1
vote
0answers
42 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 ...
0
votes
0answers
3 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 ...
-8
votes
0answers
13 views

who give best web responsive design service?

Have you seen your website on a laptop, iPad, or smartphone? How does it look? Is it hard to read? If so, that means your design is not “responsive.” When a design is responsive, it means it ...
1
vote
1answer
22 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
29 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 ...
4
votes
0answers
76 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 $B_{dR}^+$ ...
4
votes
1answer
80 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 ...
1
vote
0answers
6 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 ...
1
vote
3answers
83 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 $\delta(G)\leq\eta(G)$?
0
votes
1answer
23 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, ...
4
votes
1answer
46 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 ...
5
votes
0answers
45 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
22 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
32 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 ...
11
votes
0answers
107 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 ...
24
votes
2answers
2k views

Why is this new result such a big deal?

This popular article reports a recent result in reverse mathematics, showing that a certain theorem in Ramsey theory is provable from RCA$_0$, the base theory in SOSOA. Then there are a bunch of ...
2
votes
1answer
86 views

(quasi)metric on Riemannian manifolds via Brownian Motion?

Given points $a$ and $b$ on a Riemannian manifold $M$, I would like a (quasi)metric that corresponds to the average commute time from $a$ to $b$ under Brownian Motion (or rather, to $\epsilon$-ball $B ...
0
votes
0answers
48 views

How to find a basis of weight vectors? [on hold]

I have to following Lie Algebra $L=\{x\in End(\mathbb{C}^6)\colon x^tS+Sx=0\}$, where $S=[\begin{smallmatrix} 0&I_3 \\ I_3&0 \end{smallmatrix}]$, and the subalgebra $H$ given by the diagonal ...
-1
votes
0answers
247 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 ...
3
votes
1answer
151 views

Divisibility of Dirichlet L-functions

Let $k$ be an even integer and $p$ a prime number such that $p-1|k$. Suppose that $p$ does not divide $L(1-k,\chi)$ and $L(1-k,\psi)$, where $\chi$ and $\psi$ are quadratic characters. Can we deduce ...
1
vote
1answer
161 views

Density of Sophie Germain $3\bmod 4$ primes

Is there any reason to expect the density of primes $p$ such that $2p+1$ is also a prime where $p=3\bmod4$ holds would be different from case of $p=1\bmod4$? What if $2p+1$ is replaced by $2p-1$ and ...
0
votes
0answers
29 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 ...
2
votes
1answer
124 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 ...
2
votes
0answers
89 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 ...
1
vote
1answer
106 views

projectivity with assumption of big and semi-amplness

Let $X$ be a compact Kaehler manifold with $D$ be an effective divisor on $X$ such that $K_X+D$ is semi-ample and big then $X$ is projective?
-6
votes
0answers
22 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
2
votes
0answers
26 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 ...
1
vote
1answer
141 views

s(n) = kn or s(n) = n/k? [on hold]

This is not an important question, just for fun. Definition: $\sigma (n)$ = sum of the positive divisors of $n$. $s(n)$ = sum of the proper positive divisors of $n$. For $s(n) = kn$ , where $k$ ...
0
votes
0answers
36 views

SVD alternatives for symmetric matrices

Given any symmetric real valued matrix $A \in \mathbb{R}^{n\times n}$, I can decompose $A$ as the product of two complex matrices $$ A = E'E $$ Practically this can be done easily using SVD ...
-4
votes
0answers
29 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): ...
-1
votes
1answer
48 views

Hadwiger number of total graph

Let $G=(V,E)$ be a finite, simple, undirected graph, and let $T(G)$ be its total graph. The Hadwiger number $\eta(G)$ is the maximum $n\in\mathbb{N}$ such that $K_n$ is a minor of $G$. Is there an ...
7
votes
0answers
70 views

What are the indecomposable $U_q\mathfrak g$-modules?

Let $\mathfrak g=\mathfrak{sl}(2)$. Let $\zeta$ be a primitive root of unity of even order. Say $\zeta=e^{2\pi i/6}$, for concreteness. Let $U_q\mathfrak g$ be Lusztig's integral form of the ...
3
votes
0answers
40 views

Correspondence between dual center and linear characters of finite reductive group

Let $(G,F)$ be a connected reductive group defined over $\mathbb{F}_q$ via the Frobenius $F$ and let $(G^*,F^*)$ be a group in duality with $(G,F)$ with respect to rational maximal tori $T \subseteq ...
0
votes
0answers
24 views

Mixed PDE/finite difference equation

I have the following mixed pde/finite-difference equation for $f(t,x,y)$: $a x^2 f_{xx} + bxf_x + f_t - bxy + c\sinh(d\delta) = 0$ subject to $f(T,x,y)=0$, $x>0,\ t\geq 0,\ y\in\mathbb Z$, ...
1
vote
0answers
80 views

Presentation of hyperbolic groups [on hold]

Is it true that all hyperbolic groups are finitely presented? If yes, what is the right reference for that?
9
votes
0answers
234 views

What's wrong with Advanced Studies in Contemporary Mathematics (Kyungshang)?

By some reason the Journal mentioned in the title is no longer covered by the AMS Math. Reviews. On the MathSciNet web page it says: Last Issue: 24, no. 1  2014 Indexed cover-to-cover Status: No ...
-2
votes
0answers
21 views

Cumulative distribution function and sum of random variables [on hold]

For two continuous (iid) random variables $X$ and $Y$, we have (ref): $$ \mathbb{P}(X+Y \le a) =\int_{-\infty}^\infty \int_{-\infty}^{c-x} \big ( f(x,y) dy \big ) dx$$ with $f$ being the joint density ...
2
votes
0answers
38 views

How are $\alpha$ and $f(\alpha)$ obtained from the calculated values of $h(q)$ in the Multifractal analysis? [on hold]

In most papers they mention some kind of Legendre transform but I'm not entirely clear about the process, sine they don't mention enough details, at least for me, I tried reading the cited references ...
-5
votes
0answers
35 views

Homomorphism, Group Theory [on hold]

Let G=Z4, the group of integers modulo 4, and let H be the Klein four group, let f: G->H be a homomorphism. Why does the kernel of f must contain the element of 2 of G?
2
votes
0answers
19 views

Multivariable Weighted shift and subnormality

I have asked this question in mathstackexchange but didn't get any answer. I hope, I will get my answer here. Let $\mathbb B^m$ denote the Euclidean ball in $\mathbb C^m.$ Does there exist a ...
0
votes
1answer
78 views

Convergence of unitary products on a Hilbert space

First: I'm sorry for the basic question--I can move it to Math SE if necessary... Let $X$ be a Hilbert space and suppose $\{U_k\}_k$ is a sequence of unitary operators on $X$. Let $||\cdot||$ be the ...
10
votes
1answer
225 views

List of Applications of the $\partial\overline{\partial}$-lemma

Quoting from Huybrecht's book Complex Geometry on the $\partial\overline{\partial}$-lemma for Kaehler manifolds: Although it looks like a rather innocent technical statement, it is crucial for ...
1
vote
1answer
156 views

Free Symmetric Operads and $\mathbb{S}$-modules

In the definition of operads, if we restrict our attention to $\mathbb{S}$-modules where the action by the symmetric groups is free, then the free operads have still an underling free ...
6
votes
2answers
177 views

Can a nowhere differentiable function preserve measurability?

I want to know whether a continuous nowhere differentiable function $f: \mathbf{R} \to \mathbf{R}$ can map Lebesgue measurable sets to Lebesgue measurable sets. More generally I'm interested to know ...
0
votes
0answers
67 views

Mean curvature and submanifold

Consider $S^{N-1}$ the unit sphere and let us focus our attention on the cap $$ G=S^{N-1}\cap\{x_N>0\} $$ with boundary $\partial G= S^{N-2}\times\{0\}$: it is quite obvious to see that $G$ is a ...
11
votes
1answer
200 views

Digital physics and “Gandy-like” machines

Various physicists, famously John Wheeler, have asserted that physical information is the central object of study in physics, in the sense that an object or concept is "physically meaningful" if it ...
-1
votes
1answer
42 views

Is every implicit function reparametrized? [on hold]

Consider a continously differentiable non-constant function $f:\mathbb{R}^2\to\mathbb{R}$. Define $$ K=\{x\in\mathbb{R}^2|f(x)=0\}. $$ I wish to know whether there is a continuously differentiable ...
2
votes
1answer
125 views

Ask for a special function related to the error function

I am wondering whether anyone knows the following integration has a named special function or a reference $$ F_{a,b}(z) :=\frac{2}{\sqrt{\pi}} \int_0^z \text{erf}(a+b y)\: e^{-y^2} \text{d}y $$ for ...
2
votes
0answers
94 views

Can we solve the FGF problem by finding an appropriate action?

If we can find an action of the free group $\mathbb{F}_2$ on a measure space $X$ such that the crossed product $M=L^∞(X)⋊\mathbb{F}_2$ is a ${\rm III}_1$ factor with core isomorphic to ...
2
votes
0answers
23 views

Points of continuity of a lower semicontinuous function have non empty interior

Let $X\subset \mathbb R^d$ having non empty interior and let $f:X\to\mathbb{R}$ be lower semicontinuous. I know that the set of discontinuities of such a function is contained in a meager set, and ...

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