0
votes
0answers
39 views

Quantiles moments and Convergence

QUESTION: Let $F$ be an absolutely continuous distribution function with density $f$, and $F_{n}$ be its nth empirical distribution. Suppose that $t\in (0,1)$ is constant. Is true the convergence ...
5
votes
0answers
337 views

Different approaches to the multiverse of sets

There are some different approaches to the multiverse of sets, in particular: 1) The approach by Woodin, 2) The approach by Sy Friedman, ..., 3) The approach by Hamkins. I wonder to know if ...
4
votes
0answers
81 views

The Alexander-Conway polynomial: from knots to braids?

The Alexander-Conway polynomial was the first knot invariant to be discovered, as far back as 1923 according to this link. Given that knots can be expressed in terms of quasi-toric braid closures, it ...
0
votes
1answer
96 views

Spectral Graph Theory

Let G be an undirected graph, then Laplacian Matrix(L(G)) = Degree Matrix (D(G)) - Adjacency Matrix (A(G)). What is the relationship between laplacian and adjacency spectrum of undirected graphs?
1
vote
0answers
44 views

Whether r.v. with p.g.f. $\exp [\sum\limits_{i = 1}^\infty {{q_i}({z^i}} - 1)]$ is overdispersion?

When discrete r.v. $X$ is not Poisson distributed and ${\rm{Var}}X,EX < \infty $, I want to know whether r.v. $X$ with p.g.f. $\exp [\sum\limits_{i = 1}^\infty {{q_i}({z^i}} - 1)],({q_i} \in ...
0
votes
1answer
49 views

Isometry group of an integer as of the corresponding $\Omega(n)$-parallelotope

Let $\prod_{i}p_{i}^{a_{i}}$ be the prime factorization of a positive integer $n$ and let's consider the $\Omega(n)$-parallelotope built with, for all $i\in I$, $a_{i}$ pairwise orthogonal vectors of ...
3
votes
1answer
180 views

Is the big cell a principal open set?

Let $G$ be a complex affine reductive algebraic group, $B\subseteq G$ a Borel with maximal torus $T$ and unipotent radical $U$. Let $w\in\operatorname N_G(T)$ be a representative of the longest Weyl ...
27
votes
1answer
536 views

For which maps $S^1\to S^1$ is the winding number defined?

There are two classes of maps $S^1\to S^1$ for which I know how to define the winding number: • Continuous maps: Using the unique path lifting property of the universal covering map $\mathbb R\to ...
4
votes
1answer
146 views

Learning representation theory of real reductive lie groups

I am interested in any sources that can be helpful for learning the representation theory of real reductive groups. I am currently reading Wallach book, but I feel that I don't understand the subject ...
0
votes
1answer
59 views

Laplacian matrix of a graph with negative weights

I am trying to calculate the Laplacian and Adjacency matrix of a graphs for positive and negative weights. If a graph be simple with only non-negative weight it is easier. But in my graph I have some ...
1
vote
3answers
205 views

Powers of $2$ and the products of initial odd primes

NOTATION: $O_x$ -- the product of all odd primes $\le x$. E.g. $O_7=3\cdot 5\cdot 7 = 105$. QUESTION: Are the three ordered pairs $\ (d\ p)=(1\ 3)\ \ (2\ 3)\ \ (4\ 5)\ $ the only solutions of the ...
2
votes
2answers
102 views

Lie group about the quantum harmonic oscillator [on hold]

We konw that in quantum harmonic oscillator $H=a^\dagger a$, $a^\dagger$, $a$, $1$ will span a Lie algebra, where $a, a^\dagger$ is annihilation and creation operator, $H$ is the Hamiltonian operator. ...
2
votes
0answers
86 views

Deterministic shifts

We consider (topological) dynamical systems $(\Omega, S)$, where $S$ is the shift $(Sx)_n=x_{n+1}$, and $\Omega$ is a compact, shift invariant subspace of $[0,1]^{\mathbb Z}$. I call $(\Omega, S)$ ...
4
votes
3answers
147 views

Quadratic twist of an elliptic curve given by non-Weierstrass model

Suppose $f(x)$ is a polynomial of degree 4 with integer coefficients and nonzero discriminant. Let $C$ be the hyperelliptic curve of genus 1 defined by $y^2=f(x)$. If we assume that $C$ has a rational ...
-4
votes
0answers
56 views

Find the Flaw in the Argument [on hold]

I have got a question. The problem is to find the composite numbers $C$ $(n)$ and $C$ $(n(n+1))$ such that we get $C$ $(n(n+1))$ $-$ $C$ $(n)$ $=$ $n$. My argument is simply this. The inequality in ...
0
votes
0answers
42 views

Number of lattice points inside a parallelogram defined by a vector on the “rhombic plane”

I will give here a specific case and try to explain the question the best I can: The rhombic plane is the plane with the x-axis the same as the Cartesian plane but the y-axis tilted at $60$ degrees. ...
0
votes
0answers
10 views

What is the maximal ideal of $z[t,t^{-1}]\otimes Q$? [migrated]

I know the $z[t,t^{-1}]$ is a localization of $z[t]$.But I do not know the maximal ideal of $z[t,t^{-1}]\otimes Q$? Many thanks!
0
votes
0answers
106 views

Homotopy equivalent type of a knot complement [on hold]

Let $S$ denote the bounded complement of a tame knot in $S^3$,then $S$ is homotopy equivalent to a finite 2-dimensional simplicial complex $K$ [Milnor's paper "infinite cyclic covering"],I do not ...
4
votes
1answer
197 views

Fermat surface known to have very few rational integer solutions

The motivation for this question is the Selmer curve, given by $$\displaystyle 3x^3 + 4y^3 + 5z^3 = 0.$$ One can show that this curve has no rational integer solutions, despite having a solution ...
4
votes
1answer
191 views

How can I solve a cubic equation in a finite field with characteristic 2?

I need to solve the usual cubic equation x^3 + ax^2 + bx + c = 0 over a finite field GF(2^n). This is to avoid doing a brute-force Chien search in a BCH decoder. I read in a paper about an easy way ...
1
vote
2answers
126 views

Is there an intuitionistic generalized boolean algebra (of Stone)?

A "boolean algebra without the greatest element" was called by Stone "generalized boolean algebra" and he axiomatized it. Is there any publication about "preudo-boolean algebras without the greatest ...
13
votes
0answers
155 views

Unoriented bordism and homology, reference?

The following has undoubtedly been known to the experts for years, but I only noticed it the other day. Can anyone give a reference? One can prove Thom's theorem to the effect that every mod $2$ ...
0
votes
0answers
48 views

Surjectivity of $f\colon M\rightarrow \Gamma_{pR_p}(M_p)$

Let $R$ be a Noetherian ring and let $M$ is finitely generated $R$-module.Suppose $p$ is a minimal prime in $\text{Supp}_RM$. Then $f\colon M\rightarrow \Gamma_{pR_p}(M_p)$ that $f(m)=m /1 $ is ...
0
votes
0answers
106 views

Moment map of CP^1 as rational normal curve

I am little confused about some basic symplectic geometry about Hamiltonian actions on sphere. I appreciate your comments. Consider sphere $S^2 = \mathbb{C}P^1$ with its standard symplectic (Kaehler) ...
1
vote
1answer
95 views

Elliptic curves with square conductor

Is there a characterization of elliptic curves over $\mathbb Q$ whose conductor is a square? Does this property have a geometric meaning?
1
vote
1answer
199 views

An infinite product: combinatorial interpretation

It is an undergraduate exercise to show that the generating function for the sequence of unrestricted integer partitions $p(n)$ is the celebrated infinite product ...
2
votes
0answers
53 views

Poincaré Duality of a quasi-free algebra

I'm completely stumped on this one (yet I feel it is obviously true or obviously false) If $A$ is a quasi-free algebra, then must it satisfy Poincaré duality? All i need to find is a protective ...
1
vote
1answer
151 views

When are completely positive maps monic/epic?

In the category of C*-algebras and $*$-homomorphisms, a morphism is monic precisely when it is injective, and epic precisely when it is surjective (see Mono- and epi-morphisms for C*-algebras). Is ...
1
vote
0answers
44 views

Intuitive explanation for Hardy-Littlewood maximal function

I came across the Hardy-Littlewood maximal function in an analysis course. Could someone help me intuitively understood what the purpose of this map is, and why it is useful? Thank you. Regards ...
1
vote
1answer
139 views

Proof of the Belyi's theorem: where it is really used the hypothesis?

Consider the Belyi's theorem: If a smooth projective curve $X$ is defined over $\overline{\mathbb Q}$, then there exists a finite morphism $X\longrightarrow\mathbb P^1(\mathbb C)$ with at most ...
2
votes
0answers
55 views

Genericity of maps which are transverse when restricted to a submanifold

Let $M$ and $N$ be smooth manifolds, and $A\subset M$, $B\subset N$ be smooth embedded submanifolds. I am looking for a reference for a theorem on the following lines: The set of smooth maps $h\in ...
7
votes
1answer
314 views

Hilbert Class Field Galois over Q?

So if we have a Galois extension $K/\mathbb{Q}$, then the Hilbert Class Field $H$ of $K$ is certainly Galois over $\mathbb{Q}$. But is the converse true? I know many examples of nongalois ...
1
vote
1answer
45 views

$L^p$ estimate for (powers of) a Laplacian with inverse square potential

I need an estimate of the form $$ \|v\|_{L^p} \le C \|(K-\Delta- c|x|^{-2})^s v\|_{L^p} $$ where $K>0$ can be large if necessary, $c$ is positive but below the Hardy constant $(n-2)^2/4$, where $n$ ...
3
votes
1answer
152 views

Reference for $p$-adic Hodge theory with coefficients

Let $K$ be a $p$-adic field and $L$ be a finite or infinite extension (maybe algebraic ?) of $\mathbb{Q}_p$. Is there a reference for $p$-Hodge theory for representations $\rho : Gal_K \rightarrow ...
0
votes
0answers
64 views

$C^\infty$ approximations of $f(r) = |r|^{m-1}r$ [migrated]

Consider $f(r) = |r|^{m-1}r$ where $m \geq 1$. Is it possible to find $C^\infty$ functions $f_n$, such that $f_n \to f$ uniformly on compact subsets of $\mathbb{R}$, $f_n' \to f'$ uniformly on ...
1
vote
0answers
40 views

For Finite Dual when is $(A \otimes A)^o = A^o \otimes A^0$?

Let $A$ be any $k$-algebra. The finite dual or restricted dual of $A$ is $$ A^o = \{f \in A^* ~ | ~ f(I)= 0, \text{ for some ideal } I \subseteq A, \text{ such that } \text{dim}_k(A/I) < \infty\}. ...
2
votes
1answer
102 views

Properties of representations attached to p-adic modular forms

I found an old MOF post about representations attached to p-adic modular forms: Representations attached to p-adic modular forms and I have some follow up questions on the same topic. If we have a ...
9
votes
1answer
348 views

Roots of unity near 1 in Z / p Z

Let $r \ge 3$ be a fixed integer. I'm interested in primes p such that no integer in the interval $(-\sqrt{p}, \sqrt{p})$, except $1$ (and $-1$ if $r$ is even), is an r-th root of unity modulo p. The ...
1
vote
1answer
57 views

Does a BCL algebra define a partial order?

A BCL algebra is a universal algebra with a binary operation denoted as "$*$" and a $0$-ary operation (constant) denoted as "$0$", satisying the following axioms: (1) $x * x = 0$; (2) if $x * y = 0$ ...
3
votes
0answers
275 views

Continued fraction representation of Zeta

A question at math.SE is asking for references. The fraction is quite nice! Check it out and post some references if you know of any. I found this at arxiv, but it doesn't apply to Zeta.
-4
votes
0answers
50 views

Easy Question - A function with some proprietys [closed]

I have a problem: A group of employers {e1, e2, ..., en} with salaries {s1, s2, ..., sn} and a number dependents {d1, d2, ..., dn} (the employer + his family, di >= 1) wants to make a contract of ...
2
votes
0answers
35 views

successive schur complements

If I have a large (e.g. 6000x6000), sparse, positive definite matrix $M$ (which may have individual entries everywhere, but most non-zero entries are on / around the diagional). Divide $M$ into blocks ...
0
votes
1answer
128 views

Irreducible polynomial on $\mathbb{F}_{2}[x]$

For some reason I need some irreducible polynomial $f$ on $\mathbb{F}_{2}[x]$ where $\deg f \in [10^3,10^6]$. Could someone give information about this? Thx.
0
votes
1answer
28 views

Reduction along an Orbit for C.-M. systems

I am having trouble in understanding the section of this paper http://www-math.mit.edu/~etingof/zlecnew.pdf where the author introduces the Calogero-Moser system as the reduction of a manifold $M$ on ...
1
vote
0answers
59 views

Are injective modules flabby on basic open sets?

In order to give a simple proof of a basic fact about quasi-coherent modules (see below), I'm interested in knowing whether the following statement holds: Statement: If $A$ is a commutative ring and ...
3
votes
0answers
120 views

Symmetric matrices with $\rho(A)\gg\|A\|_\infty$

For a symmetric real matrix $A$, denote by $\rho(A)$ the spectral radius of $A$, and by $\sigma(A)$ the largest absolute row sum of $A$; that is, $\sigma(A)=\max_i \sum_j |a_{ij}|$, where $a_{ij}$ are ...
0
votes
0answers
104 views

Is there an accepted measure of the degree of coverage of different partial proofs of Fermat's last theorem? [closed]

For example, granting that, for co-prime $a,b$ (primitive cases), Fermat himself proved that $a^n+b^n=c^n$ has no solution for $n = 4$, and Euler next proved it for $n = 3$, one could say that FLT was ...
-1
votes
0answers
26 views

Is there a program for convenient working with equations and coefficients? [migrated]

I perform some calculations with one differential equation. Then I got a huge expression depending on $x$ and its degrees/powers. E.g. $$\alpha x+(4-x+\sqrt[3]{x})^2-(\beta\sqrt{x}+\frac12(x^3+1))^3 + ...
0
votes
0answers
24 views

Is the autocorrelation of one function the same if one term is flipped on the y axis? [closed]

I have some questions about autocorrelation. They are very related, so I thought that one single post was appropriate for the topic. The first question is already illustrated in the subject: if I ...
0
votes
1answer
261 views

What is the current status of representations of $GL_n(F)$ (and other algebraic groups)?

What is the current status of representations of $GL_n(F)$ (and other algebraic groups)? When $F$ is a local field, the representations of $GL_n(F)$ are classified by Bernstein and Zelevinsky in ...

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