0
votes
0answers
5 views

Techniques to solve a non linear differential equation related to curvature

Many years ago, I considered the following non linear differential equation: $y=y''.(1+y'^{2})^{-3/2}$ This equation expresses the equality between the value of a given function $y\in C^{2}(R)$ and ...
0
votes
0answers
7 views

Can the extragradient method be computed only based on proximal steps?

As we know, for solving saddle point problems, the forward-backward algorithm is generally not guaranteed to converge. But the extragradient method converges Structured Prediction via the ...
0
votes
0answers
16 views

System of diophantine equations with restricted set of solutions

I'm engineer, not mathematician, so excuse me for wrong terminology, but I hope you'll understand the problem. Example situation: I have N electronic components. Each of them has reactance and ...
1
vote
0answers
12 views

busby invariant of extensions of $C^*$-algebras

I have a question of an explicit example of a busby invariant of a extension, which can be found in Blackadars book "K-theory for Operator Algebras". Let $0\to B\to E\to A\to 0$ be a short exact ...
0
votes
1answer
90 views

What is the best currently proven bounds on prime gaps?

I did some digging around on the internet but I found tons of different equations on both lower and upper bounds for the largest possible prime gap g(n). I was wondering what are currently the best ...
-4
votes
0answers
18 views

Newton's second law [on hold]

enter image description here Which is the speed for x=4m? Given a mass equal to 3kg.
0
votes
0answers
36 views

Irreducible root system decomposition

I am looking for the name of and a good reference on the following theorem Theorem: let $G$ be a connected, compact and semisimple Lie group, and $T \subset G$ a maximal torus of $G$, there exists a ...
1
vote
0answers
25 views

Regularization by mean curvature flow

I have a $C^{1,\alpha}$ surface defined as the graph of some function $\varphi : B \to \Bbb{R}_+$ ($B$ is a ball). This surface has positive and bounded mean curvature in the weak sense (since the ...
-1
votes
0answers
71 views

Does an isogeny always define a covering map?

Consider a map $f: G_1 \to G_2$ between two topological groups. If $f$ is an isogeny when viewing $G_1,G_2$ as algebraic groups does $f$ always define a covering map when viewing $G_1,G_2$ as ...
2
votes
1answer
30 views

Operators on Hilbert $C^*$-module and families of Fredholm operators

If $A$ is a $C^*$-algebra, there is a notion of Hilbert $A$-module (which is something like Hilbert space but the inner product takes values in $A$). The standard example is ...
-4
votes
0answers
45 views

Sine, Cosine and Tangent functions [on hold]

Is the input of a Sine, Cosine and Tangent function always an angle?
0
votes
0answers
40 views

Algorithm for checking linear independence of algebraic numbers

Is there any if and only if condition for checking $Q$-linear independence of given a set of numbers say $\alpha_i$ ? More precisely how to check linear independence of given $n$ algebraic numbers ...
2
votes
0answers
45 views

Nonvanishing of the dual Euler totient on boolean intervals of finite groups

The rank $n$ boolean lattice $B_n$, is the subset lattice of $\{1,2, \dotsm n \}$. Let $[H,G]$ be a boolean interval of finite groups. Its Euler totient is defined by $$\varphi(H,G):=\sum_{K \in ...
2
votes
0answers
45 views

Wave trace on $\mathbb{S}^1$- $\langle w,\varphi\rangle=\int_{\mathbb{S}^ 1} (\sum_{k \geq 1} e^{it \sqrt{\lambda_k}}) \varphi(t) dt$ [on hold]

An exercise asks to find the wave trace $w(t)=\operatorname{tr} \left(e^{it \sqrt\Delta}\right)=\sum_{k \geq 1} e^{it \sqrt{\lambda_k}}$ as a distribution (or generalized function) of the Laplacian ...
2
votes
1answer
133 views

Does there exist a non-hyperelliptic Riemann surface with automorphism group $C_2\times A_4$?

Does there exist a non-hyperelliptic Riemann surface of genus 5 with automorphism group $C_2\times A_4$?
0
votes
0answers
18 views

LP or IP necessary? Network Flow Problem with no cycle-condition (unimodularity?) [on hold]

I need your help with a optimization problem. Recap: Normal mincost flow networks optimization problems have a constraint matrix which is total unimodular. This is a nice feature since a linear ...
0
votes
0answers
16 views

Optimal ordering in Jacobi SVD algorithm

In Jacobi SVD algorithm as given here every pair of columns of the matrix is orthogonalized until convergence. I want to know that how does the order of selection of the pair of columns affect the ...
1
vote
0answers
69 views

Is there a non-integer in the dimension spectrum for the Heisenberg group?

Let $\Gamma = \langle a,b,c \ | \ c=aba^{-1}b^{-1}, \ ac=ca, \ bc = cb \rangle$ be the discrete Heisenberg group. Let $\ell: \Gamma \to \mathbb{N} $ be the word length on $\Gamma$. This group has a ...
1
vote
0answers
52 views

Kunneth decomposition of the relative diagonal of a projective bundle

Let $\mathcal{E}$ be a projective bundle of rank $r$ over a smooth complex quasi projective variety $B$, and form its associated projective bundle $\chi :=\mathbb{P}(\mathcal{E})$. Let $\pi : \chi ...
-3
votes
0answers
36 views

Find function $h$ so that $h(U,V)$ equals density of $f(a)da$ for $f(a)=\frac{1}{2}e^{-\small|a|} ,a \in \mathbb R$ [on hold]

Let $f(a)=\frac{1}{2}e^{-\small|a|}$, $a \in \mathbb R$ and let $U,V$ be two independently uniformly distributed random variables on $[0,1]$. Now I want to find a function $h$ so that $h(U,V)$ is ...
2
votes
0answers
77 views

Semistability of a sheaf on nodal curve

Suppose $X$ is a projective, connected, nodal curve (can be reducible) over an algebraically closed field $k$ of arbitrary characteristic. Let $F$ be a pure sheaf on $X$ and denote by $\pi^{*}(F)$ its ...
-5
votes
0answers
34 views

Difficult derivative of the log of a function [on hold]

Can someone help me figure out how the derivative of log p(x) wrt. theta becomes to solution below ? $ -\frac{\delta logp(x)}{\delta \theta} = \frac{\delta F(x)}{\delta \theta } - \sum p(x) ...
3
votes
0answers
46 views

How many unimodular lattices does it take to fill a cube with high probability?

Consider $C_a$ in $\Bbb Z^n$ a cube of height $a$ at origin in positive coordinates with one corner at origin. Consider the set $M_c$ of all unimodular matrices in $\Bbb Z^{n\times n}$ with each ...
3
votes
0answers
36 views

Singular reduction in infinite dimension

In 1991, Sjamaar and Lerman [1] introduced the notion of stratified symplectic spaces. Namely, if $M$ is a symplectic manifold and $G$ a Lie group acting properly (but not necessarily freely) on $M$ ...
2
votes
0answers
33 views

Are Bipartite Matching and General Matching Really Different Problems?

Questions: Have there been attempts to either prove or disprove, that every general matching problem can be transformed into a bipartite matching problem, from whose solution the solution ...
0
votes
0answers
47 views

Reference request: Uniformly totally bounded classes of compact metric spaces are Gromov-Hausdorff precompact

The following Theorem can be found for instance here (Theorem 7.4.15): Theorem. (author ?) Any uniformly totally bounded class $\mathfrak X$ of compact metric spaces is pre-compact in the ...
6
votes
0answers
55 views

Determinants of octonionic hermitian matrices

For quaternionic hermitian matrices (i.e. quaternionic square matrices $(a_{ij})$ satisfying $a_{ji}=\bar a_{ij}$) there is a nice notion of (Moore) determinant which can be defined as follows. ...
0
votes
0answers
16 views

Lower bound for smallest eigenvalue of symmetric doubly-stochastic Metropolis-Hasting transition matrix

For my master's thesis research, I stumbled upon a question concerning the Metropolis-Hasting transition matrix $W$. Context $\quad$ Let me start with some context. I consider connected undirected ...
0
votes
0answers
69 views

Mathematical consulting or bioinformatics related careers for mathematicians with good statistics and coding experience in West Europe [on hold]

Before I start, apologies if the question is very specific, but these are exactly what I want to be. I should mention that I already studied: "Industry"/Government jobs for mathematicians ...
1
vote
0answers
19 views

A good version of truncated real radical ideal?

Suppose $\mathbb{R}[X]$ is the normal multivariate polynomial ring where $X = x_1...x_n$. $\mathbb{R}[X]_t$ is the truncated set such that $\mathbb{R}[X]_t =\left\{f: f \in \mathbb{R}[X], deg(f) \leq ...
0
votes
1answer
42 views

IFS maps on circle

A systems $<f_0,f_1>$ is minimal if the set $\{h(x): h=f_{i_n}\circ f_{i_{n-1}}\circ...\circ f_{i_1}, i_k \in \{0,1\},n>0\}$ is dense in $S^1$, for every $x\in S^1$. Consider $f:S^1 \to S^1, ...
1
vote
1answer
32 views

Maximizing joint entropy?

I'm stuck trying to find the maximum entropy probability distribution taking into account a joint distribution. Basically, I want to find the maximum entropy expression for $p(x,y)$ when the marginal ...
0
votes
0answers
50 views

Derandomizing AP existence in $A\subseteq \{1,\ldots,N\}$ for $\delta(A) \geq 1/k$

In the answer to the mathoverflow question here, it was established that if we let $p$ be the probability of including point $v$ in $A\subseteq \{1,\ldots,N\}$ and this is done independently for all ...
8
votes
0answers
90 views

Measuring the failure of pushforward to commute with Steenrod squares

Let $f \colon X \rightarrow Y$ be a map of topological spaces. Let's say that they are (closed) manifolds (not necessarily orientable), though to be honest I'm really interested in the more general ...
3
votes
0answers
31 views

Real interpolation of weighted Sobolev spaces with different weights

Let $\Omega \subseteq \mathbb{R}^n$ be open and let $w_0$ and $w_1$ be measurable and almost everywhere positive and finite functions defined on $\Omega$. Let $L^2_{w_0}(\Omega)$ be the weighted ...
1
vote
0answers
60 views

Decompositon of the Euler class in the ideal generated by Weyl-invariant polynomials

Let $G$ be a complex reductive Lie group, $B$ be a Borel subgroup, $T\subset B$ be a maximal torus, $W$ be the Weyl group. Then the space $X:=G/B$ is a complex manifold of dimension $n$, denote by ...
0
votes
0answers
47 views

Splitting of totally geodesic Riemannian foliations

Let $\mathcal F$ be a non-singular Riemannian foliation on $(M,g)$ whose leaves are totally geodesic. Suppose further that the leaves are Riemannian products of irreducible manifolds $L=L_0\times ...
5
votes
1answer
130 views

Bounding the degree of an algebraic extension containing solutions to polynomials

Also posted on math.stackexchange... Let $F$ be a field, and let $f_{1},\ldots, f_{s}$ be polynomials in $F[x_{1},\ldots, x_{t}]$. Assume that the degree of the polynomials is bounded by $d$, by ...
5
votes
1answer
91 views

Density of non-algebraic leaves in the characteristic foliation

Let $X$ be a compact complex manifold equipped with a holomorphic symplectic form $\omega$. Let $D$ be a smooth divisor on $X$. At each point of $D$, the restriction of $\omega$ to $D$ has ...
6
votes
0answers
146 views

Universal Property of Fontaine's Period Ring $B_{dR}^+$

In the introduction to his Asterisque Expose "Le Corps des Periodes p-Adiques", Fontaine announces a characterization of $B_{dR}^+$ by some universal property. Unfortunatly, at least for $B_{dR}^+$ ...
0
votes
0answers
33 views

On a count of certain number of primes in an interval

Fix a prime $p$, $\alpha\in(0,1)$ and $\beta\in(1,2)$ and let $\mathcal U$ be primes in $[p^\alpha,\beta p^\alpha]$ such that if $b\in\mathcal U$ and if $d$ is multiplicative inverse of $b$ in $\Bbb ...
1
vote
3answers
102 views

Hadwiger number and minimal degree

Suppose $G$ is a finite simple graph and $\eta(G)$ is the maximal $n\in\mathbb{N}$ such that $K_n$ is a minor of $G$. If $\delta(G)$ is the minimal degree, do we have $\delta(G)\leq\eta(G)$?
11
votes
0answers
137 views

Concept associated to the Eudoxus reals

I am aware of three different constructions of the field of real numbers : The Cauchy sequence construction : in this case, we see the field $\mathbb{Q}$ as a metric space and $\mathbb{R}$ is the ...
0
votes
0answers
271 views

Becoming a Mature Mathematician [on hold]

I am currently a sophomore in my undergraduate mathematics program. It has taken me a while to take school seriously; I was one of "those" students who just skated by without studying until Linear ...
2
votes
0answers
108 views

Are these moduli problems of curves “well-behaved”?

Let X be a smooth projective surface over $\mathbb C$, and let $d\geq 3$ be an integer. Suppose that all smooth hypersurfaces of degree $d$ are of genus $g\geq 2$. Let $H_{X,d}$ be the Hilbert scheme ...
-6
votes
0answers
25 views

applications that involves the Legendre Polynomials [on hold]

i am requested to make a basic research about the applications that involve the Legendre Polynomials.. thanks in advance
1
vote
1answer
152 views

harmonic analysis on $p$-adic $x^2 + y^2 + z^2 = 1$?

Are there p-adic analogues to spherical harmonics? In the case of $K = \mathbb{R}$, the spherical harmonics form a basis to $L^2 [SO(3)]$ where What happens in the $p$-adic case? Is there sphere ...
1
vote
0answers
15 views

History of the Vertex Disjoint Cycle Cover with Minimal Edgeweight Sum

Questions: who first posed the problem of determining a collection of (directed) cycles, whose edgeweight sum is minimal and, for which each vertex belongs to exactly one of the cycles? who came up ...
2
votes
0answers
32 views

If $f$ is dynamically coherent, is there a unique invariant foliation tangent to $E^{c}$?

Let $f$ be a diffeomorphism of a closed manifold $M$ such that $f$ is partially hyperbolic if the tanget bundle of $M$, $TM$ splits into three invariant sub-bunbles $$ TM = E^{s} \oplus E^{c} \oplus ...
-4
votes
0answers
32 views

finding eigenvector [on hold]

I have where λ1 = λ2 = 6 and λ2 = λ3 = 0. I wish to find the eigenvectors for these eigenvalues above. I've tried to turn it into equations and trying to solve them (this is for λ1 & λ2): ...

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