# All Questions

0answers
122 views

### Coefficients of $f(t)=(\sum_{m=0}^{+\infty}e^{2\pi im^4t})(\sum_{m=0}^{+\infty}e^{2 \pi inm^4t})$

I want to prove that $\forall n \in \mathbb{N}$ at least one of the Fourier coefficients of $f(t)=(\sum_{m=0}^{+\infty}e^{2\pi im^4t})(\sum_{m=0}^{+\infty}e^{2 \pi inm^4t})$ is striclty greater than ...
1answer
254 views

### Are chain complexes over a field always injective?

Question: Let $\mathbb{F}$ be an algebraically closed field of characteristic zero and let $\mathrm{Ch}_{\mathbb{F}}$ be the category whose objects are chain complexes (of $\mathbb{F}$-modules) and ...
1answer
196 views

### Confusion with proof about a fact $\mathbb{P}$-name [on hold]

Let $\mathbb{P}$ be poset. Let $B$ be a set. We say that a $\mathbb{P}$-name $\dot{b}$ is a nice name for member of $B$ if there is a maximal antichain $A\subseteq\mathbb{P}$ and a function ...
0answers
28 views

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18 views

### Simulate correlated random field of probabilities [on hold]

Hi I am trying to simulate a spatial latent random field that are probabilities not correlated binary data as specified in other posts. The goal is to have the probabilities correlated by distance. ...
0answers
62 views

### On a property of split short exact sequences [migrated]

Let $A_{\bullet}, B_\bullet$ and $C_\bullet$ be three short exact sequences of groups (not necessarily abelian) out of which $A_\bullet$ and $B_\bullet$ are split. Assume that there is again a short ...
1answer
111 views

### Rademacher average based Hoeffding Inequality

I am following these lecture notes: Given the i.i.d. $\mathcal{Z}$-valued random variables $Z_1,\dotsc,Z_m$ and $\mathcal{G}$ is a set of bounded functions $g\colon \mathcal{Z}\to[a,b]$. Corollary ...
0answers
108 views

### Torsion in cohomology

Suppose to have a short exact sequence of chain complexes of $\mathbb{Z}$-modules: $$0\to A^\bullet\to B^\bullet\to C^\bullet\to 0$$ such that $A^k,B^k,C^k$ are non zero for $k=0,1,2$. Moreover, ...
1answer
164 views

### Loop space structures on $RP^\infty$

I am interested in infinite loop structures on the infinite dimensional projective space $\mathbb{R} P^\infty$. Is it unique? I think this has to be known in work of May, and If so, then I presume its ...
0answers
72 views

### Proalgebraic completion [on hold]

For a finitely generated group, say Γ, what is the meant by of the proalgebraic completion of Γ? I came across this while seeing a paper on Representation Growth for Linear Groups by Larsen and ...
0answers
64 views

### Are all (graded) Artinian complete intersections like this?

I'm trying to prove some stuff (it's not important what) about (graded) Artinian complete intersections $R=\mathbb{C}[x_1,\ldots,x_n]/I$, where the $x_i$ have certain positive weights and where $I$ is ...
1answer
411 views

### A group whose automorphism group is cyclic

Is there an Abelian group $A$ which is not locally cyclic whose automorphism group is cyclic ? This question was first posted here.
0answers
40 views

### Pumping Lemma CFL [on hold]

L={ab^n ab^n ab^n: n ≥ 0} I've just started learning pumping lemmas, but this one confuses me. How can I show that this is not context free?
0answers
43 views

### Enumeration, selective intersect labs(::) [on hold]

{2,3,4,5::1,5,6,8::3,4,5,6} 2×3×4×5=120 1×5×6×8=240 3×4×5×6=360 (561×8=(234×5)+(156×8)+(345×6)) Preorder to 4488(yπ+) at (2345+1568+3456)/3.141592653...: 4+4+3+3=2+3+4+5 4+4+3+3+2+2=3+4+5+6 ...
2answers
236 views

### Combinatorial designs textbook recommendation

Good evening, I am currently taking a class which has combinatorial designs as the first topic, we are using Peter Cameron's book Designs, Graphs, Codes and their Links which I am finding extremely ...
0answers
68 views

### How to characterize the class of $(\mathfrak{g},K)$-modules with a fixed lowest K-type in the framework of D-modules?

Let $G$ be a real semisimple Lie group, $K$ be a maximal compact subgroup. Let $\mathfrak{g}_0$ and $\mathfrak{k}_0$ be their real Lie algebras respectively. Let $\mathfrak{g}$ and $\mathfrak{k}$ be ...
0answers
66 views

### “Exceptional components” of the exceptional divisor of a blow up

Assume we are blowing up an ideal $I$ on an affine variety $X$, let $E$ be the exceptional divisor, and $P$ be a (closed) point in $V$, the zero set of $I$. Is there any algorithm to check that $E$ ...
0answers
96 views

### Existence and local compactness of the p-adic number field without Axiom of Choice [on hold]

I think we can prove the existence and local compactness of the p-adic number field without using Axiom of Choice. Am I right?
0answers
31 views

### Techniques for finding the stationary state of a continuous-state, discrete-time Markov process

I'm interested in a continuous-state, discrete-time Markov process. Let the distribution at time $t$ be $f_t(x)$. The update equation has the form f_{t+1}(x) = \int f_t(x') g(x', x) ...
0answers
93 views

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55 views

### Theory of Numbers. PROOF using division algorithm and well ordering theorem [on hold]

I really help with the following two questions. 1) Assume that b>0. Show that there exists k an element of Z, s.t a+kb>0. (Use the division algorithm) 2)Use Theorem 3.8 (well ordering theorem) to ...
0answers
78 views

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199 views

### Mathematical urban legend - Best second tier mathematician [on hold]

A few years ago I heard a story about a talk given at Stanford by a famous probabilist, perhaps Kai-Lai Chung. The speaker got into some sort of argument with a mathematician in attendance, and called ...
1answer
139 views

### liftings of principal bundles

I would like to know what structure has the category of liftings of a principal bundle. Let me be more precise. Fix $k$ an algebraically closed field and $X$ a smooth projective variety over it (for ...
0answers
78 views

### Weak Foundation in Math [on hold]

I read this article http://www.xamuel.com/five-ways-to-be-better-at-math/ and was wondering if anyone can help me with references or advice to get better at math. I always considered myself weak at ...
0answers
74 views

### Adding a row to a Young Tableau via Novelli-Pak-Stoyanovskii

Let $T_{\lambda}$ be the set of standard young tableaux (SYT) of shape $\lambda_1\geq \lambda_2\cdots\geq \lambda_n$. Now consider pushing a row $\mu$ with $\mu\geq \lambda_1$ onto $Y$ to give shape ...
0answers
66 views

### Deformation with fixed ramification

Suppose that $f : X \to Y$ is a finite, surjective morphism of normal varieties. I want to know about the space of first-order deformations of $X$ over $Y$ with fixed ramification, i.e. the ...
1answer
76 views

### Intersection multiplicty and global sections

Let $X$ be a smooth projective variety, $V, W$ closed subschemes in $X$ such that $V \cap W$ is finitely many points. Let $\mathcal{L}$ be a line bundle on $X$. Is there any relation between ...
1answer
60 views

### About preserving real-rootedness of multivariable polynomials

Say $f_i(z_1,z_2,..,z_m)$ are polynomials real rooted in the $z$s for a bunch of polynomials indexed by $i$. When can one say that $\sum_{i} p_i f_i(z_1,z_2,..,z_m)$ is also real rooted? If ...
1answer
61 views

### Is there an irreducible subfactor with an infinite homogeneous single chain lattice?

We know that we can build an irreducible subfactor realizing a finite single chain lattice containing any finite index irreducible maximal subfactors, by using the free composition (see here). Is ...
0answers
33 views

### Finding a random variable with a density function [on hold]

So I have this homework I'm having a really hard time starting: For the random variable X with density function f(x) = 4x , 0 < x ≤ 1/2 4 − 4x , 1/2 < x ≤ 1 0 , otherwise Determine the ...
0answers
24 views

### Problem implementing Ramez algorithm [on hold]

I'm implementing the Ramez algorithm for optimal polynomials, and I'm having problems. That is, I'm getting worse and worse approximations. Repo: https://github.com/nmiculinic/dismat2[1] Viewer: ...
1answer
125 views

### Is this structure a Banach bundle?

Let $X$ be a Banach space. Put $Y=\{ \phi\in X^{*}\mid\;\; \parallel \phi \parallel\leq 1\;\; \&\;\; \phi \neq 0\}$ which is a locally compact Hausdorf space with the weak star topology. ...
0answers
27 views

### normality of truncated arc space

Let $X=Spec(A)$, with $A$ a normal $k$-algebra of finite type, $k$ is a field. For any integer $n$, let $X(k[t]/(t^{n}))$ the $n$-th truncated arc space, is it also normal? Same question for ...

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