# All Questions

2answers
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 ...
0answers
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 ...
1answer
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?
1answer
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 ...
5answers
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 ...
2answers
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 ...
2answers
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 ...
0answers
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) ...
0answers
59 views

2answers
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 ...
0answers
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 ...
0answers
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 ...
0answers
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 ...
1answer
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 \\ ...
0answers
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 ...
0answers
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 ...
4answers
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 ...
1answer
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 ...
0answers
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 ...
1answer
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 ...
2answers
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 ...
0answers
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 ...
0answers
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 ...
1answer
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 ...
1answer
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 ...
0answers
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 ...

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