# All Questions

**-3**

votes

**0**answers

29 views

### Question about LP Programming model [closed]

I have a aggregate production planning problem. As the company want to have a stable output, the quantities produced per month should (x) not fluctuate to heavily from a specified amount, say g.
So ...

**-1**

votes

**0**answers

33 views

### Random selection probability [closed]

A test was given to a group of students. The grades and gender are summarized below:
...

**6**

votes

**1**answer

291 views

### Distribution of the sequence $\bigl (\frac{\phi(n)}{n}\bigr )_{n=1}^{\infty}$ in $[0,1]$

Maybe this is a well-know problem.
What do we know about distribution of the sequence $\bigl (\frac{\phi(n)}{n}\bigr )_{n=1}^{\infty}$ in $[0,1]$? (Where $\phi$ is the Euler's totient function).
In ...

**1**

vote

**1**answer

111 views

### university press specialized in math books [closed]

I am thinking of writing a book for graduate students, on graph theory.
Apart from AMS book, does someone of you could suggest a university press that acccept submission on these arguments.
I ...

**0**

votes

**0**answers

68 views

### Does an ISI journal need to have Impact Factor? [closed]

There are a bunch of journals in Springer and Elsevier without having impact factors.
Are they considered ISI journals?

**5**

votes

**0**answers

151 views

### What is the kernel of the map $Out(\widehat{F_2})\rightarrow GL_2(\widehat{\mathbb{Z}})$?

Let $F_2$ be the free group on two generators, and $\widehat{F_2}$ its profinite completion. Let $Out(\widehat{F_2})$ be the outer automorphism group of $\widehat{F_2}$, ie, $Out(\widehat{F_2}) = ...

**4**

votes

**0**answers

94 views

### Is Hankelability NP-hard?

This question was previously asked on cstheory but with no answers or substantive comments.
I am trying to write code to detect if a matrix is a permutation of a Hankel matrix. Here is the spec.
...

**2**

votes

**0**answers

214 views

### Programming workbooks in C++ and Research Math [closed]

I know the basics of C++ by taking a few courses and going through "C++ Primer" by Lippman. As a math graduate student, I would love to get my hands on some programming-math exercises geared towards ...

**3**

votes

**2**answers

188 views

### What are the easiest examples of irreducible, but not big, monodromy representations

Let $\rho: \pi_1(S,s_0) \to GL(V)$ be the monodromy representation associated to a local system of $\mathbb Q$-modules $\mathbb V$ with $\mathbb V_{s_0} = V$.
Let $H$ be the Zariski closure of the ...

**0**

votes

**0**answers

54 views

### non-degenerate closed forms in local coordinates [closed]

Take $\psi$ a 4-form non degenerate and closed on a $4n$-dimensional manifold. Is it true that locally $\psi$ can be written as
$$\sum_{k:1}^n a_I dx_{4k-3}\wedge dx_{4k-2}\wedge dx_{4k-1}\wedge ...

**0**

votes

**0**answers

65 views

### is there a collected works of J.P. Lagrange? [closed]

Is there a collected works of Lagrange? How about detailed history of Lagrange multipliers?

**0**

votes

**0**answers

39 views

### On isolated points of the approximate point spectrum of a bounded operator

Let $X$ be a complex Banach space and $T$ be a bounded operator acting on $X$.
Let $\sigma(T)$ and $\sigma_{ap}(T)$ denote the spectrum and approximate point spectrum of $T$, respectively.
Let ...

**5**

votes

**2**answers

267 views

### References for the moduli space of complex structures

I am looking for references where the moduli space of complex structures on a complex manifold is well explained: in particular the infinitesimal deformations, the obstructions, the elliptic complex ...

**1**

vote

**0**answers

53 views

### Energy inequalities for Sobolev spaces of negative integer

I asked this question in mathematics stackexchange and couldn't get an answer.
Let $\phi\in H^{s}$ such that the following energy inequality is true:
$$\|\phi(t,\cdot)\|_s \le\int^t_0 C \| ...

**1**

vote

**0**answers

56 views

### Real algebraic surface

Let $f(u,v,z)\in \mathbb{Q}[u,v,z]$ be a polynomial in three variables such that $X_{\mathbb{R}}\subset \mathbb{R}^{3} $ (the associated surface of real solution) is smooth. Suppose that the set of ...

**10**

votes

**1**answer

224 views

### Is there something like “Noncommutative geometry internal to a category”?

I have heard that one can do algebraic geometry internal to symmetric monoidal categories. Topological quantum field theories also exist internal to symmetric monoidal categories, and the usual ...

**-1**

votes

**0**answers

57 views

### Sum of the k+l \choose l [closed]

I am tring to prove the following equality :
$\displaystyle \sum_{k=0}^n {k+l \choose l} = {n+l+1 \choose l+1} $
However, I did not manage to find a proof... Do you have any ideas ?
Thanks !

**1**

vote

**1**answer

87 views

### Iinterchanging limits for doubly indexed random sequences

I've encountered the following problem which seems to be quite standard but for which I can't find any proper references (asking on mathematics SE didn't bring up any answers so I'm reposting my ...

**0**

votes

**0**answers

31 views

### Rees rings and a formula

Could someone help me to solve this question?
Let $(R,\frak m)$ be a commutative, Noetherian, local, and complete domain. and let $R(I)=\bigoplus _{n \geqslant 0} I^n t^n$ be be Rees ring of $R$ ...

**4**

votes

**1**answer

155 views

### Does nuclearity pass to un-tensoring?

Let $A$ be a C*-algebra such that $A \otimes_{\min} A$ is nuclear.
Does it follow that $A$ is nuclear?

**-4**

votes

**0**answers

31 views

### Link between two products [closed]

Could someone help me to solve this problem :
Let's denote by $A_i$ the following product,
$$ A_i = \prod_{\substack{k=1 \\ k\neq i}}^n (a_k - a_i) $$
Is there any link or simple formula between ...

**-5**

votes

**0**answers

39 views

### How do I show that {R}^{nxn} = {R}_{sym}^{nxn} + {R}_{skew}^{nxn} [closed]

How can I show that $\mathbb{R}^{nxn} = \mathbb{R}_{sym}^{nxn} + \mathbb{R}_{skew}^{nxn}$, where $\mathbf{} \mathbb{R}_{sym}^{nxn} = \{ A \in \mathbf{R}^{nxn} | A^{t} = A\}$ and $\mathbf{} ...

**1**

vote

**2**answers

161 views

### Examples of quotients by infinitesimal group schemes

I'm looking for examples of explicit actions of the infinitesimal group schemes $\alpha_{p^n}$ on schemes (maybe as simple as the affine plane) in characteristic $p$ or mixed characteristic, and their ...

**2**

votes

**0**answers

67 views

### Non-compact and maximal non-$T_2$ [migrated]

Is there a space $(X,\tau)$ that is not compact, not $T_2$, but for every topology $\tau'\supseteq \tau$ with $\tau'\neq\tau$ the space $(X,\tau')$ is $T_2$?

**2**

votes

**1**answer

158 views

### Automorphisms of complete local rings

Let $k$ be a field and $(A,m)$ be the completion of the local ring of a smooth point of a $k$-variety. Let $x_1,x_2\in m\backslash m^2$ be regular elements. I am interested in knowing if one can find ...

**3**

votes

**0**answers

118 views

+50

### What is the complexity of determining Ramsey Number?

In the notation of Garey and Johnson [1], two problems related to Ramsey Problem were defined:
$\textbf{ARROWING}$
Instance: (Finite) graphs $F$, $G$ and $H$.
Question: Does $F\rightarrow (G, H)$?
...

**1**

vote

**1**answer

72 views

### Multiplicity of the intersection of a Rational curve in a quadric with a tangent plane

Consider a rational map $u : \mathbb{CP}^1 \to \mathbb{CP}^4$ of degree~$d$, such that the image lies in a fixed 3-dimensional quadric $Q^3$. In other words, its image is a rational curve in $Q^3 ...

**0**

votes

**1**answer

105 views

### Area of a plane surface that gives a lot of theoretical problems

Let $\mathbf{r}:(a,b)\times (0,1)\to\mathbb{R}^2\subseteq\mathbb{R}^3$ be a injective application, given by:
$$\mathbf{r}(u,v)=A(u)+v\cdot (B(u)-A(u)), \forall\ (u,v)\in (a,b)\times (0,1)$$
where ...

**1**

vote

**1**answer

69 views

### Derivative of a time evolution operator w.r.t. a parameter

Let $N\geq1$ be an integer and let $H:[0,1]^2\to\mathbb C^{N\times N}$ be a pointwise hermitean matrix valued function.
For $y\in[0,1]$ and $0\leq a\leq b\leq 1$, let $U_y(b,a)$ be the time evolution ...

**6**

votes

**1**answer

212 views

### 3-manifolds with isomorphic fundamental groups

There are many non-homeomorphic 3-manifolds with isomorphic fundamental groups, for example the lens spaces $L(p,q_1)$ and $L(p,q_2)$ with $q_1 \ne \pm q_2^{\pm 1}\mod p$. Also, Seifert fibered spaces ...

**-1**

votes

**0**answers

12 views

### Is it possible to create hierarchy basis? [migrated]

An eigenbasis is defined as basis consisting entirely of eigenvectors of a linear transformation. On the other hand a Schauder basis is also a basis except they allow for infinite sums. I could not ...

**5**

votes

**2**answers

151 views

### Extending hyperconnected spaces

A hyperconnected space is a topological space such that every two non-empty open sets have non-empty intersection. Let's call a space $(X,\cal{T})$ maximally hyperconnected if it is hyperconnected and ...

**0**

votes

**0**answers

30 views

### A source for integral operators in the context of Arthur-Selberg trace formula

Could you suggest a textbook for integral operators
(in the context of Arthur-Selberg trace formula)?

**-4**

votes

**0**answers

78 views

### Showing two Rings are nor isomorphic [closed]

I have the two rings $R[x,y]/(x^2+y^2-1)$ and $R[x,y]/(x^2-y^2-1)$ and I am trying to show they are not isomorphic over the real numbers.
I have been playing around and I got that each polynomial in ...

**2**

votes

**0**answers

73 views

### Do copairings provide dualities in derived categories?

Here is an elementary fact about vector spaces. Let $V,W$ be vector spaces over a field $\mathbb K$ and let $c : \mathbb K \to V \otimes W$ be an element of the tensor product. Then $c$ determines ...

**-2**

votes

**0**answers

61 views

### categorical constructions surfaces [closed]

Is there any literature where construction of the sphere realize know , the banda , bull, klein bottle , the projective plane etc... Using the language of category theory for example through pullback ...

**9**

votes

**1**answer

170 views

### Dyer-Lashof operations and the homology of GL_n

For any ring R, $\bigsqcup_n {BGL}_n(R)$ is an $E_\infty$-space. Are there examples of rings where people have calculated $H_*(\bigsqcup_n {BGL}_n(R);\mathbb{Z}/2)$ and determined the Dyer-Lashof ...

**0**

votes

**0**answers

74 views

### Boundedness of heat semigroup on $L^1(\Omega)$

On a bounded domain $\Omega \subset \mathbb{R}^n$ with smooth boundary, consider the Laplacian $-\Delta$ with either the Dirichlet or Neumann boundary conditions. More generally, one can also consider ...

**-1**

votes

**0**answers

28 views

### Improvement of Minimum description length (MDL) estimate [closed]

I earnestly request apology if this question is inappropriate for the forum. The question has two parts one technical and the other is not technical. I would appreciate any response.
Let me consider ...

**17**

votes

**0**answers

208 views

### Guess that group via product queries

Suppose someone (person B) knows a finite group $G$ of order $n$.
You (person A) know only the order $n$,
and that $1$ is the name of the identity element.
The group elements are named $1,2,\ldots,n$ ...

**1**

vote

**0**answers

21 views

### Simplifying closed form for Meta Operator

I was consider the set of linear operators:
$$O_{a,k} = \frac{f(ax^k) - f(x)}{ax^k - x} $$'
Particularly I am looking for the closed forms of the eigenfunctions of this operator, that is the ...

**1**

vote

**0**answers

34 views

### Antisymmetrization of the Hochschild cocycle

Let $A$ be a commutative (unital, complex) algebra and let $\varphi$ be a $n+1$-linear functional on $A$ (we will call it cochain). Define ...

**3**

votes

**1**answer

96 views

### LES for relative cohomology via sheaves

I was unable to find a suitable answer for the following question:
Once one learns that singular cohomology is the same as cohomology with coefficients in locally constant sheaf, it is natural to try ...

**-4**

votes

**1**answer

85 views

### Elliptic Curve Multiplication [closed]

What would happen if I performed Elliptic Curve multiplication on some random point within the FiniteField that wasn't actually on the curve? I assume that I would get a point in return but would that ...

**1**

vote

**0**answers

40 views

### Question about existence of forms with small $h$-invariant satisfying certain property

Given a form $f \in \mathbb{Q}[x_1, ..., x_n]$ of degree $d>2$, we define $h(f)$ to be the smallest positive number $h$ such that we can write
$$
f = u_1v_1 + ... +u_h v_h,
$$
where each $u_i$, ...

**2**

votes

**1**answer

51 views

### Quotient sigma-algebra generated by quotient-measurable generating sets

Let $X$ be a measurable space whose $\sigma$-algebra is generated by a family $\mathcal{G}=\bigcup_n \mathcal{G}_n$ of subsets of $X$, where $(\mathcal{G}_n)$ is a sequence of $\sigma$-algebras on $X$ ...

**9**

votes

**1**answer

191 views

### Are there any exact results for Hausdorff Measure?

The computation of the Hausdorff measure is extremely difficult due to the infinum appearing in its definition. This has made the calculation of the Hausdorff measure for nearly all fractals difficult ...

**2**

votes

**2**answers

356 views

### Exact sequences of pointed sets - two definitions

It seems to me that there are (at least) two notions of exact sequences in a category:
1) Let $\mathcal{C}$ be a pointed category with kernels and images. Then we call a complex (i.e. the composite ...

**2**

votes

**0**answers

108 views

### What can be said about a Boolean-valued structure from what the Boolean-valued forcing extension thinks about it?

Suppose that $\phi$ is a formula in the language of set theory such that
there are some $n_{1},...,n_{k}$ such that if $V\models\phi(x)$, then $x=(X,R_{1},...,R_{k})$ and ...

**4**

votes

**0**answers

83 views

### Integer decomposition of dilated integral polytopes

For $n > 0$, let $P$ be an integral polytope, that is, the convex hull in $\mathbb{R}^n$ of points in $\mathbb{Z}^n$. Suppose that $\dim(P) = n$.
Question: Given $d > n + 2$ is it true that
$$ ...