# All Questions

**0**

votes

**1**answer

33 views

### Adjusting matrix in generalized eigenvalue problem for the design of eigenfunctions

Take two matrices $A,B \in \mathbb{R}^{n\times n}$. I am considering the generalized eigenvalue problem ($\gamma \in \mathbb{R}, \phi \in \mathbb{R}^n$)
$$A\phi = \gamma B\phi.$$
Is there a ...

**1**

vote

**1**answer

66 views

### dual (p,q)-property

If the set system $(X,S)$ has the $(p,q)$-property does its dual system also have the property? (Possibly, for different $p$ and $q$.)
Explicitly, I am asking about the equivalence of the following ...

**4**

votes

**1**answer

100 views

### Maximum sets of lattice points such that only a few points collinear

Consider all the integer points $\in [0,n]\times[0,n]$, I want to find the maximum subset $S$ of which such that there are at most $n^\varepsilon(0<\varepsilon<1)$ points in $S$ collinear.
So, ...

**0**

votes

**1**answer

108 views

### Degree of a Segre variety (without Hilbert polynomial)

Algebraic Geometry is not my topic of research and I am having troubles in understanding the following:
In Harris book, Algebraic Geometry, a firs course, Example 18.15, there is a proof of the ...

**4**

votes

**2**answers

120 views

### Minimum number of transitive paths in tournament

Let $T$ be a tournament with $n$ vertices (i.e., between every pair of vertices there exists an edge in exactly one direction.) For any $k$, the vertices $A_1,A_2,...,A_k$ form a transitive path if ...

**0**

votes

**1**answer

48 views

### Global sections in negative degree line bundles over singular curves

Let $C$ be a local complete intersection projective curve in $\mathbb{P}^3$. Assume that $C$ is integral. Let $\mathcal{L}$ be a line bundle on $C$ of negative degree. We know that if $C$ is smooth ...

**0**

votes

**0**answers

66 views

### An inequality for moments of a random variable

I'm interested in a class C of $R^1$-valued random variables $\xi$ which satisfy
an inequality of the type
$$
(1) \qquad E|\xi|^p \leq F(E|\xi|^2),
$$
where $p>2$, $F$ is a certain ...

**2**

votes

**0**answers

113 views

### $S^{3}$-valued harmonic analysis

Edit:
Note that $S^{3}$ with the quaternion operation is a group. For a locally compact Abelian group $\Gamma$ we consider
$$\tilde{\tilde{\Gamma}}=\{\phi:\Gamma \to S^{3} \mid ...

**5**

votes

**2**answers

117 views

### Algorithm for determining when polynomial iteration is bounded?

Let $f: \mathbb{Q}\to \mathbb{Q}$ be a polynomial map with rational coefficients. Let $p\in \mathbb{Q}^n$. Is there a known algorithm that given this data determines whether or not the iterates ...

**-4**

votes

**0**answers

174 views

### Can there ever be symbolic formalism (of importance) without intuitive heuristics? [closed]

Problem solving consists of using generic or ad hoc methods, in an orderly manner, for finding solutions to problems. Some of the problem-solving techniques developed and used in artificial ...

**4**

votes

**1**answer

182 views

### When does convolution preserve the `size' of a function?

For a positive function $f$ and positive measures $\mu, \nu$, does
$$\mu\ast f\leq \nu\ast f \Rightarrow \|\mu\|\leq \|\nu\|?$$
More details: Let $G$ be a locally compact group, $C(G)$ be the space ...

**2**

votes

**1**answer

180 views

### Irreducible representation of Heisenberg group with characteristic 2?

As we all know that the irreducible representation for Heisenberg group can be classified easily when the group is over a finite field $\mathbb{F}_q$, where $q=p^n$ and $p$ is a prime greater than ...

**1**

vote

**1**answer

69 views

### Markov chain Monte Carlo: why is non-reversible MC MC not as popular?

I am new to methods for simulating Markov chains in order to sample from the target, unknown distribution. After a couple days of reading, I found out that even though people have realized that ...

**2**

votes

**0**answers

27 views

### When is the solution to a n initial value problem matrix differential equation invertible? [migrated]

Suppose $A (t,s)$ a $n\times n$ matrix is the solution of the initial value problem below, where $B_s$ is also an $n\times n$ matrix, invertible for all $s$:
$$\dfrac{d A(t,s)}{ds} = B_s A(t,s)$$
$$ ...

**0**

votes

**0**answers

11 views

### Hello, everyone, I want to ask you a question about a proof in the Terence Tao's Real Analysis notes [migrated]

everyone. I am using Terence Tao's Real Analysis notes to self learn Analysis 1. There is one thing in the proof of Theorem 27 (Least Upper Bound Property) in “week 2 note” that I don’t understand ...

**0**

votes

**0**answers

54 views

### Why does the Fourier transform of bounded domain, e.g., [-1 1], differs from that of complete domain, e.g., real line. [closed]

Recently, I asked a question about proving the positive semidefiniteness of following kernel function.
$$ k(x, x') = 1 - 2|x-x'|$$
When using the Bochner's theorem, showing psd of the kernel ...

**0**

votes

**1**answer

136 views

### Composition of a transcendental function with a rational function [closed]

The problem is: let $f: \mathbb{R}\to \mathbb{R}$ be an analytic transcendental function and let $\psi(x)=\frac{x}{2(1+x^2)}$. Is the function $f(\psi(x))$ transcendental?

**1**

vote

**1**answer

97 views

### Representations of parabolic subgroups of the general linear group over the complex numbers

In all that follows, we are working over $\mathbb{C}$. Let $B \subseteq P \subseteq {\rm GL}(n)$ be a parabolic subgroup. Can you say anything in general about the representations of $P$? I suspect ...

**-3**

votes

**0**answers

69 views

### biproduct and tensorial product [closed]

Let $\mathcal{C}$ be a monoidal abelian category. Let A,B, C $\in$ $\mathcal{C}$.There is an isomorphisms between this objects?
(A$\bigoplus$B)$\otimes$C;
A$\otimes$(B $\bigoplus$C)

**0**

votes

**0**answers

34 views

### Sufficient Conditions For Monotonic Decreasing of Multivariate Function

I found the following theorem on sufficient conditions for decreasing monotonicity of an absolutely continuous function $\phi : \mathbb{R} \rightarrow \mathbb{R}$, I would like to know if it is ...

**1**

vote

**0**answers

99 views

### Standard name for a Monoid/Semigroup with a+b <= a, b?

I have seen suplattice and inflattice being used when dealing with a lattice. What about when you don't have a lattice?
For instance, for positive reals a, b define a |+| b === 1/((1/a) + (1/b)), you ...

**8**

votes

**1**answer

771 views

### What is the arithmetic Nullstellensatz?

The only precise statement (coming from a reliable source) of the "arithmetic Nullstellensatz" I can find is in Gowers's book, stating that two polynomials with integral coefficients have the same ...

**1**

vote

**0**answers

42 views

### “embedding” various matrix equivalences into the equivalence of particular linear map

Consider the square matrices over a (local) ring $R$, up to conjugation, $A\rightarrow UAU^{-1}$, where $U$ is an invertible matrix over $R$. Such an equivalence embeds into the "left-right" ...

**5**

votes

**0**answers

120 views

### Operator connected with Hermite polynomials

For $n \geq 1$, define the following operator $M_n$ on the ring of all polynomials with real coefficients.
$$M_n P(x) = nP(x)^2 - x \int_0^x (P'(t))^2 \, \mathrm{d}t$$
Monomials $x^k$ are mapped to $n ...

**1**

vote

**2**answers

52 views

### Largest eigenvalue adjacency matrix-link deletion

Let G be a connected undirected graph and G\e be a graph obtained by removing a random link e from the graph G. Let $\lambda_1(A(G))$ be the largest eigenvalue of the adjacency matrix of graph G. Is ...

**6**

votes

**1**answer

173 views

### When is the profinite completion a pro-$p$ group?

My research area is mainly pro-$p$ groups and profinite groups. However, in the last few year I became also interested in discrete groups. Therefore, it seems to me a natural problem to look for ...

**7**

votes

**1**answer

165 views

### Block Matrix determinant

Consider the $k \times k$ block matrix:
$ C = \left(\begin{array}{ccccc} A & B & B & \cdots & B \\ B & A & B &\cdots & B \\ \vdots & \vdots & \ddots & ...

**0**

votes

**1**answer

73 views

### Absolute irreducibility of a symmetric square?

This is a question I received today by email, which somebody more experienced with finite group representations can probably answer directly. Take $F:=\mathbb{F}_q$ for some prime power $q$, so ...

**1**

vote

**0**answers

42 views

### Minimal density hitting set for k-length arithmetic progressions

This is problem which came up in the process of designing a game. Thus, I don't know any previous work relevant to the problem.
Fix a small set $D$ of a natural numbers. For example, $D=\{1,2,3\}$. ...

**16**

votes

**4**answers

721 views

+50

### What arrangement of unit cubes minimizes surface area?

For each of these two questions, one can assume that the arrangements are polycubes (for which a definition can be found in the excerpt-image below).
Question A. How does one arrange $n$ unit cubes ...

**8**

votes

**0**answers

120 views

### Which forcing types preserve the axiom of determinacy?

Do we have some rudimentary understanding of some properties that a forcing can have in order to guarantee that it doesn't violate the axiom of determinacy?
To be more specific, in Which forcings ...

**4**

votes

**1**answer

210 views

### “Is it possible to give a restricted set-theoretical definition of addition of natural numbers in terms of successor?” [Tarski]

In his paper "Restricted set-theoretical defintions in arithmetic" Raphael Robinson cites a problem posed by Tarski:
Is it possible to give a restricted set-theoretical
definition of addition of ...

**1**

vote

**1**answer

76 views

### Results for resolution of equations in polynomial ring

Is there any reference for resoluttion of equations in a polynomial ring, such as $x^2+y^2=z^2$ in $\mathbb{C}[t]$? Thanks!

**5**

votes

**1**answer

208 views

### Which axioms of ZF are used for finite choice?

Apologies if this is a silly question, not an expert in set theory but just wondering about it.
ZF implies finite choice. But let's suppose one wanted to work without it. The thinking here is being ...

**19**

votes

**1**answer

510 views

### $f(x)$ is irreducible but $f(x^n)$ is reducible

Does there exist an irreducible polynomial $f(x)\in \mathbb{Z}[x]$ with degree greater than one such that for each $n>1$, $f(x^n)$ is reducible (over $\mathbb{Z}[x]$)?

**1**

vote

**1**answer

235 views

### questions on steenrod algebra

I plan to give a talk on Steenrod algebra in a student seminar. but there are some questions that I didn't find an answer to, and it seems to me that I'm missing something:
if the algebra of ...

**-3**

votes

**3**answers

102 views

### if V(f) is irreducible, then how to show that the polynomial f itself is irreducible? [closed]

V(f) is the zero locus of the polynomial f in the polynomial ring k[x1, x2, ..., xn] with k an algebraically closed field.
If V(f) is irreducible, then how to show that 'f' is irreducible?

**-2**

votes

**0**answers

53 views

### prime number sequence and the tendency [closed]

before I ask..
I'm not good at english. (because I'm not an English.)
so you may..not be able to understand what I want to say.
1> definite new sequences
prime number sequence
{Pn} =
2 3 5 7 11 13 ...

**0**

votes

**2**answers

180 views

### Weil restriction

I've already asked a similar question in SE, without success, so I've decided to post here a more general version of my question.
Let $f: Y \to X$ be a finite etale morphism of smooth proper ...

**5**

votes

**2**answers

203 views

### What are TQFTs that are multiplicative under connected sums? Do bordisms with connected sum as monoidal product exist?

In general, one extracts a manifold invariant from a TQFT by interpreting the closed manifold as a bordism from the empty set to the empty set. The TQFT sends this bordism to a homomorphism of the ...

**0**

votes

**1**answer

332 views

### Counterexample to Pólya's conjecture

It is known that Polya's conjecture is false and the smallest counter-example is about $10^9$.
Assuming that we are searching for a counter-example not knowing that it exists. What useful information ...

**1**

vote

**0**answers

81 views

### Kempe chain color swaps in a partially colored map

Crossposted from math.stackexchange.com:
http://math.stackexchange.com/questions/904932/kempe-chain-color-swaps-in-a-partially-colored-map
Question: In this partially Tait's colored map, using ...

**2**

votes

**0**answers

85 views

### Inverse Function Theorem on Zygmund Spaces, is the inverse in the same Zygmund Space?

Preliminary Definition
We define the Zygmund spaces $C^r_{*}$ with $r>0$, $r \in \mathbb{R}$ in the following way: (all the functions are allowed to have values in $\mathbb{R}^m$, via working with ...

**1**

vote

**2**answers

238 views

### Asymptotics on prime divisors

Somewhat inspired from the Zsigmondy's theorem is my question. Suppose Let $a_{1}> a_{2}> \cdots > a_{k}$ be nonzero integers, with $k \geq 2$. Let $a(n) : = a_{1}^{n}+\cdots+a_{k}^{n}$ for ...

**3**

votes

**1**answer

128 views

### Rational homogenous spaces and symmetric spaces

What are the complex rational homogenous spaces $G/P$ ($G$ a semi-simple complex Lie group, $P$ a parabolic subgroup) such that the set of real points $(G/P)(\mathbb R)$ is a (compact) riemannian ...

**3**

votes

**0**answers

45 views

### Polynomials connected with Gale's condition and cyclic polytopes

I was reading about cyclic polytopes and (I think naturally) became interested in polynomials $f(X) \in \mathbb{R}[X]$ which have a factorization of the form $f(X)=g(X)g(X+1)$ for some $g(X) \in ...

**2**

votes

**2**answers

144 views

### What is an extragradient method?

I've searched Google, but it seems that only research journal papers appear in search results, where some new, improved, or specialized extragradient method is discussed. I've also searched Wikipedia ...

**0**

votes

**0**answers

58 views

### reference help indecomposable representations of SL(2,R)

Let $\mathfrak{g}$ be the Lie algebra $\mathfrak{sl}_2(\mathbb{C})$, $K=SO(2)$ the maximal compact subgroup of $SL_2(\mathbb{R})$. Then the classification of irreducible admissible ...

**1**

vote

**0**answers

45 views

### symmetric theta structures and arithmetic subgroups

A symmetric theta structure is a theta structure that commutes with (a lift of) the natural involution $\imath: A \to A$ an an abelian variety. For simplicity I will assume that $A$ is a surface.
...

**0**

votes

**1**answer

78 views

### A special class of random variables

I'm interested in classes C of $R^1$-valued random variables which possess the following properties:
1) the sum of two independent random variables from class C belongs to class C;
2) for any ...