# All Questions

**0**

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4 views

### A decreasing sequence involving the divisor function?

Define $N_k \geq 6$ to be the $k-th$ primorial number and let $\sigma(n)$ be the divisor function.
It seems that $u_k = \dfrac{\sigma(N_k)}{N_k \log\log N_k}$ is a decreasing function ?
By ...

**0**

votes

**0**answers

3 views

### Sqare wave in the limit of infinite frequency

What is the new function obtained when one takes the limit of the square wave function when the frequency is taken to infinity?
Does it depend on how the function is written down (e.g. defined as ...

**4**

votes

**1**answer

16 views

### Definition of the differential of the Cone of a morphism of complexes

Let $(F^\bullet,d_F)$ and $(G^\bullet,d_G)$ be two complexes in an abelian category $\mathbf{A}$.
The complex cone $Cone(\varphi)^\bullet$ of a morphism of complexes $\varphi:F^\bullet \to G^\bullet$ ...

**0**

votes

**0**answers

8 views

### CLT for sums of an infinite sequence of rv with an asymptotic distribution

Excuse me if the question is ill-posed. I'll do my best to explain the problem.I have a vector $(x^{(n)}_1, x^{(n)}_2, \ldots x^{(n)}_n),$ whose individual components can be shown to be asymptotically ...

**1**

vote

**1**answer

23 views

### Symplectic group over integers and finite fields

For $H=\left( \begin{smallmatrix} 0 & I_n \\ -I_n & 0 \end{smallmatrix} \right)$ and a commutative ring $F$, the symplectic group $Sp(2n,F)$ is the set of all matrices $M\in F^{2n\times 2n}$ ...

**5**

votes

**0**answers

30 views

### Is the restriction map for embeddings of manifolds with boundary a fibration?

Let $M$ and $W$ be smooth manifolds (possibly with boundary) and $V\subseteq W$ a submanifold. We have a map between embedding spaces
$$Emb(W,M)\rightarrow Emb(V,M)$$ given by restriction.
Richard ...

**1**

vote

**0**answers

18 views

### If $u \in L^2(0,T;X_0)$ with $u_t \in L^2(0,T;X_2)$, then is $u \in L^\infty(0,T;X_1)$?

Let $X_0 \subset X_1 \subset X_2$ be continuous embeddings, with $X_0 \subset X_1$ compact.
Suppose $u \in L^2(0,T;X_0)$ with $u_t \in L^2(0,T;X_2)$.
Is then $u \in L^\infty(0,T;X_1)$?
To apply ...

**0**

votes

**0**answers

65 views

### Has the attempt of proof of the Frankl conjecture by Vladimir Blinovsky been checked?

I found his article in arxiv: http://arxiv.org/pdf/1507.01270.pdf. But i didn't find any response to the article and as I'm an undergraduate I have no knowledge to judge if this approach is promising.
...

**0**

votes

**1**answer

25 views

### Does continuity in one variable and locally Lipschitz in another imply uniformity in the first?

I understand the definition of Lipschitz functions when talking of functions of single variables. However, I have trouble understanding it when it is a multivariable function.
Suppose $ f(t,x):D ...

**3**

votes

**0**answers

31 views

### A non locally compact group of finite topological dimension?

Is there a topological group which is Hausdorff, first countable,
locally connected and has finite topological dimension, yet fails
to be locally compact?

**1**

vote

**0**answers

29 views

### Looking for Severi varieties

Let $K$ be an algebraically closed field of characteristic $0$, and let $\mathbb{O}$ be the Cayley algebra over $K$. Let
$$
\mathfrak{J}_{3}=\{A\in\mathcal{M}_{3}(\mathbb{O}):A\text{ is Hermitian}\},
...

**7**

votes

**0**answers

104 views

### Have Grothendieck's notes in Montpellier already been investigated?

Grothendieck, who passed away on November 13, 2014, left a huge amount (around 20.000 sheets) of personal notes in the University of Montpellier that he thought he was the only one to be able to ...

**-4**

votes

**0**answers

19 views

### Integral of cos(x) wrt t when integral of sin(x) wrt t is known [on hold]

If $\int_0^T sin(\theta) dt = A$, where $\theta$ is a variable, A is constant.
Then can we find out $\int_0^T cos(\theta) dt$ = ?

**0**

votes

**0**answers

25 views

### smoothness of boundary under Riemann mapping

Suppose there is a smooth Jordan curve separating the complex plane. For complicity, assume the curve is given by a graph $(x, \phi(x))$, where $\phi(x)$ is smooth, bounded, and derivatives are ...

**0**

votes

**0**answers

5 views

### Frobenius series of Fuchsian PDEs

I'm interested in the analyticity of Frobenius-like series solutions to a PDE in $z=(z_1,\ldots ,z_N)\in\mathbb{C}^N$ with regular singular behavior at $z_\alpha=0$ for all $\alpha=1,\ldots, N$.
For ...

**0**

votes

**0**answers

12 views

### Fundamental system of neighborhoods. Self similar set

I have been reading the text "Analysis on Fractals" of Jun Kigami. There is a theorem about fundamental system of neighborhoods of a point in a self similar set.
It is stated as follows
Let ...

**0**

votes

**0**answers

7 views

### Standard term for parametrisation where heights of parameters and values are correlated

Suppose an algebraic variety over Q, or subvariety of one, has a parametrization, also over Q.
Clearly an infinite number of birationally equivalent parametrisations can be obtained from this. But ...

**5**

votes

**0**answers

51 views

### List of counting proofs instead of linear algebra method in combinatorics

I've just come across this proof of the Graham-Pollak Theorem by Sundar Vishwanathan (thanks to Konrad Swanepoel's sporadic comments about it on this site), that must be called beautiful after its ...

**0**

votes

**0**answers

35 views

### an example for fundamental group of graph of groups

suppose we have a graph $X$ with the vertex set $\left\lbrace v_1,v_2,v_3 \right\rbrace $ and the edge set $\left\lbrace e_1,e_2,e_3 \right\rbrace $ like a triangle. let $(\Gamma,X)$ be a graph of ...

**1**

vote

**0**answers

16 views

### Is support function of a convex curve in $\mathbb{R}^2$ absolutely continuous?

There is an example of a convex function of two variables that is convex but not absolutely continuous. The level set of this function is a convex curve.
To construct one example of such a function ...

**1**

vote

**0**answers

30 views

### Solvable Lie algebra whose nilradical is not characteristic

It is well known that the nilradical of a finite-dimensional Lie algebra over a field of characteristic p > 0 need not be characteristic (that is, invariant under all derivations of the algebra), but ...

**0**

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**0**answers

23 views

### HNN extension group with finitely generated base

Let $B$ be a group and let $A_1$ and $A_2$ subgroups of $B$ with $\phi :A_1\rightarrow A_2$ an isomorphism. Let $\left<t\right>$ be the infinite cyclic group, generated by a new element $t$. The ...

**-2**

votes

**0**answers

26 views

### Algorithm to rate board of tic-tac-toe [on hold]

At start I want to say that im programmer and I don't want anyone to write me code, just to help me what I can use.
Is there any algorith which I can use to rate a board of tic-tac-toe ?
What I want ...

**5**

votes

**1**answer

186 views

### Hahn-Banach theorem for arbitrary locally compact fields?

Does anyone know if the Hahn-Banach theorem is true for every locally
compact field? Specifically, let $F$ be a finite algebraic extension of
either $Q_p$, the $p$-adic completion of $Q$, or of
...

**3**

votes

**0**answers

26 views

### Can approximately periodic functions be perturbed to periodic functions on a locally compact group?

Let $G$ be a locally compact group and $H\subset G$ a closed and cocompact subgroup. I wish to consider bounded continuous functions from $G$ to $\mathbb{C}$ that are periodic in the following strong ...

**5**

votes

**0**answers

61 views

### Chern-Simons forms, characteristic numbers, and boundary terms?

For any principal $G$-bundle $P \to M$ with principal connection $\omega$, given a $G$-invariant polynomial $p: \mathfrak{g} \to \mathbb{R}$ we can construct a form $p(F_\omega)$ on $P$ which descends ...

**1**

vote

**0**answers

9 views

### Construction of point process having same pair correlations as GUE

The distribution of the pair correlations of the eigenvalues of the GUE satisfies (in the limit, when being normalized appropriately)
$$
g(u) = 1 - \left(\frac{\sin(\pi u)}{\pi u}\right)^2 + ...

**4**

votes

**1**answer

71 views

### Sufficient conditions for $\sum_{n \ge 1} a_n e^{-(a_1+\cdots+a_n) s} \sim \frac{1}{s}$ as $s \to 0^+$

Let $(a_n)_{n \ge 1}$ be a sequence of non-negative real numbers such that $\sum_{n \ge 1} a_n = \infty$, and set $\lambda_n := a_1 + \cdots + a_n$ for each $n$. Then the (generalized Dirichlet) ...

**3**

votes

**2**answers

40 views

### $V(A)$ semi group of equivalent projections in $M_∞(A)$ cancelative?

I found in the book of Murphy, C*- Algebras and Operator Theory, the Theorem 7.1.2 :
Let A be an unital C* algebra, the semi group $V(A)$ of equivalent projections (under Murray Von
Neumann ...

**4**

votes

**0**answers

35 views

### When is a crossed-product algebra a division algebra?

Let $L/K$ be a finite Galois extension with Galois group $G$. For every 2-cocycle $\gamma$ of $G$ with values in $L^\times$ there is the crossed-product $K$-algebra
$$S(L,G,\gamma) = \bigoplus_{g\in ...

**-3**

votes

**0**answers

16 views

### Get angle of Trajectory of a projectile [on hold]

Formula1
Since a view hours I'm desperately trying to solve this equation after alpha.
I can't use Formula2 because my launch starts at the height h.
Thanks for your guys guidance and help.

**2**

votes

**0**answers

75 views

### When is $(1^2+1)(2^2+1)\dots (n^2+1)$ a perfect square? [duplicate]

Find all such $n$. Natural guess is that $n=3$ is the only solution.
It is natural to try something like Bertrand's postulate for Gaussian integers with imaginary part 1, but what is known?

**4**

votes

**1**answer

135 views

### Can we always attain another prime via inserting digits between the digits of a fixed prime?

The sequence OEIS A080437 is
For n > 10, let m = n-th prime. If m is a k-digit prime then a(n) = smallest prime obtained by inserting digits between every pair of digits of m.
I don't see why ...

**2**

votes

**0**answers

16 views

### Carving a rectilinear polygon

In this question, carving a polygon $P$ means removing an axis-parallel rectangle adjacent to the boundary of $P$. Carving $P$ might break it into two or more polygons.
You are given a square $P$. ...

**1**

vote

**0**answers

17 views

### Difference between Schmidt decomposition and singular value decomposition [migrated]

Schmidt decomposition of an operator is a useful tool of quantum information theory nowadays. Let $O$ be an operator acting on the Hilbart space $\mathcal{H}_{d_1} \otimes \mathcal{H}_{d_1}$. ...

**0**

votes

**0**answers

14 views

### Points in Convex Configuration with Trivial Optimal Tour

Which property guarantees, that for set of $n$ points of the Euclidean plane, that are convex configuration, the optimal tour visiting all points consists of the $n$ shortest edges of the induced ...

**2**

votes

**0**answers

62 views

### Exponential analogue of formal connections

Let $F=\mathbb{C}((t))$. Let $G=GL_n$. Then $G(F)$ acts on $\mathfrak{g}(F)$ by gauge transformation:
$$
g.x:=gxg^{-1} + \dot{g}g^{-1},\quad \quad g\in G(F), \quad x\in \mathfrak{g}(F).
$$
Here, ...

**1**

vote

**0**answers

25 views

### A quantitative version of Pełczyński's property ($V^{*}$)

Let me first fix some notations. Let $A$ be a bounded subset of a Banach space $X$. Set $$wk_{X}(A)=\widehat{d}(\overline{A}^{w^{*}},X)=\sup\{d(x^{**},X):x^{**}\in \overline{A}^{w^{*}}\},$$ where ...

**-1**

votes

**0**answers

25 views

### finite Projective plane [on hold]

Let Z=PG(q,2) be a finite Projective plane over a finite field Fq, q a prime power. Show that there exists a commutative binary operation * in Z such
that
(i) x*y is neither x nor y for any x and y, ...

**1**

vote

**0**answers

25 views

### Stochastic calculus in $L^1$

Does there exist a more general (than Malliavin or Itô) "Stochastic calculus" defined on $L^1$ space, or some Orlicz space between $L^2$ and $L^1$?
For examples: are there:
Ito ...

**2**

votes

**1**answer

66 views

### Opposite of an E2-algebra

Suppose $C$ is the monoidal $\infty$-category of modules over an $\mathcal{E}_2$-ring spectrum $A$. Let $C' = C$ as a category, but with opposite monoidal structure to $C$. Is $C'$ the category of ...

**2**

votes

**1**answer

48 views

### Area of an irregular, n-sided, non-intersecting (edges) polygon algorithm

I need to generate an irregular, n-sided polygon of non-intersecting edges (n= 200, for example) with the smallest area possible. The position of the vertex is random and I've tried designing a couple ...

**-1**

votes

**1**answer

42 views

### Computing the inverse of a Cholesky decomposition [on hold]

I have chol(A) and I would like chol(A^-1). One way to do this is to construct the inverse positive definite symmetric matrix and then take its Cholesky decomposition (with Dpotri and Dpotrf for ...

**-10**

votes

**0**answers

84 views

### Please help me for answers to question. best regards [on hold]

Find the definition of a locale and its dual (i.e. a frame) and consider the
definition of a Grothendieck topology. Discuss the differences between this
concept and an ordinary topology on a set ...

**-2**

votes

**0**answers

76 views

### Techniques to solve logarithmic functional equations [on hold]

I would like to solve this logarithmic functional equation, but cannot find a standard technique:
$$f(f(x)) = log(x)$$

**2**

votes

**1**answer

65 views

### Discrete spectrum and almost periodicity

According to Vershik, an ergodic invertible measure-preserving transformation $T$ on a Lebesgue space $X$ has discrete spectrum if and only if for every bounded measurable function $f\colon X \to ...

**1**

vote

**2**answers

93 views

### Probability of at most $K$ consecutive zeroes in a sequence of 0s and 1s [on hold]

I want to prove that in a sequence W of length n, consisting of 1s and 0s, $P$( in $W$ there is at most $\frac{\log_2n}2$ consecutive zeroes ) $\leq \frac{K}{n} $ for some constant K. Can anyone ...

**-4**

votes

**0**answers

156 views

### What area of maths have I reinvented? [on hold]

I was trying to solve the issue of calculating (total) utilities with infinite numbers of people. This is problematic, because many infinite series are divergent, so there does not appear to be a way ...

**3**

votes

**1**answer

45 views

### Converging to moments obeying Carleman's condition

I believe that the following is true, and I'd like to make sure that it is and to have a reference. Suppose that $\mu_N$ are a sequence of measures on $\mathbb{R}$. Let $m_{N,k}$ be the $k$-th ...

**9**

votes

**2**answers

237 views

### Stable homotopy groups of $RP^{\infty}$

Are the stable homotopy groups $\pi^s_i(\mathbb R P^{\infty})$ known for small $i$? In particular, I would be interested in the values for $i = 5,6$. A quick Internet search did not lead to anything.