0
votes
0answers
5 views

Can an abelian variety/Q have no points over Q_sol?

Let $A/\mathbb{Q}$ be an abelian variety. Must there be a finite solvable extension $K/\mathbb{Q}$ such that $A(K)$ is nontrivial? This follows from the conjecture that the maximal ...
1
vote
0answers
7 views

Probability of non-negative matrix relaxation

Given matrix $M\in\Bbb\{0,1\}^{n\times n}$, take $\mathscr{M}[M]=\{Q\in R_{\geq0}^{n\times n}:Q[ij]>0\iff M[ij]=1\}$. Does ...
2
votes
0answers
19 views

flatness and derived completion

Let $A$ be a local ring of maximal ideal $\mathfrak{m}$. Let $\hat{A}$ be its completion. If $A$ is noetherian , then we know that $A\rightarrow\hat{A}$ is faithfully flat. If $A$ is not noetherian, ...
3
votes
1answer
91 views

Non-Forcing and Independence

I asked this question about two weeks ago on MSE and haven't gotten an answer, so I thought I would post the question here. Do there exists sentences which are independent of ZFC, cannot be shown to ...
0
votes
0answers
19 views

Relative nonarchimedean disks and annuli

Let $A$ be a Huber (i.e. f-adic) ring, meaning a topological ring with an open subring $A_0$ which is adic and has finitely generated ideal of definition. Is there a good notion of closed disk of ...
-2
votes
0answers
35 views

What does this graph notation mean? E\S [on hold]

I am studying graph theory right now but I am confused what E\S means where both E and S are sets of edges. What does the "\" indicate?
2
votes
1answer
55 views

Unitary representation with fixed Casimir

Let $G$ be a connected reductive real Lie group with Lie algebra $\mathfrak{g}$. We denote by $\widehat{G}_u$ the unitary dual, that is the set of isomorphism classes of unitary reprensentation of ...
2
votes
0answers
22 views

Properties of Integral Closure and Reduction ideal

Definition (Reduction Ideal). Let $ I $ and $ J $ be ideals of $ R $. Then $ J $ is called a reduction of $ I $ iff $ J \subseteq I $ and there exists an $ n \in \mathbb{N} $ such that $ I^{n} = J ...
0
votes
0answers
18 views

Are there compact riemannian manifolds whit Q-curvature negative?

Are there known examples of compact compact riemannian manifolds whit Q-curvature negative?
2
votes
0answers
64 views

3D models of the unfoldings of the hypercube?

There are (apparently) 261 distinct unfoldings of the 4D hypercube, a.k.a., the tesseract, into 3D.1 These unfoldings (or "nets") are analogous to the 11 unfoldings of the 3D cube into the plane.2 ...
-2
votes
0answers
66 views

Lie algebra and Lie groups [on hold]

A complex Lie algebra $L$ has a representation on $Der(L)$ by just putting $x.D=-ad_{Dx}$. For semisimple Lie algebras, by Weyl's theorem, $Der(L)$ decomposes into irreducible subspaces $D_i$. Then my ...
-2
votes
0answers
26 views

Population and date values [on hold]

Use the population data values below. North= 18,200 South=12,900 East=17,600 West=13,300 If there are 26 representatives for all districts how many ...
-2
votes
1answer
73 views

Combinatorical meaning of such expression [on hold]

Any combinatorical meaning or interpretation of $$1^{\alpha_1}2^{\alpha_2}3^{\alpha_3}...s^{\alpha_s}\alpha_1!\alpha_2!...\alpha_s!$$ for partition ...
0
votes
1answer
64 views

Completeness of a set of propositional formulas [on hold]

A set $\sum$ of formulas in propositional logic is complete if for each propositional formula $\phi$ either $\sum \vdash \phi$ or $\sum \vdash \neg \phi$. Clearly every inconsistent set of formulas ...
2
votes
1answer
41 views

Classification of ergodic measures for circle expanding maps

Let us consider the classical self-covering of the circle $S^1=\mathbb{R}/\mathbb{Z}$ given by $$\times_d(x) = dx \mod 1$$ where the degree $d$ is any integer greater than $1$. There are a wealth of ...
0
votes
1answer
48 views

Totally non fixed point property

Edit: According to the comment of Pietro Majer, I revise the question Is there a non singleton compact connected Hausdorff topological space $X$ for which the following property hold?: "Constant ...
2
votes
0answers
108 views

Reference for Arakelov's theorem: $K^2_f=0$ iff $f$ is locally trivial

Let $f:X\longrightarrow B$ be a family of curves, with $f$ relatively minimal, over a fixed curve $B$ ($B$ is projective, irreducible and smooth). The fibration $f$ is said locally trivial if all ...
0
votes
0answers
82 views

Characterizing matrices based on ranks

Given matrix $M\in\Bbb Z_{\geq0,\leq b}^{n\times n}$, denote $$\mathscr{M}[M,a]=\{Q\in\Bbb R_{\geq a}^{n\times n}:Q[ij]\neq0\implies M[ij]=1\}$$ ...
5
votes
0answers
53 views

A jump operator for Borel equivalence relations

It is well-known that with respect to Borel reducibility the class of Borel equivalence relations on a standard Borel space does not admit a maximal element. We can use the well-known Friedman-Staley ...
8
votes
1answer
151 views

Translates of meager sets

Does there exist a meager set of reals M such that every meager set can be covered by countably many translates of M? This is the category analogue of the following.
-1
votes
0answers
48 views

Name and theorems of transitive/Galois groups of quadratic (even) and cubic power polynomials: cyclic group extensions [on hold]

What is the transitive group details of a polynomial where only the third power terms occur? That is ${x}^{3n}+{a}_{n−1}{x}^{3(n−1)}+\cdots+{a}_{1}{x}^{3}+{a}_{0}$. I need the basic theorems that ...
2
votes
2answers
125 views

boundary homomorphism in the homotopy exact seqeunce of principal $SO(9)$ bundle over $S^8$

Consider principal $SO(9)$ bundles over $S^8$.They are in 1-1 correspondence with $$[S^8,BSO(9)]\cong \pi_7(SO(9))\cong \mathbb{Z}$$ Now pick up one such bundle $\xi$,we have the long exact sequence ...
-1
votes
0answers
36 views

Orthogonal vector to arbitrary vector in R3 [on hold]

I got a vector $(0, 0, 0)^T \neq v \in R^3$. Now I want a closed formula for some orthogonal vector to $w$ (I don't care which). My problem is that if I, for instance, fix $w_1$ and $w_2$ then $w_3 = ...
-4
votes
0answers
62 views

Prove an equation is always false [on hold]

How can I prove an equation is always false? For example: b = b + 1 is false for all values of b. Very simple to see. Now given a more complicated equation, such as: b = sin(sin(b) - .56)) ...
0
votes
1answer
63 views

How to minimize this sparse quadratic function?

There is a problem when I'm reading a paper. Equation: $min_p|p-p^*|^2+\alpha |R(p)|^2 + \beta |D(p)-\delta|^2$, where $p, p^*, R(p), D(p), \delta$ are all $M\times N$ matrices, and $p^*, R(), D(), ...
5
votes
1answer
96 views

Symmetry type of non-cohomological automorphic forms

By Katz-Sarnak philosophy a family of $L$-functions would have a symmetry type which would reflect the statistics of $L$-functions, such as low lying zeros and moments. Shin-Templier's paper on ...
18
votes
5answers
562 views

On an example of an eventually oscillating function

For $x\in(0,1)$, put $$f(x):=\sum_{n=0}^{\infty}(-1)^{n}x^{2^{n}}.$$ This function possesses interesting properties. It grows monotonically from $0$ up to certain point. Then it starts to oscillate ...
0
votes
0answers
54 views

Inductive/Projective Limits of Topological Algebras

It is common to form inductive/projective limits of Banach/Frechet spaces in order to come up with natural topologies for common vector spaces. For instance, For $k \ge 0$ and $K_n$ compact ...
2
votes
0answers
118 views

When does a perverse sheaf occur in the decomposition theorem?

Suppose I am in the setting of the decomposition theorem, i.e., we have the decomposition of the direct image $f_*\mathbb Q_\ell$, where $f:X\to Y$ is proper. Then the direct image decomposes into a ...
-1
votes
0answers
10 views

How to test the significance of covariance [on hold]

I'm using the Mutual Informacion covariance in RNA sequences and I want to know if there exits a way to test if some covariance is significant, let's say, an associated p-value. Thanks to all for ...
-1
votes
0answers
14 views

Combining the output of two functions smoothly for a droplet effect [on hold]

I'm trying to write a function which generates this droplet effect implicitly. I've got a function which generates both of the shapes and I'm looking for a way to somehow combine these two in such a ...
-2
votes
1answer
116 views

Degree of a rational function [on hold]

I would like to have the (simplest) proofs for the following theorem (there may be more than one interesting approach): Let $f=\frac{p}{q}:\mathbb{C}\longrightarrow\mathbb{C}$ be a quotient of ...
4
votes
2answers
363 views

How close to an integer can a polynomial root be?

Suppose I have a polynomial $p(x) = a_n x^n + ... + a_0$ where $a_n, \dots, a_0$ are integers. I would like to show that any root of this polynomial is either an integer or is far from an integer. ...
2
votes
1answer
42 views

Maximizing Frobenius Norm of Commutator (an opposite Procrustes problem)

I was wondering if anybody has any suggestions on the following problem: Let $S$ be an $n\times n$ positive definite symmetric matrix. I wish to find an $n\times n$ orthogonal matrix $R$ which ...
1
vote
1answer
139 views

Why can we not always take a Kähler class to be in rational cohomology?

Given a Kähler manifold $(X,\omega)$ we know that its Kähler class lies in an open cone of $H^{1,1}(X) \cap H^2 (X,\mathbb{R})$. Since $\mathbb{Q}$ is dense in $\mathbb{R}$ we should be able to find a ...
-4
votes
0answers
33 views

Partially ordered set [on hold]

Show that a subset $C$ of a preordered space $(X, ≤)$ is a chain if and only if $C × C ⊂ A ∪ A^{−1}$, where $A := \{(x, y) : x ≤ y\}$, $A^{−1} := \{(x, y) : (y, x) ∈ A\}$.
0
votes
0answers
27 views

Upper and Down Bound,directed,cofinal [on hold]

I'm learning a partially ordered set.Can you give me some example of each these definition: 1.Upper and Down Bound : ...
-6
votes
0answers
70 views

Can you give me some example of each these definition [on hold]

I'm learning a partially ordered set.Can you give me some example of each these definition: 1.Upper and Down Bound : ...
-4
votes
0answers
67 views

every(ultra)filter on set I is principle if and only if I is finite [on hold]

1)the filter generated by{a,b} is not ultra filter? 2)the filters generated by singleton are precisely the principle ultrafilters. 3)every(ultra)filter on set I is principle if and only if I is ...
1
vote
1answer
77 views

Base of a cone in a vector space: can one always choose a convex base?

Let $C$ be a pointed convex cone in a vector space $V$. This means that $C$ satisfies the three following axioms: $C + C \subset C$, $\mathbb{R}_+ \cdot C \subset C$, and $C \cap (-C) = \{ 0 \}$. ...
-4
votes
0answers
49 views

izomorphism of finite abelian group [on hold]

Please help me with rezolving this problem from Romanian "Gazeta Matematica" : "an finite abelian group G have |End G | and |Aut G | coprime numbers. Show that |G| is square free. Thank you!
0
votes
1answer
51 views

Decomposition of semi simple local systems

I found A question similar to this, but the answer wasn't clear to me and I'm not supposed to ask for further clarification in the answer section. Let $L$ a semi simple local system defined over an ...
0
votes
0answers
48 views

Optimal covering

Let consider a problem of optimal covering of Hamming space. So we have Hamming space $\{0,1\}^n$ and some integer $r$. We want to find a set $A \subseteq \{0,1\}^n$ such that any point from ...
-6
votes
0answers
33 views

Summation of Geometric Series [on hold]

Im really desperate please help!!! how can you show that a. the sum oscillates between the two values a and b for the summation of geometric series {a*r^(n-1)}` provided that this is divergent? ...
3
votes
1answer
66 views

Finiteness properties for graph of groups decompositions

My curiosity was raised by the following question and the huge variety of comments and suggestions it attracted. I wondered if a converse statement might be equally interesting. Let $G$ be a finitely ...
0
votes
0answers
22 views

Interchange summation and differentiation [migrated]

I asked this question already on math.stackexchange, but did not receive any answers see here Let $f = \sum_{n=0}^{\infty} a_n e_n $ where $e_n$ are an ONB of $L^2[0,1].$ Now assume we have that ...
3
votes
1answer
87 views

Covering finite groups by kernels

Let $G$ be a finite group. When does there exist a finite group $H$ such that every $h\in H$ is in the kernel of some epimorphism $H\to G$? This is well-known to be true for $G$ abelian, for example ...
-5
votes
0answers
42 views

Summation of geometric series divergence [on hold]

The summation of some geometric series a*r^(n-1) is divergent. But what i don't understand is this: If the summation of a geometric series is divergent, then one of its sum is: a. the sum oscillates ...
2
votes
0answers
117 views

Octonions product: inversion in the right and identity in the left

Once octonions product is studied, together with the relations with $Spin(8)$ and $SO(8)$ geometry (see for instance Robert Bryant's notes), one realises that the key fact bringing all the phenomena ...
1
vote
0answers
59 views

Asymptotic expansion square root matrix

I am looking for an asymptotic expansion for $\underline\gamma$ which is the "square root" matrix of a symmetric $p\times p$ matrix $\gamma$. Here $\underline\gamma$ is assumed to be symmetric, e.g. ...

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