# All Questions

**2**

votes

**1**answer

95 views

### recognising weak equivalences of simplicial sets

$\require{AMScd}$ I am interested in detecting using a lifting property when a map $f:X\to Y$ in $sSet$ (with the standard Kan model structure) is a weak equivalence. In the paper Weak Equivalences ...

**-2**

votes

**0**answers

17 views

### Can we predict next sample using the existing samples? [on hold]

Suppose that I have 18 data points and I'm sampling 3 data points each time. Suppose that I have 60 samples (each has 3 data points). Can we predict the next sample (of 3 points) from the existing ...

**0**

votes

**0**answers

31 views

### Can we conclude that $\varphi(L_xf_0)\neq0$ for every $x\in G$?

Let $H$ be a compact subgroup of locally compact topological group $G$ and $A=\{f\in L^1(G); R_hf=f(a,e)\forall h\in H\}$ as a subalgebra of $L^1(G)$ by convolution of $L^1(G)$. If $\varphi \in ...

**2**

votes

**0**answers

85 views

### Does this symmetrization operator have a name? Any theory?

Consider a function $f(x_1,\ldots,x_n)$ of $n$ complex variables. Define
$$f_{\mathrm{symm}}(x_1,\ldots,x_n) =
2^{-n}\sum_{\varepsilon_1,\ldots,\varepsilon_n=\pm 1}
...

**1**

vote

**0**answers

44 views

### Are A and A^T unitarily equivalent over a p-adic field?

Let $E/F$ be a quadratic extension of p-adic field. Let $U=\{u\in GL_2(E): uu^*=1\}$ be the unitary group of rank 2.
My question is: given a matrix $A\in GL_2(E)$ can we find $u_1,u_2\in U$ such ...

**-4**

votes

**0**answers

48 views

### Convert 1-5 Grading Scale to 1-100 Grading System [on hold]

I am creating a formula in Excel to convert 1-5 Grading Scale to 1-100 Grading System
Suppose that I have the following table:
97-100 = 1.00
94 - 96 = 1.25
91-93 = 1.50
88-90 = 1.75
85-87 = 2.00
...

**0**

votes

**0**answers

32 views

### Linear elliptic estimates

i am interested in solutions of the following
$$-\Delta \phi =f \; \; \; A_\lambda, \qquad \phi=0 \; \; \partial A_\lambda,$$ where $ A_\lambda=\{ x \in R^N: \lambda <|x|<1 \}$ with $ ...

**0**

votes

**0**answers

69 views

### Computations of derivations, $d^2$, of a (Grothendieck) spectral sequence

The maps $d^1:E_1\rightarrow E_1$ have a nice description. Is there any text providing us with a description of the higher derivations $d^2:E_2\rightarrow E_2$ arising from a Grothendieck spectral ...

**0**

votes

**0**answers

20 views

### Examples of Sigma-Adequate Links that are not simply Adequate in A and B type sense?

I am looking to see if anyone has constructed explicit examples of $\sigma$-adequate links a la Makoto Ozawa's Essential State Surfaces for Knots and Links? This technique is centered around taking ...

**-3**

votes

**0**answers

88 views

### What is the interpretation of f'(x)/f(x)? [on hold]

I'm studying Fisher information and the function d/dx ln(f(x)) thus f'(x)/f(x) appears. I'm trying to interpretate what this is quantier could represent in a function. Thank you.

**1**

vote

**2**answers

292 views

### Popular books written by great mathematicians [on hold]

I read:
H. Poincare. Value of science
F. Klein. Development of Mathematics in the 19th Century
J.E. Littlewood. A Mathematicians Miscellany
G.H. Hardy. A Mathematician’s Apology
R. Courant, ...

**3**

votes

**0**answers

53 views

### reference for higher spin - not gravitational nor stringy

Other than the papers of Berends,Burgers and van Dam, are there any papers that study
the general case of deforming a free field theory with higher spin fields to be interactive?

**2**

votes

**0**answers

33 views

### Does there exist duality/symmetry between Fuchsian differential equations, like in the case of confluent hypergeometric?

My question is about whether certain dualities or symmetries hold between pairs of Fuchsian differential equations, but I need to give a bit of background to explain what I want to ask. Thank you for ...

**4**

votes

**0**answers

271 views

### Survey of Erdős' “Tricks” [on hold]

Is there a kernel of "tricks", techniques and tools that Paul Erdős was particularly fond of and therefore employed a lot in his research work? Could you point out some survey papers that deal with ...

**1**

vote

**0**answers

39 views

### Free profinite products

Let $F$ be a nonabelian finitely generated free profinite group, and let $x \in F$. Must there be some $1 \neq y \in F$ such that $\langle x,y \rangle$ is isomorphic to the free profinite product of ...

**1**

vote

**0**answers

93 views

### Hodge structures generated by cohomology groups of varities with dimension less than $n$

Let $X$ be a smooth projective variety over $\mathbb{C}$ with dimension $n$. Is it true that for every $i<n$, the Hodge structure on $\mathrm{H}^i(X,\mathbb{Q})$ is generated by Hodge structures of ...

**2**

votes

**0**answers

56 views

### The level set of convolution

Suppose $u\in C^2(\bar \Omega)\cap C^\infty(\Omega)$ is a function which is compact supported on $\Omega$ with $u\equiv 0$ at $\partial\Omega$, and $\Omega\subset \mathbb R^3$.
We also assume that ...

**2**

votes

**2**answers

221 views

### cohomological obstructions and rational points

Let $X$ a (nice) scheme over $\mathbb{Q}$. Are there cohomolgical obstructions answering the following questions:
1) is $X(\mathbb{Q})$ an empty set ?
2) is $X(\mathbb{Q})$ a finite (non empty) set ...

**0**

votes

**0**answers

30 views

### Laplace equation between circles [on hold]

I need to solve the simple Laplace equation $$\nabla^2f(r,\theta)=0$$
with boundary conditions:
$$f(a,\theta)=g(\theta)$$
$$\lim_{A\rightarrow\infty}f(A,\theta)=1$$
where $a$ is a fixed real radius. ...

**0**

votes

**1**answer

93 views

### Alexeev's projective torus embeddings

I'm reading Alexeev's "Complete moduli in the presence of semiabelian group action" and I just started to study toric geometry.
In chapter 2 in order to obtain an affine toric variety he takes ...

**0**

votes

**0**answers

42 views

### Integration of independent Brownian motions

I am wondering if the following integral of stochastic Brownian motions has an analytical solution?
$$
\int_{0}^{t}e^{\nu \tilde{V}_{\tau} - \frac{1}{2}\nu^{2}\tau}d\tilde{W}_{\tau}
$$
where ...

**7**

votes

**1**answer

114 views

### Dual of Banach-valued $L^p$

Let $X$ be an infinite-dimensional Banach space and let $p\in(1,+\infty)$. We may define $L^p(\mathbb R;X)$. Is it always true that the topological dual of $L^p(\mathbb R;X)$ is $L^{p'}(\mathbb ...

**3**

votes

**1**answer

133 views

### Proof of a Proposition regarding the reduction of N-torsion groups on elliptic curves

In Diamond-Shurman A first course in Modular forms p.334 Prop. 8.4.4. It is stated,
For E elliptic curve over $\bar{\mathbb{Q}}$ with good reduction at the prime ideal $\mathfrak{p}$ the reduction ...

**0**

votes

**0**answers

22 views

### Separating Two Groups of Data using Fisher's Linear Discriminant

I found an article (starting on page 8) that gives a neat method for finding the line/plane/hyperplane that maximizes the separation between two groups of data points in n-dimensions. It uses Fisher's ...

**7**

votes

**1**answer

118 views

### Orders in Central Simple Algebras. Applications

It is known that orders in quaternion algebras (over a number field) are used for constructing geometric objects like hyperbolic orbifolds and Shimura curves. Moreover, if one knows embedding ...

**0**

votes

**0**answers

40 views

### Extending natural transformations of triangulated functors on $D^b(\mathbb P^1)$

Let $\mathcal T = D^b(\mathbb P^1)$, the bounded derived category of $\mathbb P^1$ over a field $k$. It is well known that $\mathcal T$ admits a strong and full exceptional sequence $\{\mathcal O, ...

**0**

votes

**1**answer

58 views

### Genus of Covering Space of 3-Manifold

Let $M_g$ and $M_h$ be closed orientable 3-manifolds of genus $g$ and $h$ respectively and suppose that $M_g$ is an $n$-sheeted cover of $M_h$. Is there a formula that would allow us to compute $g$ if ...

**6**

votes

**1**answer

193 views

### A question on compact sets

Let $K\subset \mathbb{R}^N$ be a compact set. We say
$K$ is "good" if the following property holds:
Given a set of open neighborhoods $\{x\in U_x\subset \mathbb{R}^N\}_{x\in K}$ there exists a finite ...

**0**

votes

**0**answers

41 views

### Completeness of spaces $\Lambda(\varphi, p)$

Definition 1. Let $f$ be measurable function on a mesurable subset $E\subset \mathbb R^n$. Non-increasing rearrangement of $f$ is a function $f^\ast(x)=\inf\{s>0: \operatorname{mes} E[|f| > s] ...

**4**

votes

**0**answers

57 views

### Is a finitely generated subgroup of a free profinite group virtually a retract?

Let $F$ be a nonabelian finitely generated free profinite group, and let $H \leq F$ be a finitely generated closed subgroup. Must there be some open subgroup $H \leq U \leq F$, and a closed normal ...

**7**

votes

**0**answers

77 views

### Closed geodesics avoiding points in hyperbolic surfaces

Let $\Sigma$ be a closed hyperbolic surface. Is it true that for any finite collection of points $x_1,\ldots,x_n\in\Sigma$ there exists a closed geodesic $\gamma$ containing none of them?
Remark: It ...

**2**

votes

**1**answer

62 views

### Limiting Ratio of Solutions to Ordinary Differential Equations [on hold]

I'm trying to find the limit of the ratio of two functions
$ \lim_{t \rightarrow \infty} \frac{f(t)}{g(t)} $ but only have the initial conditions and the differential equations they solve, but the ...

**5**

votes

**0**answers

90 views

### Have heat kernels for generalized Laplacians on non-compact manifolds been constructed?

Let $M$ be a non-compact Riemannian manifold which is "nice enough", and $D$ a generalized Laplacian on it. The construction of the heat kernel for the Laplace-Beltrami operator on $M$ seems to be ...

**5**

votes

**1**answer

178 views

### Examples of Symplectic Questions Solved by ``Mirror Symmetry Translation'' to Complex Questions

According to the proponents of homological mirror symmetry, when a complex and symplectic manifold are mirror symmetric, we can take difficult questions about the symplectic space and transfer them ...

**1**

vote

**0**answers

17 views

### Density of restrictions of $p$-harmonic functions on a hypersurface

Let $\omega,\Omega\subset\mathbb R^n$, $n\geq2$, be bounded smooth domains so that $\bar\omega\subset\Omega$.
Let $1<p<\infty$.
Define the boundary space $B=W^{1,p}(\omega)/W^{1,p}_0(\omega)$; ...

**0**

votes

**0**answers

31 views

### BPP with expected polynomial time [on hold]

Suppose we change the definition of BPP to require the TM to run in expected polynomial time (such as in ZPP).
Will the resulting class be equal to BPP, or larger?
Thanks.

**1**

vote

**0**answers

20 views

### Optimization of a multilinear function over a product of hypersimplices

Let $P = \Delta_1 \times \cdots \times \Delta_N$ be the Cartesian product of $N$ hypersimplices. Let $f : P \to \mathbb{R}$ be a multilinear function of $N$ variables, ie $x_i \mapsto f(x_1, \ldots, ...

**3**

votes

**1**answer

189 views

### Is an anticanonical Weil divisor in $\mathbb{Q}$-Gorenstein variety Calabi-Yau?

Let $P$ be a normal, $\mathbb{Q}$-Gorestein variety with terminal singularities. Let $X \subseteq P$ be a normal, irreducible Weil divisor such that $X \sim_{\mathbb{Q}} - K_P$, that is ...

**3**

votes

**0**answers

207 views

### Is there a hidden symmetry in the prime numbers distribution?

Under Goldbach's conjecture, let's consider once again the map $r_0\colon n\mapsto r_{0}(n)$ such that $r_{0}(n)$ is the smallest non negative integer $r$ such that both $n-r$ and $n+r$ are prime.
...

**2**

votes

**0**answers

47 views

### Geometric automorphism of free group respect to nonorientable suface

An outer automorphism $[ϕ]\in Out(F_n)$ is geometric if it is induced by a surface homeomorphism h:M→M, where M is a compact surface with nonempty boundary. I am wondering is it enough we only ...

**9**

votes

**1**answer

247 views

### singularize the least inaccessible?

Is it consistent that there is some partial order $\mathbb P$ and some inaccessible cardinal $\kappa$, which is the least inaccessible, such that $\mathbb P$ forces $\kappa$ to be singular while ...

**4**

votes

**3**answers

85 views

### Linear intersection number and vertex covering number

A linear hypergraph is a pair $\pi=(X, L)$ where $X\neq \emptyset$ is a set and $L\subseteq {\cal P}(X)$ has the following properties:
for $e\in L$ we have $|e|\geq 2$;
if $e_1\neq e_2 \in L$ then ...

**0**

votes

**0**answers

13 views

### Algebra textbook recommandation for person already familiar with algebra [migrated]

Can you guys please recommend me a good textbook on algebra, given that I am already familiar with lots of algebra stuff and I want to revisit, and deepen my knowledge?
(Little backstory: I started ...

**-1**

votes

**0**answers

42 views

### smallest (sub-) sigma algebra containing a null set [on hold]

Given a probability space ($\Omega,\mathcal{A} ,P$) and $N \in \mathcal{A}, N \ne \emptyset$ with $P(N) = 0$
What is the smallest sub-sigma algebra of $\mathcal{A}$ containing $N$.
I'm kind of ...

**1**

vote

**0**answers

52 views

### pushforward of universal objects along canonical morphisms of stacks

The kind of question I'm interested in has the following flavor: having two moduli stacks with one being an enhanced (i.e more data) version of the other with the natural "forgetting" map between them ...

**5**

votes

**0**answers

78 views

### An Interesting Markov Chain Mixing time question (coupling of random variables)

Consider a simple markov chain called reproduction process. Let $N>0$ be fixed. At each time $t$, there are $N$ balls, in which $x$ balls are colored white, and $N-x$ balls are colored black. We ...

**2**

votes

**0**answers

105 views

### How many points does 'the-most-point-contained-circle' contain at least?

Question : Given any $n$ distinct points $S$, consider the $\binom n2$ discs $D_{pq}$ formed by picking a pair of points $p,q$ from $S$ and using them as a diameter. For each disc $D_{pq}$, let ...

**0**

votes

**0**answers

112 views

### A relation that commutes with logical equivalence? [on hold]

I would like help with proving or disproving a conjecture concerning logical equivalence.
Say that a set $S$ of occurrences of formulas within a formula $\varphi$ is simplifiable (with respect to ...

**6**

votes

**1**answer

84 views

### What is the original reference for disorientations on tangle diagrams?

There are several invariants whose "natural" domain is a category of disoriented tangles, that is tangles which are piecewise-oriented, but which contain points called `disorientations' at which the ...

**3**

votes

**0**answers

75 views

### Maximal compact subgroup of SL(2,|H)

The exceptional isomorphism $Spin(5,1)\simeq SL(2,\mathbb{H})$ is well-known, and I can find references that say the maximal compact of $Spin(5,1)$ is $Spin(5) \simeq Sp(2)$. So I know the answer to ...