2
votes
0answers
8 views

Does the Turaev-Viro theory for the generalized $E_6$ subfactor for $\mathbb{Z}/7$ distinguish $L(7,1)$ and $L(7,2)$?

In the paper Sato-Wajui "COMPUTATIONS OF TURAEV-VIRO-OCNEANU INVARIANTS OF 3-MANIFOLDS FROM SUBFACTORS" they compute certain Turaev-Viro-Ocneanu invariants of certain lens spaces. One of the results ...
1
vote
0answers
8 views

Density of prime divisors of $a^n + b$

Suppose $a > 1, b \neq 0$ be two rational numbers. Is it known in general that the set of prime divisors of (the numerator of) $a^n + b$ has a positive relative density?
0
votes
0answers
14 views

which is the relationship between infinite set and the orbits of their points?

I have been studying the proof of the following theorem: Theorem: Let's suppose that $X$ is some metric space and $X$ is a infinite set. If $f:X\to X$ is transitive and has dense periodic points the ...
1
vote
1answer
23 views

Asymptotic formula for average geodesic length on graph?

If $G$ is a finite, connected simple graph then is there an expression for the average geodesic length? That is suppose I know two nodes $n_1$ and $n_2$, the number of edges in my graph and at those ...
1
vote
0answers
19 views

When does effective descent of modules hold?

Let $A$ be a commutative ring with identity. I denote by $\Delta_{\leq 1}$ the full subcategory of the simplex category $\Delta$ with objects $[0]$ and $[1]$. Let $B_{\cdot} : \Delta_{\leq ...
0
votes
0answers
3 views

Can I study a global stability of equilibrium point in a fractional order system?

I have a system of fractional-order differential equations in the sense of  Caputo’s derivatives. For this model, I obtained the equilibrium points and proved that some equilibrium points are locally ...
0
votes
0answers
8 views

diffusion and potentials in several dimensions

In a Lagrangian field theory there are conserved quantities, like total energy. This allows geometric arguments to be made about the behaviour of a system with known potential. (E.g. on asymptotic ...
0
votes
0answers
21 views

Fourier analytic estimate

The following question arises naturally from applications to the image processing. Let $\alpha\in [0,1]$ and assume that for infinitely many $n\ge 1$ we have $$\sum_{k=1}^n\frac{1-|\cos(2\pi ...
0
votes
1answer
48 views

Is there any infinite set which is Dedekind finite and weakly Dedekind finite?

Is there any infinite set which is Dedekind finite and weakly Dedekind finite? If $X$ is a weakly Dedekind finite amorphous set, can we show that $\mathcal P(X)$, the power set of $X$, is also weakly ...
1
vote
0answers
16 views

How are $\alpha$ and $f(\alpha)$ obtained from the calculated values of $h(q)$ in the Multifractal analysis?

In most papers they mention some kind of Legendre transform but I'm not entirely clear about the process, sine they don't mention enough details, at least for me, I tried reading the cited references ...
1
vote
0answers
12 views

Points of continuity of a lower semicontinuous function have non empty interior

Let $X\subset \mathbb R^d$ having non empty interior and let $f:X\to\mathbb{R}$ be lower semicontinuous. I know that the set of discontinuities of such a function is contained in a meager set, and ...
3
votes
0answers
71 views

Solving polynomial equations modulo $1$

Let $P\in \mathbb{R}\lbrack x\rbrack$ be given. (In practice, the coefficients could be given as, say, decimals to sufficient precision.) Let $M\geq 1$, and let $I$ be an interval in ...
-1
votes
0answers
58 views

Closed subgroups of $SO(4)$

My question is quite simple : we know all closed SO(3) subroups ; is it also known for the closed SO(4) subgroups ?
0
votes
0answers
32 views

Let $f:R\to S$ be a local finite monomorphism .If $M$ is an Artinian $S$-module, is it an Artinian $R$-module?

Let $(R,m)$ and $(S,n)$ be local rings (commutative Noetherian with 1). Let $f:R\to S$ be a local homomorphism/monomorphism ($f(m)=n$), such that the natural induced homomorphism $R/m\to S/n$ is an ...
5
votes
1answer
123 views

On property of monic polynomial with integer coefficients

For a monic polynomial with integer coefficients $f$ where $\partial f = 2$, we have $$ \textrm{inf}(f(x)) > 0 \implies \textrm{inf}(f(x)) \geq \frac{3}{4} . $$ Could we generalize this (for ...
-1
votes
1answer
31 views

Is every implicit function reparametrized? [on hold]

Consider a continously differentiable non-constant function $f:\mathbb{R}^2\to\mathbb{R}$. Define $$ K=\{x\in\mathbb{R}^2|f(x)=0\}. $$ I wish to know whether there is a continuously differentiable ...
4
votes
1answer
70 views

Motivating the existence of Canonical Bases for Representations

In Representation Theory, the theme of the existence of a canonical basis has been explored quite a lot. I will limit myself in this question to the kind of canonical bases that arise from the ...
2
votes
1answer
30 views

Smooth dependence on the initial condition of the integral of an ODE

I am considering an ODE $\dot{x}=f(x)$, with $x\in\mathbb{R}^d$ and $d<\infty$. $f$ is a $C^k$ function and I denote by $\Phi_t x$ be the value of the solution at time $t$. I assume that my ODE ...
1
vote
0answers
21 views

Monotonicity of integral of Bessel functions

Is it known, and if yes how does one show, that the function $$ \psi(n):=n\int_0^{+\infty} e^{-x}I_0\left(\frac{x}{n}\right)^{n-1}I_1\left(\frac{x}{n}\right)\mathrm{d}x$$ is decreasing for all $n\ge ...
6
votes
1answer
46 views

What are types of coalgebras that are more naturally described by cooperads?

Let $\mathsf{C}$ be a symmetric monoidal category. An object $X \in \mathsf{C}$ has two operads "naturally" (the two constructions aren't functorial) associated to it: the operad of endomorphisms and ...
-5
votes
0answers
18 views

Currency SHL Questions [on hold]

if the exchange rate for sterling and euro continue to increase every day by the same amount of rupee as today,in how many more days would a Euro buy more Rupees than one pound of Sterling? [On ...
0
votes
1answer
76 views

Finding out $p$-torsion elements of an elliptic curve $E$ over $\mathbb{Q}_p$

Let $E$ be an elliptic curve over $\mathbb{Q}$. Then how to compute the $p$-torsion elements of $E$ over the $p$-adic field $\mathbb{Q}_p$ using SAGE or any other means ? At least can we say whether ...
5
votes
2answers
128 views

Finding a closed form for $\sum_{k=1}^{\infty}\frac{1}{(2k)^5-(2k)^3}$

I'm looking for a closed form for the expression $$ \sum_{k=1}^{\infty}\frac{1}{(2k)^5-(2k)^3} $$ I know that Ramanujan gave the following closed form for a similar expression $$ ...
-5
votes
0answers
51 views

trying to understand n^5 - 5n^3 + 4n is divisible by 120 from “Number Theory” (Andreescu) [on hold]

I'm trying to understand this derivation: n + 2 n^5 - 5n^3 + 4n = 5! ( ) 5
0
votes
1answer
49 views

Total chromatic number and total clique number

Let $G=(V,E)$ be a finite, simple, unconnected graph. We define the total graph $T(G)$ of $G$ as follows: $V(T(G)) = (V\times\{0\}) \cup (E\times\{1\})$, $E(T(G)) = E_v \cup E_e \cup E_{v+e}$, where ...
0
votes
0answers
22 views

Generating tournaments inductively

This is a somewhat vague question, but I'm interested in ways to create a strong tournament from one or more smaller tournaments. Obviously, the disjoint union of two tournaments is a new tournament, ...
2
votes
0answers
12 views

Multivariable Weighted shift and subnormality

I have asked this question in mathstackexchange but didn't get any answer. I hope, I will get my answer here. Let $\mathbb B^m$ denote the Euclidean ball in $\mathbb C^m.$ Does there exist a ...
5
votes
2answers
129 views

Can a nowhere differentiable function preserve measurability?

I want to know whether a continuous nowhere differentiable function $f: \mathbf{R} \to \mathbf{R}$ can map Lebesgue measurable sets to Lebesgue measurable sets. More generally I'm interested to know ...
-1
votes
0answers
42 views

Ddifference between deduct and deduce [on hold]

In the context of logic, the term "deduction" was used as a way of thinking. I think, apparently, the verb of "deduction" should be "deduct", hence it is natural and reasonable to use the term ...
3
votes
0answers
83 views

$\Bbb A^1$-Localisation of Schemes, and $\Bbb A^1$-Rigid Schemes

Question 1: Are there some publications or preprints that provide $\Bbb A^1$-fibrant replacements of certain classes of (smooth) schemes? Of course, smooth schemes that are $\Bbb A^1$-fibrant are ...
2
votes
0answers
71 views

Dessin d'enfant and moduli space of bordered/punctured hyperbolic Riemann surfaces

Belyi's theorem states that if a Riemann surface could be defined as an algebraic curve over an algebraic number field, then this Riemann surface could be described by a Dessin d'enfant. I have two ...
0
votes
1answer
34 views

Convergence of unitary products on a Hilbert space

First: I'm sorry for the basic question--I can move it to Math SE if necessary... Let $X$ be a Hilbert space and suppose $\{U_k\}_k$ is a sequence of unitary operators on $X$. Let $||\cdot||$ be the ...
0
votes
0answers
39 views

Arnold chord conjecture

Recently I've started learning about the Arnold conjecture for the number of Reeb chords on a Legendrian submanifold of a contact manifold. It says that under some conditions, the number of Reeb ...
0
votes
0answers
67 views

“Sheaf” on the nerve of a category

So I have the nerve of a category and want to communicate information about the sets at each level in the simplicial set (nerve). Is there a way to regard the nerve as a category itself? Then one ...
-4
votes
0answers
43 views

Probability problem - no idea where to start [on hold]

I have been working on this question for a few days and I am completely lost on how to solve it. Any suggestions, comments, hints are greatly appreciated. Participants are competing in a ...
0
votes
0answers
46 views

Number of solutions to a modular congruence

What methods are there for determining the number of solutions to modular congruences of the form $a^m \equiv b^n k \pmod{p}$ with $1 \leq a,b \leq p-1$ where $p$ is a prime? In the case $m,n$ ...
0
votes
1answer
132 views

Normalization of complete intersection [on hold]

Let $A$ be an integral complete local ring over a field which is complete intersection. Let $B$ be a normalization of $A$. Q. Is $B$ Gorenstein? I guess that even the normalization of Gorenstein ...
0
votes
0answers
41 views

Mean curvature and submanifold

Consider $S^{N-1}$ the unit sphere and let us focus our attention on the cap $$ G=S^{N-1}\cap\{x_N>0\} $$ with boundary $\partial G= S^{N-2}\times\{0\}$: it is quite obvious to see that $G$ is a ...
0
votes
0answers
32 views

Groebner basis of algebraic system of polynomials [on hold]

I have 8 polynomials with 8 unknowns as {p,L,x1,x2,y1,y2,z1,z2}, and the remaining are all known coefficients. The polynomials are as follows: f1=h1*p - L*(h1*xb*y2 - h2*x1*y1 - h3*x2*y1) + h4; ...
-1
votes
0answers
66 views

Taylor-Series e^e^x [on hold]

I'm new to the whole topic of Taylor-Series and I am trying to figure out the Taylor-Series of $e^{e^x}$. I got the derivatives but that doesn't help right now. I think I need the n-th derivative, ...
-2
votes
0answers
56 views

Could it be possible to check if Pi is a normal number? [on hold]

So currently we don't know if Pi is a normal number and if it really contains all finite number sequences. Is it possible that we will know this in the future? Can we be sure one day?
0
votes
0answers
23 views

Is the Lopatinski-Shapiro condition invariant under diffeomorphism?

If a PDE (eg. the heat equation with Robin BCs, or the elliptic version) on a bounded smooth domain $U$ satisfies the Lopatinski-Shapiro condition (for a definition see eg. Wloka), and if $T:U \to W$ ...
8
votes
2answers
241 views

Homotopy groups of Moore spaces

Is there anything known about the homotopy groups of the Moore spaces $M(\mathbb Z_m,n)$ if $m\neq 2$ and $n \geq 2$?
0
votes
0answers
74 views

Is the category Cat complete? [on hold]

Let $Cat$ denote the 2-category of small categories. Is $Cat$ complete? That is, given a diagram $\phi:J\rightarrow Cat$, does the limit over the diagram exist in $Cat$?
2
votes
0answers
37 views

Reflexive subspaces of dual spaces

If $X$ is a Banach space, is it true that $X^{*}$ must contain an infinite dimensional reflexive subspace? I know of Gowers' example of a Banach space not containing $c_0$, $l_1$, or reflexive, but I ...
2
votes
0answers
147 views

Show that $SL_2(\mathbb{F}_p)$ is quasi-random

Terry Tao gives this oblique definition of quasirandom group in his notes 3 $G$ is quasi-random (of order $D$) if all non-trivial unitary representations $\rho: G \to U(H)$ have dimension at ...
0
votes
0answers
39 views

Finding the right σ-algebra. Question on uncertainty related to the secretary problem

Assume a number of iid. items is presented and the task was to stop under the objective of picking the best item. In this setting it is relevant what is the distribution of the values of the ...
-3
votes
0answers
88 views

Math notation with no possible syntax errors [on hold]

It surely is possible for e.g. simple integer arithmetic to invent a notation where every statement is syntactical correct, just enumerate them - "#" means "0=0", "##" "0=1", maybe "#...#" (239 of ...
10
votes
1answer
172 views

Digital physics and “Gandy-like” machines

Various physicists, famously John Wheeler, have asserted that physical information is the central object of study in physics, in the sense that an object or concept is "physically meaningful" if it ...
1
vote
0answers
28 views

What is the relation between roots of classical and Atkin modular polynomial?

Modular polynomials are a good tools in elliptic curves. I need to find the roots of $l$-th classical modular polynomial $\Phi_l(X,Y)$ over the prime field. Unfortunately the coefficients of these ...

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