# All Questions

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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 $B_{dR}^+$ ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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?
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### 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
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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 $$TM = E^{s} \oplus E^{c} \oplus ... 1answer 141 views ### s(n) = kn or s(n) = n/k? [on hold] This is not an important question, just for fun. Definition: \sigma (n) = sum of the positive divisors of n. s(n) = sum of the proper positive divisors of n. For s(n) = kn , where k ... 0answers 36 views ### SVD alternatives for symmetric matrices Given any symmetric real valued matrix A \in \mathbb{R}^{n\times n}, I can decompose A as the product of two complex matrices$$ A = E'E $$Practically this can be done easily using SVD ... 0answers 29 views ### finding eigenvector [on hold] I have where λ1 = λ2 = 6 and λ2 = λ3 = 0. I wish to find the eigenvectors for these eigenvalues above. I've tried to turn it into equations and trying to solve them (this is for λ1 & λ2): ... 1answer 48 views ### Hadwiger number of total graph Let G=(V,E) be a finite, simple, undirected graph, and let T(G) be its total graph. The Hadwiger number \eta(G) is the maximum n\in\mathbb{N} such that K_n is a minor of G. Is there an ... 0answers 70 views ### What are the indecomposable U_q\mathfrak g-modules? Let \mathfrak g=\mathfrak{sl}(2). Let \zeta be a primitive root of unity of even order. Say \zeta=e^{2\pi i/6}, for concreteness. Let U_q\mathfrak g be Lusztig's integral form of the ... 0answers 40 views ### Correspondence between dual center and linear characters of finite reductive group Let (G,F) be a connected reductive group defined over \mathbb{F}_q via the Frobenius F and let (G^*,F^*) be a group in duality with (G,F) with respect to rational maximal tori T \subseteq ... 0answers 24 views ### Mixed PDE/finite difference equation I have the following mixed pde/finite-difference equation for f(t,x,y): a x^2 f_{xx} + bxf_x + f_t - bxy + c\sinh(d\delta) = 0 subject to f(T,x,y)=0, x>0,\ t\geq 0,\ y\in\mathbb Z, ... 0answers 80 views ### Presentation of hyperbolic groups [on hold] Is it true that all hyperbolic groups are finitely presented? If yes, what is the right reference for that? 0answers 234 views ### What's wrong with Advanced Studies in Contemporary Mathematics (Kyungshang)? By some reason the Journal mentioned in the title is no longer covered by the AMS Math. Reviews. On the MathSciNet web page it says: Last Issue: 24, no. 1 2014 Indexed cover-to-cover Status: No ... 0answers 21 views ### Cumulative distribution function and sum of random variables [on hold] For two continuous (iid) random variables X and Y, we have (ref):$$ \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 ... 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 ... 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? 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 ... 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 ... 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 ... 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 ... 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 ... 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\} $$with boundary \partial G= S^{N-2}\times\{0\}: it is quite obvious to see that G is a ... 1answer 200 views ### Digital physics and “Gandy-like” machines Various physicists, famously John Wheeler, have asserted that physical information is the central object of study in physics, in the sense that an object or concept is "physically meaningful" if it ... 1answer 42 views ### Is every implicit function reparametrized? [on hold] Consider a continously differentiable non-constant function f:\mathbb{R}^2\to\mathbb{R}. Define$$ K=\{x\in\mathbb{R}^2|f(x)=0\}. $$I wish to know whether there is a continuously differentiable ... 1answer 125 views ### Ask for a special function related to the error function I am wondering whether anyone knows the following integration has a named special function or a reference$$ F_{a,b}(z) :=\frac{2}{\sqrt{\pi}} \int_0^z \text{erf}(a+b y)\: e^{-y^2} \text{d}y  for ...
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 ...
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 ...