# All Questions

**2**

votes

**0**answers

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

**0**answers

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

**0**answers

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

**1**answer

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

**0**answers

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

**0**answers

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

**0**answers

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

**0**answers

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

**1**answer

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

**0**answers

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

**0**answers

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

**0**answers

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

**0**answers

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

**0**answers

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

**1**answer

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

**1**answer

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

**1**answer

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

**1**answer

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

**0**answers

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

**1**answer

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

**0**answers

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

**1**answer

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

**2**answers

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

**0**answers

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

**1**answer

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

**0**answers

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

**0**answers

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

**2**answers

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

**0**answers

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

**0**answers

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

**0**answers

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

**1**answer

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

**0**answers

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

**0**answers

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

**0**answers

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

**0**answers

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

**1**answer

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

**0**answers

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

**0**answers

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

**0**answers

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

**0**answers

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

**0**answers

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

**2**answers

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

**0**answers

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

**0**answers

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

**0**answers

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

**0**answers

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

**0**answers

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

**1**answer

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

**0**answers

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 ...