# All Questions

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### Find examples non compact surface satisfy properties every point is hyperbolic for Gaussian curvature [closed]

Find examples non compact surface satisfy the following properties for Gaussian curvature: (a) every point is hyperbolic. (b) every point is elliptic. (c) every point is parabolic. (d) that the point ...
302 views

### Polynomials of low degree that clone polynomials of higher degree

Let $f(x_1,\dots,x_{16})=(x_1+x_2+x_3+x_4)(x_5+x_6+x_7+x_8)(x_9+x_{10}+x_{11}+x_{12})(x_{13}+x_{14}+x_{15}+x_{16})\in\Bbb R[x]$. Let $\mathcal{Z}$ be the zero set of $f$ in ...
56 views

### how to show a function is non-conservative? [closed]

So I have this question ...
338 views
+50

### What is the universal property of quotienting a normaliser of the subgroup?

Let $G$ be a group, $H$ a subgroup and $X$ a $G$-set. By taking orbits $X/H = X \times_H 1$ or fixed points $X^H = \mathrm{Hom}_H(1,X)$ we obtain a set on which $H$ acts trivially, and we've destroyed ...
166 views

### Coaction of a group

Suppose $G$ is a finite group which acts on a $C^*-$algebra which we denote by $A$. I was wondering if there is a naturally induced coaction on $A\otimes C(G)$, here $C(G)$ denotes functions on $G$. I ...
458 views

### Is forcing computable?

By results similar to Tennenbaum's theorem we know that there exist no computable models of $ZF$. But suppose we are given, as a sort of oracle, access to some model of $ZF$ (e.g. we can make oracle ...
74 views

### Local time of Brownian motion + Lipschitz continuous function

Let $\mathrm{ Lip} (M)$ denote the space of all functions on $[0,T]$ with Lipschitz constant and $L^\infty$ norm bounded by $M$. Let $(B_t)_t$ be a Brownian motion defined on the probability space ...
43 views

### Integrating factors and integrability of an ODE system

The following argument is from a paper about the Bendixson-Dulac Theorem. Consider a smooth differential equation on the plane $$x'=g(x,y),\quad y'=h(x,y).$$ Suppose there exists a function ...
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### Ext and cup products and subvarieties

I am trying to understand Remark 11.3 in Huybrechts's amazing book on derived categories (FM transforms in AG). He starts with smooth projective varieties $j\colon Y \subset X$ and aims to describe ...
562 views

### Zeros of the derivative of Riemann's $\xi$-function

The Riemann xi function $\xi(s)$ is defined as $$\xi(s)=\frac12 s(s-1)\pi^{-s/2}\Gamma(s/2)\zeta(s).$$ It is an entire function whose zeros are precisely those of $\zeta(s)$. Since $\xi$ is real ...
100 views

### Criterion for normality of a schematic image

Consider a projective flat morphism $$f\colon X\to Y$$ between normal varieties. Let's say over the complex numbers. The geometric fibers of $f$ are all irreducible. I would like a criterion to ...
723 views

### textbooks on modern algebraic geometry for 21st-century starters

As for learners in algebraic geometry in 21st century, is there a textbook, lecture note or anything like that to introduce algebraic geometry utilizing the language of derived categories and stacks? ...
20 views

### Combining Pearson correlations [closed]

I have variables a, b, c, x I know sample values A, B, C, but not X I know Pearson correlations pairwise: ax, bx, cx (and ab, ac, bc too if it helps) Now what is the most likely value for X? ...
34 views

### Odd-cycle inequality [closed]

Consider the stable set problem. An odd hole is a cycle with an odd number if nodes and no edges between nonadjacent nodes of the cycle. Show that if H is the node set of an odd hole, the following ...
91 views

### Rademacher type of a Banach space is always less than or equal to 2

Before I ask my question I will provide a brief introduction. I came across the notion of Rademacher type while reading Assaf Naor's article An introduction to the Ribe program, which can be found ...
94 views

### A surface on which all regular curves have nowhere vanishing curvature

Let $S$ be a surface in $\mathbb{R}^{3}$ such that every regular curve $\gamma\subset S$ has nowhere vanishing curvature, that is $\kappa(z)\neq 0$ for all $z\in \gamma$. Does this imply that ...
47 views

### Groups arising as direct limits of a stationary system of primitive matrices over the integers

I am interested in the kinds of groups of the form $\displaystyle\lim_{\longrightarrow}(\mathbf{Z}^k,M)$ where $M$ is a primitive (some power of $M$ has strictly positive components) $k\times k$ ...
162 views

### Maths to take a user chosen number to a predictable number [closed]

As part of simple card trick, I want to allow a user to choose a number between 1 and 100 and then ask them to do various maths to lead them to the same number so their choice becomes irrelevant. One ...
82 views

### Contractibility of a poset-indexed colimit

Let $(X,\leq)$ be a poset with distinguished element $p$, and let $P'$ be the poset of "finite chains which weakly descend to $p$" given by all $\sigma = (x_0 \geq x_1 \geq \cdots \geq x_k \geq p)$ ...
30 views

### Boolean algebra 1´=0 ; 0´=1 ; x+1=1 [closed]

Hi I have a problem to solve, in Boolean algebra. I have to prove that 1´=0 ; 0´=1 ; x+1=1 I solve the first problem x*0=0 -> x*0=x*0+0=x*0+x* x´=x*(0+x´)=x*x´=0 previous 3 problems ...
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102 views

### what are the possible approximations for ideals

(Fix some local ring $(R,\mathfrak{m})$ over a field of zero characteristic.) Suppose an ideal $J$ is defined by some complicated formula/procedure. And there is no hope of computing it/or writing ...