# All Questions

**2**

votes

**2**answers

235 views

### Is it true that all sphere bundles are some double of disk bundle?

Let's consider a smooth sphere bundle over a smooth manifold with structure group is equal to the diffeomorphism group of sphere. Then, can we say that this is a double of some disk bundle? Thank you ...

**1**

vote

**0**answers

68 views

### Moving from $\Re(s) = 1+\epsilon$ to $\Re(s) = \frac{1}{2}$ in the proof of the Weil-Guinand explicit formula

In all proofs of the Weil-Guinand explicit formula, there's this step (this is from Paul Garrett's notes):
Now consider this:
(1) $\frac{\zeta^\prime(s)}{\zeta(s)}$ has poles at $s=1$ and ...

**-3**

votes

**0**answers

29 views

### Compute score for a set of data [on hold]

So let's explain my problem. I have a set of items which have a score from 0 to 100. This set is dynamic which means that several values are expected to be added from moment to moment. In each item is ...

**6**

votes

**1**answer

52 views

### Horizontal distribution of a totally geodesic foliation

Let $\mathbb{M}$ be a $n+m$ dimensional manifold. Consider on $\mathbb{M}$ a rank $n$ sub-bundle $\mathcal{H}$ of the tangent bundle. We assume that $\mathcal{H}$ is endowed with a fiber wise inner ...

**8**

votes

**1**answer

317 views

### Why do we denote (co)ends with integral notation (beyond Fubini's Theorem)?

I know that (co)ends (i.e. universal wedges) follow Fubini-like relation, i.e.
$$ \int_{\langle c,d\rangle} F(c,d,c,d) \cong \int_c\int_d F(c,c,d,d) \cong \int_d\int_c F(c,c,d,d) $$
where we regard ...

**0**

votes

**0**answers

29 views

### Sobolev norm of a composition with a singular homeo

Let $H_p^t(\mathbb{R})$ be a fractional Sobolev space with the standard norm. The with $p>1$, $0<t<1$. Take some smooth $\phi$ from this space. Let $T$ be an ivertible homeomorphism of ...

**1**

vote

**0**answers

26 views

### Zero-dimensional $F$-space which is not strongly zero-dimensional

Does anyone know of an example of a (Tychonoff) $F$-space which is zero-dimensional but not strongly zero-dimensional?
By an $F$-space we mean every cozeroset is $C^*$-embedded.
By zero-dimensional ...

**3**

votes

**0**answers

70 views

### Green's Function for a Kernel with Symmetric Fourier Transform $\nabla^2-x^2$

I am trying to find the inverse of the following kernel in 3 dimensions
$$
\nabla^2-x^2,
$$
where,
$$
x^2=\vec{x}.\vec{x}
$$
It seems quit simple and one would think there should already be solutions ...

**2**

votes

**0**answers

92 views

### Derived Categories provide a good Framework for Sheaf Cohomology?

I'm a bit new to this sheaf cohomology business. Can someone explain how derived categories provide a good setting for Sheaf Cohomology? I understand that sheaf coho arises as right derived functors, ...

**3**

votes

**1**answer

142 views

### Reference request: The consistency of a tall tower in $\mathbb{N}^\mathbb{N}$

A $\kappa$-tower in $\mathbb{N}^\mathbb{N}$ is a sequence
$\langle a_\alpha : \alpha<\kappa\rangle$ in $\mathbb{N}^\mathbb{N}$
that is $\le^*$-increasing with $\alpha$
and has no $\le^*$-upper ...

**1**

vote

**1**answer

66 views

### Find the Picard Fuchs operator of a four parameter fundamental period

In my research, we have constructed a Calabi-Yau as a hypersurface of a toric variety and we could compute the fundamental period of the complex moduli, which is a series in four parameters. Say
...

**11**

votes

**3**answers

423 views

### Nice things that can be proved easily with characteristic classes

A bit of context for this question: as a project for my master's degree my supervisor asked me to understand the construction of Milnor's exotic spheres. After learning the heavy material (I knew very ...

**5**

votes

**0**answers

63 views

### In $(\mathbb{R}^4,\omega_{std})$ is positive symplectic area enough to guarantee a pseudoholomorphic disc representative?

I will present my question in the context that I encountered it, although I believe it probably applies in general context.
Consider $\mathbb{R}^4 \cong \mathbb{C}^2$ with the standard symplectic form ...

**14**

votes

**1**answer

209 views

### Does the injection $\text{Aut}(F_n) \hookrightarrow \text{Aut}(F_{n+1})$ split?

Let $F_n$ be the free group on $n$ letters.
The question is as in the title: letting $i:\text{Aut}(F_n) \hookrightarrow \text{Aut}(F_{n+1})$ be the natural injection, does there exist a homomorphism ...

**-2**

votes

**0**answers

16 views

### If derivative of f(x) is f'(x), then what is the integral of (f'(x))^2 in terms of f(x)? [migrated]

Is there some procedure for figuring this out or am I venturing into unsolved territory here?

**1**

vote

**0**answers

99 views

### Finding the Chern Class of a the pushfoward of a invertible sheaf

I am trying to understand what happens to the Chern Classes of an invertible sheaf $F$ over a complete intersection reduced curve of genus $g$ and degree $d$, when viewed as a invertible sheaf of ...

**2**

votes

**0**answers

147 views

### Normal bundle to fibers of a rational morphism

Let $f:X\dashrightarrow C$ be a rational fibration from a 3-dimensional variety $X$ to a curve $C$ such that generic fiber is smooth and different fibers intrsect in smooth curves. Take $S$ to be a ...

**0**

votes

**0**answers

15 views

### Sampling functions [on hold]

Suppose there were two spaces $A$ and $B$, A consists of functions that computes a scalar from an array of values($x$) that have coefficients($w$); $B$ consists of functions that does some ...

**1**

vote

**0**answers

126 views

### Stronger version of Bertini's theorem

In char 0, is there a generalised version of Bertini's theorem that will ensure that for a proper map $f: Y\rightarrow X$ between smooth projective varieties and for every point $x\in X$ we can find ...

**-4**

votes

**0**answers

31 views

### Question on logarithm Exponentiation [on hold]

I know it's not the best title but I had no idea how to be specific about it. Also sorry if I mess up the Latex syntax :/
Basically what I'm looking for is a rule that states how [log^2(a^{f(x)})]
...

**0**

votes

**0**answers

26 views

### Lower bound of general bilinear form [on hold]

Suppose I have a bilinear form $X^TAY$ where $X \in R^n, Y \in R^m$ and $Α \in R^{n \times m}$. All elements of $A$ are bounded, that is $\exists \bar a_{ij}>0:|a_{ij}|\le \bar a_{ij}, \forall ...

**2**

votes

**3**answers

178 views

### Existence of special graph

Let $G$ be a $n$-vertices graph and $\lambda_1$ is the largest eigenvalue of this graph. If $\lambda_1$ is an integer value, we can easily find the $\lambda_1$- regular graph with $n$ vertices. Now, ...

**1**

vote

**0**answers

38 views

### Matrix transformation [on hold]

I want to show that
$(I-H^T(-s)H(s))^{-1}$ has no poles on the imaginary axis
with $H(s)=C(sI-A)^{-1}B$ and $H^T(-s)=-B^T(sI+A)^{-T}C^T$
is equivalent to $M_\gamma$ has no purely imaginary ...

**0**

votes

**0**answers

15 views

### amplitude at exact frequency in wide band signal [on hold]

Could anyone suggest the most computationaly efficient method for finding amplitude of exact frequency having a noisy wide band signal.
To be more specific about a task. I have some physical ...

**2**

votes

**0**answers

68 views

### Computing the order of elements in a non abelian exterior square of a finite group

If we have an explicit group $G$, and we pick two elements $g,h \in G$, could we find the order of the element $g \wedge h \in G \wedge G$?
The best thing I could find is Theorem 1.1 in Ellis' Book ...

**2**

votes

**0**answers

28 views

### When is a linear operator on $C^{0,\alpha}(\overline{\Omega})$ a multiplication?

The title says it all, really. Suppose that I have a linear operator $T$ from $C^{0,\alpha}(\bar{\Omega})$ into itself, where $\Omega$ is a smooth bounded domain in $\mathbb{R}^d$ (e.g. the unit ball ...

**4**

votes

**0**answers

65 views

### Automorphism group of a structure without the SAP

A few years ago, a number of examples were given of Fraisse structures without the SAP in answer to the question raised in A Fraïssé class without the strong amalgamation property.
It is ...

**2**

votes

**0**answers

74 views

### Conditions to check whether a prime ramifies in a certain way

Let $p$ be a prime number and let $f = a_n x^n + \cdots + a_0$ be an irreducible polynomial of degree $n \geq 3$ with a root $\alpha$. We say that $p$ ramifies in a powerful way over $K = ...

**2**

votes

**0**answers

33 views

### The Socle of locally nilpotent $p$-group infinte rank

The Socle (is the subgroup generated by the minimal normal subgroups of $G$) of abelian $p$-group of infinite rank has infinite rank. (The term “rank” in the sense of the Mal’cev special or ...

**0**

votes

**1**answer

89 views

### 3-form torsion and Cartan structural equations

First, my level of math isn't very high as I come from the physics world.
I am trying to understand the derivation of Cartan's 3-form torsion.
I've read Robert Bryant's answer in this thread:
Relating ...

**4**

votes

**0**answers

87 views

+100

### Derivation of a stochastic Navier-Stokes equation under the assumption of perturbed particle trajectories

Let
$d\in\left\{2,3\right\}$
$\mathcal V_t\subseteq\mathbb R^d$ be the bounded domain occupied by an incompressible Newtonian fluid at time $t\ge 0$
$\Phi_t:\mathcal V_0\to\mathcal V_t$ such that ...

**2**

votes

**1**answer

159 views

### Is there a matrix that converts the gradient of every possible function to gradient of other function?

I have already asked this question on math.stackexchange.com
http://math.stackexchange.com/questions/1789476/is-there-a-matrix-that-converts-the-gradient-of-any-function-to-gradient-of-othe
Now I ...

**0**

votes

**0**answers

32 views

### Weak solutions and strong solutions of SDE [on hold]

What is the differences and connections between weak solutions and strong solutions of stochastic differential equations ?
Thank you in advanced!

**0**

votes

**1**answer

43 views

### Absolutely continuous and rectifiable boundary

Assume that $\gamma$ is a Rectifiable curve in $\mathbf{C}$ and ssume that $f$ is a bounded holomorphic function on the unit disk $U$ such that
if $z_n$ converges to a boundary point of $\mathbf{U}$, ...

**1**

vote

**0**answers

17 views

### Reference needed for exact sequence of ACM curves with homogeneous coordinate ring.

Let $C\subset\Bbb{P}^n$ be an ACM (arithmetically Cohen-Macaulay) curve with homogeneous coordinate ring $R$. Then there is an exact sequence
$$0\to \text{Tor}_i(R,\Bbb{C})_k\to ...

**-3**

votes

**0**answers

36 views

### Are Undirected Edges and Directed Edges disjoint sets? [on hold]

Many graph processing and storage frameworks assume that, in their graphs, all edges are directed. There are no edge whose type is undirected under the hood. There is only an interpretation, when ...

**4**

votes

**0**answers

80 views

### Auslander-Reiten theory for Gorenstein algebras

In the paper "Cohen-Macauley and Gorenstein artin algebras", Auslander and Reiten have a short section about Auslander-Reiten theory in Gorenstein algebras (I always assume we have an artin algebra ...

**7**

votes

**1**answer

189 views

### Characters of simply connected semsimple algebraic groups over local fields

Let $G$ be a semisimple algebraic group over $\mathbb{Q}_p$. Then by definition $G$ admits no non-trivial algebraic characters, i.e. homomorphisms $G \to \mathbb{G}_m$.
However, it is quite possible ...

**2**

votes

**1**answer

38 views

### Set of singular points for momentum map (with coisotropic action)

Let $G$ be a Lie-group acting on a connected symplectic manifold $M'$ in a hamiltonian way, with an $\operatorname{Ad}^*_G$-equivariant momentum map. Assuming $G$ acts properly on $M'$, we can ...

**3**

votes

**0**answers

50 views

### On the principal eigenvector of an elliptic operator

Suppose I have an open domain $U \subset \mathbb{R}^n$ and an elliptic operator $L$ acting on all square-integrable $C^2$ functions $\rho:U\to \mathbb{R}$ which converge to zero at $\partial U$:
...

**0**

votes

**0**answers

115 views

### Hadamard product (Schur product) in $L^2[0,1]$

Let's consider the separable Hilbert space $\mathcal{H} = L^2[0,1]$ of square-integrable functions on the interval $[0,1]$ with orthonormal basis $(e_j)$. For $x,y \in \mathcal{H}$, the Hadamard ...

**3**

votes

**1**answer

92 views

### Reference request: Principal series are equal in the Grothendieck group

In the usual setup, consider the category of Harish-Chandra $(\mathfrak{g},K)$-modules with given central character (if the central character is regular, this is equivalent to $K$-equivariant ...

**-8**

votes

**0**answers

41 views

### 0/0=2? How is this possible? [closed]

Is there anything wrong I am doing here?
0/0 =100-100/100-100
=10^2 - 10^ 2 /10(10-10)
=(10+10)(10-10)/10(10-10)
=20/10
=2

**2**

votes

**0**answers

112 views

### Uniform bound on the Mordell-Weil rank of elliptic curves

I want to know that if there is an uniform upper bound for the rank of elliptic curves over $\mathbb{C}(t)$, the rational function field over complex numbers, and generaly over the function field of ...

**5**

votes

**0**answers

123 views

### Any similar Lagrange's identity inequality

we have known Lagrange's identity
$$(a^2_{1}+a^2_{2}+a^2_{3})(b^2_{1}+b^2_{2}+b^2_{3})=(a_{1}b_{1}+a_{2}b_{2}+a_{3}b_{3})^2+\sum_{i=1}^{2}\sum_{j=i+1}^{3}(a_{i}b_{j}-a_{j}b_{i})^2$$
then we have ...

**8**

votes

**1**answer

102 views

+100

### Explicit calculations of small homotopy limits of CDGAs

I would like to carry out explicit calculations of homotopy limits of certain simple diagrams of CDGAS. My set-up is the following : I have a finite graded poset $R$ with minimal element $0$ and a ...

**5**

votes

**1**answer

213 views

### j-invariants for isogenous elliptic curves

Let $E$ be a smooth complex elliptic curve, and $\sigma$ translation of $E$ given by a point $p$ on $E$ of finite order, with respect to some fixed origin.
What are the $j$-invariants related with ...

**1**

vote

**1**answer

138 views

### Methods of showing a variety is stably rational

As anyone who follows the algebraic geometry tag on arXiv will probably know, there has been a lot of papers recently showing various varieties are non-stably rational. What I am interested in however ...

**0**

votes

**0**answers

28 views

### Generalizing Integration by parts for general bounded continous measure

Consider a probability measure $d\mu = w(t) dt$ with $w(t)\in L^1(I)$, $I =\left[ 0,1\right]$. What are the minimal assumption I can take on two functions $f,g:I\ \to \mathbb{R}$ so that an ...

**1**

vote

**0**answers

71 views

### Exceptional primes in Kummer-Dedekind theorem

Suppose that $A$ is a Dedekind domain with fraction field $K$, $L$ is a finite separable extension of $K$, and $B$ is the integral closure of $A$ in $L$. Suppose that $t$ is a primitive element for ...