2
votes
1answer
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
0answers
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
0answers
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
0answers
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
0answers
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
0answers
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
0answers
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
0answers
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
0answers
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
0answers
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
2answers
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
0answers
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
0answers
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
0answers
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
0answers
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
0answers
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
0answers
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
2answers
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
0answers
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
1answer
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
0answers
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
1answer
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
1answer
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
0answers
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
1answer
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
0answers
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
1answer
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
1answer
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
0answers
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
0answers
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
0answers
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
1answer
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
0answers
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
1answer
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
0answers
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
0answers
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
0answers
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
1answer
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
0answers
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
0answers
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
1answer
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
3answers
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
0answers
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
0answers
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
0answers
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
0answers
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
0answers
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
0answers
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
1answer
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
0answers
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 ...

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