# All Questions

36 views

### Text for studying group representation in the context of (abstract) harmonic analysis

I would like to study elements of representation theory as I often encounter it when reading texts on harmonic analysis. I was therefore curious if someone could recommend a book for this. When ...
23 views

4 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 ...
11 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 ...
37 views

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
52 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 ...
24 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, ...
14 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 ...
139 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 ...
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 ...
90 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 ...
72 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 ...
47 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 ...
40 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 ...
70 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 ...
46 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 ...
72 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 $m,n$ ...
179 views

### Normalization of complete intersection

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 ...
42 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 ...
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; ...
68 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, ...
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?
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 $T:U \to W$ ...
250 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 $n \geq 2$?
75 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 $Cat$?
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 ...
### 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 ...