# All Questions

**2**

votes

**0**answers

53 views

### Lemma 2.1.1.4 in Lurie's HTT

I have encountered a problem in understanding Lurie's proof of the following fact:
"Given a left fibration between simplicial sets $q:X \to S$, there exists a functor $$ho(S) \to Ho(sSet)$$ which is ...

**1**

vote

**0**answers

26 views

### When is a Hankel matrix invertible?

I would like to have some conditions that render a general Hankel matrix of the form
\begin{pmatrix}a_1 & a_2 & a_3 &\cdots & a_n \\ a_2 & a_3 & a_4 & \cdots & a_{n+1} ...

**5**

votes

**0**answers

34 views

### Relations between functors in a recollement

Consider a recollement situation like the following
by the very definition of the various functors it follows that $i^* j_*=0$, and $j^! i_* = 0 = j^* i_!$. Also, $j^! i_! = 0 = j^* i_*$ by ...

**-3**

votes

**0**answers

25 views

### Discrete Mathematics [on hold]

Consider the following sets.
A = {a ∈ Z | a = 4k + 2 for some integer k}
B = {b ∈ Z | b = 8n + 2 for some integer n}
C = {c ∈ Z | c = 4m for some integer m}
a) Prove: B ⊆ A.
b) Disprove: A ⊆ B.
c) ...

**1**

vote

**1**answer

62 views

### Brauer-Manin obstruction to surfaces of Kodaira dimension 1

Roughly speaking, the Kodaira dimension is an invariant of a variety that corresponds to curvature. One can show that curves of genus $\geq 2$ have Kodaira dimension 1 using Riemann-Roch. In Corollary ...

**-1**

votes

**0**answers

29 views

### problem in one of H. LlEBECK paper [on hold]

in OUTER AUTOMORPHISMS IN NILPOTENT p-GROUPS OF CLASS 2, H. LlEBECK page 1
let G be p-group of class 2 and let G be such that G/G' is direct product
\begin{equation}
\prod gp( a_jG')
\end{equation}
...

**0**

votes

**0**answers

35 views

### Some inequality

Assume that $f:[0,2\pi]\to [0,2\pi]$ is a diffeomorphism, and let $\underline f = \min f'$ and $\overline f = \max f'$ and define $$g(s) = \int_0^s e^{if(t)} dt.$$ Assume that $g(0)=g(2\pi)$. It seems ...

**1**

vote

**0**answers

32 views

### Hypercube edge-coloring problem

Question: Is there a pairing (a fixed point free involution) of the vertices of the $n$-dimensional cube graph, and a $2$-coloring of its edges such that the number of color changes needed to get from ...

**0**

votes

**0**answers

22 views

### Cayley graphs for finitely presented Lie algebras

I have seen that an important tool of finitely presented groups consists in writing down its Cayley graph with respect to a given set of generators, and then try to extract data like the coarse ...

**1**

vote

**0**answers

22 views

### About the small set expansion conjecture.

Given a graph $G=(V,E)$ and a $\delta > 0$ one wants to calculate $h(G,\delta)=min_{\vert S\vert \leq \delta \vert V \vert } \phi(S)$. ($\phi(S) = \frac{ E(S,\bar{S}) }{d min \{\vert S \vert , n - ...

**-1**

votes

**0**answers

75 views

### Writing mathematics for your website? [on hold]

I am an undergraduate student in Computer Science, me and some of my friends are interested in creating a website to teach programming languages and some mathematics topic which are required to be a ...

**-3**

votes

**0**answers

35 views

### does exist any group that it's derivation be S3? [on hold]

my question is that does exist any group that it's derivation be S3? at all, when we have a group, how we can find another group that it's derivation be the order one?

**-2**

votes

**0**answers

47 views

### compute singular (co)homology and topological fundamental group of algebraic variety over finite field(or other arithmetic base fields) [on hold]

I was told that singular (co)homology and topological fundamental group do not behave well in varieties and that's why we should have the etale substitution. However I am curious of how these things ...

**0**

votes

**0**answers

22 views

### Self-diffeomorphisms of fibered knot complements

A knot $K \subset S^3$ is fibered if the complement $S^3 \setminus K$ of (a small open neighborhood of) $K$ is a fiber bundle over $S^1$. (The fiber will be a surface with one boundary component.)
...

**-4**

votes

**0**answers

43 views

### how can I make a grid [on hold]

I have 16 numbers, 1 to 16.
16 rows.
4 columns.
I want each number to appear in each column but to only appear on a row with each of the other 15 numbers once.

**0**

votes

**0**answers

11 views

### Uniform Boundedness of the Szasz-Durrmeyer Operators on Variable $L^{p(\cdot)}$ Spaces

I am stuck with the uniform boundedness problem associated with the Szasz-Durrmeyer Operators on $L^{p(\cdot)}$ spaces. The Szasz-Durrmeyer operator can be defined as
$$M_{n}(f;x)=\sum ...

**2**

votes

**1**answer

123 views

### Infinite sequence avoiding a countable set of words

As an application in group theory, I would need an infinite sequence over a finite alphabet, that avoids a sequence of words $w_i$, where the length of $w_i$ is such that $l(w_i) > 10^8 ...

**2**

votes

**1**answer

97 views

### Periodic points in C^2

I came up with a problem which is similar to the following quesitons:
Consider a map: $f(x,y)=(y^2-2,xy-2)$. It is seems that the number of periodic points of given period is bounded.
I want to ...

**1**

vote

**0**answers

26 views

### $IM=mM$. can we say that $I$ is a reduction ideal of $m$?

Question. Let $(R,m)$ be a Noetherian local ring and $M$ be a finite faithful $R$-module. Let $I$ be an ideal of $R$ such that $IM=mM$. Can we say that $I$ is a reduction ideal of $m$? Recall that $I$ ...

**2**

votes

**0**answers

103 views

### Can someone elaborate on a categorical/homotopical point made in the proof that $\Sigma 2 = S^1$, given in the HoTT book? [migrated]

In chapter 6, specifically in the section about suspensions a proof is given that $∑2 = S^1$.
The book says that $\mathrm{transport}^{x \mapsto g(f(x)) = x}(\mathrm{refl}_N, \mathrm{merid}(y)) = ...

**2**

votes

**1**answer

254 views

### Topological Grothendieck Construction

Let $C$ be a small category and $F\colon C^{op}\rightarrow Set$ a functor. The Grothendieck construction is the category $F\wr C$ with objects being pairs $(c,x)$ where $c$ is a object of $C$ and ...

**0**

votes

**0**answers

94 views

### Why does the critical line for Riemann's zeta function lie at real part 1/2 rather than real part 0? [on hold]

Sorry for the un-mathematical way of formulating this question in the title, feel free to edit the title if that seems more appropriate. What I actually like to know is:
Is this yet another instance ...

**0**

votes

**1**answer

55 views

### Homotopy bounds in simply connected complete Riemannian manifolds

Let $M$ be a simply connected complete Riemannian manifold, and let $x\in M$. Does there exist a nondecreasing function $R:\mathbb R_+\to\mathbb R_+$ such that, for every $r>0$ and all paths ...

**1**

vote

**2**answers

86 views

### Matrices congruent to each other via a permutation

Consider the collection of all integer matrices and partition them via an equivalence relation $A\sim B\Leftrightarrow \exists$ a permutation matrix $P$ such that $B=PAP^T$. Is some canonical form ...

**2**

votes

**0**answers

79 views

### Explict form of $E_\infty$-morphisms between differential graded commutative algebras

This is a partial duplicate to this MO question, I apologize for that. I'm asking since the answers there still do not allow me to work out an answer to my question, which is a bit more specific.
...

**0**

votes

**0**answers

38 views

### regular locus of an affine domain

Let $A$ be an affine domain over a field $k$ (need not be algebraically closed). Let $\mathfrak{p}$ be a prime ideal of $A$, such that $A_{\mathfrak{p}}$ is a regular local ring. Does there always ...

**1**

vote

**0**answers

52 views

### Aperiodic graphs

The concepts of being non-periodic and aperiodic for tilings have obvious versions for connected graphs with a countable set of vertices and a finite number of edges meeting at each vertex. A graph ...

**1**

vote

**1**answer

28 views

### Linear intersection number and maximum degree

This question is inspired by a Andrew D. King's comment in Linear intersection number and coloring (not chromatic) number
A linear hypergraph is a pair $\pi=(X, L)$ where $X\neq \emptyset$ is a set ...

**-2**

votes

**0**answers

36 views

### Inverse Trigonometric Functions [on hold]

I have the following question:
for which I need to prove the above to be x/2
I tried to first convert it to :
then multiply and divide by
to get this:
But have no idea what to do next , ...

**15**

votes

**4**answers

1k views

### Maryam Mirzakhani's works

Maryam Mirzakhani has made several contributions to the theory of moduli spaces of Riemann surfaces.
Mirzakhani was awarded the Fields Medal in 2014 for "her outstanding contributions to the dynamics ...

**2**

votes

**0**answers

62 views

### K-theory of coherent sheaves on complex manifolds: references and gamma-filtration?

For a complex manifold $X$ one has an exact category of locally free coherent sheaves; so it seems to be no problem to define certain $K$-theory (I do not know whether the $K$-groups given by the ...

**0**

votes

**0**answers

44 views

### Norm on C$^*$-algebra [on hold]

Given two orthogonal elements $a,b$ in a C$^*$-algebra $A$ (i.e. $a b^* = b^* a=0$) we have $\| a + b\| = \max\{ \|a\|, \|b\|\}$. How do I show?

**8**

votes

**3**answers

283 views

### Abstract connectedness

Is there an abstract structure that characterizes connectedness, analogously to how topological spaces characterize continuity?
Here's one way to make this question more precise: if $(X,T_X)$ is a ...

**2**

votes

**1**answer

123 views

### Exact reference for Liouville theorem

It seems hard for me to find that the solution of the following equation
$$
\Delta u+e^u=0
$$
defined on a simply-connected domain $D\subset R^2$ must be of form
$$
...

**8**

votes

**5**answers

311 views

### Application of Fraïssé construction in set theory

As you know Fraïssé limit construction and its generalization, Hrushovski's construction, have many applications in model theory to build models with interesting property.
Now I would like to know ...

**0**

votes

**0**answers

53 views

### Matrices over a finite field with given Jordan normal form over the algebraic closure [migrated]

Can one describe the (conjugacy classes of) square matrices over a finite field such that over the algebraic closure of this finite field their Jordan normal form consists of one Jordan block? (Such ...

**0**

votes

**0**answers

16 views

### Alternative form for weighted least squares

Coefficients $\beta$ can be estimated from $y$ by weighted least squares with:
$ \beta = (X^T\Sigma^{-1}X)^{-1} X^T \Sigma^{-1} y $
where $\Sigma$ is the covariance matrix of the noise.
Let $N$ be ...

**4**

votes

**1**answer

144 views

### Averages over integer points of the sphere

A paper of William Duke sketches a proof that integer points on the sphere are equidistributed.
$$ V_N = \{ (x,y,z) \in \mathbb{Z}^2 : x^2 + y^2 + z^2 = N \} $$
Up to reflections across the $x$, $y$ ...

**2**

votes

**0**answers

27 views

### Reference that contains examples of absolutely indecomposable representations of quivers over a finite field

Is there a reference that lists/discusses examples of absolutely indecomposable representations of quivers over a finite field (absolutely indecomposable = does not decompose into a direct sum over ...

**1**

vote

**2**answers

92 views

### $\lim_{t\rightarrow 0}P\left(X_t >0\right)=\frac 1 2$ for continuous semimartingales?

I am trying to prove the following Lemma, which seems intuitive, but I still have doubts:
Lemma
Given a Brownian motion $\{W_t,\mathcal F_t:0\le t \le1\}$, two progressivley measurable processes, ...

**3**

votes

**1**answer

140 views

### Dihedral extension of 2-adic number field

Sorry if the question is too long and maybe elementary.
I am reading a paper by Hirotada Naito on "Dihedral extensions of degree 8 over the rational p-adic fields". To generate dihedral extension ...

**11**

votes

**1**answer

133 views

### Variety acquiring rational point over any quadratic extension

Does there exist a variety $X$ over $\mathbb{Q}$ (or a number field) such that it has no rational points over $\mathbb{Q}$ but acquires points over any quadratic extension $\mathbb{Q}(\sqrt{d})$?
If ...

**3**

votes

**1**answer

125 views

### Converse to Weil Restriction of Scalars

Let $k$ be a field of characteristic zero (I'm only interested in number fields), and let $\mathbb{G}_{/k}$ be a linear algebraic group defined over $k$ which is almost $k$-simple (all normal ...

**5**

votes

**0**answers

83 views

### Degenerate linear recurrence sequences

Let $(u_n)_{n \geq 0}$ be a linear recurrence given by
$$u_n = a_1 u_{n-1} + \cdots + a_k u_{n-k} \quad \forall n \geq k ,$$
where $u_0, \ldots, u_{k-1}, a_1, \ldots, a_k \in \mathbb{Z}$. We recall ...

**1**

vote

**0**answers

38 views

### Diffusion in a bounded domain

Let us consider an $\mathbb{R}^d$ diffusion
$$dX_t = dW_t +\mu(X_t)dt.$$
Let further $D\subset \mathbb{R}^d$ be a bounded connected open domain. By $Y^D$ we denote the diffusion $X$ restricted to ...

**0**

votes

**0**answers

22 views

### Integral Domains [migrated]

I have to proof that ($\ N_A,1_A,T)$ are a Peano system where $\ T:N_A\rightarrow N_a$ $\ x \mapsto x+1_A , x \in N_A$ and $\ N_A= \{n 1_A|n\epsilon N \} $ where N are the natural numbers and A is an ...

**1**

vote

**0**answers

33 views

### $H^1$ convergence of eigenfunctions of Schrödinger operators [migrated]

Consider the Schrödinger-Operator with Potential $V\in L^\infty(\Omega)$ with Dirichlet boundary conditions
$$ H^D=-\Delta + V $$
and let $u_{i,n}\in H_0^1(\Omega)$ be the first, nonnegative ...

**0**

votes

**0**answers

52 views

### Asymptotic sequence and asymptotic expansion [on hold]

If $(f_k(x))$ is an asymptotic sequence as x to infinity and $\phi=a_0f_0+a_1f_1+a_2f_2+...$ (equality) where $a_i$ are constant.
Is $a_0f_0+a_1f_1+a_2f_2+...$ an asymptotic expansion of $\phi$?

**1**

vote

**0**answers

85 views

### Good covering of a sphere

Consider a sphere $S_r(0)$ with center at zero and radius $r$ in the Hamming space $\{0,1\}^n$.
We will be interested in covering this sphere with balls of radius $\rho < r$.
We know that there ...

**0**

votes

**0**answers

46 views

### The right expansion of a square root matrix

I have some issues in finding an asymptotic expansion for a square root matrix and I have already posted a question (Asymptotic expansion square root matrix). Somebody redirected me to a post where ...