0
votes
0answers
37 views

What is the state of art MIQP solver

I used Gurobi with a MIQP with 26 binary variables and 26*4 interaction term without any other constraint. The speed is very slow already.... I want to ask what is the state of art of MIQP solvers. ...
0
votes
0answers
40 views

Intersection points of closed curves inscribed in a convex polygon

Suppose that I have two distinct simple closed curves, $C_1$ & $C_2$, and each is inscribed in a convex polygon, D. By inscribed, I mean tangent to each side of D. In particular, I am most ...
-2
votes
0answers
86 views

Arranging books into bags [on hold]

I'm trying to find an algorithm to answer the following question (informal): given a (finite) set of distinct books of different (positive integer) sizes and a (finite) set of bags of different ...
-4
votes
0answers
50 views

In Dedekind' construction of real numbers, what's wrong with this understanding [on hold]

in this prove, every cut corresponds to a real number. and a cut is a subset of Q.and cut have these three properties.1.is not empty 2.if p belong to this cut,any qp so in my understanding, every cut ...
-5
votes
0answers
44 views

transitive actions of automorphism group [on hold]

Can a finite group be extended to a group whose group of automorphisms acts transitively on the first group. Or more generally, given any finite module, can we extend this module so that the group ...
-2
votes
0answers
52 views

The space $W = \{u \in L^2(0,T;V) : u_t \in L^2(0,T:V^*)\}$ without having identified $H$ and $H^*$ [on hold]

Let $V \subset H \subset V^*$ be a Gelfand triple with the Hilbert space $H$ identified with its dual space and $V$ a reflexive separable Banach space. Define $W = \{u \in L^2(0,T;V) : u_t \in ...
4
votes
1answer
107 views

A lower bound on the $L^2$ norm of a Dirichlet polynomial

The Question. Suppose $0 < \alpha < \beta$ are fixed, and $a_n$ is an arbitrary sequence of real numbers. Is it known how to bound from below \begin{equation*} \int_0^{T} \Big| \sum_{\alpha T ...
3
votes
1answer
118 views

Is the fundamental group of an open arithmetic Riemann surface contained in $\Gamma(2)$

Let $X$ be a non-compact Riemann surface with universal covering $\mathbb H$ and suppose that the fundamental group of $X$ is an arithmetic subgroup of $\mathrm{Aut}(\mathbb H) = ...
0
votes
1answer
135 views

How to solve $e^{f(x)} + a f(x) + bx = 0$ [on hold]

How should determine solutions to equations of this form? $$e^{-f(x)} + b f(x) = ax$$ Here $f(x)>0$ is real valued. Also $a>0$, $b>0$.
2
votes
0answers
42 views

Finite extension of K(x) with extra structure: definable over field of invariants?

Let $K$ be an algebraically closed field, and let $\sigma$ be an automorphism on $K$. Set $k=K^\sigma$. Consider the rational function field $K(x)$ and extend $\sigma$ to $K(x)$ by $\sigma(x)=x$, ...
-4
votes
0answers
22 views

How to solve the following integral [on hold]

Do you have any idea how to solve the following integral: $\int\limits_0^a {{e^{ - \frac{{by}}{{c - dy}} - ey}}dy}$, where $a$, $b$, $c$, $d$ and $e$ are constants? Thank you very much.
2
votes
2answers
74 views

Finite series with reciprocal factorials

I asked the question at MSE http://math.stackexchange.com/questions/982388/simple-finite-series-with-reciprocal-factorials but got no answer or comment (it is not a homework). I'm trying to find the ...
4
votes
0answers
167 views

Any counterexamples known for the Generalized Tate conjecture?

One can state the generalized Tate conjecture over arbitrary finitely generated fields; to this end one should just define Galois representation to be effective if the eignevalues of the actions of ...
3
votes
1answer
31 views

Polynomial (non-)embedding of a simplex in euclidean space

Let $\Delta$ be a standard $k$-simplex, and let $f:\Delta\to\mathbb R^N$ be a polynomial map with known numerical coefficients. What sort of practical computational algorithms can be used to ...
5
votes
2answers
247 views

$j$-invariants of elliptic curves over finite fields

Let $K$ be a finite field, and $\overline{K}$ its algebraic closure. It is well known that two curves are isomorphic over $\overline{K}$ if and only if they have the same $j$-invariant. If two such ...
12
votes
2answers
1k views

Is every number the sum of two cubes modulo p where p is a prime not equal to 7?

If p is a prime other than 7, can every integer be written as sum of two cubes modulo p? Has Waring's problem mod p for cubes been proved simply and directly? Thanks for your proof. Lemi
5
votes
2answers
206 views

Which groups are LERF?

A finitely generated group $G$ is called LERF if every finitely generated $H \leq G$ is closed in the profinite topology on $G$ (equivalently, there is a family of finite index subgroups of $G$ ...
0
votes
0answers
50 views

2x3 = 5+1 AND 2+3 = 5x1. How many other examples of this type? [migrated]

I noticed the following: 2x3 = 5+1. If you switch the operators, it is still true: 2+3 = 5*1. There is another obvious/trivial example where you can swap the operators: 2x2 = 2+2. I think these ...
3
votes
1answer
118 views

Reference for a fact (?) on homeomorphic knot complements

Does somebody have a reference (or an argument why it should be true) for the following statement? “Let $K$ and $K'$ be knots in $S^3$. If there is an orientation-preserving homeomorphism $h : S^3 ...
1
vote
0answers
24 views

How to infer missing nodes from a path?

I have a first data set which is a list of train stops with coordinates (lat, lon), but not the "links" between the nodes/stops (this could thought of as a null or empty graph). I have a second data ...
2
votes
0answers
97 views

Marshall Hall's theorem for surface groups [on hold]

Let $\Gamma_g$ be a surface group of genus $g \geq 2$, that is we have a presentation: $$\Gamma_g = \langle x_1,y_1 \dots, x_g,y_g \vert \prod_{i = 1}^g [x_i,y_i] = 1\rangle$$ Let $H \leq \Gamma_g$ ...
3
votes
1answer
225 views

Doing some homological algebra in triangulated categories

It's well known that chain complexes are an abelian category, and in particular we can consider chain complexes of chain complexes, i.e. double complexes. Given a double complex $A^{\bullet\bullet} ...
0
votes
1answer
36 views

Existence of half-planes with respect to regular open sets of the Euclidean plane

I initially asked this question at math.stackexchange.com but there was no reaction, so I thought this may be a good idea to transfer it to mathoverflow.net Let ...
11
votes
0answers
94 views

When is a group Fibonacci sequence contained in a single conjugacy class?

First a definition: a Fibonacci sequence in a group is a sequence in which the first two elements may be arbitrary, and from there on each element is a product (using the group operation) of the ...
4
votes
2answers
210 views

Topological characterization of injective metric spaces

Let $\ (X\ d)\ \,(Y\ \delta)\ $ be arbitrary metric spaces. A function $\ f:X\rightarrow Y\ $ is called a metric map (with respect to the given metrics $\ d\ \delta$) $\ \Leftarrow:\Rightarrow\ ...
1
vote
1answer
56 views

Does restriction to an open subgroup preserve projective smooth representations?

Let $G$ be a locally profinite group and $K \le G$ an open subgroup. Does the restriction functor $\mathrm{Res}^G_K$ from the category of smooth $\mathbb{C}$-linear representations of $G$ to smooth ...
1
vote
0answers
18 views

Central automorphisms of groups act transitively on Krull-Schmidt decompositions

(Cross posted from math.SE) I'm looking for a modern reference to the subject line, preferably one that doesn't use Ore's generalizations to modular lattices. To clarify terminology... Suppose we ...
9
votes
0answers
134 views

Reinhardt cardinals and iterability

Work in $ZF$. Let $j:V\to V$ be a non-trivial elementary embedding which is iterable, so that we can iterate it and form models $M_\alpha, \alpha\in ON,$ with $M_0=V,$ and elementary embeddings ...
1
vote
1answer
73 views

Name for (function, set) pairs?

Right now I'm working on a topological graph theory problem. To prove a theorem I introduced some objects. Has anyone heard of something similar before? I would like to call them by the right name. ...
0
votes
0answers
34 views

Nonlinear ODE system

Let $\Psi(a) = \frac{a}{2}$ if $a>0$ and $0$ if $a\le 0$. Now we consider the following coupled system of nonlinear ODEs: $$\begin{aligned}&\frac{1}{2}\sigma_1^2 u_1''(x) + \mu_1 u_1'(x) + ...
-1
votes
0answers
43 views

Particular case of every sequence has a Cauchy subsequence? [on hold]

A metric space (X,d) has the following property: Given $\epsilon >0$ and non-empty finite subset $X_\epsilon \subset X$ $$ \inf \{ d(x,p) : p \in X_\epsilon \} < \epsilon$$ I would like to ...
2
votes
1answer
91 views

Compact induction as a tensor product

Let $G$ be a locally profinite (i.e., locally compact Hausdorff and totally disconnected) topological group, $H \le G$ a closed subgroup, and $(W, \sigma)$ a representation of $H$ over $\mathbb{C}$ ...
2
votes
0answers
66 views

Lattice model for Affine Grassmannians of non type A

There is a Lattice model for affine Grassmannians of type A, due to Lusztig. It describes affine Grassmannians of type A as the moduli space of certain subspaces in an infinite-dimensional ...
0
votes
0answers
46 views

Sequence of cosine converges? [on hold]

Does the following sequence $$(\cos (\pi \sqrt{ n^2 + n}))_{n=1}^\infty $$ converge? Can I use the ratio or root test?
0
votes
0answers
55 views

Bolzano-Weierstrass application? [on hold]

I am having problems proving the following claim: Given a bounded set $A \subset R^n$, I want to prove the existence of $a_1, \dots, a_N \in R^n$ and numbers $r_1, \dots, r_N \in [0, +\infty)$ such ...
7
votes
0answers
116 views

Countable choice in $L(\mathbb{R}^*_G)$

Let $\lambda$ be a singular strong limit cardinal and let $G \subset \text{Col}(\omega,\mathord{<}\lambda)$ be a $V$-generic filter. Let $\mathbb{R}^*_G = \bigcup_{\alpha < \lambda} ...
4
votes
1answer
267 views

How to visualise Bollobas' 1965 theorem?

Theorem $[n]=\{1,\ldots,n\}$. Let $\lbrace (R_i, S_i), i \in I \rbrace, R_i, S_i \subset [n]$ be such that $R_i \cap S_i = \emptyset, R_i \cap S_j \ne \emptyset (i \ne j)$. Then $$\sum_{i \in I} ...
0
votes
0answers
29 views

how to compute bergman kernel

i have a question to determin if the asyptotic expansion of Bergman kernel has a log term. Is there anyone can show me is there any general way to tell?
-1
votes
0answers
10 views

How to best fit for linear vs sinusoidal curve [on hold]

I have to analyze a series of data points for my environmental science class, but I've never taken statistics. I want to determine whether a line or sinusoidal curve (with a very large period -- ...
0
votes
0answers
70 views

Solving matrix equation (AX)^2+(BY)^2=D [on hold]

Is there any method that can solve the matrix equation in such a form (AX)^2+(BY)^2=D? A and B are matrix, X, Y and D are column vectors. (Solve for X and Y) I originally have two equations such as ...
1
vote
0answers
85 views

Reference request: functional analysis results used in Taubes paper (1980)

I'm studying Taubes paper 'Arbitrary N-vortex solutions to the first order Ginzburg-Landau equations'. I'm looking for a reference of three following theorems: Let $f(x)$ be a convex funtional ...
2
votes
0answers
59 views

Computing Euler Charactistics of Line bundles on Hilbert Schemes of points on Surfaces

Let $S^{[2]}$ be the Hilbert scheme of two points on a smooth projective surface (actually, right now I am particularly interested in del Pezzo surfaces). Let $B$ be the exceptional divisor of the ...
0
votes
1answer
123 views

Free action of symmetric groups

What type of compact manifolds, can be acted freely by symmetric group $S_{m}$ for some $m>2$? Is there a compact manifold which can be act freely by all symmetric ...
-5
votes
0answers
124 views

Talking about the abc-conjecture [on hold]

What is the latest news about the abc-conjecture?
8
votes
1answer
192 views

How do I check that this is a Frobenius algebra?

Let $f_1,f_2,\ldots,f_n\in \mathbb C[z_1,\ldots, z_n]$ be such that the quotient ring $$A:=\mathbb C[z_1,\ldots, z_n]/(f_1,f_2,\ldots,f_n)$$ is finite dimensional (in other words, it's a ...
1
vote
1answer
54 views

Special retraction from a metric space onto an arc

Suppose $X$ is a metric space and $A$ is a subspace of $X$ homeomorphic to $[0,1]$ with its usual topology. Let $v$ an end point of $A$, that is $v$ does not disconnect $A$. Is there a retraction $r$ ...
0
votes
0answers
50 views

Sequence from count [on hold]

I need to generate a formula for a programming project. The formula will assist in the positioning of elements on screen. I would like a formula that produces the following sequence indefinitely: 1, ...
0
votes
1answer
83 views

Braids, pure braids and Dehn twists

Consider the braid group with $n$ strands $B_n$. Each braid can be drawn (say) from bottom to top as $n$-intertwining strictly monotonic strands. Moreover, the group $B_n$ is generated by $n-1$ ...
10
votes
1answer
197 views

Diffeomorphisms and homotopy equivalences sliced over BO(n)

There are some classical results stating sufficient conditions on a manifold $\Sigma$ such that every homotopy equivalence $\Pi(\Sigma) \stackrel{\simeq}{\longrightarrow} \Pi(\Sigma)$ is homotopic to ...
-2
votes
0answers
79 views

Prove irrationality for the supplied exercise [on hold]

How can I prove that the product of cube root of 2 and the cube root of 4 is irrational ? 3 sqrt(2) * 3 sqrt(4) = irrational. Thanks!

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