0
votes
0answers
21 views

Question on Posets and open sets

i'm sorry if my question is really trivial but this one is really bugging me out.. So let's have a partially ordered set $I$ with the topology in which the open sets are the increasing ones: $i\in U$ ...
1
vote
0answers
17 views

Intersections in almost complex manifolds

Suppose $(M,J)$ is an almost complex manifold, and $X$ and $Y$ are two almost complex submanifolds (i.e. $J(T(X)) \subset T(X)$ and $J(T(Y)) \subset T(Y)$). Then must $X \cap Y$ also be an almost ...
0
votes
0answers
25 views

decomposition of polynomials over a field [on hold]

$K|F$ has this property that every polynomial $f(x)∈F[x]$ has a root in $K$.is it true that every polynomial $f(x)∈F[x]$ can be completely decomposed on $K$? i think it is false,because if we write ...
-5
votes
0answers
17 views

How to find secret key and public key for ECC cryptosystem? [on hold]

Develop an ECC cryptosystem based on E31(1;1), point G = (0,1) which has order 32. nA value of 6. What is the secret key? What is the public key?
0
votes
1answer
18 views

On the existence of compactly supported functions whose its Fourier transform satisfies a given condition

My question is concerned with the existence of compactly supported functions whose its Fourier transform satisfies a given condition: For $\gamma\ge 1$, one can prove that there is no compactly ...
-3
votes
0answers
25 views

How to compute 3P from elliptic curve where P is (28, 8) [on hold]

Consider the elliptic curve E31(1,1): Calculate 3P, where P = (28,8).
2
votes
0answers
59 views

Is the ISC kaput [on hold]

The very useful Inverse Symbolic Calculator is showing me this What's up? multiple choice (a) No, it's fine at that address: idiot Edgar did something wrong... (b) It is off-line at that ...
0
votes
1answer
120 views

Disruptive innovations in mathematical notations [on hold]

I am wondering whether there are examples of mathematical notations that, once introduced, have drastically changed or simplified the way to address a problem or a mathematical area, or that have ...
-2
votes
0answers
46 views

Complexity Dick Word in Turing Machine single tape [on hold]

(I precise I don't have a good level in english so I can rewrite if you want) The probleme : I just have two symbols O(open) for "(" and C(close) for ")" The probleme consist to implement an ...
0
votes
0answers
22 views

Connectedness of the symplectic automorphism of the 2-sphere $S^2$

The 2-sphere, endowed with the round Riemann metric with constant curvature 1, is a symplectic manifolds. My question is: Is the group of symplectic automorphisms of $S^2$ with respect to this ...
0
votes
0answers
27 views

trigonometric sum and inequalities

let $x\in\mathbb{R}-\mathbb{Z}$ and $e(x)=e^{2\pi ix}$. If we have this sum $$\left|\overset{q}{\underset{h=1}{\sum}^{*}}e\left(h\, x\right)\underset{\underset{p\equiv h\,\textrm{mod}\, q}{p\leq ...
0
votes
0answers
34 views

Studies of Specific Kinds of Beurling Primes?

I know that Beurling developed a notion of generalized primes (and integers. However, does anyone know if Beurling, or anyone else, studied subclasses of the broader class of Beurling primes that ...
-3
votes
0answers
64 views

About Gödel's incompleteness theorems [on hold]

I think maybe I found the mistake of Gödel's incompleteness theorems first,these are something I suppose 1、the content of Proof must be able to be transformed to formal logic So my point is ...
0
votes
0answers
5 views

Rearranging a sequence to minimize a series function on its subsequences

Given an arbitrary nonempty sequence of integers $Q$ with $p$ elements: Let $R$ be a rearrangement of $Q$. Let $A$ be the solution set of $1\leq n\lt m\leq p$, where $n,m\in \mathbb{Z}$. $F(n,m) = ...
1
vote
0answers
7 views

Second order term of the Fedosov quantised product

In Fedosov's version of quantisation of functions on a symplectic manifold, the product is given in terms of a symplectic connection. I have looked through Fedosov's book in deformation quantisation, ...
0
votes
1answer
37 views

What is the expression of first eigen function of Laplacian on Hyperbolic plane?

Let $\Delta$ be the Laplacian (a positive operator) on $H^2$ the hyperbolic plane. My question is what is the expression of the eigenfunction $\Delta f= f/4$? (say in the ploar coordiante)
0
votes
0answers
25 views

algorithms math help [on hold]

I can't understand the basic math behind algorithms. For example, here's a question: If f(n) = O(g(n)) is ...
0
votes
0answers
40 views

The sixth power integral moment of automorphic L-function attached to Maass Forms

It is known that the sixth power integral moment of automorphic L-function attached to Cusp Forms has been proved by M. Jutila, that is $\int_{0}^{T}|L(1/2+it,f)|^{6}dt \ll T^{2+\varepsilon}$. And ...
-1
votes
0answers
54 views

Galois group of equation [on hold]

Let the equation $5x^6-12x^5-12x^4+204x^3+81x^2-792x+414=0$ The Galois group of $P(x)=5x^6-12x^5-12x^4+204x^3+81x^2-792x+414$ have solvable to be or not?
-3
votes
0answers
42 views

How to verify a vector has a steady gradual increase mathematically? [on hold]

I rank the values inside my vector then look to verify the values have a gradual but steady increase. Ideally if I had 10 numbers the smallest would occur first and the second smallest would rank ...
3
votes
0answers
70 views

Hyperbolicity of Deligne-Mumford stacks

Let $X$ be a smooth finite type separated connected Deligne-Mumford stack over $\mathbb C$ (with trivial generic stabilizer if necessary). This question is about "hyperbolicity" and it is motivated ...
5
votes
0answers
44 views

Universality with respect to quotients

Is there an infinite cardinal $\kappa$ for which the following statement (S) true? (S) : There is a topology $\tau_\kappa$ on $\kappa$ such that for all topological spaces $(X,\tau)$ with $|X|\leq ...
-2
votes
0answers
49 views

Identification of Hilbert space with dual follows from another identification? [on hold]

Let $X$ be a Hilbert space with inner product $(\cdot,\cdot)_X$, and let $Y$ be another Hilbert space with inner product $(\cdot,\cdot)_Y$. Suppose there is a bijective continuous linear operator $F:X ...
18
votes
0answers
201 views

Does every smooth, projective morphism to $\mathbb{C}P^1$ admit a section?

Possibly this has already been asked, but it came up again in this question of Daniel Litt. Does every smooth, projective morphism $f:Y\to \mathbb{C}P^1$ admit a section, i.e., a morphism ...
7
votes
3answers
225 views

Characterize the category of rings

(Sub)categories of many well-studied mathematical objects have been characterized purely in terms of their morphisms. Some (famous) examples: Sets and functions, due to Lawvere. Modules over some ...
0
votes
0answers
90 views

A question on the Euclidean domain $\mathbb{Z}[\omega]$ [on hold]

Let $\omega=\frac{-1+i\sqrt{3}}{2}=e^{\frac{2 \pi i}{3}}$ be a complex cube root of unity, and $\mathbb{Z}[\omega]$ the Euclidean domain. In view of that $\int_0^\infty e^{ix} ...
-2
votes
0answers
41 views

Existence of minimizer in Sobolev space $H^{1,2}(\Omega)$ [on hold]

I am looking at a functional $$\frac{\int_{\partial \Omega} u^2 \mathrm{dx}}{ \left(\int_{\Omega} u^q \mathrm{dx} \right)^{2/q} }$$ And i want to know if the minimizer exists in the space ...
8
votes
1answer
169 views

A linear category with objects of infinite length but which is otherwise finite?

Fix a ground field $k$. By a linear category I will mean an Abelian category which is compatibly enriched over $k$-vector spaces. A linear category is called finite if it satisfies the following four ...
0
votes
0answers
26 views

Computing row-sum scaled unsigned Stirling nos. of the 1st kind

As the title suggests, I would like to compute probability vectors with elements proportional to (unsigned) Stirling numbers of the first kind by row. For easy reference, here is the Wiki page. For ...
1
vote
0answers
31 views

Semigroup nilpotents and compostional inversion

The integer coefficients of a general partition formula for the compositional inverse of a function are a refined version of the coefficients of the generating series for the number of nilpotents in a ...
0
votes
0answers
73 views

Is holomorphic 2-form on Moduli of Higgs bundle in Biswas' paper is non-degenerate

In Biswas' paper, Geometry of moduli of Higgs bundles, he defined a holomorphic 2-form on moduli of stable Higgs bundles, using Kodaira-Spencer map and Petersson-Weil metric. I want to know whether ...
3
votes
1answer
61 views

Probability that a sum of intependent random variables hits a point

Let $X_1,\ldots,X_n$ be independent random elements of a normed space $X$. Suppose that $\sup_{x\in X}\mathbb{P}(X_i=x)=p_i$. What is the best known upper bound for $$\sup_{x\in X} ...
0
votes
0answers
142 views

Conjecture Reference Request

If Second Hardy-Littlewood Conjecture is true then we can claim that $\pi(x)-\pi(y)\leq \pi(x-y)$. Thus the conjecture gives an upper bound for the number of primes between $x$ and $y$. I have found ...
3
votes
1answer
81 views

a question about minimal non-abelian groups

Let $G$ be a minimal non-abelian group with cyclic Sylow $p$-subgroup $P$ and normal Sylow $q$-subgroup $Q$ , see [ Huppert, Endlich Gruppen I, Aufgaben III, 5.14]. My quesion is, if there is another ...
10
votes
2answers
451 views

Is a group uniquely determined by the sets {ab,ba} for each pair of elements a and b?

This is a cross-posted question, originally active here on math.stackexchange. For a given group $G=(S,\cdot)$ with underlying set $S$, consider the function $$ F_G:S\times ...
0
votes
0answers
70 views

Is the parallelogram rule an axiom or a theorem in euclidean geometry? [on hold]

I am aware of the proof of the rule in inner product spaces. Excluding the geometry of Descartes, is it possible to prove parallelogram rule or is it an axiom?
2
votes
1answer
37 views

lower bound of a trace quadratic form [on hold]

i want to find a lower bound on the following expression: $tr(AXA^T)$ in terms of $tr(X)$ where A is real $n\times n$ matrix and $X>0$ is positive symmetric. It seems that the following bound is ...
0
votes
1answer
173 views

Is there any algorithm to decide whether a series with integral coefficiens is a algebraic function?

Given a series with integral coefficiens as following: $$F(x)=\sum_0^i a_i x^i,\text{where }a_i\in \mathbb{N}\bigcup 0 $$$$\text{and there is a computable function $\psi$ such that } \forall i ...
5
votes
0answers
77 views

Does $\mathsf{fReR}_0$ prove the existence of the cartesian product of two sets

$\mathsf{fReR}_0$ is the set-theoretical system whose axioms consist of: (1) Axiom of extensionality: $\forall z\in x\ (z\in y)\wedge\forall z\in y\ (z\in x)\rightarrow x=y$ (2) Axiom of empty set: ...
1
vote
0answers
95 views

Equations over $\mathbb{Z}[[T]]$ vs. equations over $\mathbb{Z}_p$

This question might be deemed totally unanswerable, unless there is an obvious counterexample. Answers to either effect would be welcome. Question. Let $X$ be a finite-type scheme over ...
1
vote
0answers
30 views

Cohomological dimension of transcendental p-adic extensions

Let $k = \mathbb{Q}_p$ for any prime $p$ and set $L = k(t_1,..,t_n)$. The u-invariant of a field $u(k)$ is defined by $u(k):=\{ max (\mathrm{rank}(q)) $ | $ q $ is anisotropic over $k\}$. It is ...
2
votes
2answers
126 views

A metric associated with a continuous surjective map $f:X\to Y$

Assume that $f:(X,d_{1})\to (Y,d_{2})$ is a continuous surjective map between compact metric spaces. We define another metric $d_{f}$ on $Y$ With $$ d_{f}(a,b)=Hd(f^{-1}(x), f^{-1}(y))$$ ...
3
votes
1answer
136 views

Characterizing the real analytic Eisenstein series

Consider the classical real analytic Eisenstein series $$ E(z,s)=\left(\pi^{-s}\Gamma(s)\frac{1}{2}\right)\sum_{(m,n)\neq(0,0)}\frac{y^s}{|mz+n|^{2s}}, $$ where $z=x+iy$. We think of $E(z,s)$ as a ...
0
votes
0answers
67 views

Zero-mean assumptions concerning r.d.'s when reading graduate-level probability texts [on hold]

I'm reading through T. Taos book on random matrices (to be found here), and it is frequent to make without-loss-of-generality certain reductions when proving theorems as for example Hoeffdings ...
0
votes
1answer
54 views

Nagakami behavoir

Is the sum of square Nagakami random variables Erlang distributed? What is the distribution of euclidean norm of complex Nagakami? Cheers!
0
votes
1answer
48 views

Help in finding distribution of the following function of random variable

Let $X_1$ and $X_2$ be independent complex Gaussian random variables, $$X_1 \sim \mathcal{CN}(0,\sigma)$$ $$X_2 \sim \mathcal{CN}(0,\sigma)$$ If $X= aX_1 + bX_2$ where $a,b$ are constants then the ...
-5
votes
0answers
48 views

What is induction to n^(n-1) >= n! for n=9,10 [on hold]

Can somebody help me? How do I prove n^(n-1) >= n! for n=9,10..... by induction?
4
votes
0answers
97 views

A homological criterion for collapsibility?

On page 256 of Kirby and Siebenmann one finds the following lemma (its proof an "elementary exercise", so they only give a hint): Taking $A$ to be a point and iterating this collapsing lemma, this ...
5
votes
1answer
241 views

Parity of primes [duplicate]

While working on a completely different (combinatorial) problem, I ran a simple program to calculate the parity of the first ~50000 primes (number of 1s in their binary representation modulo 2). The ...
6
votes
2answers
107 views

Are sums of 0-1 Pareto efficient vectors Pareto efficient?

Does there exist an $m \times n$ matrix $A$ and a vector $x \in \mathbb{R}^m$ such that: The entries of $A$ are $\in \{0, 1\}$. For all pairs of columns $u, v$ of $A$ the entries of $u - v$ are ...

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