# All Questions

**1**

vote

**1**answer

68 views

### Any two bivariate algebraically dependent polynomials are always in the same ring generated by some bivariate polynomial?

If $f(x,y)$ and $g(x,y)$ are two algebraically dependent polynomials over some field $k$, is it true that there exists a bivariate polynomial $p(x,y)$ such that both $f(x,y)$ and $g(x,y)$ are in the ...

**4**

votes

**0**answers

80 views

### An extension of group schemes admitting Neron models

Let $R$ be a discrete valuation ring, $K$ its field of fractions, and
$$ 0 \rightarrow G_K' \rightarrow G_K \rightarrow G_K'' \rightarrow 0$$
a short exact sequence of smooth $K$-group schemes of ...

**2**

votes

**1**answer

72 views

### On transforming pair of bivariate polynomials to pair of univariate polynomials by applying polynomial map

We know that a polynomial map $f(x,y), g(x,y)$ is polynomial automorphism if there exists polynomials $p(x,y)$ and $q(x,y)$ such that $f(p,q)$=x and $g(p,q)=y$. Jacobian conjecture tries to ...

**-6**

votes

**0**answers

27 views

### Writing an integral for a bounded volume [on hold]

Good day folks!
I'm trying to write an integral which could represent the volume of the shaded area below. However my integral calculus is quite poor, so I need some help on that equation.
...

**22**

votes

**3**answers

708 views

### Graduate program applications that require questionnaires and other non-letter material

In the December 2014 AMS Notices, a letter to the editor (http://www.ams.org/notices/201411/rnoti-p1311.pdf) by Deconinck and Medlock addresses the problem of (math) graduate programs requiring letter ...

**4**

votes

**1**answer

278 views

### Is the space of real conics with a singular point an orientable manifold?

Consider the space of non zero real homogeneous degree $2$ polynomials in three variables upto scaling. This space is $\mathbb{R} \mathbb{P}^5$. The zero set
of such a polynomial gives a real curve ...

**0**

votes

**1**answer

140 views

### A question in Sasakian geometry

Let $(S,\eta, \xi)$ be a Sasakian manifold with killing vector field $\xi$, then we have the following exact sequence $$0\to <\xi>\to TS\to \frac{TS}{<\xi>}\to 0$$.
Can
...

**14**

votes

**2**answers

302 views

### ULU Decomposition of a matrix

Let $g \in GL_n(\mathbb{F}_q)$. Is it true that we can always write $g = u_1lu_2$, where $u_1$ and $u_2$ are upper-triangular and $l$ is lower-triangular? Note that I'm not requiring that the matrices ...

**-1**

votes

**0**answers

38 views

### Gaussian Elimination for Orthogonal groups [on hold]

We known the classical Gaussian elimination algorithm where we can reduce any invertible matrix to a diagonal matrix by row-column operations. Is there row-column operations and Gaussian elimination ...

**0**

votes

**0**answers

88 views

### Roots in the solution

It is known that for a one-dimensional self-adjoint operator with periodic boundary conditions, the number of roots is directly related to the eigenstate this eigenfunction belongs to.
Now it is ...

**3**

votes

**1**answer

56 views

### Hypergeometric function 2F1 convexity proof:

Suppose $F$ is the Gaussian hypergeometric function 2F1, $x\in \mathbb{N}$, $t>x \in \mathbb{N}$, $\mu \in (0,1)$. Is the function: $$f(\mu)=\mu^{x+1} F(x,-t+x,2+x,\mu),$$ convex in $\mu$? I've ...

**12**

votes

**2**answers

219 views

### Classifying set theories whose standard models sharing the same ordinals are equal

Let's say that a (recursively axiomatizable) set theory $T$ extending ZF is "ordinal-categorical" if, whenever $M$ and $N$ are standard models of $T$ sharing the same ordinals, one has $M = N$. For ...

**5**

votes

**1**answer

184 views

### p-adic Stein spaces

The higher cohomology of coherent sheaves vanish on Stein spaces (both complex and p-adic). In the case when the space ($X$) is a curve and we're working in the complex world, this shows that all ...

**3**

votes

**1**answer

68 views

### Do we need Feller condition if the process jumps?

Consider the SDE:
\begin{equation}
dv_t = k(\theta - v_t) dt + \xi \sqrt{v_t} dW^{v}_{t}
\end{equation}
It describes a process $v_t$ which is a strictly positive if the drift is stronger enough, i.e. ...

**2**

votes

**1**answer

81 views

### Does the Lehmer quintic parameterize certain minimal polynomials of the $p$th root of unity for infinitely many $p$?

The solvable Emma Lehmer quintic is given by,
$$F(y) = y^5 + n^2y^4 - (2n^3 + 6n^2 + 10n + 10)y^3 + (n^4 + 5n^3 + 11n^2 + 15n + 5)y^2 + (n^3 + 4n^2 + 10n + 10)y + 1 = 0$$
with discriminant $D = (7 + ...

**0**

votes

**0**answers

54 views

### “Reciprocal” of Schoenberg's theorem

Schoenberg's theorem states that for a (say, countable group) $G$ and any real valued conditionally negative type function $\psi$ on $G$, the function $e^{-t\psi}$ is positive definite, for any ...

**5**

votes

**0**answers

406 views

+100

### Zeta function double product

Is it possible to write the following double product in terms of the zeta function?
\begin{align}
&\prod_{i=1}^{\infty}\prod_{j=1}^{\infty} \frac{1}{1-(p_i\ p_j)^{-s}}
\end{align}
Extending the ...

**0**

votes

**0**answers

16 views

### Restricted strong convexity for biconvex functions

Recently, it has been shown (arxiv paper) that non-convex functions with the restricted strong convexity (RSC) property has the interesting property that their local minima lie within a small ball of ...

**6**

votes

**1**answer

150 views

### Exotic “non-linear” (but “almost linear”) automorphisms of symplectic vector space

Let $V$ be a vector space over a field $k$ equipped with a symplectic form $\omega$. Let $f:V \rightarrow V$ be a bijective set map such that the following hold.
For all $v \in V$ and $c \in k$, we ...

**5**

votes

**1**answer

139 views

### Weil height of an Abelian Variety with everywhere (potentially) good reduction

Background: Suppose that $E$ is an elliptic curve over $\mathbb{Q}$ with everywhere (potentially) good reduction. there are many ways to define the height of $E$, and I will be concerned with the ...

**1**

vote

**0**answers

84 views

### Free abelian subgroups and distorsion

I realized that I know groups with distorted cyclic subgroups and groups all of whose free abelian subgroups are undistorted, but nothing between. Maybe it is a naive question, but:
Does there ...

**-1**

votes

**0**answers

87 views

### Deriving $\Box p \rightarrow \Box \Box p$ if we have $\Box(\Box p \rightarrow p) \rightarrow \Box p$ [on hold]

Let $F = (W,R)$ - Kripke frame, $AL \rightleftharpoons \Box(\Box p \rightarrow p) \rightarrow \Box p $
Proof if $F \vdash AL$ then $R$ if transitive

**3**

votes

**0**answers

223 views

### Question on a proof by Solonnikov,Ladyzhenskaya,Ural'tseva

I have already asked this question on Mathematics SE, because I suppose that it is not research level. But I haven't got an answer, possibly here someone can answer.
Let $G(t,x)$ be the fundamental ...

**0**

votes

**0**answers

86 views

### Kodaira-Spencer theory in d=1

Consider genus $g$ Riemann surfaces, and thier moduli space $\mathcal M_g$.
To determine dimension of $T\mathcal M_g$,
start with a complex structure, which in some coordinates can be written
...

**2**

votes

**0**answers

80 views

### Schur covering group [on hold]

It is known that every finite group has a Schur covering group.
I'm eager to know every finite group can be considered as a Schur covering group of a group.
If it is not true in general, under what ...

**7**

votes

**1**answer

121 views

### Conformal map of polygon with circle segments

I am looking for a conformal map from a "polygon" to eg the upper half plane, which consists of circle segments instead of lines. So for example, it could be a quadrilateral ABCD, but where AB is a ...

**1**

vote

**1**answer

157 views

### Vector fields whose divergence are proper maps

Let $X$ be a polynomial vector field of degree $2$ on $\mathbb{R}^{2}$. Does there exist a nonvanishing smooth function $g$ such that $Div(gX)$ is a proper map?Or at least the zero locus of ...

**7**

votes

**2**answers

303 views

### Least supersingular prime

Given an elliptic curve over the rationals, what can one say about the size of the smallest supersingular prime?

**1**

vote

**1**answer

79 views

### A subgroup of outer automorphisms group of a free product

I would like to ask a question about automorphisms of free products of groups.
More specifically, let $G = G_1 \ast ... \ G_n \ast F_r$ where $F_r$ is free group on r generators. We can define the ...

**0**

votes

**0**answers

48 views

### Schoenberg correspondence on $L^p$

Schoenberg correspondence states that $\psi: \mathbb R^d\longrightarrow \mathbb C$ is conditionally positive definite and hermitian if and only if $e^{t\psi}$ is positive definite for each $t>0$. ...

**-6**

votes

**0**answers

30 views

### convergence and divergence using a root test [on hold]

why does
infinity
sigma n^7 / 7^n
n=1
converge using a root test?
I'm a bit confused on this series..

**1**

vote

**0**answers

31 views

### Moser's iteration for non homogeneous quasilinear elliptic PDE

I want to know some reference of Moser's iteration for non homogeneous quasilinear uniformly elliptic PDE, in particular, $u_{ij}(\delta_{ij}+u_iu_j|\nabla u|^2)=0$. I want to know how to deal with ...

**2**

votes

**1**answer

80 views

### System of linear first order PDE with constant coefficients

recently in my researches I've come across the following operator
$$L\left(\begin{array}{c}
a_1\\
\vdots\\
a_n
\end{array}\right)=M_1\left(\begin{array}{c}
...

**1**

vote

**0**answers

123 views

### On Prüfer domains

Is there any Prüfer domain $R$ that has a prime ideal $P$ that is not finitely generated but $xP$ is subset of a finitely generated ideal $I$,for some $x$ in $R-P$ and $I$⊂$P$?

**-9**

votes

**0**answers

115 views

### How can I calculate the significance of an acquisition test campaign on Facebook by using chi-squared test? [on hold]

Should I use number of installs and spending or should I use impression and install numbers in Chi-Squared Test (Evan's Awesome A/B Tools)? Here is the link of the ...

**2**

votes

**0**answers

99 views

### Surjectivity of multiplication maps with respect to pullback

Given a morphism $f: Y \to X$ and a globally generated line bundle $\mathcal L$ on $X$ such that $H^0(X,\mathcal L) \otimes H^0(X,\mathcal L) \to H^0(X,\mathcal L \otimes \mathcal L)$ is surjective.
...

**-3**

votes

**0**answers

25 views

### Should simulation from a student-t copula distribution yield the input correlation matrix [on hold]

I am using mathematica to simulate random variates from a student-t copula distribution. Assuming that I input in the correlation matrix R, after generating a certain number of random variates, should ...

**11**

votes

**2**answers

278 views

### Entire function bounded at every line

I would like to ask about, does there exists an entire function which is bounded on every line parallel to $x$ - axis , but unbounded on the $x$ - axis.

**-4**

votes

**0**answers

149 views

### How to calculate math expectation [on hold]

How to calculate math expectation of maximum of difference between two lognormal random variable:
E[max(X-Y,0)] =?
How to proceed?

**-4**

votes

**0**answers

50 views

### Derangement,recursion and circular permutation [on hold]

N people are invited to a dinner party and they are sitting on a round table.
Each person is sitting on a chair there are exactly N chairs.
So each person has exactly two neighboring chairs, one on ...

**2**

votes

**0**answers

90 views

### Strange invocation of Shapiro's lemma

I'm having trouble understanding a claim in a paper I'm reading. To avoid having to explain a lot of notation, I'll abstract the claim a bit. Assume that $G$ is a group with a subgroup $H$. Also, ...

**6**

votes

**2**answers

315 views

### A proposition on cyclic group

$G$ is a cyclic group iff
$$ \forall H < G, \ \exists k, \ H = \{a^k : a \in G\}. $$
Is it right?

**0**

votes

**0**answers

30 views

### Canonical forms of symmetric/skewsymmetric quaternionic matrix

$A$ belongs to $n$-dimensional quaternion symmetric matrix, in the sense that $A=A^T$, where $T$ means transpose. Under transformation $U$, $A\rightarrow U\cdot A\cdot U^T$, where $U$ is $n$-dim ...

**-3**

votes

**0**answers

32 views

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

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 ...

**1**

vote

**0**answers

67 views

### union of planes in the positive grassmannian

Let $\mathbb{G}=\mathbb{G}(k,n)$ be the (real) Grassmannian of $k$-dimensional subspaces of $\mathbb{R}^n$ and let $\mathbb{G}^+\subseteq \mathbb{G}$ be the subset of all subspaces with strictly ...

**2**

votes

**2**answers

256 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 ...

**-6**

votes

**0**answers

52 views

**6**

votes

**1**answer

276 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 ...

**0**

votes

**1**answer

165 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 ...

**8**

votes

**1**answer

441 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 ...