# All Questions

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### Weak topology and topology by semi-norm [on hold]

Wikipédia: -The weak topology on X is the initial topology with respect to X* (let's note it T') -If the field K has an absolute value , then the weak topology σ(X,F) is induced by the family of ...
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### State of the art in the theory of integer sequences

I was going through N.J.A. Sloane's 'Encyclopedia of Integer Sequences'. In it are discussed many tricks that are used to determine the recursive definition or explicit formula for a given sequence. ...
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### Strongly asymmetric graphs

Asymmetric graphs are graphs that have a trivial automorphism group $\textrm{Aut}(G)$, i.e. the only graph isomorphism from $G$ to itself is the identity. Let's call a graph $G$ strongly asymmetric ...
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### Continuity of a Functional

A certain functional $T$ is defined as: $$T(F)=\int_{(0,1)}F^{-1}(s)M(ds)$$ where $M$ is a probability measure with support $[\alpha,1-\alpha]$,for $\alpha>0$. The result that above functional is ...
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### Hausdorff topologies on Q

Is there any description known of the Hausdorff topologies on $\mathbb{Q}$ compatible with the group operations?
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### Rational curves and Serre's construction

Why rational curves, used in Serre's construction of vector bundles, usually corresponds to unstable bundle? I saw this affirmation in Richard Thomas's paper on an obstructed bundle on a CY threefold. ...
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### Examples of weird 'modular like mathematical space' that behaves like as if it is infinite until a threshold value is reached? [on hold]

(Might be a bit layman because I don't have rigorous math term to describe the concept) Generalize it to mathematical spaces, are there spaces which are sort of like a. Consists of multiple ...
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### Decidable theorem or result that is not weaker than Tarski's theorem

I am wondering what other decidable theorem or results that is not weaker or stronger than Tarski's theorem. Could any one give reference or a simple introduction about such result known in their ...
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### Schur's lemma for antiunitary operators on complex Hilbert spaces

Suppose to have a linear irreducible unitary representation $\rho:G\rightarrow U(H)$ on a complex Hilbert space $H$ with $G$ a generic group. Let $A$ be an $\textit{anti}$-linear operator such that ...
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### Expected value of minimum of an exponential function [on hold]

Find expected value of minimum of n random variables: x = (x1,x2,x3,..,xn) The distribution is an exponential function: ...
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### Continuous versions of tensors/ Tensors with infinite indices?

In linear algebra and general relativity, we knew that vectors can be represented by a linear combination of components and a basis $$\mathbf{V}=\sum_{i=1}^n A_i\mathbf{e_i}$$ Or in Einstein ...
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### decomposition of tempered distributions by entire analytic functions

Let $\phi$ be a $C^{\infty}$ function on $\mathbb R^{n}$ with $$\operatorname{supp} \phi \subset \{\xi \in \mathbb R^{n}: |\xi|\leq 2, \phi(\xi)=1~~\text{if}~|\xi|\leq 1\}$$ Let $j\in \mathbb N$ ...
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### infinitesimally commutative diagram [on hold]

Consider $f:X\rightarrow Y$, $g:Y\rightarrow Z$, $h:Y\rightarrow Z$ morphisms of intregal and separated $k$-schemes of finite type. We assume that at at point $x\in X$, $h(x)=g(f(x))$ the level of ...
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### Why is the finite extension field of the p-adic numbers $\mathbb{Q}_p$ spherically complete? [on hold]

Here by spherical completeness it is meant that given a non-empty nest of closed balls $\{B_\alpha|\alpha\in I\}$, that is, $\forall \alpha_1,\alpha_2\in I$ either $B_{\alpha_1}\subset B_{\alpha_2}$ ...
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### On a minimal algebraic number field which satisfies the principal ideal theorem

By an algebraic number field, we mean a finite extension field of the field of rational numbers. Let $k$ be an algebraic number field, we denote by $\mathcal{O}_k$ the ring of algebraic integers in ...
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### singular point of a complete intersection surface [migrated]

Let $S:= H_1\bigcap H_2\bigcap \cdots \bigcap H_N \subset\mathbb{P} _{\mathbb{C}}^{N+2}$ be a complete intersection surface, where each $H_i$ is a hypersurface defined by a homogeneous equation $f_i$. ...
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### Ezcontour in Matlab [on hold]

I am using ezcontour to plot an ellipse in matlab, but I would like to get only level 1 contour. How can I specify that I only want level 1 contour? I can't find anything about this in the ...
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### Is there an improvement for the Schur-Horn inequalities for positive semi-definite matrices?

By the Schur-Horn inequality I am thinking of the statement that for any Hermitian matrix $H$ its diagonal n-tuple $(H_{11},H_{22},..,H_{nn})$ for any choice of basis lies in the convex hull of the ...
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Let $F_q$ be a finite field with $q$ elements. Let $g$ be a multiplicative generator of $F_{q^2}^*$. It implies that $<g^{q+1}> = F_q^*$. Let $l$ be a prime greater than $q^2-1 ... 0answers 56 views ### “Semiclassical approximation” in random matrix theory I am reading Planar Diagrams by Brezin, Parisi, Itzykson and Zuber. If you specialize the discussion in section 5 there we seem to derive the eigenvalue distribution of$N \times N$random Hermitian ... 0answers 52 views ### Let Z be the set of integers, and consider the function f : Z → Z defined f(x) = 2x. Which of the following is correct? [on hold] a) f is invertible b) f is injective c) f is bijective d) f is surjective I put b, though apparently that's wrong. Thanks :) 0answers 61 views ### translation invariance of the Laughlin wave function This is a translation into math of the following question, posted on PhysicsOverflow. Let$H:=L^2(\mathbb C)$. For every$N$, let$\psi_N\in\Lambda^N H\cong (L^2(\mathbb C^N))^{S_N}$be the function ... 0answers 31 views ### Calculating Swaps and Swaptions [on hold] Hi all I have a problem when I have to calculate swaps/swaptions. n=10-period binomial model for the short-rate, ri,j. The lattice parameters are: r0,0=5%, u=1.1, d=0.9 and q=1−q=1/2. 1.Compute the ... 3answers 272 views ### Reference for a strong intermediate value theorem for measures Let$\mu$be a finite nonatomic measure on a measurable space$(X,\Sigma)$, and for simplicity assume that$\mu(X) = 1$. There is a well-known "intermediate value theorem" of Sierpiński that states ... 0answers 58 views ### On multilinear linear combinations [on hold] If$K$is algebraically closed field, then consider$m$multilinear polynomials$f_i$for$i=\{1,\dots,m\}$in$K[x_1,\dots,x_n]$of degree$d_i$each with no common root. We know there exists$g_i$... 1answer 275 views ### Free action of$\mathbb{Z}(2^{\infty})$on a compact space Assume that$X$is a Hausdorff compact space such that$\forall n\in \mathbb{N}$, we have a free action of$\mathbb{Z/{2^{n}}\mathbb{Z}}$on$X$. Must$\mathbb{Z}(2^{\infty})$act freely on ... 0answers 61 views ### Number of graphs with M edges that does not contain K-clique [on hold] If we consider the space of graphs$G(n,M)$where$M$denotes the number of edges. Is there any known way of calculating the number of graphs within this space that does not contain any k-cliques? Can ... 1answer 140 views ### Nuclearity noncommutative torus I read that the Noncommutative torus (rotation algebra) is nuclear when$\theta\in\mathbb{R}\setminus\mathbb{Q}$. Unfortunately, I haven't found a proof. Could someone give me a reference and/or an ... 2answers 40 views ### Systems of ODEs that fulfill a matrix relationship at steady state [on hold] It is well known that for a system of linear ODE $$x'(t) = A(t) \cdot x(t) + b(t)$$ with initial condition$x(t_0) = x_0$, that for a solution at any other time point$t_1$,$x(t_1) = (z_1, \ldots, ...
Let $\phi:R\to S$ be a flat ring homomorphism and consider the induced adjoint pair $$\phi_!:R-Mod\rightleftarrows S-Mod:\phi^*,$$ where $\phi_!=(S\otimes_R -)$. The right adjoint $\phi^*$ is easily ...