# All Questions

2 views

### Comparison inequalities for Hamiltonian mechanics with convex potential - analogue to Rauch's theorem?

I'm asking about an area (Hamiltonian mechanics) that I don't know at all well; thus, I keep the question somewhat vague. In differential geometry, there are a number of results saying that geodesics ...
10 views

### The composition of a dissipative operator and a positive operator is dissipative?

Consider the following bilinear system on a open and bounded domain $\Omega$ \left\{\begin{array}{r c l} \displaystyle\frac{dy(t)}{dt} &=& Ay(t)+u(t)By(t)\\ y(0) &...
15 views

### Old question : What would be the group $G$ (with $Γ_1$, $Γ_2$) with the bijection $v$?

The question What would be the group $G$ (with $\Gamma_1$, $\Gamma_2$) with the bijection $v$? doesn't have been answered. It should be interesting to get an answer to this answer. Could anyone be ...
9 views

### Non-lattice Veech groups

I was thinking of Veech surfaces, which are translation surfaces whose stabilizer under the $\mathrm{Sl}_2(\mathbb{R})$ action is a lattice in $\mathrm{Sl}_2(\mathbb{R})$. They seem to have been ...
26 views

### Montgomery-Odlyzko and Riemann conjecture

If the Montgomery-Odlyzko law is solved, does it follow the Riemann conjecture? I think the Montgomery-Odlyzko law know well about the distribution of primes.
34 views

### Hodge conjecture for étale cohomology

It is known that Hodge conjecture is true for étale cohomology for field $k$ in characteristic zero. It means that the following pairing $$(x,y)\mapsto (-1)^{i}\langle L^{r-2i}(x),y\rangle$$ is ...
10 views

### $L^\infty(\Omega)$-regularity for strongly damped wave equation

I am interested in the following IBVP for the strongly damped wave equation: u_{tt}-c^2\Delta u-b\Delta u_t+eu_t=f(x,t) \quad \text{in} \ \Omega \times (0,T), \\ u=0 \quad \text{on} \ ...
7 views

### Matrix minimization

Is there an explicit solution to the problem of minimizing $||X-X_0||_F^2+||X^{-1}-Y_0||^2_F$, with respect to matrix X, where $X_0$ and $Y_0$ are given, and all matrices are real $n\times n$ and ...
13 views

18 views

### Projectively equivalent toric varieties

Say I have two normal lattice polytopes $P$ and $Q$ in $\mathbb{R}^n$ (lattice $\mathbb{Z}^n$) with the same number of lattice points $N+1$. Then they define two toric varieties $X_P$ and $X_Q$ which ...
22 views

### Limit of stochastic subsequence of stationary ergodic sequence

Let $\{X_k\}_{k\in\mathbb{N}}$ be a stationary ergodic sequence on a probability space $(\Omega,\mathcal{F},P)$ with shift $T$. Also, let $\{v_k\}_{k\in\mathbb{N}}$ be a sequence of random variables ...
7 views

49 views

### Advice on Family Index theorem [on hold]

I am reading Bismut's paper Family Index and Heat equation, but I have knowledge on the probability or stochastic. Could anyone give some advice or introduce some ref. on probability to understand ...
149 views

### Fermionic Wick Theorem

Assume we are given are fermionic many-particle system with creation operators $c_1^\dagger,c_2^\dagger,...$ acting on some Hilbert space $\mathcal{H}$. That is, the $c_i^\dagger$ and their ...
54 views

### An inequality in product space $V$ conjecture [on hold]

I found an inequality as following: Let $x, y, z$ be three complex numbers then: \begin{equation*} \frac{1}{2}(|y+z-x|+|x+z-y| + |y+x-z|) \le |x| + |y|+|z|+\frac{1}{2}|x+y+z| \end{equation*} (1) The ...
36 views

### Fourier transform of complex functions [on hold]

I want to know what is the meaning of Fourier transform for a complex function, say function $F:\mathbb C \to \mathbb C$? Up to my knowledge, Fourier transform is defined for real-valued or complex-...
43 views

### On the symmetricity of the Riemann zeta function [on hold]

Yesterday, i stumbled upon something quite interesting about the Riemann zeta function, and i posted it on MSE. However, i could not get a conclusive response, hence i decided to post it here, though ...
26 views

### Reference Request: “Resolutions” of $K_n$ for $n$ odd

A resolution (in the combinatorial design sense) of $K_{n}$ is a collection of sets of edges of $K_{n}$ so that within each set of edges, each vertex appears once, and over the entire collection, each ...
18 views

### Counting different residue classes of certain form modulo $4n-1$?

I like to calculate number of different residue classes of the form $b^2c$ modulo $4abc-1$, where $a,b,c$ are positive integers and $\gcd(a,b)=1$. I could prove that if $abc$ is prime there are only 3 ...
40 views

### An $n$-gon is isospectral to a regular $n$-gon

If an $n$-gon $P$ is isospectral to a regular $n$-gon $Q$, what could we say about the shape of the $P$. Otherwise, what could we say about $Q$? In fact, some hints or simply some ideas should be ...
71 views

### construction of the group $O(2,1)$ [on hold]

I am reading a paper "Proper actions and Pseudo-Riemannian space forms" by R. Kulkarni, and I am interested are there any references/papers which decribe the construction of the group $O(2,1)$ ...
65 views

### Polish Group Topologies on PSL(2,C)

Does anyone know how many Polish group topologies (or where to begin to look for this information) can be put on $\text{PSL}_2(\mathbb C)$?
49 views

### Embedding of Gorenstein orbifold as a hypersurface

I am trying to understand if three complex dimensional orbifold singularity $\mathbb{C}^3 / \Gamma$ can be embedded as hypersurface in $\mathbb{C}^4$. The condition of being Gorenstein and having ...
54 views

### Is every regular Borel outer measure topologically additive?

If $m$ is a regular Borel outer measure is it true that $m$ is topologically additive? If so what is a proof or a counterexample? Definitions: Topologically Additive: $X$ is a topological space, $m$ ...
48 views

### Simplicial Model Categories

Let $D$ be a combinatorial simplicial model category (e.g $SSet$ with the standard model structure) and let $C$ be a small simplicial category. Of course, we can consider the projective model ...
168 views

### Need help with paper written in Russian… Yorgov's paper on self-dual codes with automorphisms of odd order

I came across this paper by V.I.Yorgov named "Binary self-dual codes with automorphisms of odd order". (Actually I was first reading another paper by Borello that cited this paper. It later become ...