3
votes
0answers
95 views

Does there exist a continuous surjection? [on hold]

Let $C$ be an irreducible projective cubic in $\mathbb{P}_2$ with a singular point $p$. So consider $f: \mathbb{P}_1 \to C$ defined as follows. Identify $\mathbb{P}_1$ with the set of lines in ...
0
votes
0answers
75 views

Four kinds of generalized hypergeometric formulas for $\pi$

Given, $$\begin{array}{|c|c|c|c|} \hline n&a_n&b_n&c_n\\ \hline 1 & 6541681608 & 163096908 & -640320^3\\ \hline 2 & 85840 & 4492 & -14112^2\\ \hline 3 & 28302 ...
-1
votes
0answers
41 views

Characterize polytopes resulting from cutting a convex polytope by a hyperplane [on hold]

We have a convex polytope $P$ for which we know its set of vertices. Using this set we characterize the H-representation of $P$ as: $\mathbf{A}\mathbf{x} < \mathbf{b}$. If a hyperplane defined by ...
-4
votes
0answers
13 views

How to find the matrix of adjoint transformation R* according to the usual scalar product [on hold]

transformation R3 -> R3 is a" circle" around the line x / z = -y = z / 2
0
votes
0answers
16 views

Intersection of an irreducible curve with an exceptional divisor

Suppose $A$ is an irreducible curve on the blowup of $\mathbb{P}^2$. Then if $A$ is not equal to $E$ (where $E$ is the exceptional divisor) it has to intersect it positively. However, $A.E = c_1 ...
2
votes
0answers
123 views

Why the composition of planar tangles is well-defined?

In the planar algebra theory (see here or there section 2), a planar tangle is an isotopy class; then to define the composition of two tangles, we need to choose a representative in each classes. See ...
4
votes
0answers
93 views

What is the probability that a Gaussian random variable is the largest of three Gaussian random variables?

Consider three independent, normally distributed RVs: $YA \sim N(a,\sigma ^{2}),$ $% YB\sim N(b,\sigma ^{2})$ and $YC\sim N(c,\sigma ^{2})$. What is the probability that $YA$ is the maximum?: $$\Pr ...
2
votes
2answers
217 views

Is Eilenberg-Maclane $\wedge$ Moore space the spectrum of the cohomology theory $H^*(\ ,G)$?

In the web page http://www.encyclopediaofmath.org/index.php/Moore_space it can be found the following statement: If $K(\mathbb Z,n)$ is the Eilenberg–MacLane space of the group of integers ...
4
votes
2answers
593 views

Polish by compact is Polish?

Let $X,Y$ be separable and metrizable, with $Y$ Polish, and suppose there is a topological quotient map $f:X\to Y$ with compact fibers. Is $X$ Polish? I have a specific space in mind, so if the ...
1
vote
1answer
37 views

Intersection of complements of connected components (2)

Let $(X,d)$ be a non-compact, complete metric space and $K\subseteq X$ compact. Pick $x^* \in X\setminus K$. Let $E$ be the connected component of $X\setminus K$ that contains $x^*$. Let ${\cal C}$ ...
7
votes
2answers
100 views

Isomorphism problem on the class of induced subgraphs of a hypercube

A problem that I am currently studying translates to the problem of deciding whether two induced subgraphs of the hypercube $Q_k$ are isomorphic. Now it feels to me that this class of graphs is "too ...
4
votes
1answer
94 views

application of factorization theorem

Young's inequlity tells us that $L^{1}(\mathbb R)\ast L^{p}(\mathbb R) \subset L^{p}(\mathbb R)$ with norm inequality $$\|f\ast g\|_{L^{p}} \leq \|f\|_{L^1}\|g\|_{L^p};$$ and of course this ...
0
votes
0answers
26 views

Existence of Solution steady navier stokes with do nothing outflow condition

We consider the stationary navier stokes equation with mixed boundary conditions $$ \begin{align} -\nu\Delta u +(u\cdot\nabla) u + \nabla p &= 0\ \textrm{in}\ \Omega \\ div\ u&=0\ \textrm{in}\ ...
4
votes
0answers
89 views

finite approximation equation on free group

An equation in a free group $F$ is an identity of the form $W(x_1,..,x_n,a_1,...a_n)$ where $x_1,...,x_n$ are variables, $a_1,...,a_n$ free generators of $F$ and $W$ a word in the free group on ...
0
votes
0answers
90 views

Does the equality of product of integers modulo prime p holds in a given interval?

For any given prime $p$, does there exist $a_1,a_2,\dots,a_k,$ (not necessarily distinct) $b_1,b_2,\dots,b_m$ (not necessarily distinct) and $y_1$, $y_2$ such that ...
-1
votes
0answers
43 views

Finite groups whose non-trivial elements have no fixed points [migrated]

I am interested in finite groups $G$ acting on a finite set $X$ with the following property: (*) fix(g)=$\emptyset$ for all $g\in G\setminus\{1\}$, where fix(g):=$\{x\in X|gx=x\}$ denotes the set ...
1
vote
1answer
46 views

Limiting absorption principle

I would like to know if there is a book (or a paper) which can give me an introduction to LAP. I tried to read some papers by myself, but I don't feel comfortable. I think that I need the basic ideas ...
0
votes
0answers
56 views

Sheaves whose restriction maps are monomorphisms?

When the restriction maps of a sheaf of $\mathcal O_X$-modules are epimorphisms, the sheaf is flasque and we have a whole theory of that. Is there a detailed study of the opposite phenomenon, i.e., ...
-2
votes
0answers
51 views

Subgroups of the group $G_2 \times G_2$ [migrated]

Does the group $G_2 \times G_2$ have the group $SO(7)$ (or its double cover $Spin(7)$) as its subgroup? Here, $G_2$ is the compact exceptional group $G_2$.
3
votes
1answer
21 views

Intersection of complements of connected components

Let $(X,\tau)$ be a topological space, $S\subseteq X$ such that there is $x^*\in X\setminus S$. Let $E$ be the connected component of $X\setminus S$ that contains $x^*$. Let ${\cal C}$ be the ...
3
votes
1answer
43 views

Normal Hopf ideals and Hopf subalgebras, quotient group schemes

There is a following theorem: $H$ is a commutative Hopf algebra over a field $k$. Then there exists a bijective correspondence between $$\{ \textrm{Hopf subalgebras }K\subset H \} \quad ...
-4
votes
0answers
21 views

Compute eigenvalues and lash1e vectors (2n + 1) X (2n + 1) matrix: [on hold]

middle row: 1 ... 1 0 1 ... 1 middle column: 1 ... 1 0 1 ... 1 In the unmarked places are zero. Calculate at least in the case, when n=2 I have really no idea how to start.
0
votes
0answers
10 views

Cardinality of maximum independent set for a given degree distribution

Consider undirected graph $G(V,E)$. Assume that $f_n(k)$ be the probability mass function of degree of a vertex in $G$. Further, assume that $f_n(k)$ is an strictly decreasing function of $k$ with ...
4
votes
2answers
137 views

Closure of the graph of a function

Let $X_1, X_2$ be non-empty sets and let $R\subseteq X_1\times X_2$ such that for all $x\in X_1$ there is $y\in X_2$ such that $(x,y)\in R$. Are there topologies $\tau_i$ on $X_i$ for $i=1,2$ and a ...
-4
votes
0answers
29 views

Cartopolar curve

Is there any plane curve that has the same equation in cartesian as in polar coordinates? To be more specific, is there a function such that $f(f(x)\cos x)=f(x)\sin x, \forall x$?
2
votes
1answer
64 views

planes intersecting a convex polytope

We are given a $d$-dimensional convex polytope ${\cal P}$ in $N$-dimensional space where $d<N-1$. Consider several planes $P_i$ corresponding to inequalities $f_i(X)\ge 0$. We are given that each ...
1
vote
0answers
42 views

What is the complexity of finding a generator for the cyclic elliptic curves?

Let $E$ be an elliptic curve which is defined over a finite field $\mathbb{F}_p$, where $p$ is a prime number. If we know that $E(\mathbb{F}_p)$ is cycyclic, is there an algorithm to find its ...
3
votes
0answers
39 views

Equivalence (or not) of two Artin/Fox wild arcs

The repeating patterns in the wikipedia articles on wild arcs and wild knots seem to me to be not continuously deformable to each other. Is this true? For clarity, here is my diagram of the repeating ...
3
votes
0answers
116 views

Varieties acted upon faithfully by an abelian variety

Let $X$ be a smooth projective variety over the complex numbers. Suppose that some positive-dimensional abelian variety $A$ acts faithfully on $X$. Examples of such varieties $X$ are provided by ...
3
votes
1answer
177 views

When a smooth algebra is regular?

Let $A \subseteq B$ be noetherian integral domains, $A$ regular (=every localization at maximal ideal is a regular local ring) and $B$ is a smooth $A$-algebra. For the definition of a smooth algebra, ...
13
votes
2answers
667 views

Origin of the term “Diophantine equation”

It seems that the term "Diophantine equation" has been around at least since the second half of the 19th century, since the historian Hermann Hankel writes (polemically) in the chapter on Diophantus ...
23
votes
1answer
733 views

When is there a submersion from a sphere into a sphere?

(First posted on math.SE, with no answers.) That is: For which positive integers $n, k \ge 1$ does there exist a submersion $S^{n+k} \to S^k$? The discussion at this math.SE question has ...
-2
votes
0answers
33 views

positiv Martingale using Itô [on hold]

I would to like to prove that the process: $$e^{\int_{0}^{T}\theta _{s}dW_{s}-\frac{1}{2}\int_{0}^{T}\theta _{s}^2ds}$$ is a martingale which is positiv and has a mean=1 $$\theta is continuous ...
-4
votes
0answers
48 views

Matrix 5th rooth - how to find it? [on hold]

I kindly ask you to help me with an example of calculating 5th rooth of 3 over 3 matrix. Thank you
3
votes
0answers
241 views

What's the name of this branched covering?

I've come across a double cover of $\mathbb P_1(\mathbb C)$, ramified at $[1:1]$ and $[-1:1]$ in homogeneous coordinates, given as the quotient by the natural $\mathbb Z/2\mathbb Z$-action generated ...
4
votes
1answer
69 views

Numerical equality testing

I am working on developing an online homework system. One thing I would like to have is something which compares a student's answer (like $2\sin(x)\cos(x)$) with the intended answer (maybe ...
9
votes
1answer
178 views

Nontrivial finite group with trivial cohomology in prescribed degree

For any non-trivial finite group $G$ there exists some $j > 0$ such that $H^{aj}(G) \neq 0$ for all $a = 1,2,3,\dots$, see e.g. this question: Non-vanishing of group cohomology in sufficiently high ...
-3
votes
0answers
58 views

How to prove that $h^*(A)$ exists and $h^*(A)=\{x\in ON : x \leq^* A\}$? [on hold]

Definition : $h^*(A)$ is the least aleph such that $\not\leq^* A$. $Z \not\leq^* X$ means theie is no map from $X$ onto $Z$. How to prove that $h^*(A)$ exists and $h^*(A)=\{x\in ON : x \leq^* ...
2
votes
0answers
82 views

Naive G-spectrum representing geometric equivariant cobordism

Let $G$ be a finite group. By the transversality results of Wasserman $G$-equivariant bordism (say real) should be a naive homology theory, and as such it should be represented by a naive G-spectrum. ...
0
votes
0answers
45 views

Sum of the series with Stirling numbers [on hold]

Yesterday I worked on one problem in discrethe math and in the process of decision I came across this series. Try to do it with generating functions, but there is no success for me. So, what do you ...
0
votes
0answers
34 views

Function series involving a suite of imprimitive Dirichlet characters and a zero of $L(\chi,s)$

I have difficulties to understand the behavior of following suite of functions near zero : $$F_P(x)= \sum\limits_{n=P}^{\infty} \chi_P(n) f(nx)$$ With $f(x) = x^{-s_0} e^{-x}$ where $s_0$ is a non ...
3
votes
2answers
100 views

Maximizing entropy under constraints

This question is about an extension of the variational principle in thermodynamical formalism when one adds linear constraints to the measures. Consider the one-sided shift ...
2
votes
1answer
143 views

On the number of irreducible components of an exceptional divisor

Let $X$ be a complex, affine variety and $Z\subseteq X$ a closed subset of $X$ (i.e. a closed, reduced subscheme). Let $E$ be the exceptional divisor of the blow-up $\pi:\tilde X\to X$ of $X$ with ...
5
votes
1answer
72 views

Simultaneous approximation of arbitrary functions in Hölder space and in $L^2(\mu)$ by a smooth function and its derivative

Let $\mu$ be a probability measure on the circle $S^1=\mathbb{R}/\mathbb{Z}$ which is singular with respect to the Lebesgue measure $\lambda$. Consider the functions spaces $L^2(\mu)$ on the one hand, ...
3
votes
0answers
106 views

Differences associated with differences of primes: are they all 1,2,3?

Let $d_k$ be the $k^{th}$ difference sequence of the primes; that is, $$d_k = \sum_{i=0}^{k} (-1)^i {k \choose i} P_{k+1-i},$$ where $P_i$ denotes the $i$-th prime number. Let $(s_n)$ be the ...
0
votes
0answers
79 views

Problem with operator and Fourier transform

I am currently dealing with a problem in functional analysis where I want to show the following. Let $\phi_{k+1}(x):=\sqrt{2} \sum_{n \in \mathbb{Z}} h(n) \phi_k(2x-n)$ and $\phi_0= \chi_{[0,1]},$ if ...
-3
votes
0answers
16 views

Calculate coordinate transformation matrix [on hold]

Calculate coordinate transformation matrix A in the base [1; x; x2]. In the space R2 [x] of real polynomials highest rate? D is given a scalar product. Sebi-adjoint transformation of A: R2 [x]! R2 ...
2
votes
2answers
171 views

Convergence of a sum with the ranks of homotopy groups

Let $F$ be a (nontrivial) topological space that satisfies the following conditions: 1) $\pi_n(F)$ has a trivial action of $\pi_1(F)$ for $n>0$ and 2) its homology groups are finitely generated. ...
0
votes
0answers
21 views

Definite integral involving Legendre Polynomial [on hold]

Does anyone know the answer to the following definite integral: $\displaystyle \int_{0}^{\pi}P_{\ell}(\cos\theta)\sin^{k}\theta\, d\theta $, for $k\geq 1$, where $P_{\ell}(x)$ is the $\ell$-th ...
8
votes
2answers
200 views

Radial limit does not exist almost everywhere

Problem 4 in Chapter 4 of Stein's book "Real Analysis" says $\sum_{n\geqslant 0}z^{2^n}$ doesn't have radial limit as $z$ approaches the unit circle from inside almost everywhere. It's fairly easy ...

15 30 50 per page