# All Questions

**3**

votes

**1**answer

88 views

### Balanced binary code that “resists” local decoding?

I am looking for a construction that can be stated as the following coding problem: a binary code with good distance ($d = \Omega(n)$ where codeword length is $n$) that "resists local decoding" in the ...

**7**

votes

**0**answers

111 views

### Higher moments of information and Renyi entropy

For a given discrete probability distribution, Shannon entropy can be though as an expectation value $\langle - \log p \rangle$ (see also: What is entropy, really?, What is the role of the logarithm ...

**4**

votes

**0**answers

132 views

### abelian $\ell$-adic representations in $\widehat{SL(2,Z)}$

In Grothendieck's Esquisse he claims that the action of
$$\text{Gal}(\mathbb Q)\to\text{Out}(\pi_1(M_{1,1})=\text{Out}(\widehat{SL(2,Z)})$$
obtained from the homotopy exact sequence of the étale ...

**11**

votes

**2**answers

252 views

### A bit of history of Verdier duality

I was wondering who originated the presentation of Verdier duality as an equivalence between categories of sheaves and cosheaves ?
I learnt it reading Jacob Lurie's Higher Algebra and Justin Curry's ...

**13**

votes

**1**answer

269 views

### Lurie's approach to the bar-cobar adjunction

I've been trying to read Jacob Lurie's approach to the bar-cobar constructions (Higher algebra §5.2 in the 2014-09 version) but I don't recognize what I know about these constructions. I wonder if ...

**-4**

votes

**0**answers

26 views

### Inverse Laplace Transformation [on hold]

I have a question about laplace transformation.
$\frac{8s+4}{s^2+23}$
I tried to split them. $\frac{8s}{s^2+23}$ is similar to cos and $\frac{4}{s^2+23}$ is similar to sin. Can anyone help?
...

**1**

vote

**1**answer

52 views

### Limit involving modified Bessel Function of the second kind

I'm looking for the following limit
$$\lim_{x\rightarrow 0} \frac{\sqrt{\frac{\text{BesselK}^{(2,0)}(0,x)}{\text{BesselK}(0,x)}}}{\log (x)}$$
I believe the limit is finite, and is near -0.578. ...

**4**

votes

**1**answer

375 views

### Modular forms and “too many symmetries”

How do we interpret Barry Mazur's quote of
Modular forms are functions on the complex plane that are inordinately symmetric. They satisfy so many internal symmetries that their mere existence ...

**3**

votes

**1**answer

146 views

### Coherent cohomology of an abelian scheme and base change

Let $f\colon A \rightarrow S$ be an abelian scheme of dimension $d$. I would like a reference or an argument for the fact that $R^1f_* \mathcal{O}_A$ is locally free of dimension $d$ and that its ...

**8**

votes

**1**answer

295 views

### Is a free group a product of f.g subgroups of infinite index?

Let $F$ be a free group, and let $H,K \leq F$ be finitely generated subgroups of infinite index in $F$. Is it possible that for the set of products we have $HK = F$ ?

**3**

votes

**1**answer

184 views

### A More Advanced Version of Aluffi's Chapter 0

This is a crosspost of this question from MSE.
Paulo Aluffi's Book, Algebra, Chapter 0 aims to teach basic algebra from a categorical viewpoint. The first chapters of the book, however, introduce ...

**0**

votes

**0**answers

62 views

### Connected components $0-1$ matrices [on hold]

Let $M$ be a $0-1$ matrix.
Here a matrix has one component means we can traverse from a matrix entry $(i,j)$ which is $1$ to any other one by moving step of $(i\pm1,j),(i,j\pm1),(i\pm1,j\pm1)$ where ...

**0**

votes

**0**answers

56 views

### Complete solution set of a Convolutional Equation?

Here is a problem that am I stuck and I appreciate any help. In essence, I am trying to show that the only solutions for the described problem are the ones provided below. Best..
Setup: In what ...

**3**

votes

**1**answer

142 views

### A question on models of set theory and Lebesgue measure

In a question and an answer at MO, Joel David Hamkins showed that (if ZFC is consistent) there are models of ZFC in which $V\neq HOD$ and every $\Sigma_2$-definable set has a definable member.
Let ...

**0**

votes

**1**answer

93 views

### equivalence in simplicial category

Let $(\mathcal{C},W)$ be a category with weak equivalences. One can build from $(\mathcal{C},W)$ its hammock localization $L^{H}(\mathcal{C},W)$ which is a simplicial category $\textit{ie}$ a category ...

**3**

votes

**1**answer

95 views

### automorphism of prime order for group of Lie type in

Thanks for any help.
Suppose $S$ is a simple group of Lie type of prime characteristic $p$. we know that every automorphism of $S$ is composite of inner, diagonal, field and graph automorphism of ...

**0**

votes

**0**answers

28 views

### How do these two extensions of Sobolev spaces relate to each other?

In nonparametric statistics, the following space is often used
$$H_{per}^\beta := \left\{f:[0,1]\to\mathbb{R}:\,D^{\beta-1}f\,\text{absolutely continuous and } D^\beta f\in L^2[0,1], \\D^{k}f(0) = ...

**2**

votes

**0**answers

67 views

### Algorithm to minimally connect line segments in Euclidean plane

Suppose you have finitely many line segments in the Euclidean plane. How do you "connect them to form one chain of line segments of minimal length?"
More formally and generally, what I'm looking for ...

**3**

votes

**1**answer

171 views

### cycle class as Chern class

Let $X$ be a smooth projective complex variety and $Z \subset X$ a codimension $p$ closed algebraic subvariety. Then one can define the class of $Z$ in singular cohomology
$[Z] \in H^{2p}(X, ...

**-9**

votes

**0**answers

57 views

### Using the intuition from the arithmetic of cardinal numbers to ascribe values to functions on the extended real line? [on hold]

Please note, this question is about ascribing exact values to indefinite forms, not about fining corresponding limits, so please do not answer "there is no such limit, so it is indeterminate".
First ...

**17**

votes

**2**answers

371 views

### Unstable homotopy groups of spheres beyond Toda's range

In 1962 Toda published his book "Composition methods in homotopy groups of spheres", which contains computations of $\pi_{n+k}(S^n)$ for $k\le 19$ and $n\le 20$. The values of these groups are ...

**1**

vote

**0**answers

43 views

### “Generators” for fusion rings

It's a rather obvious idea in the area of fusion rings, but I haven't found a
reference yet. Start with the usual rules for a rank n fusion ring
$X_i\bigotimes{X_j}=\Sigma_k{T_{ij}}^kX_k$
and ...

**0**

votes

**0**answers

36 views

### Baire sets in locally compact Hausdorff spaces

I posed this on 14 Dec. at http://math.stackexchange.com/questions/1067751/baire-sets-in-locally-compact-hausdorff-spaces, but there has been no response:
(This is a follow-up to ...

**1**

vote

**0**answers

34 views

### finding dominating cycles in $2K_2$-free graphs

A cycle $C$ in a connected graph $G$ is called dominating if its complement $V(G)-V(C)$ is an independent set. H.J. Veldman proved in 1983 (Disc. Math. v.43, 281-96) a general result that in ...

**2**

votes

**0**answers

53 views

### Varieties with few monomials and the n-conjecture

The n-conjecture
is a generalization of abc and basically says that the if
$a_1 + \ldots + a_n=0$, no proper subsum vanishes and $a_i$
are coprime, then the radical of $a_1\cdots a_n$ can't be
too ...

**1**

vote

**1**answer

42 views

### Is the orthogonal complement of an admissible subcategory admissible itself?

I´m studying Huybrechts book "Fourier-Mukai transforms in algebraic geometry" and I came up with the following: as an example of semi orthogonal decomposition of a triangulated category $\mathcal{D}$ ...

**5**

votes

**0**answers

60 views

### Unbalanced equipartitions

Let $K$ be a compact convex set in the plane.
Say that a perimeter-halving partition of $K$
is a partition of $K$
into two pieces by a chord (a segment with endpoints
on the boundary $\partial K$) ...

**4**

votes

**1**answer

264 views

### Cap product à la Poincaré

Recently, it became apparent to me that I was not the only one who always first thought in terms of cap product before actually computing a cup product. There is no denying this is evil, but I found ...

**-8**

votes

**1**answer

137 views

### Do the mathematicians really know the exact values of what usually called “indeterminate forms”? [on hold]

First of all I would point out that exact value of a function and the limit of the function in that point do not necessarily coincide. For instance, it is often assumed that $0^0=1$ even though the ...

**0**

votes

**0**answers

51 views

### Reference : Special case of Banach-valued function integration by parts

Let $u \in L^p (0,T; L^1(\Omega))$ with $\partial_t u \in L^p(0,T; L^1(\Omega))$ and $v \in L^q (0,T; L^\infty(\Omega))$ with $\partial_t u \in L^q(0,T; L^\infty(\Omega))$ (with $1/p+1/q=1$ and $p \in ...

**3**

votes

**0**answers

53 views

### Is there an efficient way to visualize the bifurcation locus of this family of functions?

I have been trying to help out with this question from math.stackexchange. It concerns the family of functions:
$$f_\alpha(z,w) = \frac{\alpha + z}{1 + w}.$$
and an iteration scheme:
$$z_{n+1} = ...

**9**

votes

**0**answers

163 views

### Is every projective space curve a set-theoretic intersection of two surfaces? What is known about this question?

I am sorry if this question has been already asked, couldn't find anything similar myself. I have recently recalled this long standing open problem of whether every curve in $\mathbb{P}^3(\mathbb{C})$ ...

**0**

votes

**0**answers

32 views

### Extension of homomorphism to place in quotient field, or of local ring to valuation ring in quotient field

Let be given a domain $R$ (that can be supposed to be integrally closed if this can help), and $\varphi$ an homomorphism of $R$ into a field $F$.
$\varphi$ extends uniquely to a homomorphism ...

**1**

vote

**1**answer

113 views

### intuitive interpretation of analytic spread

I am studying analytic spreads from Bruns-Herzog's book. The definition is clear but calculation of the analytic spread of an ideal is hard for me in practice. I wonder if it is hard for you too.
...

**1**

vote

**1**answer

37 views

### Retractions and left-factoring morphisms

Let $\mathcal{C}$ be any category and let $A, B$ be objects.
A retraction is a morphism $r: A\to B$ such that there is $s:B\to A$ such that $r\circ s:B\to B$ is the identity.
A morphism $l: A\to B$ ...

**2**

votes

**0**answers

61 views

### What are interesting open problems in pseudo-differential operators?

May I ask what are some interesting open problems in the field of micro-local analysis (or classical analysis, semi-classical analysis, etc) using pseudo-differential operators? To my knowledge the ...

**1**

vote

**0**answers

50 views

### (Affine) Schemes and the point of view of morphisms with values in a field

Let $A$ be a commutative ring with unity. If $\varphi_1 : A \rightarrow K_1$ and $\varphi_2 : A \rightarrow K_2$ are ring morphisms from $A$ to fields, $\varphi_1$ and $\varphi_2$ are said to ...

**0**

votes

**0**answers

60 views

### sufficient condition of complete intersection [on hold]

According to Corollary 2.8 and the front part of Section 3 of this paper,
if $X:= Q_1\bigcap Q_2\bigcap Q_3\subset \mathbb{P} _{\mathbb{C}}^{4}$ be a connected and purely $1$-dimensional intersection ...

**-4**

votes

**0**answers

58 views

### Flow in graph. Proof [on hold]

Let $(S_1, \overline{S_1} ) , (S_2, \overline{S_2} )$ be minimum cuts in some network. Is it true that $(S_1 \cap S_2, \overline{S_1 \cap S_2)}$ is a minimum cut in this network?

**-4**

votes

**0**answers

101 views

### show that L(X,Y)banach then Y banach

Let {Xα}α∈A be a collection of Banach spaces. It is easy to show that P={(xα):supα∥xα∥<∞} with ∥(xα)∥=supα∥xα∥ is a banach space.
If the indexing set A is finite, then it is easy to show that P ...

**1**

vote

**1**answer

65 views

### Any two bivariate algebraically dependent polynomials are always in the same ring generated by some bivariate polynomial?

If $f(x,y)$ and $g(x,y)$ are two algebraically dependent polynomials over some field $k$, is it true that there exists a bivariate polynomial $p(x,y)$ such that both $f(x,y)$ and $g(x,y)$ are in the ...

**4**

votes

**0**answers

70 views

### An extension of group schemes admitting Neron models

Let $R$ be a discrete valuation ring, $K$ its field of fractions, and
$$ 0 \rightarrow G_K' \rightarrow G_K \rightarrow G_K'' \rightarrow 0$$
a short exact sequence of smooth $K$-group schemes of ...

**2**

votes

**1**answer

71 views

### On transforming pair of bivariate polynomials to pair of univariate polynomials by applying polynomial map

We know that a polynomial map $f(x,y), g(x,y)$ is polynomial automorphism if there exists polynomials $p(x,y)$ and $q(x,y)$ such that $f(p,q)$=x and $g(p,q)=y$. Jacobian conjecture tries to ...

**-6**

votes

**0**answers

27 views

### Writing an integral for a bounded volume [on hold]

Good day folks!
I'm trying to write an integral which could represent the volume of the shaded area below. However my integral calculus is quite poor, so I need some help on that equation.
...

**22**

votes

**3**answers

698 views

### Graduate program applications that require questionnaires and other non-letter material

In the December 2014 AMS Notices, a letter to the editor (http://www.ams.org/notices/201411/rnoti-p1311.pdf) by Deconinck and Medlock addresses the problem of (math) graduate programs requiring letter ...

**4**

votes

**1**answer

275 views

### Is the space of real conics with a singular point an orientable manifold?

Consider the space of non zero real homogeneous degree $2$ polynomials in three variables upto scaling. This space is $\mathbb{R} \mathbb{P}^5$. The zero set
of such a polynomial gives a real curve ...

**0**

votes

**1**answer

137 views

### A question in Sasakian geometry

Let $(S,\eta, \xi)$ be a Sasakian manifold with killing vector field $\xi$, then we have the following exact sequence $$0\to <\xi>\to TS\to \frac{TS}{<\xi>}\to 0$$.
Can
...

**13**

votes

**1**answer

249 views

### ULU Decomposition of a matrix

Let $g \in GL_n(\mathbb{F}_q)$. Is it true that we can always write $g = u_1lu_2$, where $u_1$ and $u_2$ are upper-triangular and $l$ is lower-triangular? Note that I'm not requiring that the matrices ...

**-1**

votes

**0**answers

38 views

### Gaussian Elimination for Orthogonal groups [on hold]

We known the classical Gaussian elimination algorithm where we can reduce any invertible matrix to a diagonal matrix by row-column operations. Is there row-column operations and Gaussian elimination ...

**0**

votes

**0**answers

87 views

### Roots in the solution

It is known that for a one-dimensional self-adjoint operator with periodic boundary conditions, the number of roots is directly related to the eigenstate this eigenfunction belongs to.
Now it is ...