# All Questions

**1**

vote

**0**answers

46 views

### “Generators” for fusion rings

It's a rather obvious idea in the area of fusion rings, but I haven't found a
reference yet. Start with the usual rules for a rank n fusion ring
$X_i\bigotimes{X_j}=\Sigma_k{T_{ij}}^kX_k$
and ...

**0**

votes

**0**answers

41 views

### Baire sets in locally compact Hausdorff spaces

I posed this on 14 Dec. at http://math.stackexchange.com/questions/1067751/baire-sets-in-locally-compact-hausdorff-spaces, but there has been no response:
(This is a follow-up to ...

**1**

vote

**0**answers

36 views

### finding dominating cycles in $2K_2$-free graphs

A cycle $C$ in a connected graph $G$ is called dominating if its complement $V(G)-V(C)$ is an independent set. H.J. Veldman proved in 1983 (Disc. Math. v.43, 281-96) a general result that in ...

**2**

votes

**0**answers

58 views

### Varieties with few monomials and the n-conjecture

The n-conjecture
is a generalization of abc and basically says that the if
$a_1 + \ldots + a_n=0$, no proper subsum vanishes and $a_i$
are coprime, then the radical of $a_1\cdots a_n$ can't be
too ...

**1**

vote

**1**answer

46 views

### Is the orthogonal complement of an admissible subcategory admissible itself?

I´m studying Huybrechts book "Fourier-Mukai transforms in algebraic geometry" and I came up with the following: as an example of semi orthogonal decomposition of a triangulated category $\mathcal{D}$ ...

**6**

votes

**0**answers

68 views

### Unbalanced equipartitions

Let $K$ be a compact convex set in the plane.
Say that a perimeter-halving partition of $K$
is a partition of $K$
into two pieces by a chord (a segment with endpoints
on the boundary $\partial K$) ...

**4**

votes

**1**answer

289 views

### Cap product à la Poincaré

Recently, it became apparent to me that I was not the only one who always first thought in terms of cap product before actually computing a cup product. There is no denying this is evil, but I found ...

**-8**

votes

**1**answer

141 views

### Do the mathematicians really know the exact values of what usually called “indeterminate forms”? [on hold]

First of all I would point out that exact value of a function and the limit of the function in that point do not necessarily coincide. For instance, it is often assumed that $0^0=1$ even though the ...

**0**

votes

**0**answers

51 views

### Reference : Special case of Banach-valued function integration by parts

Let $u \in L^p (0,T; L^1(\Omega))$ with $\partial_t u \in L^p(0,T; L^1(\Omega))$ and $v \in L^q (0,T; L^\infty(\Omega))$ with $\partial_t u \in L^q(0,T; L^\infty(\Omega))$ (with $1/p+1/q=1$ and $p \in ...

**3**

votes

**0**answers

62 views

### Is there an efficient way to visualize the bifurcation locus of this family of functions?

I have been trying to help out with this question from math.stackexchange. It concerns the family of functions:
$$f_\alpha(z,w) = \frac{\alpha + z}{1 + w}.$$
and an iteration scheme:
$$z_{n+1} = ...

**10**

votes

**0**answers

175 views

### Is every projective space curve a set-theoretic intersection of two surfaces? What is known about this question?

I am sorry if this question has been already asked, couldn't find anything similar myself. I have recently recalled this long standing open problem of whether every curve in $\mathbb{P}^3(\mathbb{C})$ ...

**0**

votes

**0**answers

49 views

### Extension of homomorphism to place in quotient field, or of local ring to valuation ring in quotient field

Let be given a domain $R$ (that can be supposed to be integrally closed if this can help), and $\varphi$ an homomorphism of $R$ into a field $F$.
$\varphi$ extends uniquely to a homomorphism ...

**1**

vote

**1**answer

130 views

### intuitive interpretation of analytic spread

I am studying analytic spreads from Bruns-Herzog's book. The definition is clear but calculation of the analytic spread of an ideal is hard for me in practice. I wonder if it is hard for you too.
...

**1**

vote

**1**answer

40 views

### Retractions and left-factoring morphisms

Let $\mathcal{C}$ be any category and let $A, B$ be objects.
A retraction is a morphism $r: A\to B$ such that there is $s:B\to A$ such that $r\circ s:B\to B$ is the identity.
A morphism $l: A\to B$ ...

**2**

votes

**0**answers

66 views

### What are interesting open problems in pseudo-differential operators?

May I ask what are some interesting open problems in the field of micro-local analysis (or classical analysis, semi-classical analysis, etc) using pseudo-differential operators? To my knowledge the ...

**1**

vote

**0**answers

53 views

### (Affine) Schemes and the point of view of morphisms with values in a field

Let $A$ be a commutative ring with unity. If $\varphi_1 : A \rightarrow K_1$ and $\varphi_2 : A \rightarrow K_2$ are ring morphisms from $A$ to fields, $\varphi_1$ and $\varphi_2$ are said to ...

**0**

votes

**0**answers

66 views

### sufficient condition of complete intersection [on hold]

According to Corollary 2.8 and the front part of Section 3 of this paper,
if $X:= Q_1\bigcap Q_2\bigcap Q_3\subset \mathbb{P} _{\mathbb{C}}^{4}$ be a connected and purely $1$-dimensional intersection ...

**-4**

votes

**0**answers

59 views

### Flow in graph. Proof [closed]

Let $(S_1, \overline{S_1} ) , (S_2, \overline{S_2} )$ be minimum cuts in some network. Is it true that $(S_1 \cap S_2, \overline{S_1 \cap S_2)}$ is a minimum cut in this network?

**-4**

votes

**0**answers

109 views

### show that L(X,Y)banach then Y banach

Let {Xα}α∈A be a collection of Banach spaces. It is easy to show that P={(xα):supα∥xα∥<∞} with ∥(xα)∥=supα∥xα∥ is a banach space.
If the indexing set A is finite, then it is easy to show that P ...

**1**

vote

**1**answer

73 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

113 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

75 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

28 views

### Writing an integral for a bounded volume [closed]

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

734 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

281 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

147 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
...

**15**

votes

**2**answers

328 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

39 views

### Gaussian Elimination for Orthogonal groups [closed]

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

89 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

57 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

227 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 ...

**6**

votes

**1**answer

192 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

74 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

82 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

55 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

446 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

17 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

155 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 ...

**6**

votes

**1**answer

178 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

86 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

90 views

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

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

317 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

87 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

85 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

124 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

158 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

306 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

80 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

49 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 [closed]

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