**1**

vote

**1**answer

83 views

### Uniqueness of $\partial_t u -u\Delta u=0$ with $u(0,\cdot)=1$

Is there anything known about uniqueness of classical solutions to
$$
\partial_t u -u\Delta u=0\quad u(0,\cdot)=1
$$
on smooth domains $[0,T]\times D$ without boundary conditions? I know that ...

**3**

votes

**0**answers

120 views

### Integrations of Ricci curvature of the Weil-Petersson metric on the moduli space of varieties of general type is a rational numbers?

It is known that the integrations of Ricci curvature of the Weil-Petersson metric on the moduli space of Calabi-Yau varieties is a rational numbers
My question is on moduli space of varieties of ...

**1**

vote

**1**answer

77 views

### How to prove the Hölder continuity of a function $u$ by evaluating $\int_{B_{\rho}(x_0)}\frac{|Du(x)|^{2}}{|x-x_0|^{n-2}} dx$?

I'm looking at a video on thin obstacle problem given by Arshak Petrosyan.
In his lecture, he uses the following results:
Let $0<\alpha<1$, and $B_1$ be the unit ball centered at origin in ...

**1**

vote

**0**answers

42 views

### Regularity on Neumann problem on polygonal domain

I asked a similar question before but didn't get any responses. So I will attempt again (the prior question was regarding Holder continuity).
Let $ \Omega$ denote a cube in $ R^n$ and consider ...

**5**

votes

**3**answers

231 views

### family of polynomials with square discriminant

The title pretty much sums it up: do people know of nice parametrized families of polynomials (with integer coefficients) with square discriminant. I should say that one such family consists of ...

**0**

votes

**1**answer

37 views

### Compact embedding and fractional Sobolev spaces in unbounded domain

It is known that there exists a compactness results involving fractional sobolev spaces in bounded domain. What about unbounded domain? More precisely, Under which conditions, we can extend the ...

**3**

votes

**0**answers

70 views

### Information and intuition packed in the Chern character for coherent sheaves

even after quite some time learning it, I still get somehow puzzled by the Chern character. Let me recall some stuff to get notation and setting.
Let us consider a smooth projective algebraic variety ...

**21**

votes

**4**answers

570 views

### Deep/precise relationship between two approaches to FLT for polynomials, $n = 3$

David Speyer commented the following here.
I saw Brian Conrad give an excellent one hour talk to undergraduates where he proved that there do not exist nonconstant, relatively prime, polynomials ...

**-1**

votes

**0**answers

14 views

### How to calculate error for 3D-trilateration [closed]

I'm developing a 3D positioning system that uses four anchor nodes of known location to position a fifth node of unknown location. I'm calculating the position by using trilateration, MATLAB code ...

**14**

votes

**0**answers

168 views

### What is higher equivariant homotopy?

In Lurie's "Survey of elliptic cohomology" it is claimed that there exists some mystical "2-equivariant homotopy theory" for elliptic cohomology. The classical equivariant elliptic cohomology is ...

**3**

votes

**1**answer

51 views

### Convergence of local stable manifolds

This question is a kind of local version of a previous post (MO224171).
Let $\ f_n \ $ be a sequence of Morse functions on $\mathbb{R}^d$, converging, in the $C^\infty$-topology, to a limit Morse ...

**2**

votes

**0**answers

74 views

### Name for the variety of preimages of a finite morphism

If $f:X\to Y$ is a finite morphism of degree $d$ between two varieties, you get a closed subset of the symmetric product $X^{(d)}$ (or perhaps rather the Hilbert scheme $X^{[d]}$), defined as the ...

**2**

votes

**2**answers

136 views

### Bound that random walk stays within with constant probability?

For one-dimensional random walk, it is well-known that if the walk goes for $n$ steps, with constant probability it ends within $\pm\sqrt{n}$.
What is the bound, in terms of $n$, such that if the ...

**2**

votes

**1**answer

227 views

### rational numbers and triangular numbers

This question is an offshoot of Ratio of triangular numbers. Suppose $ka(a+1)=nb(b+1)$, where $k,n >1$ are relative prime integers, and $a,b \geq 0$ are integers. Which $k,n$ pairs have no solution ...

**0**

votes

**0**answers

61 views

### Modifying tensor to be positive definite everywhere [on hold]

Consider a (0,2)-tensor. It is known that it is positive definite somewhere and it is negative definite otherwise. Is there a theory how to "make" that tensor positive definite everywhere, while ...

**0**

votes

**0**answers

75 views

### Euler Characteristic of simple sheaves

Let $X$ be a projective curve over a field $K$ (any characteristic). Let $\mathcal{F}$ be a coherent simple sheaf
(In the sense, that $\mathcal{F}$ doesn't have non-trivial subsheaves). What is the ...

**0**

votes

**0**answers

58 views

### Onsager-Machlup function for special matrix-valued diffusion process

Potentially useful background info
For standard vector-valued diffusion processes the following result is well-known:
Suppose we have a diffusion $X_{t}$ on $\mathbb{R}^{m}$ given by
\begin{align*}
...

**1**

vote

**0**answers

62 views

### Pull back of a semistable vector bundle to a product is semistable?

Let $X$ be a smooth projective surface over $\mathbb{C}$. Let $L$ be an ample line bundle on $X$. Let $F$ be a $\mu_L$ semistable rank 2 vector bundle on $X$ (semistability in the sense of ...

**0**

votes

**0**answers

65 views

### Divergence free vector field on compact surface

I get a free divergence field $X$ on a compact surface $(\Sigma, g)$ and I would like to integrate it.
On the sphere $X=\nabla^\bot f$ since the spher is simply connected.($\nabla^\bot =J\circ ...

**3**

votes

**0**answers

136 views

### Does the reference letter writer know which school his/her letter is sent to? [closed]

I am using AMS Mathjob. I am wondering:
If a reference letter writer could write different letters for different schools.
To do that, He/She needs to know which school his/her letter is sent to. Can ...

**2**

votes

**1**answer

56 views

### Definitions of negative order Sobolev spaces

I am having a problem with the definition of the space $W^{-k,p}$. I use Adams's definition
$$
W^{-k,p} = \left\{T \in D'(\Omega) \ \middle| \sum \limits_{0 \leq |i| \leq k} (-1)^{|i|} \int_{\Omega} ...

**-2**

votes

**0**answers

42 views

### heat equation in 2D with absorbing and reflecting boundary conditions [closed]

could you please help me with solving the following problem
$$u_{xx}+u_{yy}=u_t, \quad t>0,x∈(−∞;∞),y>0$$
initial conditions :
$$u(x_0,y_0,0)=δ(x−x_0,y−y_0)$$
boundary conditions:
\begin{align}
...

**5**

votes

**1**answer

221 views

### Which Banach spaces are realcompact?

I have a question about the topological space underlying a Banach space.
A topological space $X$ is realcompact iff it is homeomorphic to a closed subset of an infinite product of the form $\mathbb ...

**0**

votes

**0**answers

56 views

### Wild automorphisms of profinite groups

Is there a profinite group $G$, a continuous automorphism $\alpha$ of
$G$ and a topologically finitely generated closed subgroup $H \leq G$
such that $\alpha(H) \lneq H$ ?
Note that if an ...

**0**

votes

**0**answers

64 views

### Hoeffding's lemma for unbounded r.v with bounded exponential map

Let $X$ be a real r.v with $E[e^{\lambda X}] < \infty $ for all $\lambda \in [-c,c]$.
Is it possible to get an Hoeffding's lemma like bound on $E[e^{\lambda(X-EX)}]$. That is, an upper bound: ...

**1**

vote

**0**answers

34 views

### Fully residually free groups and completion

Let $G$ be a fully residually free group with a finitely generated profinite completion. Is $G$ necessarily finitely generated?

**6**

votes

**0**answers

261 views

+100

### “The” natural double complex associated to a principal $G$-bundle?

Let $\pi: P \to M$ be a principal $G$-bundle. We have the associated adjoint bundle $ad(P)= P \times_{ad} \mathfrak g$ whose sections correspond to infinitesimal guage trasformations.
Consider the ...

**5**

votes

**1**answer

188 views

### number of maximal subgroups of the symmetric group

What is the asymptotics of the number of the maximal subgroups of $S_n$ (as a function of $n$)? This must be written down somewhere...
EDIT I am actually more interested in the number of conjugacy ...

**4**

votes

**1**answer

178 views

### Goldbach for certain classes of $n$

Asked on MSE without response here.
$\#$ of ways even $n$ can be represented by prime additions is heareafter denoted $G(n)$.
The Wiki article on the Goldbach conjecture states that
In 1975, ...

**2**

votes

**3**answers

430 views

### The number of submodules of $\mathbb{Z}_q^n$

Observe $\mathbb{Z}_q^n = \mathbb{Z}_q \times \cdots \times\mathbb{Z}_q$ as a module over $\mathbb{Z}_q\equiv\mathbb{Z}/q\mathbb{Z}$, for general $q$.
I am interested in the following questions:
How ...

**1**

vote

**1**answer

72 views

### Intuition about Skorohod integral

I'm teaching myself Malliavin calculus and Skorohod integrals and with this kind of math I find myself following the logic through but lacking solid intuition about what is going on.
In particular ...

**0**

votes

**1**answer

135 views

### On the number of divisors in a given range

Given $\alpha\in\Bbb N$, can there be more than $(\log N)^4$ divisors (composites allowed) of $N$ in $\big[\frac\alpha2,\alpha\big]$ when $\sqrt N\in\big[\frac\alpha2,\alpha\big]$?
What is the ...

**0**

votes

**1**answer

57 views

### On a theorem by Mooney and Khavin on the weak sequential completeness of the predual of $H^\infty(\mathbb{D})$

There is a theorem by Mooney http://msp.org/pjm/1972/43-2/pjm-v43-n2-p.pdf#page=185 and independently proved by Havin which says that the predual of $H^{\infty}(\mathbb{D}),$
$L^{1}/H^{1}_{0}$ is ...

**8**

votes

**2**answers

505 views

### Did Bishop, Heyting or Brouwer take partial functions seriously?

The partial μ-recursive functions which may or may not be provably total seem to have some direct relation to the initial motivations for intuitionistic mathematics. (Following Kronecker, one ...

**1**

vote

**0**answers

69 views

### The normalizer problem for group rings

I recently studied about The Normalizer problem (NP) which states that given an integral group ring $\Bbb{Z}G$, $N_{\cal{U}}(G)=G\frak{z}$ where $\frak{z}$ denotes centre of $\cal{U}$ = ...

**0**

votes

**0**answers

60 views

### A PDE problem on the Heat-Like differential equations

I came across the following questions in part of my work:
Consider the Heat-Like equation of the form $\frac{\partial u}{\partial t}=\hat{H}u + f(x,t)u + g(x,t)$ where $\hat{H}$ is a Sturm-Liouville ...

**0**

votes

**0**answers

45 views

### Is there a function with a fixed point but does not satisfy the Banach contraction principle? [closed]

This is my question
Is there a function which does not satisfy the Banach contraction principle, but has a fixed point?
thank

**4**

votes

**0**answers

139 views

+50

### Cartesian square root of a measure preserving action

Let $G \curvearrowright (X,\nu)$ be probability measure preserving action of a countable discrete group. When does there exist a probability measure preserving action $G \curvearrowright (Y,\mu)$ such ...

**1**

vote

**1**answer

116 views

### Determining conjugacy class of a subgroup from the sizes of its intersections with the conjugacy classes

Let $C_1,C_2,\ldots,C_n$ be the conjugacy classes of a finite group $G$. It is possible that there are two non-conjugate subgroups $K \leq G$ and $H \leq G$ such that $|H \cap C_i|=|K \cap C_i|$ for ...

**9**

votes

**0**answers

176 views

### Homological stability for orthogonal groups

In Vogtmann's paper "Spherical posets and homological stability for $O_{n,n}$" it is shown that for all fields different than the field $F_2$ with two elements the homology groups of the orthogonal ...

**0**

votes

**0**answers

54 views

### a question on warped product

This question is on J.Cheeger and Tobias H.Colding's paper "lower bound on Ricci curvature and the almost rigidity
of warped products".
For a warped product $M=(a,b)\times_f N^{n-1}$ with metric $g$. ...

**9**

votes

**1**answer

170 views

### A Graph-Theory Related Question

Let $n$ be a positive integer and partition a grid of $4n$ by $4n$ unit squares into $4n^2$ squares of sidelength $2$. (The squares with sidelength $2$ have all of their sides on the gridlines of the ...

**-3**

votes

**0**answers

16 views

### Test correlation between 3 variables by hand [closed]

Do the three areas (courtside, lower deck, upper deck) differ in soda sales per hour?
Courtside Lower Deck Upper Deck
38 35 11
42 37 25
40 ...

**4**

votes

**0**answers

49 views

### General approaches to extension theorems as Caratheodory

I would like to know if there are some general studies about extension-like theorem, in the sense which i'm going to describe. This paragraph is not rigorous; I just would like the idea to be clear.
I ...

**0**

votes

**0**answers

15 views

### Is there a shelling of a (threshold)shifted complex, such that any partial shelling is still (threshold)shifted?

first the relevant definitions:
A complex $\Delta \subset 2^{[n]}$ is a family of subsets of $[n]$ that is closed downwards, i.e. if $A \subset B$ and $B \in \Delta$, then $A \in \Delta$.
A complex ...

**1**

vote

**0**answers

59 views

### Cubic, divisor of rational function $x/z$? [closed]

Let $k$ be a field, and let $a \neq 0$, $1 \in k$. Let $C = V(y^2z - x(x-z)(x - az))$. What is the divisor of the rational function $\psi([x, y, z]) = x/z \in k(C)$?

**-1**

votes

**0**answers

88 views

### $C = V(x^3 - xz^2 - y^2z)$, linear equivalence [closed]

Let $C = V(x^3 - xz^2 - y^2z) \subset \mathbb{P}^2(\mathbb{C})$. Let $p_0 = [0, 1, 0]$, $p_1 = [0, 0, 1]$, $p_2 = [1, 0, 1]$, $p_3 = [-1, 0, 1]$. I have two questions.
Is $2p_0$ linearly equivalent ...

**10**

votes

**0**answers

460 views

### Quaternions: ellipse effect

I would be interested in an explanation of the "six ellipse effect" produced by the pseudocode below (I also wonder how close are these to being actual ellipses). Note the code is somewhat similar to ...

**0**

votes

**0**answers

17 views

### Bayesian model to estimate the parameter of a Bernoulli law

Suppose we have iid boolean variables $X_1,...,X_T = X_{1:T}$ and the associated deterministic parameters $k_1,...,k_T=k_{1:T}$ and $c_1,...,c_T=c_{1:T}$, where for each $t \in \mathbb{N}$, $k_{t} \in ...

**3**

votes

**1**answer

136 views

### Is the localization of the maximal abelian extension still a maximal abelian extension?

Let $K$ be a number field and consider the maximal abelian extension $K^{ab}$ of $K.$ For a finite prime $p,$ letting $K_p$ be the completion of $K$ at $p,$ we have an extension $K_p \subset K_p ...