# All Questions

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### Is there a Hochschild-Serre spectral sequence for unramified cohomology?

Similar to the Hochschild-Serre spectral sequence for etale cohomology ($H^p(G, H^q_{et}(X_L, \mathcal F|_{X_L})) \Rightarrow H^{p+q}_{et}(X, \mathcal F)$ for a Galois field extension $L/k$ with ...
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### Nonsingular curve $C$ of degree 4, exists rational function $f: C \to \mathbb{CP}^1$ of degree 2?

Suppose $C \subset \mathbb{CP}^2$ is a nonsingular curve of degree $4$. Does there exist a rational function $f: C \to \mathbb{CP}^1$ of degree $2$?
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### Divisors of a quadratic trinomial

Let $P(n)$ be a quadratic trinomial with integer coefficients. For each positive integer $n$, the number $P(n)$ has a proper divisor $d_{n}$ (i.e. $1 < d_{n} < P(n)$), such that the ...
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### Constant spinors from constant forms

Let $X$ be a $m$-dimensional complex spin manifold and let us denote by $S_{\mathbb{C}}$ its complex spinor bundle. Then: $S_{\mathbb{C}}\simeq \Lambda_{\mathbb{C}}(X)$ Let $\nabla$ be any ...
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### A circulant coin weighing puzzle

We are given $n$ coins, some of which are "real" and weigh $1$ and some of which are "fake" and weigh $0$. We have one "spring scale" which can weigh any subset of the coins. A classic question asks ...
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### Connection and reduction of the structure group

I apologize for this question which is not really research-level, but I don't get any answer on mathStackExchange, and I asked a professor in my university... which couldn't find the solution. I am ...
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### Strange maps between operations in the operad of probability distributions

Summary: There is an operad $O$ of probability distributions on finite sets, with a strange sort of map between certain morphisms of different arities in $O$. I'd like to understand how to think about ...
1answer
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### How do I Calculate :$\int_{0}^{1}x^{k}\psi(x)dx$ where $k\geq 3$ is an integer?

How do I Calculate, if possible, in terms of well-known constants the integral : $\int_{0}^{1}x^{k}\psi(x)dx$ , where $k\geq 3$ is an integer ? note: $\psi(x)$ is digamma function. Any help is very ...
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### 3 possible tensors in 2-categories?

let $\mathcal{A}$ be a 2-category, consider: $$\mathcal{A}(W \otimes_i A, X) \simeq_i \mathcal{C}at(W, \mathcal{A}(A, X)) \;\;\; i = 1, \: 2, \: 3.$$ where $W$ is a category, and $A$, ...
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### Existence of finite set of points in the revolving circles

Let $k$ and $n$ be two fixed integers. Let $C$ denotes the circle with radius $4n$ (in the plane $\mathbb{R}^2$). Suppose $\{C_1,C_2\}$ shows the set of two arbitrary tangent circles with radius $2n$ ...
1answer
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### Using Jacobi fields to approximate parallel transport along geodesic:is the following limit true?

I apologize if this is not a research level question (already tried asking http://math.stackexchange.com/questions/1303288/relation-between-parallel-transport-and-jacobi-field-iion stack exchange with ...
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### On the use of the symmetric asymptotic upper density on $\mathbf Z$

The upper asymptotic density on $\mathbf Z$, viz. the function $${\sf d}^\ast: \mathcal P(\mathbf Z) \to [0,1]: X \mapsto \limsup_{n \to \infty} \frac{|X \cap [1,n]|}{n},$$ has a ''symmetric ...
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### Is there a $\Sigma^0_3$-complete ideal on $\omega$?

In Kechris's book "Classical Descriputive set theory" Chapter 23 (Exercise 23.4), it claim that there is a $\Sigma^0_\xi$-complete ideal on $\omega$ for each $\xi\geq 3$. There is a candidate ...
2answers
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### u.p (unique product) group which is not Right ordered ($RO$)

I am looking for an example of a u.p (unique product) group which is not Right ordered. Almost any group I pick up (obviously torsion free, as u.p. group cannot have torsion element, so no use ...
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### Details for Woodin's forcing argument for a saturated ideal from the Levy collapse

Theorem 2.65 in Woodin's book shows that a saturated ideal on $\omega_1$ exists after Levy-collapsing a Woodin cardinal $\delta$ to $\omega_2$. I am confused about the part of the argument where he ...
2answers
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### Special connection of vector bundle over real manifold

Let $E \rightarrow M$ be a vector bundle over a smooth manifold $M$ and let $g$ be a bundle metric. Does there exists a conection (maybe unique) $\nabla$ which is compatible with $g$. By this I mean: ...
1answer
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### Can there be a tree of height $\omega_2$ having all levels countable, with no cofinal branch?

For many years I had the idea that if a well-founded tree is both very tall and very narrow, then it must have a cofinal branch. For example, it is a fun exercise to show that any $\omega_1$-tree ...
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### About properties of polynomials with common interlacing

Say $\{a_1,a_2,..,a_n\}$ and $\{b_1,b_2,...,b_n\}$ be the real roots of two monic polynomials of degree $n$ which have a common interlacing. (say I have arranged the roots in increasing order) Can ...
1answer
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### Segal maps for Segal precategories

A Segal precategory is just a simplicial space $X:\Delta^{op} \to sSet$ such that its $0$-th space is discrete (i.e. constant). A Segal category is defined everywhere in the literature as a Segal ...
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Let $k$ be an algebraically closed field. Consider the map $\phi:X:=\mathbb{A}^{1}\times\mathbb{A}^{\mathbb{N}}\rightarrow Y:=\mathbb{A}^{\mathbb{N}}$ given by $(\lambda,x(t))\mapsto (t-\lambda) ... 1answer 62 views ### Find the probability that the product of these numbers is a multiple of 3 [on hold] From the sequence of natural numbers randomly select a pair of numbers. Find the probability that the product of these numbers is a multiple of 3. 0answers 40 views ### What is the idea behind a projection operator?what does it do? [on hold] I need the idea behind this not the definitions of the examples can someone help? 1answer 80 views ### Computing a transversal of a subgroup$H$of$G$in expected$O(|G : H|^2 \log |G : H| + |H|)$time I have the book "Handbook of Computational Group Theory", by Derek Holt, and in it is a section on finding the transversal of a subgroup. Recall a transversal of a subgroup$H$of$G$is a single ... 0answers 8 views ### Laplacian Matrix for weighted Adjacency? [on hold] I have seen definitions for Laplacian matrix in many resources as follows : L = D − A where D and A are the degree and ... 0answers 170 views ### Excellent rings If A is an excellent commutative ring and G is a finite group of automorphisms of A, is the invariant subring A^G still excellent ? I think this is false -- because if not it would probably be written ... 1answer 52 views ### Evolution operator for a linear parabolic equation Let$A(t)$be a smooth family of positive definite operators on a Hilbert space$H$. Consider the operator $$D:= \frac{d}{dt}+A(t)$$ and let$U(t):H\to H$be the evolution operator, i.e.,$U(0)=I$and ... 0answers 48 views ### TOPOLOGY DATA ANALYSIS [on hold] actually i am PHD student and my research in TOPOLOGY DATA ANALYSIS (TDA) what I dream about to understand this artcile cran.r-project.org/web/packages/TDA/vignettes/article.pdf may you help me: 1- MY ... 0answers 61 views ### Relation between Kahler form and Kahler potential [on hold] Let us consider an example. Take$\mathbb{C}^m$which is identified with$\mathbb{R}^{2m}$. Now, the Kahler form is given by $$\Omega = \frac{i}{2} \sum_{i=1}^m dz^i \wedge d\bar{z}^i$$ Now, how can ... 0answers 81 views ### The existence of proper schemes under complection Let$R$be a regular local ring,$\hat{R}$be its completion,$X$be a proper scheme over$\text{Spec}(\hat{R})$. In what case there exist a proper scheme$Y$over$\text{Spec}(R)$, such that$X$is ... 1answer 139 views ### Direct proof that$U$is an$E_\infty$-space An immediate consequence of Bott periodicity is that the infinite unitary space is an infinite loop space and so an$E_\infty$-space. I wonder if there is a direct proof (not using$U = \Omega^2 U$) ... 0answers 33 views ### why group completion of configuration space is the iterated suspension space In Lecture notes in mathematics Vol. 533, The homology of$C_{n+1}$-spaces,$n\geq 0$, F. Cohen, page 226, Corollary 3.3:$\alpha_{n+1}: C(\mathbb{R}^{n+1};X)\to \Omega^{n+1}\Sigma^{n+1}X$is a ... 0answers 68 views ### Endomorphism algebras of abelian surfaces with real multiplication Given an abelian variety$A$over a field$F$, one may consider the ring of endomorphisms$End(A)$, the ring of$F$-rational maps$A \to A$respecting the group structure on$A$. We may also consider ... 0answers 62 views ### Has solution of Brocard's Equation n!=m^2-1 [on hold] Brocard conjecture in 1904 that the only solution of are n=4,5,7. There are no other solutions with .(Berndt and Galway n.d).Another of Brocard’s conjecture is that there are at least four primes ... 0answers 40 views ### Sobolev-Poincaré inequality for curl-integrable functions Let$B=B(r)$denote a ball of radius$r$in$\Omega \subset \mathbb R^d$and $$u_B := \frac1{|B|}\int_B u \, dx.$$ The standard Sobolev-Poincaré inequality states that if$u \in W^{1,p}(\Omega)$, ... 1answer 68 views ### Infinite graphs with “similar” Hom-sets Let$G,H$be infinite simple undirected graphs with the property that for any graph$X$we have$|\text{Hom}(X,G)| = |\text{Hom}(X,H)|$. Does this imply that$G$is isomorphic to a subgraph of$H\$, ...

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