3
votes
1answer
273 views

A good book on adeles and ideles

Many results in number theory are stated either in a classical language or in an adelic one. I am often impressed of the efficiency and the satisfactory computational properties of the adelic setting, ...
5
votes
1answer
379 views

Is fourier analysis necessary to prove this?

I have a couple of inequalities that I want to prove. The proof is easy using fourier analysis but I am wondering whether there is a proof that does not use fourier analysis. 1) For any $c, s > ...
-3
votes
0answers
74 views

Inequality with five variables [on hold]

Let $a$, $b$, $c$, $d$ and $e$ be positive numbers. Prove that: $\frac{a}{a+b}+\frac{b}{b+c}+\frac{c}{c+d}+\frac{d}{d+e}+\frac{e}{e+a}\geq\frac{a+b+c+d+e}{a+b+c+d+e-3\sqrt[5]{abcde}}$ Easy to show ...
-2
votes
0answers
33 views

triangular inequality [on hold]

If $|a_n-L|\leq \epsilon$ and $|a_n-L'|\leq \epsilon$, then by the triangular inequality $|L-L'|\leq 2\epsilon$ I know that the triangular inequality says if $|a-b| \leq |a|+|b|$. However, I could ...
-2
votes
1answer
153 views

A calculus question [on hold]

Fix $q>1$. Define the function $$ f_q(c):=\int_e^\infty \frac{e^{-c r^2}r}{\log(r)^q}d r. $$ The problem is whether the following is true, $$ \lim_{c\rightarrow 0} c \log(1/c)^q f_q(c) = C \in ...
3
votes
1answer
154 views

Is $G \rightarrow G/P$ surjective on $K$-points over a local field?

Let $K$ be a local field, $G$ a (connected) reductive $K$-group, and $P \le G$ a parabolic subgroup. Is the map $G(K) \rightarrow (G/P)(K)$ necessarily surjective, and, if so, then why?
0
votes
0answers
77 views

Big polynomial similar to a small rational function on a subset of points

Consider a real polynomial $p(x_1,x_2,\dots,x_n)$ that when evaluated on $x_i\in \{0,1\}$ takes values only in $\{0,1\}$. It is clear that $p(x_1,x_2,\dots,x_n)$ can be multilinear (multiaffine) ...
-5
votes
0answers
54 views

Fermat's little theorem with smaller powers [on hold]

I am having some trouble using Fermat's Little Theorem: (a^p-1) = 1 (mod p) I am able to solve something where the power is larger than what we are dividing by, but how would I go about solving ...
1
vote
0answers
190 views

Is the upper half plane an algebraic stack?

Here by algebraic stack I mean an algebraic stack over the etale site $\textbf{Sch}/\mathbb{C}$. So I've read from various nonrigorous sources that the upper half plane $\mathcal{H}$ is a fine moduli ...
0
votes
0answers
47 views

Guess A Property Of The Integral Average Value Function [on hold]

Let $f$ be a function that is defined on $[a,b]$ and Riemann integrable on $[a,b]$. Def 1. $$\hat f(x)=\begin{cases} f(x),& \text{if }x\in[a,b], \\ f(a),& \text{if }x<a, \\ ...
5
votes
0answers
118 views

Quotient of the hyperbolic plane with respect to commutator group of $\pi_1(\Sigma_g)$

Let $\Sigma_g$ be a Riemann surface of genus $g\geq 2$ and $G=\pi_1(\Sigma_g)$. Let $\pi\colon \mathbb{H}\to \Sigma_g$ be the universal covering map. What kind of surface is $\mathbb{H}/[G,G]$? ...
-2
votes
0answers
59 views

Stable curves and degenerations of smooth ones [on hold]

i'm approaching the study of Deligne-Mumford compactification for the moduli space of smooth curves of genus $g$. I'm trying to understand the geometrial meaning of stable curves: i know they have a ...
0
votes
0answers
28 views

How is constrained optimization done? [on hold]

I am trying to implement an optimizer described in http://arxiv.org/pdf/1406.2572v1.pdf I have an objective function, gradient and hessian. The algorithm for unconstrained optimization is described ...
0
votes
1answer
66 views

About the regularity of the boundary of a set

Consider $\Omega_1, \Omega_2$ two convex, bounded domains in $R^n$ with $\Omega_1 \supset \overline{\Omega_2}$ and suppose that $\operatorname{dist}(x, \partial \Omega_2) =\min_{y \in \partial ...
1
vote
0answers
44 views

Is there an efficient way to compute the “complete subset regression”?

Background: Let $X \in \mathbb{R}^{N\times K}$ and $y \in \mathbb{R}^{N\times 1}$ be data for a regression problem. The aim is to find $\beta \in \mathbb{R}^{K\times 1}$ such that $X\beta \approx y$ ...
5
votes
1answer
202 views

Associative Ring Spectra and Derived Completion

So, I was thinking before that this might have some nice, simple topos theoretic explanation, but Jacob disabused me of that notion. However, I'm still very interested in the following question: Is ...
3
votes
2answers
115 views

A lower bound on $\|\cdot\|_{p_{\ast}}$ image of $\ell^{q_{\ast}}$ vectors

The motivation for this question comes from this paper where we study lower bounds on the complexity of convex optimization algorithms (BTW, if you find a better title for my question, please let me ...
10
votes
3answers
339 views

Take contraction wrt a vector field twice and define kernel mod image. Does that give anything interesting?

I apologize in advance if this question is too vague for mathoverflow. My main aim is to get some references for a concept. First, we make the following observation: let $X: M \rightarrow TM $ be a ...
0
votes
0answers
44 views

Convergence of Selberg type Zeta function

Let $X=G/K$ be a Riemannian symmetric space without compact factor. We can assume $G$ is connected and real reductive. $K$ is a maximal subgroup of $G$. Let $\Gamma$ be a discrete torsion free ...
0
votes
2answers
151 views

Equidistribution of rational points on an algebraic variety

Suppose that we have a variety $X \subset \mathbb{P}^{n}$ defined over $\mathbb{Q}$. Suppose we have $S$ many rational points on $X$ inside the box defined by $|x_i| \leq B_i$ for $i = 0, \cdots, n$, ...
0
votes
0answers
43 views

quadratic knacksack problem, state of art [on hold]

What is the current status to quadratic knacksack problem? Say, how many variables can the state of art solver handle? Thank you.
0
votes
0answers
13 views

Pierce's Law in HOL Light [migrated]

Im fairly new to HOL light and ocaml. Could someone please explain to me how Pierce's Law can be written in HOL Light. Thanks in advance.
0
votes
1answer
129 views

Discriminant of a polynomial in two variables

I want to compute the discriminant of the following polynomial $$ F(X,Y)=X^mY^n+\sum_{i=0}^{m-1}\sum_{j=0}^{n-1}c_{ij}X^iY^j. $$ Here the discriminate means the equation $D(c_{i,j})$ in the variables ...
-2
votes
0answers
34 views

Demonstrate by extension with 3 changing value [on hold]

I want to demonstrate by extension this : Z x Z U Z It should give some stuff like , {x} element of Z I don't know how to demonstrate by extension because there will be 3 changing values, i, j and ...
6
votes
1answer
160 views

Center of one-point stabilizer in 2-transitive groups

In this MO question it was mentioned that the following fact seems to be true: If $G$ is doubly transitive on $X$ and the one-point stabilizer $G_x$ has a non-trivial center, then $G$ is of ...
1
vote
1answer
87 views

How to formulate approximation from above?

(This is perhaps a stupid question. If so, please give me a hint and a down vote.) I have a sequence of Banach spaces $X_{1}\supset X_2\supset ...$ and a sequence of elements $x_j\in X_j$ ...
2
votes
0answers
128 views

Tate's conjecture and symmetry of Hodge-Tate weights

I'm reading Bellaiche's notes on the Block-Kato conjecture (Hawaii summer school). Here is the link http://people.brandeis.edu/~jbellaic/BKHawaii5.pdf At page 10 he claims that an indirect ...
0
votes
0answers
52 views

Hill's discriminant and spectral properties of Schrödinger operator

I am currently reading this paper on Schrödinger operators see here. On page 6 and 7 they talk about Hill's discriminant and how this is connected with the spectral properties. They also show some ...
0
votes
1answer
48 views

Reference request for stably free modules

I am looking for some references on the theory of stably free modules. I will call (F) the following property for a ring $R$: every f.g. stably free module over $R$ is free. 1) Is there a standard ...
3
votes
1answer
93 views

Operator norm versus Hlawka inequality

Let $E$ be a finite dimensional normed vector space. If $E$ is $\ell^1$-embeddable, then the norm satisfies Hlawka inequality ...
7
votes
2answers
298 views

Rep-tiles of order 2

A 2-rep-tile is a geometric shape that can be partitioned into exactly 2 smaller (dilated) copies of itself. Although there are many rep-tiles of higher orders, the only 2-rep-tiles I could find ...
2
votes
2answers
102 views

Witt index of the sum of 24 squares

Consider the quadratic forms $q(x)=x_1^2+\dots +x_8^2$ in 8 variables and $p(x)=x_1^2+\dots+x_{24}^2$ in 24 variables over the field of rational numbers $\mathbb{Q}$. Let $E/\mathbb{Q}$ be a field ...
6
votes
0answers
83 views

Fibrations of the injective model structure on G-simplicial sets

Let $G$ be a discrete group. Consider the category of $G$-simplicial sets endowed with the injective model structure, i.e. cofibrations are the injective maps and weak equivalences are the maps which ...
3
votes
0answers
95 views

On a problem of Berkovich

What is the real history of the following problem proposed by Berkovich [Y. Berkovich, Z.Janko, Groups of prime power order. Volume 2, Expositions in Mathematics, 56, Walter de Gruyter, New York, ...
0
votes
0answers
38 views

Combining binary numbers [on hold]

Assume you have n n-digit binary numbers, for example: ...
4
votes
1answer
139 views

Shift-invariant symmetric functions in representation theory?

The connection between symmetric functions and representation theory is well-known. Now consider the subspace of symmetric functions that are shift-invariant, that is, functions satisfying ...
4
votes
1answer
88 views

Euler characteristic of open varieties as degree of Chern class of logarithmic differentials

Let $U$ be a smooth variety over a subfield $k$ of $\mathbb{C}$. Let $X$ be a smooth projective variety containing $U$ as the complement of a normal crossings divisor $D$. Denote by $\chi(U)$ the ...
1
vote
0answers
45 views

The normalization axiom of a quantization

Guillemin, Ginzburg and Karshon explain a quantization in their book [Chap 6,MR1929136] as follows. The quantization is a process which associates to a symplectic manifold $M$ a Hilbert space ...
5
votes
0answers
76 views

The topology on the Robba ring

I've been reading Kedlaya's paper http://arxiv.org/abs/math/0208027 on finiteness of rigid cohomology and there's something I can't quite resolve in my understanding of the topology on the Robba ring. ...
3
votes
2answers
139 views

Schrödinger operators on a sphere

if you have a Schrödinger operator on a sphere ( $\mathbb{S}^2$) $-\Delta_{\theta,\phi} \psi(\theta,\phi) + V(\theta) \psi(\theta,\phi) = E\psi(\theta,\phi),$ where the potential does not depend on ...
3
votes
1answer
232 views

Tangent space describes the manifold's first order characteristic. Is there something like tangent space describes higher order characteristic?

I'm learning differential geometry. I'm curious that when we learned analysis, we learned higher order derivative, while in differential geometry, first order derivative is generalized to element of ...
0
votes
0answers
88 views

Can I find a resolution of singularities that is both smooth and projective? [on hold]

Let $X$ be a scheme of finite type over a field $k$. Can I find $X'$ that is both smooth and projective along with a birational, surjective, proper morphism $p:X'\longrightarrow X$? I have been ...
3
votes
1answer
88 views

If $ F(x,\bullet) \in {L^{\infty}}(G,B) $ for all $ x \in G $, then is $ x \mapsto F(x,\bullet) $ strongly measurable?

Let $ (X,\Sigma,\mu) $ be a $ \sigma $-finite measure space and $ B $ a Banach space. A function $ f: X \to B $ is said to be strongly $ \mu $-measurable iff it is the almost-everywhere pointwise ...
3
votes
1answer
66 views

Singularities induced by the toric ambient spaces

Let $\Delta \subset \mathbb{R}^4$ be a (reflexive) polytope and $X$ be the hypersurfacedefined by a generic section of the any-canonical bundle of the toric variety $\mathbb{P}_{\Delta}$. Are there ...
-2
votes
0answers
34 views

Numerical method of lines for solving PDEs [on hold]

Could you please advise some literature about the numerical method of lines (MOL) for parabolic PDEs? It is a method of solving PDEs with discretizing only by space but not by time. A system of ODEs ...
2
votes
1answer
43 views

A Possible characterization of F.D or AF commutative $C^{*}$ algebras

By F.D or AF $C^{*}$ algebra,we mean finite dimensional or approximately finite dimensional $C^{*}$ algebra. Let $A$ be a unital commutative $C^{*}$ algebra with the property that for every ...
-4
votes
0answers
47 views

A fixed point problem about the iterated mappings [on hold]

Assume that the vector set $Ω$ is an $n$-dimensional Euclid space, and is closed and bounded as well. Now we define a mapping $f$ on $Ω$, which only satisfies the following two conditions: (a). For ...
9
votes
1answer
246 views

Guessing the larger integer: A game-theoretic twist

The starting point for this question is the old chestnut, already discussed on MO, about a game show on which the host has chosen two distinct integers and the contestant gets to reveal one of them at ...
0
votes
2answers
86 views

Asymptotics for Hitting the sphere from the Outside

The problem is: consider A a solid ball centered at 0 and the exterior starting point $x\in A^{c}$, what is the behavior of $P_{x}(T_{B_{r}(0)}>t)$ for $d\geq 3$ as $t\to \infty$,where ...
0
votes
0answers
26 views

unable to use mysql for Python in mac os 10.9 [closed]

I am very new to python and was trying to work with mysql. I followed the below link to install the package (OS x 10.9.5) (http://www.tutorialspoint.com/python/python_database_access.htm) After ...

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