# All Questions

**2**

votes

**2**answers

148 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

116 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

93 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

127 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 ...

**15**

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

91 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

148 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

32 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

36 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 ...

**-4**

votes

**0**answers

43 views

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

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

188 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

166 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

144 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

76 views

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

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

58 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

61 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

85 views

### Graph Theory text for a social scientist [closed]

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

547 views

### How can we construct an $S^1$-equivariant cohomology theory over an elliptic curve in positive characteristic?

Author's note: The original question was "How is an $S^1$-equivariant elliptic cohomology affected as we continuously vary the underlying theory elliptic curve?" This was not answered, so I altered ...

**9**

votes

**0**answers

93 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 [closed]

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

381 views

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

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

54 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

73 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

94 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

139 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

58 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

156 views

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

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

268 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 ...

**4**

votes

**1**answer

185 views

### Does the proof of Picard's theorem become simpler by increasing the number of points that are not attained?

Let $f$ be an entire analytic function which attains all but $k$ complex numbers $z_1,\ldots,z_k$. Is there any elementary proof, for some $k$, that $f$ is constant?

**0**

votes

**0**answers

50 views

### Duality results for quadratic equality constrained optimization problem

Consider the optimization problem
$$
\begin{align}
\min_{x\in\mathbb{R}^n}&\quad f(x) = x^TA_0x+b_0^Tx+c_0\tag{P1}\\
\nonumber \text{subject to } \quad & g_i(x) = x^TA_ix+b_i^Tx+c_i = ...

**27**

votes

**2**answers

2k views

### A curious determinantal inequality

In my study, I come across the following curious inequality, which I do not know a proof yet (so I am asking it here).
Let $A, B$ be $n\times n$ (Hermitian) positive definite matrices. It is very ...

**1**

vote

**0**answers

60 views

### Type theory: can multiple elimination rules be defined, in principle?

I'd like to ask a question on type theory:
Consider the usual type theoretical definition of the natural numbers. We could give an elimination rule in the form:
or in the form:
I called the ...

**4**

votes

**0**answers

121 views

### inequality in a shape of inclusion exclusion formula

I have two inequalities to show, both of which describe some probabilities. First I know how to handle, and it follows from applying arithmetic-harmonic mean inequality:
consider 9 numbers ...

**0**

votes

**0**answers

71 views

### How can I keep the roots of f(x)^n+g(x)^m far away from the roots of f and g?

More specifically, suppose for example I have $h(x)=\sum_{i=1}^k (x-i)^{d_i}$. Can I get any handle on the roots of $h(x)$?
Can I somehow guarantee that the roots of $h(x)$ are not arbitrarily close ...

**6**

votes

**1**answer

168 views

### Decidability of an Algebraic System in Real Numbers

Is there an algorithm to decide whether an algebraic system
\begin{gathered}
{f_1}({x_1}, \ldots ,{x_n}) = 0 \hfill \\
\vdots \hfill \\
{f_m}({x_1}, \ldots ,{x_n}) = 0 \hfill \\
...

**-2**

votes

**0**answers

20 views

### projection of point, Coordinates [closed]

Please see the link below
http://mathworld.wolfram.com/Point-LineDistance3-Dimensional.html
I can get 'd' from the above link
How about getting the intersection point? Do we have any relation for ...

**-1**

votes

**0**answers

49 views

### square classes of quadratic extensions of 2-adic fialds [migrated]

I have a question about square classes of quadratic extensions of 2-adic fields. I appreciate anybody help me to understand.
Why all elements of $1+\mathfrak{p}^5$ are square in ...

**12**

votes

**4**answers

337 views

### Maximum of the Vandermonde determinant / minimum of the logarithmic energy

The problem is to find the asymptotics (as $n\to\infty$) of the maximum (say $M_n$) of the Vandermonde determinant
$$V_n:=\prod_{0\le i<j\le n-1}(a_j-a_i)
$$
over all $a_0,\dots,a_{n-1}$ such ...

**0**

votes

**1**answer

175 views

### Does unique factorization for automorphic L-functions imply a weakened form of Ramanujan conjecture?

Selberg orthonormality conjecture for automorphic L-functions was proven under Ramanujan conjecture, and SOC itself implies unique factorization for those L-functions.
My question is: does the ...

**0**

votes

**0**answers

110 views

### What is known about order of torsion of jacobian of hyperelliptic curve over finite field? [on hold]

Suppose $J$ is jacobian of hyperelliptic curve $C$ over $F_p$ of genus $g$. Suppose $T$ is torsion of $J(F_p)$.
What is known about order of $T$?
Are there some bounds on order of $T$? Can one say ...

**1**

vote

**1**answer

89 views

### Diffeomorphism variation of the Christoffel symbol

Under an infinitesimal diffeomorphism the Riemann metric changes by the Lie derivative
$$
\delta g_{\mu\nu} = ({\mathcal L}_\xi G)_{\mu\nu}=\nabla_\mu \xi_\nu+\nabla_\nu \xi_\mu
$$
and under a change ...

**4**

votes

**2**answers

236 views

### Definition field of isogeny between abelian varieties

Let $K$ be a number field. Let $A$ and $B$ be abelian varieties over $K$. Assume that $A$ and $B$ are isogenous over $\bar{K}$, the algebraic closure of $K$. We further assume that the endomorphism ...

**3**

votes

**0**answers

59 views

### Braid relations $n_\alpha n_\beta n_\alpha \ldots = n_\beta n_\alpha n_\beta \ldots $ in arbitrary reductive groups

I'm currently trying to prove or disprove the following claim. First let me set up some notation.
Let $G$ be a connected reductive group over a field $K$, let $S \leq Z \leq N \leq G$ be respectively ...

**2**

votes

**0**answers

94 views

### Gauge freedom in the tetrad

I'm reading the following paper about Petrov type D space times called "Type D vacuum metrics":
http://scitation.aip.org/content/aip/journal/jmp/10/7/10.1063/1.1664958
by Kinnersley. I have a ...

**2**

votes

**1**answer

67 views

### Is this series involving hyperbolic functions uniformly convergent?

Suppose that
$\mu_k$ is an increasing sequence of numbers such that $0 < \mu_1 \leq \mu_2 \leq ..$ with $\mu_k \to \infty$ as $k \to \infty$
$\sum_{k=1}^\infty |u_k|^2 < \infty$ and ...

**3**

votes

**1**answer

69 views

### Non-field example of a commutative, local, dual ring with nilradical $N$ such that $ann(N)\nsubseteq N$

I asked this question on math.stackexchange a month ago with no progress, even after a bounty. I hope to eliminate one if the other receives a satisfactory answer.
For an ideal $I\lhd R$ in a ...

**5**

votes

**0**answers

140 views

+50

### How to get a polygon from a translation surface $(X,\omega)$

Let $S_g$ be a compact topological surface of genus $g$. I know there is the correspondence
$\{$Abelian differentials on compact Riemann surfaces of genus g$\}\leftrightarrow\{$ Translation surfaces ...