# All Questions

**1**

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**0**answers

18 views

### Natural probability on integers

This is a follow-up to this classical question asked recently here: we now (e.g. using the second Borel-Cantelli Lemma) that no probability measure on $\mathbb{Z}$ has the property that $n\mathbb{Z}$ ...

**2**

votes

**0**answers

23 views

### divisible by all standard prime numbers

This question is about prime numbers in nonstandard models of Peano Arithmetic. Every such model looks like N+AxZ, where A is a dense linear order without end points.
There are many nonstandard ...

**-1**

votes

**0**answers

18 views

### References request: are there some references about simple modules of group algebras?

Are there some references about constructing the simples, determining the dimensions of simple modules and describing decompositions of tensor products of simple modules of group algebras? Thank you ...

**1**

vote

**0**answers

12 views

### The intersection of two $l_1$ balls

Let $B_1$ and $B_2$ be two balls in $\mathbb{R}^n$ with respect to the $l_1$ norm that have different radii and different centers. Is there an upper bound for the number of vertices that $B_1\cap ...

**1**

vote

**0**answers

14 views

### Equivariant Harmonic Maps to R-tree and Korevaar-Schoen Convergence

Thank you for spending time on the following question.
I am trying to make an explicit example of Korevaar-Schoen convergence. The problem I am facing is that I can not find the limit of the harmonic ...

**0**

votes

**0**answers

12 views

### persistence of regularity for nonlinear Klein-Gordon equation

I have been reading the paper on nonlinear Klein-Gordon equation(NLKG) for initial data in modulation space: For detail please see the paper "Klein-Gordon Equations on Modulation Spaces (2014)" ...

**1**

vote

**0**answers

38 views

### Do we know any bound on $lcm(2^1-1, 2^2-1,…,2^n-1)$?

We know that lcm(1,...n) is approximately $e^n$ and and also we know that $gcd(2^a-1, 2^b-1)=2^{gcd(a,b)}-1$.
I wonder if there exists an upperbound/lowerbound/approximation for $lcm(2^1-1, ...

**-2**

votes

**1**answer

61 views

### Which function is $f(x)=x$ when $x>=0$ and $f(x)=0$ when $x=-1$ [on hold]

This is a very simple question that will not be a problem for any mathematician. With enough time I could come up with a non-optimal solution myself, but I know some of you may just provide the ...

**2**

votes

**0**answers

28 views

### Carleman Estimates in a Riemannian manifold

Suppose $(\Omega,g)$ is a Riemannian manifold where $\Omega$ is a domain in $\mathbb{R}^3$ with smooth boundary. Furthermore suppose there exists a global coordinate chart $(x_i)$ such that $g= dx_1^2 ...

**0**

votes

**0**answers

27 views

### Ness and suff condition for the embedding $A^X\otimes_A A^Y\rightarrow A^{X\times Y}$

This question is related to that one
Commutation of tensor products with inverse limits in a specific case
where it received a (partial) answer.
I can complement a bit: in any case, $A$ is supposed ...

**-2**

votes

**0**answers

36 views

### Adjoint of Expoenential Map [on hold]

Can the adjoint of the derivative of the exponential map of a lie group, be understood via the ad operator?
If so how, explicitly?

**0**

votes

**0**answers

25 views

### A solvable Lie algebra

Consider the Lie algebra $\mathfrak{g}$ span by $x_1,\ldots,x_n,y_1,\ldots,y_n$ with the commutator
$\left[y_i,x_i\right]=y_i, \left[x_i,x_{i+1}\right]=y_i, \left[y_i,x_{i+1}\right]=-y_i,\quad 1\leq ...

**-4**

votes

**0**answers

37 views

### What are all the factors of n=p^2q^3r? [on hold]

n=p^2q^3r
It has a total of 24 factors. I need to show all of the factors.

**0**

votes

**0**answers

14 views

### $l$-weights and $l$-character of finite-dimensional highest $l$-weight representation of $L\mathfrak{g}$

I am trying to solve the following problem, which is related to relatively recent results, but I am not sure how to do it.
Problem
In this problem, $\mathfrak{g}=\mathfrak{sl}_{2}$. We study ...

**0**

votes

**0**answers

20 views

### Transitive closure of balanced bounded mass transport

Given two $\sigma$-finite measures $\mu$ and $\nu$ on $\mathbb{R}^n$, write $\mu \sim \nu$ iff there exist countable decompositions $\mu = \mu_1 + \mu_2 + \cdots$ and $\nu = \nu_1 + \nu_2 + \cdots$ ...

**0**

votes

**0**answers

29 views

### Upper bound involving random orthogonal projection

Let $R$ be an $n\times N$ random matrix with i.i.d. standard Gaussian entries, $n<N$, and let $M:=(RR^T)^{-1/2}R$. Let $u,v\in \mathbb{R}^N$ non-random and s.t. $u^Tv=0$ and $\|u\|>\|v\|$.
I ...

**3**

votes

**0**answers

66 views

### Writing down gerbes explicitly over the projective line

Let $X = [\mathbb P^1/(\mathbb Z/2\mathbb Z)]$, where we take the trivial action of $\mathbb Z/2\mathbb Z$ on $\mathbb P^1$. Is this DM stack over $\mathbb C$ a gerbe over $\mathbb P^1$? Is it the ...

**0**

votes

**0**answers

54 views

### Rationality of intersection of algebraic groups

Suppose that $G$ (defined over $\mathbb{Q}$) and $H$ (defined over $\mathbb{R}$) are two algebraic subgroups of a larger algebraic group defined over $\mathbb{Q}$. Assume that $G(\mathbb{R})$ and ...

**0**

votes

**0**answers

19 views

### Rate-Distortion theory: What is the distribution of distortion on an optimal encoder?

If we wish to encode a gaussian source, $X\sim\mathcal{N}(0,\sigma^2)$ at rate $R$, rate-distortion theory tells us that the lowest mean-squared-error we can achieve from encoding is $\sigma^2 ...

**-4**

votes

**0**answers

38 views

### how can i calculate the 2x2x2 (doublet tensorproduct) [on hold]

help me
the simple question
how can I calculate the
doublet@doublet@doublet
@ : tensor product
please teach me

**14**

votes

**3**answers

766 views

### Should one post a paper on the arXiv if it is not intended to be published?

A brief description: I have written a paper which contains a new result which I believe is somewhat important but not vital to the field. It is a generalization of an existing proof to get ...

**-2**

votes

**0**answers

58 views

### Can $SL(d, \mathbb{R})$ be embedded in $sp(n, \mathbb{R})$ for n large enough? [on hold]

my question is that can $SL(d, \mathbb{R})$ be embedded in $sp(n, \mathbb{R})$ for n large enough? And i also ask similar question for the Lie algebra.

**2**

votes

**2**answers

56 views

### Moment problem for discrete distributions

Let $x_1, \dots, x_N \in \mathbb R$ and consider the discrete distribution $\mu := \frac{1}{N} \sum_{i=1}^N \delta_{x_i}$, where $\delta_x$ denotes the Dirac measure, i.e. for any measurable set $B ...

**19**

votes

**8**answers

613 views

### Historical (personal) examples of teaching-based research

The phrase "teaching-based research" brings to mind research about teaching, though important, it is not what I mean. Unfortunately, I couldn't come up with a better phrase, thus please bear with me ...

**0**

votes

**0**answers

38 views

### G-delta sets and Lebesgue measure [on hold]

The set S of all subsets in R^n which are of the form G\N, where G is a
G-delta set and N a null-set (=outer Lebesgue measure zero)
coincides with the set of all Lebesgue measurable sets.
How could ...

**0**

votes

**0**answers

38 views

### Question on homogeneous measures

Let $\mu$ be a strictly positive measure ($m(a)=0$ iff $a=0$) on a Boolean algebra $B$. $\mu$ is called homogeneous if it have the same Maharam type on every $b\in B$.
By additive measure algebra I ...

**0**

votes

**0**answers

48 views

### Largest ball with fixed center in a a convex region

Let $x_0$ be a point contained inside a compact, convex set $C\subset\mathbb{R}^d$, which is of the form $C=\{x:f(x)\leq0\}$ for some explicit convex function $f$. Is there a computationally ...

**0**

votes

**0**answers

26 views

### monotonicity alike functions

assuming we have two smooth function ${f_1},{f_2}:{R^N} \to R$,
under what condition, we have
${f_1}\left( {{{\bf{x}}_1}} \right) \ge {f_1}\left( {{{\bf{x}}_2}} \right) \leftrightarrow ...

**10**

votes

**1**answer

199 views

### Existence of a “quasi-uniform” probablility distribution on $\mathbb{Z}$

Does there exist a probability distribution on $\mathbb{Z}$ such that
for every integer $n\geq 1$, the probability that a random integer $x$
is divisible by $n$ equals $1/n$?
Henry Cohn has an ...

**7**

votes

**0**answers

74 views

### Between Tietze's and Dugundji's Extension Theorems

The celebrated Tietze Extension Theorem asserts that any continuous real-valued function defined on a closed subset of a normal space, can be extended to a continuous function on the whole space. Seen ...

**0**

votes

**0**answers

21 views

### What is $T>0$ large enough such that $\mu\left(B\right)<\varepsilon$?

Let $\left(M,\sigma,\mu\right)$ where $\sigma$ is a Borell $\sigma$-algebra
and $\mu$ is a probability $f$-invariant. Let $x\in M$, $E\subset M$ measurable
and $f:M\rightarrow M$ a measurable ...

**-2**

votes

**0**answers

21 views

### $\mu$ is a $f$-invariant measure [on hold]

Let $\left(M,\sigma\left(\tau\right),\mu\right)$ a measure space
where $\mu$ is a measure finite, $\tau$ is a topology in $M$, i, e, $\sigma\left(\tau\right)$
is a Borel $\sigma-$algebra. Let ...

**1**

vote

**1**answer

46 views

### Local Uniform Convergence

Suppose $f(x)$ is a positive continuous function on $[0,\infty)$ and that $f(x+u)-f(x)\to 0$ as $x\to\infty$ for every given $u\in[0,\infty)$. Prove that, given any $a>0$, $f(x+u)-f(x)\to 0$, as ...

**3**

votes

**1**answer

156 views

### Character table of $\mathrm{SL}_2(\mathbb{Z}/p^n\mathbb{Z})$

Is there any reference where I can find the character table of $\mathrm{SL}_2(\mathbb{Z}/p^n\mathbb{Z})$? A simple search in google gave me this paper of Philip C. Kutzko on "The characters of the ...

**-1**

votes

**0**answers

48 views

### Is Ш a good parameter for the failure of Global-Local principle for abelian varieties? [on hold]

Comparing to class group cases : we have an isomorphism
$Cl(K)\rightarrow \prod \left(K^\times \backslash K_p^\times /O_p^\times \right)$ for a number field $K$.
Similarly, for an elliptic curve ...

**4**

votes

**1**answer

96 views

### Existence of $\kappa$-Suslin trees above a measurable cardinal

We have learned from Joel David Hamkins and Monroe Eskew that:
Answers:
Having a measurable cardinal $\delta$ we can force a $\kappa$-Suslin tree for many $\kappa$'s above $\delta$.
But is the ...

**3**

votes

**2**answers

413 views

### What's the name of this geometric mathematical modeling problem?

There is a right angle corner with width 1 in both directions. One wants to find the largest area shape which can pass through this corner.
I know that this is a famous problem, but what is it called?
...

**0**

votes

**1**answer

76 views

### Equivalence of Lie subalgebras, within a (irreducible) representation

Lie subalgebras inside simple Lie algebras (of type ABCDEFG) have been classified up to equivalence, and linear equivalence (by Dynkin et al). How does one classify embeddings of a Lie algebra h ...

**2**

votes

**3**answers

212 views

### Is every algebraic $K3$ surface a quartic surface? [on hold]

Algebraic $K3$ surface means the $K3$ surface admits an ample line bundle. So the question is equivalent to asking whether every algebraic $K3$ surface can be embedded in $\mathbb{P}^3$.

**0**

votes

**1**answer

26 views

### A short problem with minimal projections and biprojections

Let $(N \subset M)$ be a finite index irreducible subfactor, $P=P(N \subset M)$ its planar algebra.
Notation: For $a,b \in P_{2,+}$ positive operators, then $\langle a,b \rangle$ is the biprojection ...

**5**

votes

**1**answer

69 views

### Decay of solutions to Schrodinger equation with local minimum in potential

Consider the one-dimensional Schrodinger operator on the real line $\mathbb{R}$ given by
$$ L = - \partial_x^2 + V $$
where $V$ is a potential with the following properties:
$V$ is non-negative, ...

**4**

votes

**0**answers

212 views

### Why does this fundamental group not have elements of finite order? [duplicate]

Let $X$ be a subset of $\mathbb R^3$ with its induced topology and let $a\in X$ be a point. Then the fundamental group $\pi_1(X,a)$ seems not to have elements of finite order (except the identity of ...

**0**

votes

**0**answers

80 views

### How large can a set of nearly equidistant points be?

Suppose that $D$ is a set of points in $\mathbb{R}^{k}$ such that all pairwise distances between them belong to $[1,1+\epsilon]$.
It seems that such a set cannot be very large and that its ...

**1**

vote

**1**answer

72 views

### Representability of deformation functors via SGA

I'm trying to understand Böckle's proof of Theorem 2.1.1 in his notes on deformation theory.
Let's start with some motivation. Let $\Gamma$ be a profinite group (I'm thinking of an absolute Galois ...

**3**

votes

**1**answer

36 views

### Is $[0,1]^\kappa$ an affine complete lattice?

A $k$-ary function $f$ on a bounded distributive lattice
$L$ is called compatible if for any congruence relation $\theta$ on $L$ and $(a_i, b_i)\in \theta$ for $i=1,\ldots,k$ we always have ...

**2**

votes

**1**answer

116 views

### Ehresmann fibration theorem for manifolds with boundary

All manifolds in consideration may have nonempty boundary and may be disconnected.
Let me fix a definition first. A map between smooth manifolds $M\rightarrow N$ is a fiber bundle, iff it's locally ...

**2**

votes

**1**answer

166 views

### Existence of a projection operator onto subspace of Hilbert space

Let $V \subset H$ be Hilbert spaces with a continuous, compact and dense imbedding. Let $\{w_j\}_j \subset V$ be a basis of $V$ and of $H$ (so finite linear combinitions are dense) which is not ...

**4**

votes

**1**answer

111 views

### Embedding of classical into intuitionistic linear logic

Following on from this recent question, there is another construction that is well-known, but I don’t know a good primary source for: the Kolmogorov-style double-negation embedding of classical into ...

**-1**

votes

**1**answer

85 views

### If $(X_n+Y_n)$ has bounded variance, is the same true for $(X_n)$ and $(Y_n)$? [on hold]

let $(X_n)$ and $(Y_n)$ be two sequences of random variables defined on the same probability space such that the variance of all components $X_n$, $Y_n$ is finite and the sequence of variances of ...

**0**

votes

**0**answers

59 views

### When does the integral of a Dolbeault-exact form vanish?

What conditions (if any) can be imposed on a Kahler manifold $M$ so that we get a Dolbeault analogue of Stokes' theorem on a closed manifold, i.e.
$\int_M \partial ( ... ) =0$
The trivial solution ...