# All Questions

**3**

votes

**1**answer

74 views

### Topology of ring of global sections of finite union of affinoid opens in a rigid analytic space

Let $X$ be a rigid analytic space over a non-Archimedean field $k$. If $U_1,\ldots,U_n\subseteq X$ are affinoid opens, then it's usually not clear whether or not the admissible open ...

**10**

votes

**3**answers

514 views

### How to write an abstract for a math paper? [on hold]

How would you go about writing an abstract for a Math paper? I know that an abstract is supposed to "advertise" the paper. However, I do not really know how to get started. Could someone tell me how ...

**3**

votes

**0**answers

69 views

### Application of finding shortest paths on Cayley graphs

For a fixed integer number $m$, Consider Cayley graph defined by all m-cycles in Symmetric group $Sym(n)$.
I know that for $m=2$,
there are some applications of finding shortest paths (or distance ...

**0**

votes

**0**answers

51 views

### Differentiating and integrating an infinite series arising from a PDE

Let us work on a bounded domain $\Omega$ with Neumann BCs, with $(\varphi_k, \lambda_k)$ being the orthonormalised eigenvectors and eigenvalues of the Neumann Laplacian. Given $u \in H^{\frac ...

**5**

votes

**1**answer

148 views

### Automorphism group of a fiber bundle surjects onto diffeomorphism group?

This should surely be well-known by I have not been able to find a good reference to the following question: Given a smooth fiber bundle $\pi\colon P \longrightarrow M$ over a smooth manifold $M$ with ...

**-1**

votes

**0**answers

35 views

### Probability/Bayes theorem/Bernoulli's experiments question [on hold]

John has rolled the dice 10 times and he said that every number form 1 to 6 has appeared at least once. Given this information find the probability of the event "number 6 has appeared at least 2 ...

**3**

votes

**1**answer

162 views

### Largest symmetric matrix given rank

Let $\mathscr{M}[n,d]$ be collection of $n\times n$ symmetric matrices with real entries from $\{0,1\}$ such that every row/column is distinct with sum of every row/column being $d$.
What is minimum ...

**2**

votes

**1**answer

111 views

### Asymptotic of min(#generators times diameter), for a Cayley graph of Sn

This post is a sequel of Diameter of symmetric group.
Let $\Sigma$ a generating subset of $S_n$, $\Gamma(S_n, \Sigma)$ the Cayley graph and $d_{\Sigma}$ the diameter of $\Gamma(S_n, \Sigma)$.
Let ...

**1**

vote

**0**answers

143 views

### Can triangulated categories be “approximated by countable subcategories” (that are triangulated but not full!)?

For a given (finite) set of (objects and) morphisms $f_i$ in a triangulated category $C$ I am interested in a (non-full!) triangulated subcategory $C'\subset C$ of "small size" that would contain ...

**0**

votes

**0**answers

41 views

### all paths between two nodes of an grid structure [on hold]

i have an 5*5 matrix numbered from 1 to 25. i wanted to print all paths between any two nodes.
...

**1**

vote

**0**answers

37 views

### Inverse Laplace Transforms of Exponential Form

I'm trying to find the velocity component of an MHD flow using Laplace transforms. R.B. Hetnarski's algorithm for inverting the laplace transforms of some exponential functions was recommended to me ...

**1**

vote

**0**answers

85 views

### Positivity of alternating series

Let $\{a_n\}_{n=0}^{\infty}$ be a sequence of positive real numbers such that $\limsup_n \frac{1}{n}\log a_n=-\infty$. Then
$$
f(x)=\sum_{n\geq 0}a_n x^n
$$
converges absolutely for all $x$. Under ...

**3**

votes

**1**answer

126 views

### Discretizing probability measures

Consider a probability distribution on $\mathbb{R}^k$, say $\mu$. Then there is a sequence of probability measures $\mu_n$ that converge weakly to $\mu$ so that each of them is discrete (takes ...

**0**

votes

**0**answers

39 views

### Does a positive-measure subset of the unit interval almost surely intersect a random translation of some countable subgroup of $\mathbb{R}$?

Please forgive me if this is a very easy question.
Let $A \subset [0,1]$ be a Borel-measurable set with strictly positive Lebesgue measure. Does there necessarily exist a countable subgroup $G$ of ...

**1**

vote

**0**answers

164 views

### What is deforming this non-complete intersection like?

Let $R = \mathbf{C}[x,y,u,v]$ be the coordinate ring of $\mathbf{C}^4$. Let $I$ be the ideal generated by $u$ and $v$, let $J$ be the ideal generated by $u$ and $y$. What are the flat deformations of ...

**2**

votes

**1**answer

126 views

### Is every weight of an integrable highest weight module in the Tits cone?

Let $\mathfrak{g}$ be a Kac-Moody algebra with Cartan subalgebra $\mathfrak{h}$, Weyl group $W$, and simple roots and coroots $\alpha_i, \check{\alpha_i}, i \in I$, respectively. Let $L$ be an ...

**-5**

votes

**0**answers

76 views

### a basic question [on hold]

If $\{A_i\}_{i=1}^{\infty}$, and $A=\bigcup_{i} A_i$ then we can
write this union as a disjoint union.
For this $B_n=A_n-\bigcup_{i=1}^{n-1} A_i$ , then
...

**1**

vote

**2**answers

71 views

### Extending GUE to a measure on operators?

Let $\mathcal H_n$ denote the space of Hermitian $n\times n$ matrices and let $\mu_{GUE}$ denote the following measure on $\mathcal H_n$:
$$
\mu_{GUE}(dM) = \exp\left( -\frac{n}{2}\text{tr}\ ...

**-1**

votes

**0**answers

89 views

### Meromorphic functions on $U^2 = T^3 + 1$, genus [on hold]

This question Asked in S.E but no, answer ,I would like to know how do i find a genus of
$F$
. Let $k$ be a field of characteristic $\neq 2$, and consider the quadratic extension $F$ of $k(T)$ ...

**2**

votes

**2**answers

145 views

### Transitivity of discriminant for flat algebras

Sorry if the question doesn't feed this site, I'm reposting it from MSE. Nobody answered it there and I couldn't find the proof in general case(whenever it was mentioned the proof was referred to as a ...

**3**

votes

**0**answers

114 views

### When there exists some “cone” of a morphism of (ind-representable) cohomological functors?

I am interested in cohomological functors from a certain small triangulated category $C$ to abelian groups.
The question is: given a tranformation $F\to G$ of two functors of this sort, is it ...

**3**

votes

**1**answer

84 views

### A differential equation with continuous coefficient and no solution in a reflexive Banach space?

Is there a reflexive Banach space $B$ and a continuous map $f:B\to B$ such that the differential equation
$$ \frac{d x (t)}{dt} = f(x(t)) $$
with some initial condition $x(0)=x_0$ has no solution?

**2**

votes

**1**answer

126 views

### Cauchy completeness of the real closure

Let $k$ be an ordered field of cofinality $cf(k)$ whose Cauchy $cf(k)$-sequences are convergent.$^{(1)}$
Let $\mathcal{R}(k)$ be its real closure.
As an algebraic extension of $k$, it has the same ...

**13**

votes

**5**answers

1k views

### How to explain the concentration-of-measure phenomenon intuitively?

One way to phrase the
"concentration-of-measure"
phenomenon is that,
for a Euclidean sphere $S^d$ in $d$ dimensions, for large $d$,
"most of the mass is close to the equator, for any equator."1
...

**3**

votes

**2**answers

68 views

+50

### What's an example of a rough path that's not Ito/Stratonovich-Brownian rough path?

The only rough path that I've ever seen discussed are the ones associated with Brownian motion. I could use a "rough path" for any nice function, defeating the point. In particular are there ...

**2**

votes

**2**answers

144 views

### A conservative, non faithful functor between triangulated categories

Suppose that we have:
1) triangulated categories $C,D$, each equipped with a $t$-structure.
2) triangulated functor $F: C \to D$ which is $t$-exact.
3) $F$ reflects isomorphisms, i.e. is ...

**1**

vote

**0**answers

27 views

### Valid KKT Constraint Qualification? Linear constraints not full rank, Jacobian of nonlinear constraints full rank and independ. of linear constraints

For a nonlinear optimization problem having only linear constraints, by the Linearity Constraint Qualification, no further constraint qualification is required for the Karush-Kuhn-Tucker (KKT) ...

**3**

votes

**0**answers

59 views

### Searching information on a certain function with a fixed point property connecting Moebius $\mu$ and Fibonacci numbers

Let $\mu$ be the Moebius function and define for $1\leq n\in\mathbb{N}$
$$
f(n) =
\left\{
\begin{array}{ll}
\mu\left(\frac{n}{2}\right) + \mu\left(\frac{n}{4}\right), & n\equiv 0, 4, 8\mod 12, \\
...

**0**

votes

**0**answers

33 views

### Largest Set of Special Unitary Matricies With Invariant Subspace For Adjoint Action

I am trying to solve the following. Given the special unitary group $SU(n)$ and its adjoint action $Ad_{U}: \mathfrak{su}(n) \rightarrow \mathfrak{su}(n)$, what is the largest subset of $SU(n)$ such ...

**2**

votes

**1**answer

41 views

### Vanishing Restricted Isometric Constant

In compressed sensing, we are interested in the restricted isometry property. Suppose the design matrix is $n$ by $p$, consisting of $np$ iid $\mathcal{N}(0, 1/n)$ entries. Assume both $n$ and $p$ are ...

**-3**

votes

**0**answers

35 views

### Number of homomorphisms between finitely generated abelian group and a finite cyclic group [on hold]

This is the situation:
Suppose we have a finitely generated group $G= \mathbb{Z}^r \times E$ with $E$ it's tortion subgroup and $m=$ exponent of $E$ i.e. the least natural number such that $x^m=1$ ...

**3**

votes

**2**answers

186 views

### Sets $X,Y \subset [0,1]$, stronger than being measure $0$, such that $X+Y = [0,2]$

A set $X\subset \mathbb{R}$ is called nice if for every $\epsilon > 0$ there are a
positive integer $k$ and $k$ bounded intervals $I_1,I_2,...,I_k$ such that
$X \subset I_1 \cup I_2 \cup ...

**2**

votes

**0**answers

164 views

### Can estimate upper bound of $|p_{i}|$ or $|q_{i}|?$

when I Find the diophantine-equation rational points $$2y^2=x^6-x^2+2$$
I using Faltings's theorem showed that there are only finitely many solutions,if we assmue that
...

**3**

votes

**1**answer

141 views

### higher dimensional analogue of EGZ theorem

The EGZ theorem states that any multiset of $2n-1$ integers has a subset of size $n$ the sum of whose elements is a multiple of $n$.
Kemnitz-Reiher theorem is a 2-dimensional analogue of EGZ. Here is ...

**-6**

votes

**0**answers

73 views

### A Paradox by a Variant of Von Neumann's coin toss [on hold]

All biased coins are fair.
If I have a biased coin whose probability of heads is $p$, and keeps tossing it, and only stops when the number of heads equals tails, then each sequence I get has a ...

**3**

votes

**0**answers

57 views

### On an automatic translation of typed lambda calculus in untyped lambda calculus

I have a question regarding the "compilation" of typed lambda calculus in untyped lambda calculus.
Take for example the inductive definition of lists, with introduction rules:
and:
We can ...

**1**

vote

**1**answer

51 views

### Gradient of distance function at cut points on Alexandrov spaces

Let $M$ be an $n$-dim Alexandrov space with curvature bounded below $sec \geqslant k$, possibly non-compact. We assume that $M$ has no boundary for simplicity. For a compact subset $K \subset M$, the ...

**-1**

votes

**0**answers

84 views

### Graph Theory text for a social scientist [on hold]

I am a graduate student in Economics. I have a decent grounding in maths, but I've never studied graph theory or combinatorics. I need to study graph theory in order to analyse production networks. ...

**10**

votes

**0**answers

514 views

### How is $S^1$-equivariant elliptic cohomology affected as we continuously vary the underlying elliptic curve?

Background:
Grojnowski constructs a $S^1$-equivariant cohomology theory $E^*_{S^1}$ which trivially satisfies $$\text{Spec }E^*_{S^1}(pt) = E$$
where $E$ is a mild modification of a complex elliptic ...

**9**

votes

**0**answers

86 views

### Is there a nice formula for the “non-crossing substitution” of linear combinatorial species?

Background
A linear species is a functor
$$F : \mathrm{Lin} \to \mathrm{FinSet},$$
where $\mathrm{Lin}$ is the category of totally ordered sets and bijections and $\mathrm{FinSet}$ is the category ...

**-2**

votes

**0**answers

44 views

### Clockwise sorting of circle point [on hold]

I have list of 3d points ( -2.03591339559,-0.560307972035,-0.474112849094),
( -2.05118196203,-0.55785528461,0.5743518821),
( -1.02999710644,1.16145402736,0.585203882893),
( ...

**2**

votes

**1**answer

371 views

### Mathematics equivalent of Feynman's Lectures in Physics? [on hold]

I'm looking for an equivalent of "Feynman's Lectures in Physics" in mathematics. I'm specifically looking for book/books that delve into, using Feynman's words, "the meaning of things".

**3**

votes

**1**answer

51 views

### Convex optimization with full subdifferential information

Can anyone direct me to any algorithms or theorems that describe the difficulty of solving a non-smooth convex optimization problem for the special case where the full subdifferential is available? ...

**0**

votes

**0**answers

72 views

### A question about Segre class

Suppose $C$ is a cone over $X$.(i.e.$C=\operatorname{Spec}S$, where $S$ is a sheaf of $O_X$ algebras.)
The Segre class $s(C)$of $C$ is the class in $A_*(X)$ defined by ...

**1**

vote

**0**answers

92 views

### Steepest descent path and Picard-Lefschetz theory

Assume that an ordinary integral of the form
$$I=\int_{-\infty}^{\infty}dx e^{-f(x)} $$
for some real function $f(x)$ is given where $f(x)$ is well defined over all $\mathbb{R}$ and the integral is ...

**2**

votes

**2**answers

134 views

### Extremal functions for Gagliardo-Nirenberg inequality

Recently I read about the Gagliardo-Nirenberg inequality. And I would like to ask about the attainability and the maximizers of the GN inequality:
$(∫|u|^{r}dx)^{\frac{1}{r}} \leq ...

**0**

votes

**0**answers

55 views

### Random Cluster Model only for bond percolation?

Can someone please tell me which of the following statements I make are true of the current state of the art:
The Random Cluster Model is a generalization of bond percolation (with possibly ...

**-3**

votes

**1**answer

155 views

### Is :$\frac{\Bbb d}{\Bbb d x}$ a chaotic operator in infinite-dimensional Hilbert space? [on hold]

I proposed this question in SE but no answer ,may I have a problem in my question, I would like to know when $\frac{\Bbb d}{\Bbb d x}$ does chaotic operator in Hilbert space ?
Let $H$=$L^2(\mathbb ...

**0**

votes

**1**answer

261 views

### On a claim of Zagier on extending a map to cocycle

Zagier, in his paper 'Some Surprising Consequences of the Cohomology of SL$_2(\bf{ Z})$' (link, p. 6), studies the action of $\Gamma=PSL_2(\bf Z)$ on a vector space $V$, denoting the action by $v\ |\ ...

**6**

votes

**0**answers

107 views

### What is the significance of having Prime Ideal Theorem in models for failure of Axiom of Choice? [migrated]

Prime Ideal Theorem says:
PIT: Every ideal on a Boolean algebra can be extended to a prime ideal.
It follows from Axiom of Choice but is weaker than it.
In many cases I saw that people check ...