query: If $\wp(u) = \wp(v)$, then $u-v$ or $u+v$ is a period of $\wp$
positive_passages.docid: 149500
positive_passages.text: Regarding Periods of Weierstrass $\wp$ function
negative_passages.docid: 138212
negative_passages.text: Please help me prove: $v(a+b)\leq v(a)+v(b)$, and $v(ab)\leq v(a)v(b)$ where $v(x)=\inf{\{\vert x^n \vert}^{1/n}: n\in\mathbb{N}\}$
negative_passages.docid: 35071
negative_passages.text: Periodic polynomial?
negative_passages.docid: 146541
negative_passages.text: Why $\dim U+\dim U^\perp=\dim V$?
negative_passages.docid: 26658
negative_passages.text: A proof for $\nabla |u|^p = p\ \text{sgn}(u)|u|^{p-1}\nabla u$.
negative_passages.docid: 19804
negative_passages.text: How to prove that $|w_{n+1}-w_n| \leq (2/3)^2 |w_n - w_{n-1}|$?
negative_passages.docid: 54737
negative_passages.text: Proof that $V = \sum_k U_k$ and $\dim V=\sum_k \dim U_k$ implies $V=\oplus_k U_k$
negative_passages.docid: 53633
negative_passages.text: Given two subspaces $U,W$ of vector space $V$, how to show that $\dim(U)+\dim(W)=\dim(U+W)+\dim(U\cap W)$
negative_passages.docid: 145600
negative_passages.text: Is it true that $ U \oplus W_1 = U \oplus W_2 \implies W_1 = W_2 $?
negative_passages.docid: 92291
negative_passages.text: $U_1, U_2, ..., U_k$ subspaces of linear space $X$ with same dimensions, prove $X=U_1\oplus V=U_2\oplus V=...=U_k\oplus V$
negative_passages.docid: 46265
negative_passages.text: Minimal polynomial of the operator $T:V\oplus W\to V\oplus W$
negative_passages.docid: 126020
negative_passages.text: pumping lemma: ww^R not regular
negative_passages.docid: 24585
negative_passages.text: Proving that $\mathbf{W}$+$\mathbf{W^{\perp}}$=$\mathbb{R^{n}}$
negative_passages.docid: 15300
negative_passages.text: How to show that $(W^\bot)^\bot=W$ (in a finite dimensional vector space)
negative_passages.docid: 30583
negative_passages.text: If $a\mid b$ and $b\mid a$, $a,b\in R$, show that $\exists w \in R^\times$ with $b=wa$
negative_passages.docid: 99821
negative_passages.text: Show that $u(x)=\ln\left(\ln\left(1+\frac{1}{|x|}\right)\right)$ is in $W^{1,n}(U)$, where $U=B(0,1)\subset\mathbb{R}^n$.
negative_passages.docid: 32589
negative_passages.text: Prove or disprove that Arg(zw)=Arg(z)+Arg(w)