All Questions
5,073 questions with no upvoted or accepted answers
1
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99
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Global approximation via convex combination of local approximations
I recently faced the problem of efficiently approximating a very large set of data points and, neither having a model of the empiric function, nor of the error distribution, my method of choice would ...
- 13.2k
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0
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81
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Ring structure for $K^{-1}$?
My questions are
whether there exists a product structure for $K^{-1}(X)$? Here $K^{-1}$ is the odd topological $K$-group, and $X$ is a compact space (or a manifold), say.
If such a ring structure ...
- 1,173
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0
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196
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Reference for a General Theory of Sequences?
Since decades, mathematicians are studying function spaces, discovering new structures more and more adapted for a general theory of functional analysis.
In that works, sequence spaces are generally ...
- 2,306
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0
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135
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Could one recover the relative K-theory from the quotient derived category?
Let $A\to B$ be a full embedding of exact categories that induces an embedding $D^b(A)\to D^b(B)$. My question is: what can one say about the relation of the homotopy cofibre $K(A)\to K(B)$ (the ...
- 16.9k
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204
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Is there inverse FFT algorithm for Fourier transform of a integer-valued random variable?
In many applications, it is possible to derive an explicit expression for the
Fourier transform of a random variable $X$
$$\varphi (\theta ) = \sum\limits_{n = 0}^\infty {{p_n}} {e^{in\theta }}$$
...
- 113
1
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249
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Game Theory - need references on analysis of particular game
My hobby AI research have led me to a thorethical game of particular design. As design is pretty simple, I was sure that such game has well-known name. But my question on math.stackexchange, where I ...
- 105
1
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217
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Periodic solution of first order ODE
There is a famous result shows that for every continuous function $f:{\mathbb R}\rightarrow {\mathbb R}$, the first order autonomous system
$$
\left\{
\begin{array}{l}
\dot{x}=f(x), \\
x(t_0)=x_0,
\...
1
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0
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192
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Ideals with norm in arithmetic progression
Let K/Q be a number field extention. Is there an asymptotic formular for the numer of ideals $\sum\limits_{\substack{N(A)\leq x\\N(A)\equiv k(q)}}1$,where $(k,q)=1$ and $A$ runs over ideals in $O_K$. ...
- 21
1
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0
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262
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$\mathfrak{q}$-ideal class bound
Let $K$ be a number field, $\mathcal{O}_K$ be its ring of integers. Let $\mathfrak{q}$ be a nonzero ideal in $\mathcal{O}_K$.
The $\mathfrak{q}$-ideal class group consists of equivalence classes of ...
- 3,320
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196
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Reference Help: Matsuki duality Orbits
I'm studying the Matsuki duality of $G_0$-orbits and $K$-orbits over a flag manifold $G/P$ where $G$ is semisimple complex Lie group and $P$ is a parabolic subgroup. I would like to study some ...
- 111
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0
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255
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An extrasensory perception strategy :-)
I asked this question at MSE some months ago
but I received only partial answers, so I put it here. The following sounds nice for me and I spent a good time during the investigation. But I am a ...
- 5,409
1
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0
answers
87
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unique types and decidability
Suppose $\mathcal{M}$ is an infinite structure which has the property that every type that is realised is realised uniquely. Also assume that every element of $\mathcal{M}$ is definable but there is ...
1
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0
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65
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Equivalence of $L^p$ harmonic functions on the ball and a representation by harmonic homogeneous polynomials
In Harmonic function theory, there is a theorem which says that if $u$ is an harmonic function on $B\left(a,r\right)$, then there exist homogeneous harmonic polynomials $p_{m}$ in $\mathbb{R}^{n}$ ...
- 325
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207
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Proofs for almost prime limits
A number $n$ with prime factorization $$n=\prod_{i=1}^rp_i^{a_i}$$
is a k-almost prime if it has a sum of exponents $$\sum_{i=1}^{r}a_i=k$$ i.e., when the prime factor (multiprimality) function $\...
- 1,903
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0
answers
42
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Harmonic Bergman spaces on graphs
Harmonic Bergman spaces on Euclidean domains are a set of harmonic functions on a domain that are from $L^{p}$ of that domain. I tried to find something on harmonic Bergman spaces on graphs because we ...
- 325
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510
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Which one is the correct assertion in the end? (projectivity of moduli of polarized varieties)
I randomly came across a 2007 article by Kollár in which the author makes a mathematical statement and explicitly states that it is in contradiction with a result contained in a 2004 article by ...
- 23.4k
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0
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493
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Complexity of Nested Linear Optimization
My question is motivated by the fact, that among other ways, it is possible to restrict a variable to two discrete values, e.g. the prototypical $0$ and $1$, via an optimization constraint:
$$\max(\...
- 13.2k
1
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0
answers
79
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Wavelets in the spaces of harmonic functions
I plan to do something with the theory of wavelets but in harmonic function theory. My question is about this interconnection between wavelets and harmonic functions. Can you recommend me some paper ...
- 325
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0
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636
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Centralizer of a maximal split torus
Can you help me find a reference for the following fact?
"If $G$ is a quasi-split $p$-adic group and $T$ is a maximal split torus in $G$, then the centralizer of $T$ is a maximal torus in $G$."
Or ...
- 11
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126
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Partially Observable Markov Decision Process - finding a hidden object with some positive probability
The following problem is example 5.1 from http://www.statslab.cam.ac.uk/~rrw1/oc/oc2013.pdf
A hidden object moves between two locations according to a Markov China with probability transition matrix $...
- 383
1
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0
answers
120
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Vanishing theorems that work in positive characteristic
Let $X$ be a smooth projective variety over a field of characteristic $p>0$ of dimension at least $2$. I am looking for some examples when $H^2(\mathcal{O}_X)$ vanishes. Is there any standard way ...
- 1,981
1
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98
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Small ball probabilities for functions of correlated normals
Let $f : \mathbb{R}^k \rightarrow \mathbb{R}$ and let $X$ be distributed k-dimensional normal with mean $0$ (with "arbitrary" covariance matrix). I am looking for references with bounds of the form: ...
- 111
1
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0
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305
views
Lagrangian complement in a symplectic vector bundle
A standard, folk result in symplectic geometry states that:
in a symplectic vector bundle $(E,\pi,B,\omega)$, any lagrangian subbundle $L$ admits a lagrangian complement $L'$.
Having to use this ...
- 4,306
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0
answers
158
views
Is the $K$-Theory of $\mathbb{P}X$ a $\lambda$-Ring?
If we let $\mathbb{P}X$ denote the free commutative algebra generated by the spectrum $X$, then we have a weak equivalence
$$
\mathbb{P}X\simeq \bigvee_r E\Sigma_{r+}\wedge_{\Sigma_r}X^{\wedge r}.
$$
...
- 535
1
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0
answers
133
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K-Exactness for groups and C*-algebras
We say that a C*-algebra $A$ is K-exact, if for any exact sequence of C*-algebras
$0\rightarrow I\rightarrow B\rightarrow B/I\rightarrow0$, the sequences
$K_i(I\otimes_{min}A)\rightarrow K_i(B\...
- 1,702
1
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0
answers
116
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Properties of the internal language of the category of sheaves
Consider a simple case of set-valued sheaves on some topological space $X$, $\operatorname{Sh}(X)$. All of these are Grothendieck toposes but clearly not all of them are equivalent.
Is there an ...
- 408
1
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0
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64
views
Complexity of in-dominating set
Is the decision problem In-Dominating Set NP-complete for digraphs of regular out-degree (greater than $\frac{n-2}{4}$, in particular)? --
I'm mainly looking for a reference.
Thanks for any answer!
1
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0
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94
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H-flux by any other name
There are more than a few papers referring to H-flux and/or H-twist etc.
Is there anywhere a survey relating these variants?
- 3,880
1
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0
answers
263
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Hopf lemma for line bundles on curves in algebraic geometry
In the paper http://arxiv.org/pdf/math/0110256v1.pdf Claire Voisin proves that all linear subspaces which lie inside of a (not too big) secant variety of a smooth projective curve must lie inside one ...
- 73
1
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0
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242
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Good factors of L-function
Let $X/K$ be a smooth projective variety over a number field $K$. I have seen two definitions of the L-function $L^i(s)$ attached to it's cohomology groups $H^i(X)$.
Both definitions agree that at a ...
- 3,555
1
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0
answers
464
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Reference request for parallel transport
I am learning about parallel transport on a Riemannian manifold equipped with an affine connexion. It seems (if I understand it well) that, in general, we might not be able to compute the parallel ...
- 119
1
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0
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272
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Possible counterexample to the strong three exponentials conjecture
There is something wrong possibly either with me or with Wikipedia.
Wikipedia's article on the strong three exponentials conjecture
defines $L^\ast$ as the set of all complex numbers of the form
$$\...
- 25.4k
1
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0
answers
327
views
Logical and alphabetological variant?
The notion of alphabetical variant is well known, so that a formula $x=x$ is an alphabetical variant of $y=y$ if $x$ and $y$ are distinct variables.
One may want to consider the set term $\{x:x \neq ...
- 3,574
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0
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612
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Is the automorphism group of a homogeneous (locally finite) tree unimodular?
I have seen somewhere (that I don't remember now) that the (full) automorphism group of a k-regular tree is unimodular. I assume a k-regular tree is the same thing as the homogeneous tree of degree k (...
user23860
1
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0
answers
236
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Volume Function on Banach Spaces
I'm looking for a reference for the following so-called Volume Function $V_n$, which is intended to be a Banach/normed vector space generalization of the determinant.
Let $X$ be a Banach space with ...
- 485
1
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0
answers
70
views
parabolic PDE with pseudomonotone operators
I am looking for a reference where well-posedness of problems
$$u_t + A(t)u = f$$
is addressed via the Galerkin method where $A$ is a pseudomonotone operator. I am aware that Roubicek's book ...
- 131
1
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0
answers
86
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Classification of involutions of the lattice $H\oplus H(k)^{\oplus2}$ for $k=5,6$?
Let $H$ denote the hyperbolic lattice (rank 2 lattice generated by $e,f$ such that $e^2=f^2=e.f-2=0$). Let $k >0$ be an integer. Is it possible to classify involutions $\iota$ of the lattice
$$
L:=...
- 1,663
1
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0
answers
123
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Six operations passage from $X_0$ to $X$ reference request
Let $X_0$ be a variety over $\mathbb F_q$ and denote by $X$ its basechange to the algebraic closure. Consider the constructible derived categories $D^b_c(X_0,\mathbb E)$ and $D^b_c(X,\mathbb E)$, ...
- 13.2k
1
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258
views
Is an exact operator, unitary equivalent to a banded operator?
Let $H$ be an infinite dimensional separable Hilbert space and $B(H)$ the algebra of bounded operators.
Definition : Let $(e_{n})_{n \in \mathbb{N}}$ be an orthonormal basis.
$T \in B(H)$ is ...
1
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0
answers
112
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What is a good reference for periodic Jacobi matrices?
I have been using Barry Simon's text "Szego's Theorem and its Descendants" and Gerald Teschl's text on Jacobi matrices to learn about the theory of periodic Jacobi matrices, but I would like to have ...
- 437
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0
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280
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Would a proof of both (G)RH and Montgomery's pair correlation conjecture imply SOC?
Would a proof of both (G)RH and Montgomery's pair correlation conjecture imply SOC?
It seems, judging by the abstract of a 2002 paper of Ram Murty and a possibly Romanian co-author published on www....
- 6,982
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0
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176
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Dold-Kan preserves weak equivalences and fibrations
It's well known that Dold-Kan correspondence is an isomorphism between simplicial vector spaces and non-negative chain complexes of vector spaces. Moreover, weak equivalences and fibrations are ...
- 1,271
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81
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Reference request: Compact metrizable semilattices with small connected semilattices are absolute retracts
Let $X$ be a compact metrizable topological semilattice with a neighbourhood base of sub-semilattices that are path-connected. I need a reference for a proof that $X$ is an absolute retract.
Here is ...
- 900
1
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0
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211
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Bound for field of definition (vs field of moduli) of an abelian variety
Let $A$ be a principally polarised abelian variety over $\mathbb{C}$ of dimension $g$.
Let $K$ be the field of moduli of $A$.
Proposition. $A$ has a model defined over an extension $L$ of $K$ such ...
- 1,500
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0
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653
views
On uniform convergence of sequences of bounded holomorphic functions with formal convergence
At some point I needed to prove that some formal (iterative) construction yielded an actual convergent power series. To do so I was led to prove the following lemma, where $\mathcal{B}(\Delta)$ is the ...
- 5,438
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0
answers
840
views
State of the game : cohomology of principal bundles
I would like to know what has been done in terms of specific calculations for the cohomology of principal bundle. For instance, it is known (see e.g. Greub, Halperin and Vanstone's "Connection, ...
- 502
1
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0
answers
117
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Is this basis of simplex polynomials known?
Put $R_n=\mathbb{R}[t_0,\dotsc,t_n]/(\sum_it_i-1)$ (the ring of polynomial functions on the $n$-simplex). Consider a monomial $t^a=t_0^{a_0}\dotsb t_n^{a_n}$. Let $(b_0,\dotsc,b_n)$ be the sequence $...
- 56.9k
1
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0
answers
95
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Generating series of free PROs
Let
\begin{equation}
G := \biguplus_{p \geq 0} \: \biguplus_{q \geq 0} G(p, q)
\end{equation}
be a bigraded set of generators and $\mathcal{F}(G)$ be the free PRO generated by $G$ (see [1] for a net ...
- 437
1
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0
answers
102
views
Notion of transversality over the field of Puiseux series.
To a given a Laurent polynomial $f$ over the field of Puiseux seris with parameter $t$, $f \in \mathbb{C} \lbrace\lbrace t \rbrace\rbrace[z_1^{\pm1},...,z_n^{\pm 1}]$, one can associate the ...
- 41
1
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0
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786
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Pontryagin Product on the Homology of $CP^{\infty}$
Is there an explicit description of the Pontryagin product on the homology of $CP^{\infty}$? Also, what is the homology of the classifying spaces $BU(n)$?
- 935