# All Questions

**0**

votes

**0**answers

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

**0**answers

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

**0**answers

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

**1**answer

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

**0**answers

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

**0**answers

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

**1**answer

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

**0**answers

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

**0**answers

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

**0**answers

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

**0**answers

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

**0**answers

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

**1**answer

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

**1**answer

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

**1**answer

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

**1**answer

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

**0**answers

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

**0**answers

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

**0**answers

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

**1**answer

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

**0**answers

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

**2**answers

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

**0**answers

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

**0**answers

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

**1**answer

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

**1**answer

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

**5**answers

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

**0**answers

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

**0**answers

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

**0**answers

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

**0**answers

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

**1**answer

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

**2**answers

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

**1**answer

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

**1**answer

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

**0**answers

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

**0**answers

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

**0**answers

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

**0**answers

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

**1**answer

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

**0**answers

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

**1**answer

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

**0**answers

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

**0**answers

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

**1**answer

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

**0**answers

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

**1**answer

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

**0**answers

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

**0**answers

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

**0**answers

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. ...