# All Questions

**2**

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16 views

### Cohen's model yet again

It has been discussed already whether a countable OD set necessarily contains an OD element. See e.g.
A question about ordinal definable real numbers
.
A negative answer was obtained in Archive for ...

**1**

vote

**1**answer

33 views

### A generalization of Erdős–Mordell inequality

I proposed my conjecture generalization of Erdős–Mordell inequality as following:
Let $A_1A_2....A_n$ be a polygon in a plane, $P$ be the point on the plane. Let $d_i$ be the distances from $P$ to $...

**0**

votes

**0**answers

10 views

### Hyperbola application [on hold]

A curved mirror is placed in a store for a wide angle view of the room. the right hand branch of x squared over one minus y squared over three equals one models the curvature of the mirror. a small ...

**0**

votes

**0**answers

9 views

### Algorithm for Longest Common Subtour

For a new kind of heuristic for the TSP I need to calculate the longest subtour, that is common to a set $T_1,\ ...,\ T_m$ of tours, that are "good" approximations of the optimal tour $T_{opt}$.
By a ...

**0**

votes

**0**answers

35 views

### Is (+, *) the only semiring over the positive reals? [on hold]

I know that there are others over the reals but I can't find any others over the positive reals.

**0**

votes

**0**answers

23 views

### How many number of finite points exists inside the circle?

I am doing project on Image processing dealing with circular images. So I need an approximate number of pixels present inside circle image of radius R and Circle center of (x,y). Please give me the ...

**0**

votes

**2**answers

26 views

### Computing canonical forms from orbit partitions

Suppose we know the orbit partition of the vertices of a graph (due to the action of its automorphism group). Is it easy (as in "polynomial time") to generate a canonical form for that graph using its ...

**0**

votes

**0**answers

8 views

### Proving that an integral of several cdf and pdf functions is increasing in a certain parameter

Basic assumptions: $n\geq3$, $a\leq b\leq c$, $b$ is simply a dummy
variable of integration, and $\rho\geq0$. $F(z)$ and $f(z)$ represent the
usual general CDF and PDF (no specified distribution here)....

**1**

vote

**0**answers

31 views

### Gauge Fixing Problem on Cylindrical

For Cylindrical $Y\times\mathbb R$, where $Y$ is a closed oriented 3-manifold.
Fix a Line bundle $L\to Y\times \mathbb R$ and a Hermitian connection $A_0$, we know that all other Hermtian ...

**3**

votes

**0**answers

25 views

### Intersection multiplicity of limit linear spaces

Let $X\subset\mathbb{P}^N$ be a smooth projective variety. Let us fix a general point $q \in X$, and let $C\subseteq X$ be a smooth curve passing through $q$.
Now let $\Lambda_{\xi, q}$, with $\xi \...

**1**

vote

**0**answers

56 views

### The current status of the conjecture on algebraic matroids

Can anyone point out some articles for the conjecture: the dual of an algebraic matroid is algebraic?
Thank you!

**0**

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**0**answers

17 views

### On balanced bipartite graphs

Of the $2^{n^2}$ balanced bipartite graphs on $2n$ vertices how many of them have $i$ perfect matchings where $i\in\Bbb N\cup\{0\}$ and $0\leq i\leq n!$ holds?

**1**

vote

**0**answers

31 views

### A priori estimates for elliptic operators

Suppose $L : L^{m,p}(M)\rightarrow L^p(M)$ is some elliptic operator of order $m$, and $(M,g)$ is a compact Riemannian manifold. Then it is known that there exists a constant $C$ such that we have the ...

**14**

votes

**0**answers

138 views

### Applications of arithmetic topology to number theory

There is a well-known analogy between 3-manifolds and number fields, with prime ideals corresponding to knots. Are there any results in number theory that have been proven using topology through this ...

**0**

votes

**0**answers

20 views

### Sums of unit vectors has a binary span after constrained permutations

Let $e_1 = (1,0,\ldots,0), \ldots , e_{m_1+m_2} = (0,\ldots,0,1)$ be the unit vectors of the standard basis $E$ of $\mathbb{R}^{m_1+m_2}$.
An enumeration $ E \cup -E = \{f_1, \ldots, f_{2(m_1+m_2)}\}...

**1**

vote

**0**answers

66 views

### A Combinatorial Game: the Snake and the Hunter

The Snake and the Hunter is a game for two players who play in two rounds interchanging the roles of snake and hunter. The game is played in a rectangular grid of points, say $6 \times 6$. In both ...

**0**

votes

**0**answers

61 views

### Selmer and free rank of Elliptic Curves

If I am not mistaken, the equality of the $p$-Selmer rank and the free rank of an elliptic curve are conjectured to be equal.
This is one of the many equivalent formulations of the Birch and ...

**3**

votes

**1**answer

50 views

### Isoperimetric inequality via Crofton's formula

I have seen various assertions that one can derive the isoperimetric inequality in the plane from Crofton's formula in geometric probability. Unfortunately, I have not managed to figure out such a ...

**3**

votes

**1**answer

52 views

### Lie subalgebra of $\chi^{\infty}(M)$ of codimension one

Assume that $M$ is a manifold.Is there a Lie subalgebra of $\chi^{\infty}(M)$, the space of smooth vector fields on $M$, whose codimension is equal to one?

**0**

votes

**2**answers

95 views

### number of partitions from 0 to n^2

You are given the numbers 0 to n^2. You must use n numbers with no number greater than n to form all the partitions of the numbers 0 to n^2. For example with n=4 you want to find the partitions of 7:...

**0**

votes

**0**answers

25 views

### Non symmetric, zero column sum, positive diagonal and negative off diagonal entries matrix bound?

Under which conditions can the A-inner product of a non symmetric, zero column sum, positive diagonal and negative off diagonal entries matrix be bounded by the L2-inner product?
$A \in \mathbb{R}^{n ...

**-2**

votes

**1**answer

123 views

### Does one need an external, peer-reviewed grant to become tenured faculty in this field? [on hold]

As a secondary question, how important is it to be awarded grants to remain employed as a PhD mathematician at an academic research institution? Is it common or uncommon for PhD mathematicians to have ...

**2**

votes

**0**answers

46 views

### Kahler Einstein metric with minimal singularities

Let $X$ be a Kahler variety with snc divisor $D$ such that $K_X+D$ is
ample. then there is a Kahler metric $\omega_E$ such that
$Ric(\omega_E)=-\omega_E$ on $E=X\setminus D$, then
$h=\frac{1}{\...

**2**

votes

**1**answer

90 views

### Elements in the group von Neumann algebra which are not summable

Let $G$ be a discrete group. I am wondering if there is a recipe which can be applied to find elements in the group von Neumann algebra which are not absolutely summable, i.e. $T \in VN(G)$ while $T \...

**0**

votes

**1**answer

34 views

### Count Functional digraph

Given a set of nodes, how can I count the number of different functional digraph containing a specific number of connected components? With a restriction that no node can have an edge point to itself. ...

**1**

vote

**0**answers

30 views

### Finding the analytic Zariski decomposition singular hermitian metric on a relative line bundle

Let $f:X\to S$ be a proper surjective projective morphism between complex manifolds with connected fibers and let $D$ be an effective $\mathbb Q$-divisor on $X$ such that
$$S^°=\{s\in S| f\text{ is ...

**5**

votes

**1**answer

117 views

### How to compute $[CP^2, G/PL]$?

Let $E^4$ be the two stage Postnikov space appearing in the homotopy type of the classifying space $G/PL$. One of its properties is that it only has two nontrivial homotopy groups $\pi_2(E)=Z/2Z$ and $...

**1**

vote

**0**answers

42 views

### Gauss Bonnett on a flat surface with border

I'm reading the article "Euler Characteristics of Teichmuller Curves in genus two" by Matt Bainbridge and there's a point I don't understand in the proof of theorem 5.5. Maybe you can help me clarify ...

**2**

votes

**0**answers

53 views

### Some queries on Moduli Space of Parabolic Vector Bundles on curve

In "Moduli of Vector Bundles on curves with Parabolic Structures"-Bulletin of the American Mathematical Society Volume 83, Number 1, January 1977 the author announces the following result on moduli ...

**2**

votes

**1**answer

55 views

### Are all zeros of $\dfrac{\Gamma'}{\Gamma^2}(s) \pm \dfrac{\Gamma'}{\Gamma^2}(1-s)$ either real or on the line with $\Re(s)=\frac12$?

In this post it was proven that, except for a finite few, all zeros of $\Gamma(s) \pm \Gamma(1-s)$ are either real or reside on the line $\Re(s)=\frac12$.
I have been searching for similar reflexive $...

**1**

vote

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31 views

### Singular canonical hermitian metric

Let $M$ be a complex manifold , take
$$K_{M,m}:=\sup \{|\sigma|^{\frac{2}{m}}; \sigma\in H^0(M,\mathcal O_M(mK_M)), |\int_M(\sigma\wedge\bar\sigma)^{\frac{1}{m}}|\leq 1\}$$
Let $$K_{M,\infty}:=\lim\...

**0**

votes

**0**answers

41 views

### What is combinatorially possible, for a singular minimal surface in $\mathbf{R}^3$?

A cubic planar graph gives a cell decomposition of a two-sphere, whose dual complex is a triangulation. If I understand Plateau's laws here, a soap film gives a cell decomposition whose dual complex ...

**-2**

votes

**0**answers

21 views

### weighted restricted integer compositions and extended binomial coefficients [on hold]

proof of
d_{S,f}(n,k) = \binom{k}{n}{(f(s)){s\in S}}

**4**

votes

**1**answer

94 views

### Stopping times for Brownian motion

Let $B_t, t\geq 0$ be standard Brownian motion.
Let $\big(\mathcal{G}_t, t\geq 0\big)$ be the natural filtration, defined by $\mathcal{G}_t=\sigma(B_s, 0\leq s\leq t)$.
Define also a filtration $\...

**0**

votes

**0**answers

37 views

### How to build C-Corn for Coq from source? [on hold]

Trying to install C-Corn via opam install. The problem is that since two weeks I do not see any progress, I see only Processing: make .
I have i7 , 8 GB RAM.
Is that normal or has something gone ...

**6**

votes

**2**answers

248 views

### Simple proof for $\sum_{i=1}^{n} a^{gcd(i,n)} $ is divisible by n

Burnside's Lemma Deduce That:
$$\sum_{i=1}^{n} a^{gcd(i,n)} $$
is divisible by n
it's a beautiful result. but i want to prove it without any abstract algebraic tools such as Burnside's Lemma...
is ...

**1**

vote

**1**answer

103 views

### Affine open subsets for algebraic group actions

Let $G$ be a reductive algebraic group over an algebraically closed field $K$ of characteristic zero.
Assume that $G$ acts on an affine variety $X$. Assume that $X$ contains an open orbit $U$ (so $\...

**0**

votes

**0**answers

20 views

### A specific spanning property of a family of vectors

Let $v_2, v_2, v_3, \dots$ be a family of vectors in $\mathbb R^n$ that span $\mathbb R^n$. Given this family, define the family of vectors
\begin{align*}
\begin{pmatrix} v_1 \\ \alpha_1 v_1 \end{...

**0**

votes

**1**answer

61 views

### Heat kernel upper bounds on a complete Riemannian manifold

Let $M$ be a complete Riemannian manifold, and $p(t, x, y)$ denotes its heat kernel. I am trying to find sufficient conditions for when the following holds:
$$ p(t, x, y) \leq Ct^{-n/2}, \forall x, y, ...

**0**

votes

**0**answers

24 views

### Evaluation modules of $U_q(L(sl_2))$

Let $a \in \mathbb{C}^{\times}$, $r \in N$. Let $W = V_q(r)$ be the $r$-dimensional irreducible type 1 representation of $U_q(gl_2(\mathbb{C}))$. In the usual basis $\{v_0, \ldots, v_r\}$, the action ...

**0**

votes

**0**answers

35 views

### $L^\infty$-contractive semigroups

Let $L^\infty(\mathbb T)$ be the space of $2\pi$-periodic and bounded measurable functions
and $\mathcal P$ be a pseudo-differential operator defined on
$\mathcal D(\mathcal P)\subset L^\infty(\...

**3**

votes

**0**answers

73 views

### Curves embedding in plane

Given two closed simple(no self-intersection point) curves $C_1,C_2$ in the plane $\mathbb R^2$, is there a good way to judge whether one curve could be embedded inside into the other one, here ...

**1**

vote

**1**answer

88 views

### a space isomorphic to $S^{p+q}$

I've asked this question few days ago in MathStackExchange, but there was no result. So, I decided to ask it there.
In one of the paper I have met that
$$\mathbb{S}^{p+q} \cong \mathbb{S}^p \times \...

**4**

votes

**1**answer

181 views

### Is the assignment of a root system to a complex semisimple Lie algebra functorial?

As described here, we have a category of root systems, where a morphism from a root system $\Phi$ in a Euclidean space $E$ to a root system $\Phi'$ in $E'$ is given by a linear map $f: E \to E'$ such ...

**0**

votes

**0**answers

35 views

### Is it possible for a quantum group algebra $U_{q}\left(\mathfrak{g}\right)$ to have a diagonal universal $R$-matrix?

I am writing a research paper and have shown that in the special case when a quantum group algebra $U_{q}\left(\mathfrak{g}\right)$ with the quantum group parameter $q$ not a root of unity has a ...

**1**

vote

**0**answers

32 views

### Concentration of functional of Gaussian random variable

Suppose I have two Gaussian distributions
$p(x) = \frac{1}{(2\pi)^{d/2}|\Sigma_p|^{1/2}}\exp(-\frac{1}{2}x^\top \Sigma_p^{-1} x)$ and $q(x) = \frac{1}{(2\pi)^{d/2}|\Sigma_q|^{1/2}}\exp(-\frac{1}{2}x^\...

**6**

votes

**1**answer

83 views

### Chevalley restriction theorem for non-split Cartan

Let $G$ be a reductive group over a field $k$ with maximal torus $H$. Let $\mathfrak{g}$ and $\mathfrak{h}$ denote the corresponding Lie algebra. If $k$ is algebraically closed, we have a theorem of ...

**2**

votes

**0**answers

42 views

### Average range of Motzkin path

Motzkin path are paths from (0,0) to (n,0) in $\mathbb{Z}^2$ such that we are allowed to move SE, E and NE.
More on this is here https://en.wikipedia.org/wiki/Motzkin_number
I would like to know if ...

**0**

votes

**0**answers

24 views

### Recast a finite-dimensional multiparameter SDE as an infinite dimensional SDE

In another question, I've asked how we can derive a stochastic Navier-Stokes equation under the assumption of perturbed particle trajectories.
More concretely, I want to obtain a SDE of type as ...

**8**

votes

**1**answer

182 views

### Groups whose word problem can be solved in constant time

Given a finitely generated group $G$, define an encoding of $G$ to be a one-to-one function $\Phi:G\to \bigcup_n \{0,1\}^n$ that sends each group element to a unique finite word. For $a,b\in G$, ...