0
votes
0answers
6 views

Extending the topology on a set to the group/vector space it generates

The multiplicative group $\Bbb Q^+$ can be viewed as a $\Bbb Z$-module. To see this, note that any rational can be decomposed into the form $2^{n_2} \cdot 3^{n_3} \cdot 5^{n_5} \cdot ...$ The tuple ...
1
vote
0answers
14 views

Relation between crystalline and perverse sheaves

Take $X$ to be a smooth complex projective algebraic variety. The Riemann-Hilbert correspondence gives an equivalence of categories between the category of perverse sheaves on $X$ and the category of ...
0
votes
0answers
24 views

Mathematical Definition of $n$-Brouillin Zone [duplicate]

I am having trouble finding a mathematical definition of the Brouillin zone beyond the first, which are basically the Voronoi cells or Wigner-Seitz cells. We could imagine the set of point closer to ...
0
votes
0answers
22 views

A certain measure on $C^{*}$algebras

Is there a reference who introduce the following measure on a $C^{*}$ algebra and investigate it from the view point of $C^{*}$ algebra or from the view point of ergodic theory?: Let $A$ be a $C^{*}$ ...
2
votes
0answers
26 views

Equivalence of questions regarding restrictions of pure states

In Davidson and Szarek's article "Local Operator Theory, Random Matrices and Banach Spaces" in the Handbook of the Geometry of Banach Spaces, the authors discuss the (now solved) Kadison-Singer ...
3
votes
2answers
277 views

Statements going against the grain of Riemann Hypothesis (R.H.)

Let $M(N) := \sum_{n=1}^N \mu(n)$) It is known that bounding $M(N)$ by $N^{1/2+\epsilon}$ implies R.H. A bound of $M(N)$ by $K\sqrt N$ for say $ K\ge2 $ is also sufficient. $K = 1$ is excluded as ...
0
votes
0answers
19 views

Solving for f given constraint involving f(x, y) and f(xy, y)

I am interested in a weighted version of the Catalan numbers. The generating function for this case, $$ f(x, y) = \sum_s \sum_n f_{s n} x^s y^n $$ (where the $y^n$ term is the weight), obeys the ...
4
votes
1answer
126 views

Power sums of p-th roots of unity

The following question was asked by a colleague of mine. For any prime $p$ consider $$ M_p:=\min_{z_1,\dots,z_p}\max_{j,k}\left|z_1^k+\dots+z_j^k\right|,$$ where $z_1,\dots,z_p$ are the complex $p$-th ...
0
votes
0answers
65 views

Spectral sequences to compute Hom's in derived category

Does anybody have a good reference that lists spectral sequences that may be used to compute Hom sets in derived categories (of coherent sheaves, say)?
1
vote
0answers
35 views

Explicit construction of a bielliptic curve

Let $C$ be a (projective smooth complex) curve such that $K_C=2(D+p)$, with $D+p$ defining a $g_7^2$; $p$ is a base point and $D$ defines a 2-to-1 map $\varphi:C\rightarrow E\subset\mathbb{P}^2$ onto ...
0
votes
1answer
51 views

Is there currently a known way to construct an injective mapping that transforms finite graphs into discrete geometric objects?

If there is such a mapping, it seems as though it could turn the graph isomorphism problem from a purely combinatorial problem to a discrete geometric one.
0
votes
0answers
59 views

In commutativity theorems in ring theory

Suppose that $R$ is a ring such that for any $x\in R$ there exists $1<n(x)\in \mathbb{N}$ such that $x^{n(x)}-x\in Z(R)$. Prove that $R$ is commutative or if it is not commutative, then the ideal ...
4
votes
0answers
52 views

What is know about maps between loop spaces of Spheres? - Reference request

What is know in general about the maps $\Omega^rS^n\rightarrow\Omega^sS^m$ between loop spaces of Spheres, or, perhaps to phrase it better, the groups $[\Omega^rS^n,\Omega^sS^m]$ for various values ...
1
vote
0answers
24 views

Sufficient condition for the unique solvability of Dirichlet problem of Hamilton-Jacobi equation

It shall be an old story in PDE. I am looking for a sufficient condition of Dirichlet problem for the existence of the unique viscosity solution of the equation in the form of $$\inf_{a \in [-1,1]} \{...
2
votes
0answers
42 views

Stabilizers of pairs of ternary quadratic forms

Let $A,B$ be two ternary quadratic forms with real coefficients, given by symmetric matrices $$\displaystyle 2A = \begin{pmatrix} 2a_{11} & a_{12} & a_{13} \\ a_{12} & 2a_{22} & a_{23}...
1
vote
1answer
39 views

suspension operad

There are many candidates of suspension operad in literature. Among them, $\Lambda= {\rm End}_{s\mathbb{K}}$ and $\Lambda'=\{s^{1-n}\mathbb{K}\otimes sgn_n\}_{n\geq 0}$ are typical ones. The oeprad ...
4
votes
0answers
54 views

Is the natural isomorphism $|FX_\bullet| \cong F|X_\bullet|$ lax symmetric monoidal?

Let $\mathcal{V_1}$ and $\mathcal{V_2}$ be cocomplete symmetric monoidal categories, each endowed with a cosimplicial object $\Delta^\bullet=\Delta^\bullet_{\mathcal{V}_i}:\Delta \to \mathcal{V}_i$. ...
1
vote
0answers
148 views

In what language do you think when doing mathemematics? [on hold]

Today, nearly all important papers are written in English. People whose mother tongue is not English nevertheless have to learn English if they want to be a mathematician. My question concerns these ...
0
votes
0answers
30 views

Compact Embeddings [on hold]

Put: $D=\{u\in L^{2}(\mathbb{R}^{2})| N=(x\frac{d}{dy}- y \frac{d}{dx})u\in L^{2}(\mathbb{R}^{2}) \}$ Why $D \hookrightarrow L^{2}(\mathbb{R}^{n})$ with compact injection? Thank you in advance.
2
votes
2answers
136 views

Reducibility of determinantal hypersurfaces

I have a determinantal hypersurface defined by $\det(A)=0$, with $a_{ij}$ homogeneous polynomial of fixed degree $d$ in $n$ variables. $A$ is not diagonal. How can I find out whether the hypersurface ...
2
votes
1answer
29 views

upper bound on the difference between two Perron-Frobenious eigen values

Let $\lambda, \mu$ be the Perron-Frobenious eigen value of the non-negative matrices $A,B$ respectively. I am interested in knowing whether there are any results available on the upper bound of $|\...
1
vote
0answers
35 views

When the tensor product of motives that are not $0$-(homotopy)-connective can be $0$-connective?

For $t$ being the homotopy $t$-structure for Voevodsky effective motivic complexes when $M\otimes N\in DM_{eff}^{t\le -1}$ ensures that either $M$ or $N$ belongs to $DM_{eff}^{t\le -1}$ (so, we use ...
0
votes
0answers
34 views

Order statistics of iid uniform RV and Pólya's urn model. Question about a.s. convergence

Let $U_1,U_2,U_3,\dots$ be IID uniform on $[0,1]$. For each $n\geq 1$ let $$U_{1:n}<U_{2:n}<\dots<U_{n:n}$$ be the order statistic of $(U_1,\dots,U_n)$. Independent of the $U$ process there ...
1
vote
1answer
55 views

Hyperplane generic to a given arrangement

At the moment, I am reading the paper "on the connectivity of the realization spaces of line arrangements" of Nazir and Yoshinaga. I would like to extend their Lemma 3.2 to higher dimension. However, ...
3
votes
1answer
105 views

A follow up question to: Number of walks on integer lattice with self-edge at zero

Let $a(n)$ be the number of lattice paths in ${\mathbb{Z}^2}$ of length $n$ which start at the origin $(0,0)$ and end up at $(n,0)$ and have only up-steps $U:(i,j) \to (i + 1,j + 1)$, down-steps $D:(...
3
votes
0answers
90 views

Fourier Mukai transform for non-quasi coherent sheaves

Let $A$ be an abelian variety and $\hat A$ be the dual abelian variety. If $P$ is the (normalized) Poincare line bundle, then Mukai defines $R\hat S:D(A)\to D (\hat A)$ via $R\hat S(?)=Rp_{\hat A,*}(...
0
votes
0answers
68 views

Can we use GAP to find index of subgroup of an infinite group? [on hold]

Can we use GAP to find index of subgroup of an infinite group? If yes, please tell how, I tried kgmag package of GAP but could not find. From various questions here, I guessed that in MAGMA, one can ...
4
votes
1answer
91 views

Are there any unitary matrices which satisfy the Yang-Baxter equation which are universal for quantum computation?

Let $H$ be a finite dimensional hilbert space. Let $L:H\otimes H\rightarrow H\otimes H$ be a unitary transformation. Then the equation $$(L\otimes I)(I\otimes L)(L\otimes I)=(I\otimes L)(L\otimes I)(I\...
3
votes
0answers
28 views

A priori $C^0$ estimates for a semi-linear vector Poisson equation

Main Question Consider a $C^2,H^2$ map $F:\mathbb{R}^m \to \mathbb{C}^n$ which satisfies the following equation: $$ -\Delta F(x) + \sum_i a_i(x)\nabla_iF(x) + B(x)F(x) + |F(x)|^2F(x) = 0 $$ Here $a_i:...
1
vote
0answers
24 views

Power spectrum of the difference of two Poisson processes with equal rates

I am studying the asymptotic properties of a dynamic a model involving the difference of two balanced Poisson processes (i.e., $\lambda_1 = \lambda_2$). I recently discovered the Skellam Distribution ...
2
votes
0answers
40 views

How do spectrums interact with bi-Lipschitz maps?

If it makes things simple, we can just stick to bi-Lipschitz maps from $S^k \rightarrow \mathbb{R}^d$ (w.r.t geodesic distance on the sphere with the standard round metric and the $2-$norm on the ...
0
votes
0answers
53 views

generic divisibility equation for two natural numbers [on hold]

Given two natural numbers N and B, so that N > B, is there a generic equation that contains only multiplications of N and B which can tell whether N is divisible by B? Basically, something like a ...
3
votes
2answers
161 views

Combinatorial interpretation for coefficients of reciprocal of power series

I've seen a number of combinatorial interpretations for the coefficients of the compositional inverse (aka reversion) of a power series. Is there a known combinatorial interpretation for the ...
-4
votes
0answers
31 views

Simplify a Trigonometric equation [on hold]

Should end in Sin(a)+Cos(a) I'm unable to decrpyt it.
3
votes
1answer
228 views

Confusion regarding statement of mirror symmetry for elliptic curves

I am a little bit unsure about the mirror symmetry statement for elliptic curves; specifically, how the flipping of the Kähler and complex moduli works. Perhaps I should say at the outset, the reason ...
1
vote
0answers
27 views

Integral of Daubechies wavelets [on hold]

For Daubechies wavelets according to this paper (above eq 19) this relation holds $$ \int_{-\infty}^{-\infty} \phi(2x-i)\phi(2x-j)dx = \frac{1}{2} \int_{-\infty}^{-\infty} \phi(x-i)\phi(x-j)dx $$ ...
0
votes
0answers
91 views

Number Theory Characterization Problem

Given any natural number $N = a_{n}a_{n-1}\ldots a_{1}$, let us associate to it the set $S_{N} = \bigcup_{j=1}^{n}\{(a_{j},j)\}$. We're going to define a d-self-contained number as any natural number ...
7
votes
0answers
66 views

Homology of inverse limits over inverse systems more complicated than towers

Most textbooks discussions of homology of inverse limits of chain complexes consider only “towers,” i.e. inverse systems indexed by the natural numbers. I’d like to find a reference that explains what ...
0
votes
0answers
38 views

Questions related to a summation of fraction equation

I am struggling the following problems. It is not ensured to solve completely because these problems are generated by myself. Particularly, I guess the second problem is very hard if we try to solve ...
4
votes
0answers
64 views

Is there a name for groups of the form $Sp(1)^n$?

A (compact) torus is a Lie group isomorphic to the product of finitely many circles: $T^n = S^1 \times \cdots \times S^1$. Such groups are extremely important in Lie theory, Differential Geometry, ...
1
vote
1answer
100 views

estimating binomial coefficients

There is a beautiful paper on the arXiv by Andrew Suk containing an asymptotic result about the Erdös-Szekeres convex polygon problem. I am struggling with one of the estimates he makes on page 4. He ...
-3
votes
0answers
31 views

How many vertical or horizontal asymptotes does this equation (x^2 - 1)y = x^2 - 4 have? [on hold]

How many vertical or horizontal asymptotes does this equation (x^2 - 1)y = x^2 - 4 have? Actual question is this(Qs11) Answer is given as C but I think there are two horizontal asymptotes
5
votes
2answers
175 views

Constructively, are all fibrations cloven?

A "cloven fibration" is a fibration for which we have an explicit choice of cartesian liftings; this is often phrased as, "We can pick a lifting without using the axiom of choice". Firstly, I'm a bit ...
0
votes
0answers
21 views

Permutation Invariant Color Class

$G$ is a $d$ regular graph, it has $n$ vertices. $S_n$ acts on $n$ vertices of graph $G$. Question: Does there exist a coloring algorithm for which color classes is invariant under all ...
3
votes
0answers
45 views

Symmetries of modular categories coming from quantum groups

This is a request for references about the computation of the braided autoequivalences of fusion categories coming from a quantum group. I could not find even the description of braided ...
8
votes
2answers
311 views

What is the intuitive meaning of the coskeleton of a simplicial set?

Consider the inclusion $i_n: \varDelta_{\leq n} \hookrightarrow \varDelta$. This induces a truncation functor $tr_n:\mathbf{sSet}\to\mathbf{sSet}_{\leq n}$, which has a left and a right adjoint, $tr_n^...
1
vote
0answers
12 views

The jump set of $SBV$ function for different value of parameter in image denoising problem

The classical Mumford-Shah image denoisng problem study the minimizer of the following functional, for each $\alpha>0$ where $\Omega\subset \mathbb R^2$ is open bounded with sommth boundary, $$ u_\...

15 30 50 per page