Recently Active Questions
159,066 questions
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Pimsner-Popa Bases
Let $N\subset M$ be a finite index $II_1$-subfactor. Let $B=\{b_i\}$ be a finite orthonormal (Pimsner-Popa) basis for $M$ over $N$. Let $d=[M\colon N]^{1/2}$. It is well known that $B_1=\{d b_{i_1} ...
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Is every left fibration of simplicial sets with nonempty fibers a trivial kan fibration?
In Lemma 2.1.3.4 of Higher Topos Theory, the statement of the lemma requires that the fibers are not only nonempty but contractible. However, in the proof, I don't see where contractibility is ...
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2
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Definition of homotopy limits
Here's a definition for homotopy limits that isn't quite right, but seems salvageable. Does anyone know how to fix it?
Suppose the category $C$ is some reasonable setting for homotopy theory, say it'...
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Difference between Beta Process and Dirichlet process
I'm trying to understand the definition of a Beta process, as given in the paper:
www.ece.duke.edu/~lcarin/Paisley_BP-FA_ICML.pdf
The problem is that from the definition it follows that every ...
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Reference for the `standard' Tate curve argument.
I'd like a reference (e.g. something published somewhere that I can cite in a paper) for the proof of the following:
Let $E$ be an elliptic curve over $\mathbb Q$ with minimal discriminant $\Delta$...
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1
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computing lengths in the A_2 affine weyl group
The A_2 affine Weyl group is the symmetry group of the triangulation of the plane by equilateral triangles. As Sean points out, it may be generated by reflections $r_1, r_2, r_3$ about the edges of a ...
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The Category of Representations of a Group
Do people study the category of representations of a compact finite group (not just irreducible ones)? I'm more interested in small cases like S_3 and SU(2) but I'd be curious about general cases ...
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Extracting integer multiplicative factors from the sum of certain sets of (finite-precision) real numbers?
Update based on Michael's answer (thanks again!) - Can the LLL or PSLQ algorithms provide a (knowably - i.e. not just incidental) unique solution for the set of integer multiplicative factors? Are ...
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2
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Non-integral scheme having integral local rings
I can show that if $X$ is a scheme such that all local rings $\mathcal{O}_{X,x}$ are integral and such that the underlying topological space is connected and Noetherian, then $X$ is itself integral.
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Realizing complexes with bases as cellular complexes
This is a question a friend of mine asked me some time ago. I suspect the answer is "no" but can't prove it.
Every free complex of abelian groups is isomorphic to the reduced cellular complex of some ...
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Expressability of an electrical circuit with probabilistic switches
Here is a purely number theoretical question that I got to know from our electrical engineering department.
Call a number $q\in \mathbb{N}$, good if one can do the following:
Given a set of "...
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3
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Characterizations of non-wellfounded models?
My question is whether there are any characterizations of non-wellfounded models of set theory. A wellfounded model is one that does not have any \epsilon-descending infinite sequences. I'm not asking ...
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yoneda-embedding vs. dual vector space
I've made the following observation: let V be a vector space over $\mathbb{R}$ with a inner product $\langle , \rangle$. then there is a "natural contravariant" injective map $V \to \hom(V,\mathbb{R})$...
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A parametrization of Heronian triangles
Let $a,b,c$ be integers which are the sides of a triangle with integral area, a so called Heronian triangle. This website attributes to Gauss the result that there must then exist integers $m,n,p,q$ ...
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Which is the correct version of a quantum group at a root of unity?
By this I mean the specialisation of the quantum group Uq(g) with q a root of unity, and the 'correct' meaning of 'correct' (enclosed in quotations since there isn't necessarily a correct answer) is ...
CommunityBot
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Homotopies of triangulations
I imagine this is pretty much standard, but surely someone here will be able to provide useful references...
Suppose $X$ is a topological space. Let me say that two triangulations $T$ and $T'$ of $X$,...
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GW invariants for varieties with negative first Chern class
Does there exist any theorem claiming that if a variety with negative first Chern class has no rational curves then every GW invariant is zero?
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Collapsing the medial axis of a polytope
Let X be a convex polyhedron in hyperbolic 3-space.
Let M be the medial axis of X.
Question: Is M collapsible?
It is easy to see that M is contractable.
In the case of Euclidian 3-space, instead ...
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Term to describe how much harder an optimization problem can become after constraining a small part of the domain?
This is a follow up to this question.
I'm interested in discrete optimization problems formulated as 0-1 integer programs; essentially, anything of the form
$$\Phi = \max_{\mathbf{x} \in \left\{0,1\...
CommunityBot
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3
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How do I calculate the discriminant of a galois closure and its other subfields?
Given a number field K of dimension d over Q, and galois closure of dimension d! over Q (i.e galois group Sd), can we relate the discriminant of the galois closure to that of the discriminant of K? ...
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2
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What does Faltings' theorem look like over function fields?
Minhyong Kim's reply to a question John Baez once asked about the analogy between $\text{Spec } \mathbb{Z}$ and 3-manifolds contains the following snippet:
Finally, regarding the field with one ...
CommunityBot
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Is this a sleight of hand or a video edit?
In another question someone linked to this video where the lady ties a knot in a seemingly impossible manner.
What I don't understand is how the end sticking out beyond her right hand gets longer as ...
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4
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Uniqueness of Force Balancing Solutions
Consider some number of charged particles on a closed interval, each with possibly different amounts of charge. Assuming some kind of 'friction' to dampen their motion, they will eventually find a ...
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12
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2
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"Kummerian" fields?
This is sort of a random, spur of the moment question, but here goes:
We define [with apologies to Conan the Barbarian] a field K to be $\textbf{Kummerian}$ if there exists
an index set I, and ...
CommunityBot
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how do i cite a contribution made by mathoverflow in my next publication ? [closed]
Ok. Here I come. Assume I am working on a paper, and I have a small side problem X related to a conjecture Y. Solving that side problem X will of course help my work as it will allow me to solve the ...
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Are Dynkin diagrams of some universal construction?
This is a general question. The classification of semisimple Lie algebras by using Dynkin diagrams has always amazed me. And these A,B,C,D,E,F,G diagrams seem to appear quite often in the realm of ...
CommunityBot
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3
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Two finite groups with the same identical relations?
An identical relation on a group G is a word w in Fr, the free group on r elements (for some r), such that evaluating w on any r-tuple of elements of G yields the identity (this just means ...
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Analysis analogue of Orlov's theorem?
Mukai's theorem states that if $X$ is an abelian variety, and $\check{X}$ is the dual abelian variety, then the Fourier-Mukai transform corresponding to the Poincare line bundle on $X \times \check{X}$...
CommunityBot
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The convergence of Eisenstein series of weight zero [closed]
Consider Eisenstein series of weight zero, i.e.
$ E_{\mathfrak{a}}(z,\ s,\ \chi) = \sum_{ \gamma \in \Gamma_{\mathfrak{a}} \backslash \Gamma } \bar{\chi}(\gamma) (Im\sigma_{\mathfrak{a}}^{-1}
\gamma ...
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0
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306
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Diagonalizing matrices over cyclotomic fields with unitaries
Let $F$ be a number field with a fixed embedding $F \hookrightarrow \mathbb{C}$ such that the restriction of complex conjugation from $\mathbb{C}$ to $F$ is in Gal$(F/\mathbb{Q})$ and fix a Hermitian ...
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8
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1
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Inequality of the number of integer partitions
I am familiar with the partition function p(k,n) where p is the number of partitions of n using only natural numbers at least as large as k.
Is there a way of determining if p(k1, n1) > p(k2, n2) that ...
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1
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A product of gamma values over the numbers coprime to n.
Let φ(n) denote Euler's totient function and k $\perp$ n denote that k, n are integers and relatively prime. Let N = φ(n) + 1. If n is not a prime power
$$ \prod_{\substack{0 < k < n, \\ ...
- 85.6k
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When f(x)-a and f(x)-b yield the same field extension
An interesting mathoverflow question was one due to Philipp Lampe that asked whether a non-surjective polynomial function on an infinite field can miss only finitely many values. In my interpretation ...
CommunityBot
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Special bases of number fields
Let K be a number field of degree n with a fixed embedding in the complex numbers. Let | . | be the normalized absolute value given by that embedding. (The square of the ordinary absolute value ...
- 8,866
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3
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Advantages of a back-propagation neural network over other function approximation methods
Hello.
Let's say I have a set of input vectors $I = \{\mathbf{x_1}, \dots, \mathbf{x_k}\} \subset \mathcal{R}^m$ and a set of output vectors $O = \{\mathbf{y_1}, \dots, \mathbf{y_k}\} \subset \...
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Models for, and motivation for, (oo,n)-categories for general n
First: Is there a precise meaning to the term "model for (oo,n)-categories"? A related question, which might actually be the same question, is: what exactly do we want to get out of (oo,n)-category ...
CommunityBot
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2
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Closed forms for Monotonic polynomial recurrences?
I have a monotonic polynomial recurrence of the following form:
c_n = 1-p + p*(c_n-1)^2
This comes from the probability that a specific branching process (Galton-Watson) will be extinct before the ...
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2
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2
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Use of the word "data" not in the statistical sense [closed]
Occasionally I see the use of the word "data" in definitions. For instance, one definition of an exact sequence starts off by saying, "An exact sequence of abelian groups (or modules or vector spaces) ...
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The "ultimate" indefinite inner product space
This can be considered as a relative of Splitting a space into positive and negative parts.
Is there a real (non-trivial) vector space $V$, endowed with a nondegenerate symmetric bilinear pairing $\...
CommunityBot
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Extremum under variations of a traceless matrix
Sorry for my precedent tentative, I was a little hasty:
Ok, I think I'd better put the original problem:
I have an action of three fields: $A$ which is the spin-connection, $B$ an skew-symmetric 2-...
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What optimization criteris should be used for this problem?
The real world version:
I have a united value (e.i. 12in, 120V 1.414 kg*m/s) where the units are specified as the rational exponents of the 5 base units; m, s, kg, C and K. Additionally, I have a set ...
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Why are non-singleton covering families often ignored?
It seems to me that frequently when discussing stack conditions and descent, people consider only singleton covering families, i.e. there is some single covering map $U\to X$, for which one constructs ...
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Asymptotics for Christoffel number
What is the order for the following sum $\sum\limits_{i=1}^{n} \frac{\lambda _i}{1-x _ i}$ where $\lambda _i$-i-th Christoffel number and $x _i$- i-th zero of n-th Legendre polynomial.
P.S
...
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What is the Zariski closure of the space of semisimple Lie algebras?
Given Leonid Positselski's excellent answer and comments to this question, I expect that the present one is a hard question. Recall that the Lie algebra structures on a (finite-dimensional over $\...
CommunityBot
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Is there a text on estimation theory online?
Where can I find graduate level, thorough, parameter estimation/ estimation theory material on the web?
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Non-smooth algebra with smooth representation variety
A not necessarily commutative algebra A (over C, say) is called formally smooth (or quasi-free) if, given any map $f:A \to B/I$, where $I \subset B$ is a nilpotent ideal, there is a lifting $F:A \to B$...
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Highbrow interpretations of Stirling number reciprocity
The number ${n \choose k}$ of $k$-element subsets of an $n$-element set and the number $\left( {n \choose k} \right)$ of $k$-element multisets of an $n$-element set satisfy the reciprocity formula
$\...
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Can Walsh-Hadmard transform be used for convolution ?
The Walsh-Hadamard transform is very fast to compute.
Can it be used to compute the convolution of two functions as it can be done with Fourier transform ?
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Can you explain a step in a proof about 2-sided surfaces in 3-manifolds?
Following is an argument given by Hempel where I am unable to understand his comment about choosing a loop close enough to a surface. Can somebody please elucidate this:
Lemma: If $F$ is a compact ...
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Finding divisors on a curve
What is the best way to find an actual divisor of an affine curve? I.E. if I am interested in finding a canonical divisor of a curve in two variables, is there a general way to go about it? Do I need ...
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