variance 方差
For $E[X^2]<\infty$, the variance is $\operatorname{Var}(X)=E[(X-E[X])^2]$.
Terminology & Translations
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vector space 向量空间
An abelian group $V$ with a unital scalar action of a field $F$, distributive in both inputs and satisfying $(ab)v=a(bv)$.
vertex cover 顶点覆盖
A vertex cover of a simple graph G is a vertex subset C such that every edge of G has at least one endpoint in C.
vertex degree 顶点度
In a finite simple graph, the degree d(v) of a vertex v is the number of its neighbors, equivalently the number of edges incident with v.
wandering point 游荡点
For a continuous self-map $T$, a point having a neighborhood $U$ such that $T^n(U)\cap U=\varnothing$ for every integer $n\ge1$.
wave equation 波方程
The constant-speed wave equation is partial_t^2 u=c^2 Delta_x u with c>0, classically for a twice differentiable space-time function; an initial value problem normally specifies both u and partial_t u at time zero.
weak convergence in a normed space 弱收敛
A sequence x_n in a normed space converges weakly to x if lambda(x_n) tends to lambda(x) for every bounded linear scalar functional lambda.
weak derivative 弱导数
For locally integrable u and v on an open Omega, v is the jth weak derivative of u if integral u partial_j phi=-integral v phi for every smooth compactly supported test phi. Higher-order derivatives use the sign…
weak mixing 弱混合
A probability-preserving map is weakly mixing if $N^{-1}\sum_{n=0}^{N-1}|\mu(A\cap T^{-n}B)-\mu(A)\mu(B)|\to0$ for every measurable $A,B$.
weak solution of a PDE 弱解
In the zero-Dirichlet Poisson problem on bounded open Omega with f in L2, a weak solution is u in H_0^1(Omega) satisfying integral gradient u dot gradient phi=integral f phi for every phi in H_0^1(Omega); other PDEs…
well-order 良序
A total order on a set in which every nonempty subset has a least element.
Yoneda lemma 米田引理
For small $C$, presheaf $P$, and $A\in C$, evaluation at $1_A$ gives $\operatorname{Nat}(\operatorname{Hom}(-,A),P)\cong P(A)$ naturally.
zero divisor 零因子
A nonzero element of a commutative ring whose product with some nonzero element is zero.