Recently Active Questions
159,064 questions
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Isolated hypersurface singularities, Chow groups and D-branes
Say a ring $R$ is an isolated hypersurface singularity if $R = k[x_1, \ldots, x_n]_{(x_1, \ldots, x_n)}/(W)$, where $k$ is a field and $W \in k[x_1, \ldots, x_n]$ is such that the ideal $(\partial_1 W,...
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Upper bound on the genus of a k-page graph
Is there an upper bound on the genus of a graph that has a book embedding on say k pages, or can the genus be arbitrarily large? If not a general bound is known, what happens for k=3?
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3
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Why are some tilings introduced as geometrical objects, not graphs?
Let's say you have a planar tiling. Quite often these tilings are introduced as geometrical objects with metrics; each tile having coordinates assigned to its vertices.
The tiling has an associated ...
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4
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What is the "right" universal property of the completion of a metric space?
I'm a little embarrassed to ask this one, but it could help for a class I'm teaching, so here goes:
Let $X$ be a metric space. We all know that $X$ admits a completion, which is a complete metric ...
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0
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linear program with zeros
Hi, I want to be able to solve a linear program that has constraints that are either zero or a range. An example below in LP_Solve-like syntax shows what I want to do. This doesnt work. In general all ...
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2
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Schur Multipliers
I'd like to know H^2(G,C^*) for a few (finite) groups I have in mind. For example, a finite abelian group. Is this information in a table somewhere? If not, ...
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Covering maps of Riemann surfaces vs covering maps of $k$-algebraic curves
In going from Riemann surface theory to the theory of algebraic curves over fields $k$ that are not necessarily $\mathbb{C}$, I would like to understand more about how the notion of a covering map ...
- 57.6k
2
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2
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773
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In what sense Fraissean view point shows Model Theory can be done without any formal syntax and deduction rule?
In this post I want to look at an issue I was in doubt when looking at the comment of F. G. Dorais in the post In model theory, does compactness easily imply completeness?
F. G. Dorais remark was:
...
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construct random variable with a fixed level of Spearman Coefficient to another
In my quest to understand all things Spearman, consider the following problem:
Given random variable $x$ with known variance, $\sigma^2$, and $p \in [-1,1]$, one can construct a random variable $y$ ...
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1
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Equivariant map preserves stabilizer
Let $G$ be a group and $X$ a set equipped with a transitive right $G$-action. Further, let $c: X\to X$ be a $G$-equivariant map. Is it true that $\text{Stab}(x) = \text{Stab}(c(x))$ for all $x\in X$?
...
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2
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Building a multi-variable regression model [closed]
I have a large set of data points which have 18 dimensions to them. I know that these data points must follow a strict polynomial formula with no possible variance. Given that I have enough data (I ...
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1
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Baccarat and the way to win it [closed]
Recently, A friend of mine tell me something about "Baccarat"--a hot game of gambling.and he want to know some way to play it that can win more money. and he guess that math can help to do this. But I ...
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2
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318
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Alternate expresion of L-series coefficients
I was hoping that someone could help clarify a source of confusion for me, I must be doing and saying something wrong but I just don't know what:
Let $E$ be an elliptic curve over $\mathbb{Q}$ and let ...
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4
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1
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"Remove a vertex" map for right-angled Artin groups
Given a finite graph $\Gamma$, one has the
right-angled Artin group $A(\Gamma )$. Its generators $s_1, \dots s_n$ bijectively correspond to vertices of $\Gamma$ and the relators are $s_is_j=s_js_i$ ...
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What primes divide the discriminant of a polynomial?
Given a monic polynomial $p(t) = t^n + ... + c_1 t + c_0$ with integer (or rational) coefficients and with roots $a_1, \dots a_n$, we can compute its discriminant, which is defined to be $\prod_{i< ...
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2
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Get rid of tr() in SVM kernel trick
I designed a kernel function (to be used within SVM) which has the expression $tr(AB)$ in it. For efficient implementation of this, I was wondering if I could write $tr(AB)$ as an inner product: $\phi(...
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An "Elementary" Math Question Generalized (Ring Theory Perhaps)
The following question is posed in the book "The USSR Olympiad Problem Book: Selected Problems and Theorems of Elementary Mathematics"
"Prove that if integers a_1, ..., a_n are all distinct, then the ...
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3
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Definition of sheaves in wikipedia
In wikipedia, sheaves were first defined in the case of concrete categories (with usual identity and gluing axioms), then in the general case. (writing it as an "exact" sequence)
Do these two ...
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5
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0
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420
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Direct integrals and fields of operators
Suppose we have a measure space $(X,\mu)$ and a measurable field of Hilbert spaces $H_x$ on it. We can form the direct integral ${\cal{H}} = \int H_x \ d \mu$, which is a Hilbert space.
Suppose now ...
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2
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Why is GL(n,C)/U(n) a CAT(0) space?
The title says it all. In one of his answers to the question "Convex hull in CAT(0)" (I don't have the points to post a link, if someone doesn't mind link-ifying this that would be cool), Greg ...
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4
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2
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Finding the codomain of a monoid homomorphism
We have a monoid M, and a function $f: M \rightarrow \{0, 1\}$. We're promised that this function factors through a (surjective) homomorphism to a finite abelian group (considered as a commutative ...
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3
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Navigation solution for frictionless vehicles.
Looked around a bit and couldn't seem to find a similar question. (either that or it was worded with vocabulary above the multivariable calculus I've taken. :))
Roughly worded: I would like to ...
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2
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Properties of monodromy of a fibration?
Sorry for a loaded question.
I'm not an expert on those things, but I do know that a fibration gives rise to the representations of pointed fundamental group of the base on the cohomology of the ...
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6
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Curriculum vitae: including grants you've applied for, not received (or not yet received).
I've heard from multiple sources now that one's CV should include grants you've applied for, even if you didn't receive them or won't find out if you've received them until after your CV goes out. I ...
CommunityBot
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3
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Number Theory and Geometry/Several Complex Variables
This is a question for all you number theorists out there...based on my skimming of number theory textbooks and survey articles, it seems like most of the applications of geometry and complex ...
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4
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3
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Complex powers in finite fields
Is it possible to compute complex powers in finite fields? Given a $\in \mathbb{F}_p$ ($p$ prime), how can one compute $a^i$ per example?
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2
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3k
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Algorithm for decomposing permutations
Is there an algorithm for solving the following problem: let $g_1,\ldots,g_n$ be permutations in some (large) symmetric group, and $g$ be a permutation that is known to be in the subgroup generated by ...
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7
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1
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Reference for equivalent definitions of the genus
Let $X$ be a (edit: nonsingular) projective complex algebraic curve. The genus of $X$ can be defined as the dimension of the space of holomorphic $1$-forms on $X$, which in turn can be defined either ...
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Where are we working when we prove metamathematical theorems?
I am posting my comment from this question as a separate question, as was recommended to me.
(EDIT: I'm sorry if it ended up being too similar a question, I just wanted to phrase it in the ...
CommunityBot
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3
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2
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392
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Homology class orthogonal to image of Chern characters?
I had this simple question when formulating the Todd class question.
Does there exist an example of proper morphism $f:X\to Y$ together with nontrivial homology class $t\in H^*(X)$ such that for ...
CommunityBot
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5
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678
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Hurwitz Encoding
In "Random Matrices and Random Permutations" by Okounkov it says, "It is classically known that every problem about the combinatorics of a covering has a translation into a problem about permutations ...
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1
vote
1
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251
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Why is the Brauer Loop Scheme Not a Variety?
I am trying to grapple with the basics of scheme theory. Is the scheme defined by Spec[C[x,y,z]/(xy,yx,zx)] a variety? What do the points look like?
I suspect it represents points satisfying xy = ...
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3
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2k
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Matrices whose nullspace is nicely shaped
I'm looking for natural conditions on $a_{ij}$ to guarantee that the null space of the $n\times m$ matrix $A=(a_{ij})$ has a nice basis.
The null space of { {1,-2,1,0,0}, {0,1,-2,1,0}, {0,0,1,-2,1} } ...
CommunityBot
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2
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Computing Integral Closures
I'm wondering if there's an algorithm, or a program I can use, to compute integral closures. Specifically, what I have in mind are variants of questions of the sort: what is the integral closure of &#...
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3
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1
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Is D-module on flag variety of Lie algebra a scheme?
This question was motivated by the answers in D-module as quasi coherent sheaves on deRham stack. What I am interested in is the case of D-module on flag variety of Lie algebra. So,in this case, if we ...
CommunityBot
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Natural models of graphs?
Motivation
I want to capture the notion of natural models of finite graphs: How can natural predicates and natural relations on a given natural base class $D$ be defined? If this succeeds the ...
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4
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Intuitive explanation to Probability question [closed]
I have \$3. I flip a coin. If I get heads, I get \$1. If I get tails, I lose \$1. The game stops when I have \$0 or \$7. What is the probability I get \$7?
I solved this by creating a system of ...
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1
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1
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A rational point in the scheme of pointed degree n rational functions [0912.2227]
The following question is related to "Remark 2.2" in Christophe Cazanave's paper "Algebraic homotopy classes of algebraic functions". I decided to add the arxiv article-id to the questions title to ...
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3
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What assumptions and methodology do metaproofs of logic theorems use and employ?
In logic modules, theorems like Soundness and completeness of first order logic are proved. Later, Godel's incompleteness theorem is proved. May I ask what are assumed at the metalevel to prove such ...
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What's the relationship between Gauss sums and the normal distribution?
Let $p$ be an odd prime and $\left( \frac{a}{p} \right)$ the Legendre symbol. The Gauss sum
$\displaystyle g_p(a) = \sum_{k=0}^{p-1} \left( \frac{k}{p} \right) \zeta^{ak},$
where $\zeta_p = e^{ \...
CommunityBot
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2
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Measure between the counting measure and the Lebegue measure
There are subsets of the real line that has infinite counting measure, but Lebegue measure 0, so the Lebegue measure is used for measuring larger sets than the counting measure. My question is: Is ...
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7
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2
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A quadratic form
Let $q$ be a power of 2. Let $P$ be the set of polynomials in
$F_q [x]$ of degree d or less.
Let $\mathbb{Z}$ be the ring of integers. For any $f \in P$, let $\psi(f)$ be the
number of distinct ...
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4
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1
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Is the scalar extension functor for Chow motives conservative?
Denote $CHM(F)$ to be the category of Chow motives over a field $F$.
Let's consider an algebraic exension $E/F$, then
there is a natural extension of scalars functor $CHM(F) \to CHM(E)$.
I was ...
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1
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a proof that L_min is not in coRE?
Define $L_{min}$ to be the language of all minimal Turing machines, in some standard encoding. (A Turing Maching is minimal if it has the shortest encoding among all the TMs recognizing the same ...
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2
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Minimum-area bounding quadrilateral algorithm
There are a few algorithms around for finding the minimal bounding rectangle (OBB) containing a given (convex) polygon.
Does anybody know about an algorithm for finding a minimal-area bounding ...
CommunityBot
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2
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2
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3k
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How to attack this diophantine equation in 3 variables?
From link:
Find integers a, b and c such that:
987654321a + 123456789b + c = (a + b +
c)³
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2
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322
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Can "premodular" be relaxed as a condition for uniqueness of Bruguieres/Mueger modularization?
Suppose that C is a ribbon monoidal category with dominant ribbon functors F_1: C->D_1 and F_2: C->D_2 such that D_1 and D_2 are modular tensor categories, does it follow that D_1 and D_2 are ...
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2
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2k
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Taylor series of a complex function that is not holomorphic
I want to create Taylor series of a complex function that has complex conjugate in it. Obviously I cannot do a total derivative but derivations over real and imag parts exist.
Bonus question: Can I ...
CommunityBot
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6
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"Every scheme as a sheaf" references?
I have sometimes hard time reading papers that are written in the language of schemes being replaced by the functors they represent (I have especially homotopy scheme theory in mind).
I think the ...
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2
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Brauer-Manin obstruction and Tate-Shafarevich group of an Abelian variety
I read that the Brauer-Manin obstruction $A(\mathbb{A}_K)^{\mathbf{Br}}$ of an Abelian variety $A$ over a number field $K$ equals (naturally?) its Tate-Shafarevich group $\mathrm{III}(A)$.
Is this ...
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