . {\displaystyle NCD_{Z}(x,y)={\frac {Z(xy)-\min\{Z(x),Z(y)\}}{\max\{Z(x)
Monomial order (1,940 words) [view diff] no match in snippet view article find links to article
{\displaystyle x} dominates). Grlex: x 2 z 2 > x y 2 z > x 3 > z 2 {\displaystyle x^{2}z^{2}>xy^{2}z>x^{3}>z^{2}} (total degree dominates; higher power of
Exponentiation (14,112 words) [view diff] no match in snippet view article find links to article
e^{z+w}=e^{z}e^{w}} . In particular, for any complex number z = x + i y {\displaystyle z=x+iy} e z = e x + i y = e x ⋅ e i y , {\displaystyle e^{z}=e^{x+iy}=e^{x}\cdot
Imaginary unit (2,859 words) [view diff] no match in snippet view article find links to article
vectors. Consider the matrix equation ( z x y − z ) 2 = ( − 1 0 0 − 1 ) . {\displaystyle {\begin{pmatrix}z&x\\y&-z\end{pmatrix}}^{2}\!\
Pre-Lie algebra (780 words) [view diff] no match in snippet view article find links to article
y ) ◃ zx ◃ ( y ◃ z ) = ( x ◃ z ) ◃ y − x ◃ ( z ◃ y ) . {\displaystyle (x\triangleleft y)\triangleleft z-x\triangleleft (y\triangleleft z)=(x\triangleleft
Probability bounds analysis (4,526 words) [view diff] no match in snippet view article find links to article
z = x + y F ( x ) G ( y ) d z = ∫ R F ( x ) G ( zx ) d x = F ∗ G . {\displaystyle H(z)=\int _{z=x+y}F(x)G(y)dz=\int _{\mathbb {R} }F(x)G(z-x)dx=F*G
Nagata's conjecture (146 words) [view diff] no match in snippet view article find links to article
Ivan P. Shestakov (2004). Nagata's automorphism is given by ( x , y , z ) ↦ ( x − 2 ( x z + y 2 ) y − ( x z + y 2 ) 2 z , y + ( x z + y 2 ) z , z ) .
Complemented subspace (2,087 words) [view diff] no match in snippet view article find links to article
complements of each other. This happens if and only if the addition map Y × ZX, which is defined by (y, z) ↦ y + z, is a homeomorphism. Note that while
Janet basis (2,290 words) [view diff] no match in snippet view article find links to article
order z x x > z x y > z x > z y y > z y > z {\displaystyle z_{xx}>z_{xy}>z_{x}>z_{yy}>z_{y}>z} and the G R L E X {\displaystyle GRLEX} order z x x > z x y
Jensen's inequality (4,211 words) [view diff] no match in snippet view article find links to article
space of T: E ⁡ | ⟨ z , X ⟩ | < ∞ {\displaystyle \operatorname {E} |\langle z,X\rangle |<\infty } , and ⟨ z , E ⁡ [ X ] ⟩ = E ⁡ [ ⟨ z , X ⟩ ] {\displaystyle
QMA (1,732 words) [view diff] no match in snippet view article find links to article
_{i}h_{i}Z_{i}+\sum _{i<j}J^{ij}Z_{i}Z_{j}+\sum _{i<j}K^{ij}X_{i}X_{j}} where Z , X {\displaystyle Z,X} represent the Pauli matrices σ z , σ x {\displaystyle \sigma _{z}
Multivariate mutual information (2,308 words) [view diff] no match in snippet view article find links to article
( Y ; Z ) {\displaystyle I(Y;Z)} will be zero, but I ( Y ; Z | X ) {\displaystyle I(Y;Z|X)} will be positive (1 bit) since once output X {\displaystyle
Heisenberg group (5,714 words) [view diff] no match in snippet view article find links to article
y={\begin{pmatrix}1&0&0\\0&1&1\\0&0&1\\\end{pmatrix}}} and relations z = x y x − 1 y − 1 ,   x z = z x ,   y z = z y {\displaystyle z_{}^{}=xyx^{-1}y^{-1},\ xz=zx
Killing vector field (1,379 words) [view diff] no match in snippet view article find links to article
connection, this is g ( ∇ Y X , Z ) + g ( Y , ∇ Z X ) = 0 {\displaystyle g(\nabla _{Y}X,Z)+g(Y,\nabla _{Z}X)=0\,} for all vectors Y and Z. In local coordinates
Semigroup (4,967 words) [view diff] no match in snippet view article find links to article
ordered pair (x, y). Associativity is formally expressed as that (x·y)·z = x·(y·z) for all x, y and z in the semigroup. Semigroups may be considered
List of drugs: X (227 words) [view diff] no match in snippet view article find links to article
H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z X-Trozine Xalatan (Pfizer) xaliproden (INN) xamoterol (INN) Xanax (Pfizer)
Neutral axis (799 words) [view diff] no match in snippet view article find links to article
undergoing uniform bending, a plane on the beam remains plane. That is: γ x y = γ z x = τ x y = τ x z = 0 {\displaystyle \gamma _{xy}=\gamma _{zx}=\tau _{xy}=\tau
Delsatia (137 words) [view diff] no match in snippet view article find links to article
sér. II a, t. 324, p. 135-140 Z. Kielan-Jaworowska, R. L. Cifelli, and Z.-X. Luo. 2004. Mammals from the age of dinosaurs: Origins, evolution, and structure
Variety (universal algebra) (1,944 words) [view diff] no match in snippet view article
operation. A sufficient defining equation is the associative law: x ( y z ) = ( x y ) z . {\displaystyle x(yz)=(xy)z.} The class of groups forms a variety
Seminormal ring (260 words) [view diff] no match in snippet view article find links to article
not normal, one can consider the non-integral ring Z [ x , y ] / x y {\displaystyle \mathbb {Z} [x,y]/xy} , or the ring of a nodal curve. In general,
Mixed Hodge structure (2,944 words) [view diff] no match in snippet view article find links to article
distinguished triangle i ∗ i ! Z XZ X → R j ∗ Z U → [ + 1 ] {\displaystyle i_{*}i^{!}\mathbb {Z} _{X}\to \mathbb {Z} _{X}\to \mathbf {R} j_{*}\mathbb
Incidence (geometry) (1,717 words) [view diff] no match in snippet view article
can be expressed as: ( x y z x 1 y 1 z 1 x 2 y 2 z 2 ) ( a b c ) = ( 0 0 0 ) . {\displaystyle \left({\begin{matrix}x&y&z\\x_{1}&y_{1}&z_{1}\\x_{2}&y_{
Bony–Brezis theorem (1,066 words) [view diff] no match in snippet view article find links to article
| 2 ≤ | zx | 2 + 2 h ⋅ ( x − z ) + | h | 2 = D ( x ) + f 0 ( h ) + | h | 2 {\displaystyle \displaystyle {D(x+h)\leq |x+h-z|^{2}\leq |z-x|^{2}+2h\cdot
Implicit surface (2,102 words) [view diff] no match in snippet view article find links to article
y 0 , z 0 ) , F z ( x 0 , y 0 , z 0 ) ) ≠ ( 0 , 0 , 0 ) {\displaystyle (F_{x}(x_{0},y_{0},z_{0}),F_{y}(x_{0},y_{0},z_{0}),F_{z}(x_{0},y_{0},z_{0}))\neq
Plus minus method (750 words) [view diff] no match in snippet view article find links to article
x ) = − z ( x ) v 1 ( x ) + E X − E S + z ( x ) v 2 ( x ) {\displaystyle \triangle \tau (x)=-{\frac {z(x)}{v_{1}(x)}}+{\frac {E_{X}-E_{S}+z(x)}{v_{2}(x)}}}
Satake isomorphism (843 words) [view diff] no match in snippet view article find links to article
= Z / p Z ( ( x ) ) {\displaystyle K=\mathbb {Z} /p\mathbb {Z} ((x))} and O = Z / p Z [ [ x ] ] {\displaystyle O=\mathbb {Z} /p\mathbb {Z} [[x]]} , p {\displaystyle
Conjugacy problem (437 words) [view diff] no match in snippet view article find links to article
problem is to determine whether there exists an element z of G such that y = z x z − 1 . {\displaystyle y=zxz^{-1}.\,\!} The conjugacy problem is also known
Euler's identity (1,880 words) [view diff] no match in snippet view article find links to article
+ 1 = 0. {\displaystyle e^{i\pi }+1=0.} Any complex number z = x + i y {\displaystyle z=x+iy} can be represented by the point ( x , y ) {\displaystyle
Presentation of a group (2,353 words) [view diff] case mismatch in snippet view article find links to article
frf^{-1}=r^{-1}\rangle } The quaternion group is a special case when n = 2 Z × Zx , y ∣ x y = y x ⟩ {\displaystyle \langle x,y\mid xy=yx\rangle } Z/mZ × Z/nZ
Pauli group (291 words) [view diff] no match in snippet view article find links to article
G 1   = d e f   { ± I , ± i I , ± X , ± i X , ± Y , ± i Y , ± Z , ± i Z } ≡ ⟨ X , Y , Z ⟩ {\displaystyle G_{1}\ {\stackrel {\mathrm {def} }{=}}\ \{\pm
Conical surface (731 words) [view diff] no match in snippet view article find links to article
{\displaystyle S(x,y,z)=0} where S ( x , y , z ) = ( x 2 + y 2 ) ( cos ⁡ θ ) 2 − z 2 ( sin ⁡ θ ) 2 . {\displaystyle S(x,y,z)=(x^{2}+y^{2})(\cos \theta )^{2}-z^{2}(\sin
Mesungulatidae (264 words) [view diff] no match in snippet view article find links to article
0026.CS1 maint: ref=harv (link) Kielan-Jaworowska, Z.; Cifelli, R.; Luo, Z.-X. (2004). Mammals from the Age of Dinosaurs: Origins, Evolution, and Structure
Exponentially modified Gaussian distribution (1,721 words) [view diff] no match in snippet view article find links to article
exponential random variables. An exGaussian random variable Z may be expressed as Z = X + Y, where X and Y are independent, X is Gaussian with mean μ and variance
Social Choice and Individual Values (3,181 words) [view diff] no match in snippet view article find links to article
z     x    y T z     (x z T y is the same ranking as x y T z, so is omitted, etc.) y x z     y T x    z z x y     z    x T y x z y     x T z    y y z
Dajnko alphabet (296 words) [view diff] no match in snippet view article find links to article
alphabetical order was as follows: A B C D E F G H I J K L M N Ŋ O P R S Ȣ Z X T U Y V Ч "Dajnkova slovnica" [The Grammar of Dajnko]. Kamra (in Slovenian)
Fixed-point combinator (4,757 words) [view diff] no match in snippet view article find links to article
formally this is not correct. Instead defining y by ∀ z , y   z = x {\displaystyle \forall z,y\ z=x} gives, λ f . let ⁡ y   z = f   ( y   z ) in ⁡ y   z {\displaystyle
Ext functor (3,121 words) [view diff] no match in snippet view article find links to article
defined as H ∗ ( X , A ) = Ext ∗ ⁡ ( Z X , A ) . {\displaystyle H^{*}(X,A)=\operatorname {Ext} ^{*}(\mathbb {Z} _{X},A).} Here Ext is taken in the abelian
Dajnko alphabet (296 words) [view diff] no match in snippet view article find links to article
alphabetical order was as follows: A B C D E F G H I J K L M N Ŋ O P R S Ȣ Z X T U Y V Ч "Dajnkova slovnica" [The Grammar of Dajnko]. Kamra (in Slovenian)
Mamenchisauridae (558 words) [view diff] no match in snippet view article find links to article
Acta Geologica Sinica 82(1) :17-26. Li, K., Yang, C.-Y., Liu, J. and Wang, Z.-X. (2010). "A new sauropod dinosaur from the Lower Jyrassic of Huili, Sichuan
Parabolic coordinates (1,057 words) [view diff] no match in snippet view article find links to article
surfaces of constant σ {\displaystyle \sigma } form confocal paraboloids 2 z = x 2 + y 2 σ 2 − σ 2 {\displaystyle 2z={\frac {x^{2}+y^{2}}{\sigma ^{2}}}-\sigma
Quadratic Lie algebra (424 words) [view diff] no match in snippet view article find links to article
and Lie bracket [ X , Y ] = Z , [ Y , Z ] = X , [ Z , X ] = Y {\displaystyle [X,Y]=Z,\quad [Y,Z]=X,\quad [Z,X]=Y} . Straightforward computation shows
Yinotheria (2,255 words) [view diff] no match in snippet view article find links to article
Linnean Society. 77: 353–84. doi:10.1111/j.1096-3642.1983.tb00859.x. Luo, Z.-X.; Cifelli, R.L.; Kielan-Jaworowska, Z. (2001). "Dual origin of tribosphenic
Hyperboloid model (3,063 words) [view diff] no match in snippet view article find links to article
{\displaystyle (w,x,y,z)} is: ( w x y z x x 2 w + 1 + 1 y x w + 1 z x w + 1 y x y w + 1 y 2 w + 1 + 1 z y w + 1 z x z w + 1 y z w + 1 z 2 w + 1 + 1 ) {\displaystyle
Submersion (mathematics) (1,183 words) [view diff] no match in snippet view article
\mathbb {R} ^{3}\to \mathbb {R} } given by f ( x , y , z ) = x 4 + y 4 + z 4 . {\displaystyle f(x,y,z)=x^{4}+y^{4}+z^{4}.} The Jacobian matrix is [ ∂ f ∂ x
Adiabatic quantum computation (1,927 words) [view diff] no match in snippet view article find links to article
_{i}h_{i}Z_{i}+\sum _{i<j}J^{ij}Z_{i}Z_{j}+\sum _{i<j}K^{ij}X_{i}X_{j}} where Z , X {\displaystyle Z,X} represent the Pauli matrices σ z , σ x {\displaystyle \sigma _{z}
Algebraic cycle (1,471 words) [view diff] no match in snippet view article find links to article
groups of cycles for varying r together form a group ZX = ⨁ r Z r X . {\displaystyle Z_{*}X=\bigoplus _{r}Z_{r}X.} This is called the group of algebraic
Ogham inscription (2,881 words) [view diff] no match in snippet view article find links to article
Y MUCOI Z (X son of Y of the tribe Z) X KOI MAQI MUCOI Y (here is X son of the tribe Y) X MUCOI Y (X of the tribe Y) X MAQI Y MAQI MUCOI Z (X son of Y
Rewaconodon (107 words) [view diff] no match in snippet view article find links to article
undescribed species may have lived in North America. P. M. Datta, D. P. Das & Z.-X. Luo (2004). "A Late Triassic dromatheriid (Synapsida: Cynodontia) from India"
Metric differential (501 words) [view diff] no match in snippet view article find links to article
Rn defined by the limit M D ( f , z ) ( x ) = lim r → 0 d X ( f ( z + r x ) , f ( z ) ) r {\displaystyle MD(f,z)(x)=\lim _{r\rightarrow 0}{\frac {d_{X}(f(z+rx)
Riesz space (4,120 words) [view diff] no match in snippet view article find links to article
properties: for all x, y, and z in X x ∧ (y ∨ z) = (x ∧ y) ∨ (x ∧ z) x ∨ (y ∧ z) = (x ∨ y) ∧ (x ∨ z) (x ∧ {\displaystyle \wedge } y) ∨ {\displaystyle
Ordered semigroup (210 words) [view diff] no match in snippet view article find links to article
that is compatible with the semigroup operation, meaning that x ≤ y implies zx ≤ z•y and x•z ≤ y•z for all x, y, z in S. An ordered monoid and an ordered
Schubert polynomial (1,474 words) [view diff] no match in snippet view article find links to article
elements. They form a basis for the polynomial ring Z [ x 1 , x 2 , … ] {\displaystyle \mathbb {Z} [x_{1},x_{2},\ldots ]} in infinitely many variables.
Pons asinorum (1,875 words) [view diff] no match in snippet view article find links to article
\|x-z\|^{2}=\|x\|^{2}-2x\cdot z+\|z\|^{2},} and x ⋅ z = ‖ x ‖ ‖ z ‖ cos ⁡ θ {\displaystyle x\cdot z=\|x\|\|z\|\cos \theta } where θ is the angle between
Shifted Gompertz distribution (1,807 words) [view diff] no match in snippet view article find links to article
{\displaystyle q/p} . Similar to the Bass model, the hazard rate z ( x ; p , q ) {\displaystyle z(x;p,q)} is equal to p {\displaystyle p} when x {\displaystyle
Let expression (5,021 words) [view diff] no match in snippet view article find links to article
substitution, ⟺ x = y ∧ ( L   z ) [ x := y ] ⟺ x = y ∧ ( L [ x := y ]   z [ x := y ] ) ⟺ x = y ∧ L   z [ x := y ] ⟹ L   z [ x := y ] {\displaystyle {\begin{aligned}&\iff
Optimal instruments (997 words) [view diff] no match in snippet view article find links to article
vector-valued function z of x, it will be the case that E [ z ( x ) ( y − f ( x , θ ) ) ] = 0 {\displaystyle E[z(x)(y-f(x,\theta ))]=0} . That is, z defines a finite
Ambondro mahabo (1,939 words) [view diff] no match in snippet view article find links to article
Luo, Z.-X., Cifelli, R.L. and Kielan-Jaworowska, Z. 2001. Dual origin of tribosphenic mammals (subscription required). Nature 409:53–57. Luo, Z.-X., Kielan-Jaworowska
Mott insulator (1,402 words) [view diff] no match in snippet view article find links to article
77i4518M. doi:10.1103/PhysRevB.77.094518. Hasan, M. Z.; Isaacs, E. D.; Shen, Z.-X.; Miller, L. L.; Tsutsui, K.; Tohyama, T.; Maekawa, S. (2000-06-09). "Electronic
Early stopping (1,774 words) [view diff] no match in snippet view article find links to article
an unknown probability measure, ρ {\displaystyle \rho } , on Z = X × Y {\displaystyle Z=X\times Y} , the goal of such problems is to approximate a regression
Stirling polynomials (2,875 words) [view diff] no match in snippet view article find links to article
{S}}_{t}(z)^{t}} , we have that S t ( z ) x = ∑ n ≥ 0 x σ n ( x + t n ) z n . {\displaystyle {\mathcal {S}}_{t}(z)^{x}=\sum _{n\geq 0}x\sigma _{n}(x+tn)z^{n}
Mapping spectrum (42 words) [view diff] no match in snippet view article find links to article
of spectra X, Y is characterized by [ X ∧ Y , Z ] = [ X , F ( Y , Z ) ] . {\displaystyle [X\wedge Y,Z]=[X,F(Y,Z)].} "homology of a mapping spectrum". MathOverflow
Sign (mathematics) (2,640 words) [view diff] no match in snippet view article
function requires the magnitude of its argument z = x + iy, which can be calculated as | z | = z z ¯ = x 2 + y 2 . {\displaystyle |z|={\sqrt {z{\bar {z}}}}={\sqrt
Basketball at the 2018 Asian Games – Men (69 words) [view diff] no match in snippet view article find links to article
quarter: 18–26, 19–12, 12–31, 17–14 Pts: Yergali 15 Rebs: Bazhin, Bykov, Marchuk 6 Asts: Yergali 7 Pts: Liu Z.X. 18 Rebs: Abudushalamu A. 11 Asts: Liu Z.X. 6
Surface of revolution (1,474 words) [view diff] no match in snippet view article find links to article
around the y-axis is described by ( r , θ , z ) = ( x ( t ) , θ , y ( t ) ) {\displaystyle (r,\theta ,z)=(x(t),\theta ,y(t))} . In Cartesian coordinates
Moment-generating function (2,406 words) [view diff] no match in snippet view article find links to article
probability-generating function is defined as G ( z ) = E [ z X ] . {\displaystyle G(z)=E\left[z^{X}\right].\,} This immediately implies that G ( e t ) = E
Boolean algebras canonically defined (7,925 words) [view diff] no match in snippet view article find links to article
(x∧y)∨(y∧z)∨(zx) and (x∨y)∧(y∨z)∧(zx) are actually the same operation. That is, we have proved the equational identity (x∧y)∨(y∧z)∨(zx) = (x∨y)∧(y∨z)∧(zx), for
Generating function (14,619 words) [view diff] no match in snippet view article find links to article
corresponding generating functions, F ( z ) x {\displaystyle F(z)^{x}} and G ( z ) x {\displaystyle G(z)^{x}} , then for arbitrary t {\displaystyle t}
Parallel axis theorem (1,984 words) [view diff] no match in snippet view article find links to article
y z 0 − x − y x 0 ] 2 = [ y 2 + z 2 − x y − x z − y x x 2 + z 2 − y z − z x − z y x 2 + y 2 ] . {\displaystyle -[R][R]=-{\begin{bmatrix}0&-z&y\\z&0&
Thin plate spline (1,485 words) [view diff] no match in snippet view article find links to article
where each entry ϕ i ( z ) = ‖ zx i ‖ 2 log ⁡ ‖ zx i ‖ {\displaystyle \phi _{i}(z)=\|z-x_{i}\|^{2}\log \|z-x_{i}\|} . Note that for TPS, the control
Function composition (3,653 words) [view diff] no match in snippet view article find links to article
binary relations, then their composition R∘S is the relation defined as {(x, z) ∈ X × Z : ∃y ∈ Y. (x, y) ∈ R ∧ (y, z) ∈ S}. Considering a function as a special
Translation surface (differential geometry) (1,661 words) [view diff] no match in snippet view article
{\displaystyle c_{2}} is a line. The elliptic paraboloid z = x 2 + y 2 {\displaystyle \;z=x^{2}+y^{2}\;} can be generated by   c 1 : ( x , 0 , x 2 )  
Monotreme (3,876 words) [view diff] no match in snippet view article find links to article
Neuroanatomy: Evolution and Adaptation. Wiley. p. 361. ISBN 978-0-471-73383-6. Luo, Z.-X.; Cifelli, R.L.; Kielan-Jaworowska, Z. (2001). "Dual origin of tribosphenic
Stokes' paradox (906 words) [view diff] no match in snippet view article find links to article
{z}}f(z)+g(z)} . Here z = x + i y {\displaystyle z=x+iy} , where i {\displaystyle i} is the imaginary unit, z ¯ = x − i y {\displaystyle {\bar {z}}=x-iy} , and f
Laplace's equation (4,855 words) [view diff] no match in snippet view article find links to article
complex analytic function both satisfy the Laplace equation. That is, if z = x + iy, and if f ( z ) = u ( x , y ) + i v ( x , y ) , {\displaystyle f(z)=u(x
Partially ordered set (3,728 words) [view diff] no match in snippet view article find links to article
Another way to combine two posets is the ordinal sum (or linear sum), Z = X ⊕ Y, defined on the union of the underlying sets X and Y by the order a
Multilinear polynomial (123 words) [view diff] no match in snippet view article find links to article
multilinear polynomial with degree 2 (because of the monomial 3xy) whereas p(x,y,z) = x² +4y is not. Multilinear polynomials are important in the study of polynomial
Källén function (369 words) [view diff] no match in snippet view article find links to article
quadratic polynomial in three variables λ ( x , y , z ) ≡ x 2 + y 2 + z 2 − 2 x y − 2 y z − 2 z x . {\displaystyle \lambda (x,y,z)\equiv x^{2}+y^{2}+z^{2}-2xy-2yz-2zx
Logarithm (11,905 words) [view diff] no match in snippet view article find links to article
may be denoted as z = x + i y = r ( cos ⁡ φ + i sin ⁡ φ ) = r ( cos ⁡ ( φ + 2 k π ) + i sin ⁡ ( φ + 2 k π ) ) , {\displaystyle z=x+iy=r(\cos \varphi +i\sin
Arithmetic rope (126 words) [view diff] no match in snippet view article find links to article
Addition X + Y = Z X knots are counted, then another Y. The total number of counted knots is Z. e.g.: 5 + 4 = 9 Subtraction X - Y = Z X knots are counted
Sum (529 words) [view diff] no match in snippet view article find links to article
fibered sum), the colimit of a diagram consisting of two morphisms f : ZX and g : Z → Y with a common domainor pushout, leading to a fibered sum in
Probability distribution of extreme points of a Wiener stochastic process (3,328 words) [view diff] no match in snippet view article find links to article
)}=}     exp ⁡ ( − 2     ( zX b ) ( zX a ) σ 2 ( b − a ) ) {\displaystyle \ \ \exp {\biggl (}-2\ \ {\frac {(z-X_{b})(z-X_{a})}{\sigma ^{2}(b-a)}}{\biggr
Mittag-Leffler distribution (651 words) [view diff] no match in snippet view article find links to article
{\displaystyle \alpha } if, for some constant C > 0 {\displaystyle C>0} , E ( e z X α ) = E α ( C z ) , {\displaystyle \mathbb {E} (e^{zX_{\alpha }})=E_{\alpha
Birkhoff's representation theorem (2,895 words) [view diff] no match in snippet view article find links to article
, z ) = ( x ∨ y ) ∧ ( x ∨ z ) ∧ ( y ∨ z ) = ( x ∧ y ) ∨ ( x ∧ z ) ∨ ( y ∧ z ) {\displaystyle m(x,y,z)=(x\vee y)\wedge (x\vee z)\wedge (y\vee z)=(x\wedge
Wick product (956 words) [view diff] no match in snippet view article find links to article
Y)-\operatorname {E} (XY).\,} ⟨ X , Y , Z ⟩ = X Y Z − E ⁡ Y ⋅ X Z − E ⁡ ZX Y − E ⁡ X ⋅ Y Z + 2 ( E ⁡ Y ) ( E ⁡ Z ) ⋅ X + 2 ( E ⁡ X ) ( E ⁡ Z ) ⋅ Y + 2 (
Legendre sieve (630 words) [view diff] no match in snippet view article find links to article
integer z < X, and then the Legendre identity becomes: S ( A , P ) = ∑ d ∣ P μ ( d ) ⌊ X d ⌋ = ⌊ X ⌋ − ∑ p 1 ≤ zX p 1 ⌋ + ∑ p 1 < p 2 ≤ zX p 1 p 2
Tetrahedron (7,055 words) [view diff] no match in snippet view article find links to article
(a+b-c+d)\,(a+b+c-d)}}{192\,u\,v\,w}}} where a = x Y Z b = y Z X c = z X Y d = x y z X = ( w − U + v ) ( U + v + w ) x = ( U − v + w ) ( v − w + U )
Källén function (369 words) [view diff] no match in snippet view article find links to article
quadratic polynomial in three variables λ ( x , y , z ) ≡ x 2 + y 2 + z 2 − 2 x y − 2 y z − 2 z x . {\displaystyle \lambda (x,y,z)\equiv x^{2}+y^{2}+z^{2}-2xy-2yz-2zx
Wick product (956 words) [view diff] no match in snippet view article find links to article
Y)-\operatorname {E} (XY).\,} ⟨ X , Y , Z ⟩ = X Y Z − E ⁡ Y ⋅ X Z − E ⁡ ZX Y − E ⁡ X ⋅ Y Z + 2 ( E ⁡ Y ) ( E ⁡ Z ) ⋅ X + 2 ( E ⁡ X ) ( E ⁡ Z ) ⋅ Y + 2 (
Transport-of-intensity equation (556 words) [view diff] no match in snippet view article find links to article
terms of irradiance and phase: 2 π λ ∂ ∂ z I ( x , y , z ) = − ∇ x , y ⋅ [ I ( x , y , z ) ∇ x , y Φ ] , {\displaystyle {\frac {2\pi }{\lambda }}{\frac
Knight shift (475 words) [view diff] no match in snippet view article find links to article
momentum operators, the K ^ i = ( K x x K x y K x z K y x K y y K y z K z x K z y K z z ) {\displaystyle {{\hat {\mathbf {K} }}_{i}}=\left({\begin{m
Geostrophic wind (1,169 words) [view diff] no match in snippet view article find links to article
using the third equation above, we have: f ⋅ v = − g ∂ P ∂ x ∂ P ∂ z = g ∂ Zx f ⋅ u = g ∂ P ∂ y ∂ P ∂ z = − g ∂ Z ∂ y {\displaystyle {\begin{aligned}f\cdot
Hilbert's nineteenth problem (3,211 words) [view diff] no match in snippet view article find links to article
properties: (1)      ∬ F ( p , q , z ; x , y ) d x d y = Minimum [ ∂ zx = p ; ∂ z ∂ y = q ] {\displaystyle {\iint F(p,q,z;x,y)dxdy}={\text{Minimum}}\qquad
Oscillator representation (21,477 words) [view diff] no match in snippet view article find links to article
relation. If ℑ z > 0 {\displaystyle \Im z>0} , then f z ( x ) = e i z x 2 / 2 {\displaystyle f_{z}(x)=e^{izx^{2}/2}} lies in L2 and is called a coherent
Probability density function (5,029 words) [view diff] no match in snippet view article find links to article
transform H {\displaystyle H} be defined as H ( Z , X ) = [ Z + V ( X ) X ] = [ Y X ~ ] {\displaystyle H(Z,X)={\begin{bmatrix}Z+V(X)\\X\end{bmatrix}}={\b
Probability distribution of extreme points of a Wiener stochastic process (3,328 words) [view diff] no match in snippet view article find links to article
)}=}     exp ⁡ ( − 2     ( zX b ) ( zX a ) σ 2 ( b − a ) ) {\displaystyle \ \ \exp {\biggl (}-2\ \ {\frac {(z-X_{b})(z-X_{a})}{\sigma ^{2}(b-a)}}{\biggr
Allotheria (497 words) [view diff] no match in snippet view article find links to article
Evolution of Mammals". The New York Times. Retrieved November 6, 2014. Luo, Z.-X.; Kielan-Jaworowska, Z.; Cifelli, R.L. (2002). "In quest for a phylogeny
Log-logistic distribution (1,903 words) [view diff] no match in snippet view article find links to article
)^{-\beta }][1+(x/\alpha )^{\beta }]}}} Defining the substitution z = x / α {\displaystyle z=x/\alpha } leads to the simpler equation: G = sin ⁡ ( π / β ) π
List of Toyota model codes (977 words) [view diff] no match in snippet view article find links to article
GSE20 = 4GR + XE20 Sienna GSL30 = 2GR + XL30 Z A N Wish ZNE10 = 1ZZ + AE10 Z X C Camry ACV30 = 2AZ + XV30 Hybrid R none W Lexus GS 450h GWS190 = 2GR + S190
Legendre sieve (630 words) [view diff] no match in snippet view article find links to article
integer z < X, and then the Legendre identity becomes: S ( A , P ) = ∑ d ∣ P μ ( d ) ⌊ X d ⌋ = ⌊ X ⌋ − ∑ p 1 ≤ zX p 1 ⌋ + ∑ p 1 < p 2 ≤ zX p 1 p 2
Ricci decomposition (2,307 words) [view diff] no match in snippet view article find links to article
( x , y , z , w ) + R ( y , z , x , w ) + R ( z , x , y , w ) . {\displaystyle b(R)(x,y,z,w)=R(x,y,z,w)+R(y,z,x,w)+R(z,x,y,w).\,} The space RV = ker b
AltGr key (2,771 words) [view diff] no match in snippet view article find links to article
The keymap with the AltGr key: â ß € r ț y u î o § „ ” ă ș đ f g h j k ł ; z x © v b n m «  » Since release 1903, versions of Windows 10 have the binding:
Moran process (4,585 words) [view diff] no match in snippet view article find links to article
\end{aligned}}} Writing Y = X ( t ) {\displaystyle Y=X(t)} and Z = X ( t − 1 ) {\displaystyle Z=X(t-1)} , and applying the law of total expectation, E ⁡ [ Y
Figure-eight knot (mathematics) (972 words) [view diff] no match in snippet view article
F(x,y,z,t)=G(x,y,z^{2}-t^{2},2zt),\,\!} where G ( x , y , z , t ) =   ( z ( x 2 + y 2 + z 2 + t 2 ) + x ( 6 x 2 − 2 y 2 − 2 z 2 − 2 t 2 ) ,   t x 2 +
Hessian form of an elliptic curve (2,157 words) [view diff] no match in snippet view article find links to article
{\displaystyle x} and y {\displaystyle y} are represented by X , Y , Z , X X , Y Y , Z Z , X Y , Y Z , X Z {\displaystyle X,Y,Z,XX,YY,ZZ,XY,YZ,XZ} satisfying the
Quantifier rank (482 words) [view diff] no match in snippet view article find links to article
quantifier rank 3: ∀ x ∃ y ∃ z ( ( x ≠ y ∧ x R y ) ∧ ( x ≠ z ∧ z R x ) ) {\displaystyle \forall x\exists y\exists z((x\neq y\wedge xRy)\wedge (x\neq
Thin plate energy functional (1,422 words) [view diff] no match in snippet view article find links to article
{\displaystyle i,j} yields Z X X = R 00 2 z x x + 2 R 00 R 01 z x y + R 01 2 z y y , Z X Y = R 00 R 10 z x x + ( R 00 R 11 + R 01 R 10 ) z x y + R 01 R 11 z y
Pseudo-Euclidean space (2,333 words) [view diff] no match in snippet view article find links to article
pseudo-Euclidean space is the plane z = x + yj consisting of split-complex numbers, equipped with the quadratic form ‖ z ‖ = z z ∗ = z ∗ z = x 2 − y 2 . {\displaystyle
Hurwitz's theorem (composition algebras) (3,717 words) [view diff] no match in snippet view article
( X ) , Y ∘ Z ) + ( D ( Y ) , ZX ) + ( D ( Z ) , X ∘ Y ) = 0. {\displaystyle (D(X),Y\circ Z)+(D(Y),Z\circ X)+(D(Z),X\circ Y)=0.} Setting Z = 1, shows
Category of rings (1,823 words) [view diff] no match in snippet view article find links to article
is the functor which assigns to every monoid X the integral monoid ring Z[X]. The category Ring is both complete and cocomplete, meaning that all small
Filter bank (6,025 words) [view diff] no match in snippet view article find links to article
components x ( z ) = d e f ( X 0 ( z ) , . . . , X | M | − 1 ( z ) ) T {\displaystyle x(z){\stackrel {\rm {def}}{=}}(X_{0}(z),...,X_{|M|-1}(z))^{T}} . Denote y
Spherical 3-manifold (1,307 words) [view diff] no match in snippet view article find links to article
group of order m with a group having presentation ⟨ x , y , z ∣ ( x y ) 2 = x 2 = y 2 , z x z − 1 = y , z y z − 1 = x y , z 3 k = 1 ⟩ {\displaystyle \langle
Ruin theory (1,440 words) [view diff] no match in snippet view article find links to article
δ τ − s X τ − − z X τ ] {\displaystyle \mathbb {E} ^{x}[e^{-\delta \tau -sX_{\tau -}-zX_{\tau }}]} w ( x 1 , x 2 ) = e − s x 1 − z x 2 {\displaystyle
R-algebroid (509 words) [view diff] no match in snippet view article find links to article
f ∗ g ) ( z ) = ∑ { ( f x ) ( g y ) ∣ z = x ∘ y } {\displaystyle \displaystyle (f*g)(z)=\sum \{(fx)(gy)\mid z=x\circ y\}} . Only this second construction
Incidence algebra (2,831 words) [view diff] no match in snippet view article find links to article
elements in an interval: ζ 2 ( x , y )   =   ∑ z ∈ [ x , y ] ζ ( x , z ) ζ ( z , y )   =   ∑ z ∈ [ x , y ] 1   =   # [ x , y ] . {\displaystyle \textstyle
Infrastructure (number theory) (2,485 words) [view diff] no match in snippet view article
nearby. To formalize this concept, assume that there is a map r e d : R / R ZX {\displaystyle red:\mathbb {R} /R\mathbb {Z} \to X} ; then, one can define
Fourier series (9,840 words) [view diff] no match in snippet view article find links to article
{r} }.} Assuming r = ( x , y , z ) = x 1 a 1 a 1 + x 2 a 2 a 2 + x 3 a 3 a 3 , {\displaystyle \mathbf {r} =(x,y,z)=x_{1}{\frac {\mathbf {a} _{1}}{a_{1}}}+x_{2}{\frac
Tarski's axiomatization of the reals (642 words) [view diff] no match in snippet view article find links to article
y ∈ Y, x < y, then there exists a z such that for all x ∈ X and y ∈ Y, if z ≠ x and z ≠ y, then x < z and z < y. To clarify the above statement somewhat
Superalgebra (1,475 words) [view diff] no match in snippet view article find links to article
_{A_{0}}A_{1}\to A_{0}} such that μ ( x ⊗ y ) ⋅ z = x ⋅ μ ( y ⊗ z ) {\displaystyle \mu (x\otimes y)\cdot z=x\cdot \mu (y\otimes z)} for all x, y, and z in
Cayley graph (2,438 words) [view diff] no match in snippet view article find links to article
y , z {\displaystyle x,y,z} . They satisfy the relations Z = X Y X − 1 Y − 1 , X Z = Z X , Y Z = Z Y {\displaystyle Z=XYX^{-1}Y^{-1},XZ=ZX,YZ=ZY} ,
Monogenic field (313 words) [view diff] no match in snippet view article find links to article
subring Z[a] of K generated by a. Then OK is a quotient of the polynomial ring Z[X] and the powers of a constitute a power integral basis. In a monogenic field
Unreachable code (1,320 words) [view diff] no match in snippet view article find links to article
fragment of C code: int foo (int X, int Y) { return X + Y; int Z = X * Y; } the definition int Z = X * Y; is never reached as the function always returns before
Tamari lattice (636 words) [view diff] no match in snippet view article find links to article
from the first by only rightward applications of the associative law (xy)z = x(yz). For instance, applying this law with x = a, y = bc, and z = d gives
Lagrange's theorem (group theory) (2,173 words) [view diff] no match in snippet view article
− z then we get a total of 3 different polynomials: x + y − z, x + z − y, and y + zx. Note that 3 is a factor of 6.) The number of such polynomials
Lelong number (309 words) [view diff] no match in snippet view article find links to article
point x of Cn is lim inf zx ϕ ( z ) log ⁡ | zx | . {\displaystyle \liminf _{z\rightarrow x}{\frac {\phi (z)}{\log |z-x|}}.} For a point x of an
Finitist set theory (7,003 words) [view diff] no match in snippet view article find links to article
denoted as z = x ∩ y {\displaystyle z=x\cap y} . The intersection of x {\displaystyle x} and y {\displaystyle y} , z = x ∩ y {\displaystyle z=x\cap y} ,
Additive inverse (877 words) [view diff] no match in snippet view article find links to article
x′ is called an additive inverse of x. If + is associative (( x + y ) + z = x + ( y + z ) for all x, y, z), then an additive inverse is unique. To see
Ekeland's variational principle (1,784 words) [view diff] no match in snippet view article find links to article
(x,y)\mapsto \epsilon d(x,y)} ). Given zX {\displaystyle z\in X} , define the functions G z := G ( z , ⋅ ) : X → R ∪ { + ∞ } {\displaystyle G_{z}:=G(z
Strong antichain (280 words) [view diff] no match in snippet view article find links to article
have a common lower bound in P, that is, ∀ x , y ∈ A [ x ≠ y → ¬ ∃ z ∈ P [ zx ∧ z ≤ y ] ] . {\displaystyle \forall x,y\in A\;[x\neq y\rightarrow \neg
Non-associative algebra (2,958 words) [view diff] no match in snippet view article find links to article
so that ex = x = xe; in that case we can define x0 ≝ e. Associative: (xy)z = x(yz). Commutative: xy = yx. Anticommutative: xy = −yx. Jacobi identity: (xy)z
T-norm (2,853 words) [view diff] no match in snippet view article find links to article
{\displaystyle \Rightarrow } on [0, 1] such that ⊤ ( z , x ) ≤ y {\displaystyle \top (z,x)\leq y} if and only if z ≤ ( x ⇒ y ) {\displaystyle z\leq (x\Rightarrow
Infinite impulse response (1,504 words) [view diff] no match in snippet view article find links to article
to be: H ( z ) = Y ( z ) X ( z ) = ∑ i = 0 P b i z − i ∑ j = 0 Q a j z − j {\displaystyle {\begin{aligned}H(z)&={\frac {Y(z)}{X(z)}}\\&={\frac {\sum
Cathaysia (688 words) [view diff] no match in snippet view article find links to article
2002, Abstract Scotese & McKerrow 1990, p. 17 Li, W. X.; Li, X. H.; Li, Z. X. (2005). "Neoproterozoic bimodal magmatism in the Cathaysia Block of South
Transfer function (2,700 words) [view diff] no match in snippet view article find links to article
transfer function is similarly written as H ( z ) = Y ( z ) X ( z ) {\displaystyle H(z)={\frac {Y(z)}{X(z)}}} and this is often referred to as the pulse-transfer
Alon–Boppana bound (1,893 words) [view diff] no match in snippet view article find links to article
Now, there exists some constant c {\displaystyle c} such that z = x − c y {\displaystyle z=x-cy} satisfies z T 1 = 0. {\displaystyle z^{\text{T}}\mathbf
Linkage principle (2,139 words) [view diff] no match in snippet view article find links to article
( zx ) W A ( z , x ) {\displaystyle \int _{-\infty }^{z}v(x,y)g(y\mid x)dy-G(z\mid x)W^{A}(z,x)} . In equilibrium, it is optimal to choose z = x and
Circular motion (3,763 words) [view diff] no match in snippet view article find links to article
z} , a complex "vector": z = x + i y = R ( cos ⁡ [ θ ( t ) ] + i sin ⁡ [ θ ( t ) ] ) = R e i θ ( t )   , {\displaystyle z=x+iy=R(\cos[\theta (t)]+i\sin[\theta