0
votes
0answers
2 views

Let Z be the set of integers, and consider the function f : Z → Z defined f(x) = 2x. Which of the following is correct?

a) f is invertible b) f is injective c) f is bijective d) f is surjective I put b, though apparently that's wrong. Thanks :)
0
votes
0answers
6 views

translation invariance of the Laughlin wave function

This is a translation into math of the following question, posted on PhysicsOverflow. Let $H:=L^2(\mathbb C)$. For every $N$, let $\psi_N\in\Lambda^N H\cong (L^2(\mathbb C^N))^{S_N}$ be the function ...
0
votes
0answers
15 views

Calculating Swaps and Swaptions [on hold]

Hi all I have a problem when I have to calculate swaps/swaptions. n=10-period binomial model for the short-rate, ri,j. The lattice parameters are: r0,0=5%, u=1.1, d=0.9 and q=1−q=1/2. 1.Compute the ...
2
votes
0answers
15 views

Reference for a strong intermediate value theorem for measures

Let $\mu$ be a finite nonatomic measure on a measurable space $(X,\Sigma)$, and for simplicity assume that $\mu(X) = 1$. There is a well-known "intermediate value theorem" of Sierpiński that states ...
-1
votes
0answers
28 views

On multilinear linear combinations

If $K$ is algebraically closed field, then consider $m$ multilinear polynomials $f_i$ for $i=\{1,\dots,m\}$ in $K[x_1,\dots,x_n]$ of degree $d_i$ each with no common root. We know there exists $g_i$ ...
1
vote
1answer
69 views

Free action of $\mathbb{Z}(2^{\infty})$ on a compact space

Assume that $X$ is a Hausdorff compact space such that $\forall n\in \mathbb{N}$, we have a free action of $\mathbb{Z/{2^{n}}\mathbb{Z}}$ on $X$. Can $Z(2^{\infty})$ act freely on $X$? Note ...
-1
votes
0answers
21 views

Number of graphs with M edges that does not contain K-clique

If we consider the space of graphs $G(n,M)$ where $M$ denotes the number of edges. Is there any known way of calculating the number of graphs within this space that does not contain any k-cliques? Can ...
1
vote
1answer
47 views

Nuclearity noncommutative torus

I read that the Noncommutative torus (rotation algebra) is nuclear when $\theta\in\mathbb{R}\setminus\mathbb{Q}$. Unfortunately, I haven't found a proof. Could someone give me a reference and/or an ...
-2
votes
1answer
22 views

Systems of ODEs that fulfill a matrix relationship at steady state

It is well known that for a system of linear ODE $$x'(t) = A(t) \cdot x(t) + b(t)$$ with initial condition $x(t_0) = x_0$, that for a solution at any other time point $t_1$, $x(t_1) = (z_1, \ldots, ...
2
votes
0answers
25 views

Exactness of an additive left Kan extension

Let $\phi:R\to S$ be a flat ring homomorphism and consider the induced adjoint pair $$\phi_!:R-Mod\rightleftarrows S-Mod:\phi^*,$$ where $\phi_!=(S\otimes_R -)$. The right adjoint $\phi^*$ is easily ...
1
vote
0answers
48 views

Can we say that $A$ is a complement for a group $G$?

Let $A$ be a frobenius complement for a group $G$ i.e. $A$ act on $G$ by automorphism s.t. $C_A(g)=e$ for all nonidentity $g$. Now, Action of $A$ can be linearly extended so that $A$ act on $F[G]$. ...
0
votes
0answers
11 views

Best s-term approximation and unit balls in weak $\ell^p$ norm

In the book "A Mathematical Introduction to Compressive Sensing" by Foucart and Rauhut there is the following asymptotic estimate at page 332, equation (11.1): $$\sup_{\mathbf{x}\in B^N_{r,\infty}} ...
-4
votes
0answers
23 views

Find solution of signle element $y_i$ in vector $y$ subject to $Ay=c$ [on hold]

I have a interesting question about linear algebra problem. Assume that I have a matrix $A^{m \times n}$ and vector $c^{n \times 1}$ are known and I want to find the solution of vector y subject to ...
-4
votes
0answers
30 views

An exercise related to Arzela- Ascoli theorem [on hold]

I am looking for some hint to prove the set A={x belonging to C[a,b]| sup|x| +sup|x'|<=1} is compact. Can you help me? I will appreciate any help!
-7
votes
0answers
62 views

How to understand mathematics [on hold]

How do I achieve a good understanding of university level mathematics in order to do research in ? How do I know that the piece of math is understood and that I can go ahead?
1
vote
1answer
14 views

A question on difficiency value for entire function

Recently I come cross a question about difficiency value for entire function. I find that many examples in the book about the dificiency value, whose difficiency values are in the singular value ...
0
votes
1answer
37 views

Question on affine buildings

Let $X$ be an affine building. Assume that $X$ is periodic, by which I mean that there exists a covering $X\to F$ of a finite simplicial complex. Let $\Gamma$ denote the group of deck transformations, ...
8
votes
1answer
219 views

Are there known cases of the Mumford–Tate conjecture that do not use Abelian varieties?

(For a formulation of the Mumford–Tate conjecture, see below.) The question As far as I know, all non-trivial known cases of the Mumford–Tate conjecture more or less depend on the Mumford–Tate ...
4
votes
1answer
31 views

Additivity of simplicial volume

I have read for example in the introduction of http://arxiv.org/pdf/math/0506338v2.pdf about the property that if we glue hyperbolic manifolds with geodesic boundary consisting of tori along some ...
19
votes
0answers
194 views

Can one properly embed a differential manifold into numerical space of double dimension?

If $X$ is a $ C^\infty$ differential manifold of dimension $n$, then there exists an embedding $f:X\to \mathbb R^{2n+1}$. This is a not too difficult theorem due to Whitney, proved in many textbooks. ...
2
votes
0answers
62 views

lower-bound for $Pr[X\geq EX]$

Given n random variables, $X_1, ..., X_n$, each takes value 0 or $a_i \in[0, 1]$. $X = \sum_{i=1}^n X_i$ and $EX \geq 1$ is the expected value of $X$. Can we get a lower-bound for $Pr[X \geq EX]$? It ...
0
votes
0answers
8 views

LYX: how to mark power set? [migrated]

This is my first time here and I did my best to figure out if such a question is in place here. If I missed something I apologize. My questions is how can I mark a power set in the lyx document ...
0
votes
1answer
66 views

Stability conditions of coherent sheaves on abelian 3-folds

My work for now consists on understanding stability conditions of coherent sheaves on abelian 3-folds. I have the book by D. Huybrechts (the geometry of moduli spaces of sheaves), But I would like to ...
0
votes
0answers
99 views

A question about a subset in R^n homeomorphic to an open subset [on hold]

Let A be a subset of n-dimensional Eucliean space R^n, A is homeomorphic to an open subset of R^n. Then whether A is also an open subset of R^n? Is it a theorem in somewhere? Thank you very much.
1
vote
0answers
39 views

Periodic Growth behaviours of Cayley graphs

This question is related to On the size of balls in Cayley graphs and Folner sequences of amenable groups of exponential growth Given a Cayley graph of a group $G$ with finite generating set ...
4
votes
1answer
62 views

Isomorphic Hadwiger graphs

Let $G$ be a graph, then we define its Hadwiger graph $\textrm{Hadw}(G)$ in the following way: $V(\textrm{Hadw}(G)) = \{S\subseteq (V(G): S\neq \emptyset\textrm{ and } S \textrm{ is connected}\}$; ...
0
votes
0answers
23 views

Density for Translated Process

Let $M$ be a (compact) Riemannian manifold. Let $v$ be a smooth vector field on $M$ with flow $\Theta_t$. Let $L$ be an elliptic second order differential operator on $M$ that generates the Ito ...
1
vote
1answer
23 views

A cascade process on a graph with positive and negative edge weights

Let $G$ be an arbitrary graph with randomly or pseudo-randomly assigned edge weights $w_i \in \mathbb{R}$ (edge weights can be both positive and negative). We model a cascading process on this graph ...
0
votes
1answer
117 views

When a proper morphism of schemes is a closed imbedding?

Let $X$ and $Y$ be finitely presented schemes over $\mathbb{C}$. Let $f\colon X\to Y$ be a proper morphism. Let us assume that for any finitely presented scheme $S$ the induced map $$Mor_{Sch}(S,X)\to ...
-2
votes
0answers
47 views

Is it true that standard R-algebra remains standard after going modulo a homogeneous ideal [on hold]

Is it true that any standard R-algebra remains standard after going modulo a homogeneous ideal?
2
votes
1answer
160 views

Counting Ribbon graphs

Let $G$ be a ribbon graph (sometimes called fat graph) with $v$ vertices and $e$ edges. Furthermore each vertex is of degree $d$. Q) What is the number of $G$ with the above properties? I mean does ...
7
votes
1answer
224 views

Is it possible to define higher cardinal arithmetics

In number theory there are several operators like ‎addition, ‎multiplication and ‎exponentiation defined from ‎$‎‎‎\omega‎‎\times‎‎\omega‎$ ‎to ‎‎$‎‎‎\omega‎$. Each ‎of ‎them ‎is defined as an ...
0
votes
0answers
25 views

asking for some basic computation of pseudodifferential operator

i am reading Kashiwara's paper"Analyse microlocale du noyau de Bergman". In the page 9 he computed the following: suppose $h=\sum_{j=1}^{n}|z_j|^4$ and $\delta(f)$ is the dirac function $Y(f)$ is ...
2
votes
0answers
74 views

Siegel Walfisz Theorem for algebraic number fields

Is there a generalization of the Siegel Walfisz to algebraic number fields? This has been done for the prime number theorem in the prime ideal theorem.
2
votes
0answers
32 views

relationship of max-sat and min-cut in theory and practice

I have been using MAX-SAT solver to obtain the exact ground state of ising spin glass model: For 1D periodic model, for systems with 50 binary variables and interaction range of 15th nearest ...
0
votes
0answers
40 views

Approximation of quadratic variation

Here $M$ and $N$ are two bounded continuous martingales with respect to some filtration $(\mathcal F_t)_t$. I found this claim in a paper I was reading: $t$ being fixed, then a.s. $$\lim_{h\rightarrow ...
0
votes
0answers
26 views

Maximum Entropy for Dirichlet with Constrained Expectation [on hold]

How would I find the maximum entropy distribution of a Dirichlet with a known expectation (i.e if I know the expected value, a multinomial, how would I find the concentration parameter that maximizes ...
0
votes
0answers
100 views

On degrees of polynomials with matching zeros in a subset

Let $S\subsetneq \Bbb R^n$ such that $|S|<\infty$ and for all partitions $S_1$ and $S_2$ of $S$ there exits a multilinear polynomial $h$ such that $h(s)=1-h(s'),\mbox{ }\forall s\in S_1\mbox{ and ...
4
votes
0answers
84 views

spectral sequence of a bicomplex equipped with a group action

Let $(A_1^\bullet,\partial_1)$ and $(A_2^\bullet,\partial_2)$ be complexes of $\mathbb{C}$-vector spaces. We suppose that $(A_1^\bullet,\partial_1)$ and $(A_2^\bullet,\partial_2)$ are equipped with ...
0
votes
1answer
40 views

Can the conservative form of the advection equation be re-written by replacing the velocity term with an integral over all other points in space?

Suppose I have a 1D advection equation in conservation (divergence) form $\partial_t u(x,t) = -\partial_x [v(x)u(x,t)],$ where $u$ is a conserved quantity in space, and $v$ gives the velocity of the ...
0
votes
1answer
142 views

Are compact complete geodesics closed?

note: I find this question In stackexchange math, I would be interest to know how I could be answer this kind of question,I pasted it here as I see it appropriate For MO. check this link: ...
0
votes
0answers
51 views

Characterizing subgroups $H$ of $\Bbb T$ with $\{(f(x),g(x))\mid x\in H\}$ dense in $\Bbb T^2$

Let $\Bbb T$ be the circle group with Euclidean topology. Is there a way to determine all $H\le \Bbb T$ such that there are $f,g\in Aut(H)$ with $\{(f(x),g(x))\mid x\in H\}$ dense in $\Bbb T\times ...
-4
votes
0answers
21 views

matrix summation and uniform convergence of matrix sequence [on hold]

I start studying summation theory and as we know a matrix is called a Schur matrix if i)lim (a)nk= x when n goes to infinity and ii)the sum of (a)nk that means the convergence is uniform in n. can ...
0
votes
1answer
67 views

Finding nodes with a particular weight in a graph

Say that an edge $e$ is incident to a node $v$ if one of its two extremes is $v$. Then we can also say that $v$ is hit by $e$. We might define the notion of "weight of a node $v$" as the sum of all ...
2
votes
1answer
92 views

On Serre's problem regarding the injectivity of Albert-Algebra cohomological invariants

In these Lecture Notes http://molle.fernuni-hagen.de/~loos/jordan/archive/cohinv/cohinv.pdf from 2006 by Garibaldi on page 21. 7.5 there is the following open problem mentioned: Is the map $g_3 ...
4
votes
1answer
185 views

Intersection of nonzero prime ideals is zero — does it have a name?

The Rabinowitch trick (in Eisenbud's Commutative Algebra with a view toward Algebraic Geometry, page 132) says that $R$ (commutative unital ring) is Jacobson if and only if for every prime ideal $P ...
0
votes
0answers
48 views

Criterion for global dimension of subring

All rings are assumed to be associative and unital. If $B$ is a commutative sub-ring of $A$ (which itself needs not be commutative) then what properties of $B$ are both necessary and sufficient for ...
4
votes
1answer
119 views

Biquadratic reciprocity for $p\equiv 1\pmod 4$ and $q\equiv 3\pmod 4$

For a prime $p\equiv 1\pmod 4$, let $\left(\frac{\cdot}{p}\right)_4$ denote the rational biquadratic residue symbol; that is, $$ \left(\frac{a}{p}\right)_4 = \begin{cases} \ \ \ ...
0
votes
0answers
56 views

Residual Intersections of a complete intersection

Let $R$ be a Cohen-Macaulay local ring and $I=(b_1,\dots,b_s)$ be a complete intersection generated by a regular sequence $\underline{b}$. Let $\mathfrak{a}\subseteq I$ such that ...
5
votes
1answer
101 views

Precise density estimates for Cantor sets

Let $C_\lambda$ be the classical Cantor set associated to a real number $0<\lambda<\frac{1}{2}$, as defined for example in the book of K. J. Falconer The geometry of fractal sets. I recall ...

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