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votes
2answers
1k views

Splitting book into chapters [closed]

I need a way to split output pdf-file (a book) into chapters on such a way that cross-references will survive. A simple example with a solution (based on answers below) can be found here
6
votes
3answers
283 views

Inverses in convolution algebras

Let $G$ be a locally compact totally disconnected group, and to make life easy let's suppose its Haar measure is bi-invariant. Let $C_c(G)$ be the space of locally constant complex functions on $G$ ...
5
votes
4answers
1k views

Patterns in Generalized Continued Fractions

According to the Wikipedia page on generalized continued fractions, $\pi$ can be given several GCF representations which have very regular structures; for example, one has the partial denominators as (...
2
votes
1answer
600 views

Understanding formula in Frenkel-Witten

I'm not the person to understand everything in Geometric Endoscopy and Mirror Symmetry, but some parts of it are reasonably clear to me. In particular, one of the main objects, mathematically ...
17
votes
2answers
2k views

Calculating the “Most Helpful” review

How would you calculate the order of a list of reviews sorted by "Most Helpful" to "Least Helpful"? Here's an example inspired by product reviews on Amazon: Say a product has 8 total reviews and ...
5
votes
3answers
921 views

Where does the generic triangle live?

This is a reformulation of my question Characterizing triangles unembeddedly. Motivation 1: There is such a thing as a generic group. In category theory this is done by constructing "theory" of ...
-3
votes
3answers
318 views

Dense section of sheaves of modules

Here is something that isn't yet very clear to me. Say, I've got a commutative ring A. I consider the affine scheme from A, so it's a sheaf of rings over Spec A. EDIT: And additionally let's say ...
8
votes
3answers
10k views

What's an efficient way to calculate covariance for a large data set?

What is the best algorithm for computing covariance that would be accurate for a large number of values like 100,000 or more?
9
votes
1answer
259 views

Factoring maps of handlebodies

Any map of finite graphs (1-dimensional CW-complexes) factors as a composition of a finite sequence of folds; an inclusion; and a finite-to-one covering map. There should be a corresponding result ...
4
votes
2answers
5k views

Finding correlation in large data, non-numeric sets

Suppose I collect a lot of data from a group of persons, like their height their weight color of eyes (chosen from eg the four categories blue/brown/black/other) sex day of the week the measurement ...
20
votes
6answers
2k views

“The” random tree

One time I heard a talk about "the" random tree. This tree has one vertex for each natural number, and the edges are constructed probabilistically. Connect vertex $2$ to vertex $1$. Connect vertex $3$ ...
11
votes
2answers
240 views

“Positive systems” in n * the (n-1)-simplex

Let S := the nonnegative integer solutions to {$a_1 + ... + a_n = n$}, and center := (1,1,1,...,1). Call a vector v generic if v.s = v.center <=> s = center. Then each generic v defines a positive ...
16
votes
3answers
2k views

Number theoretic spectral properties of random graphs

If G is a graph then its adjacency matrix has a distinguished Peron-Frobenius eigenvalue x. Consider the field Q(x). I'd like a result that says that if G is a "random graph" then the Galois group ...
22
votes
3answers
2k views

Highly transitive groups (without assuming the classification of finite simple groups)

What is known about the classification of n-transitive group actions for n large without using the classification of finite simple groups? With the classification of finite simple groups a complete ...
14
votes
3answers
3k views

References for equivariant K-theory

I want a good introduction to localization in equivariant $K$-theory. This introduction can be simple in several ways: I only care about torus actions. I only care about $K^0$. I only care about very ...
3
votes
1answer
340 views

Intuition for Nagata's altitude formula?

This is theorem 14.C on p.84 of Matsumura's commutative algebra. Let $A$ be a noetherian domain, and let $B$ be a finitely generated overdomain of $A$. Let $P \in Spec(B)$ and $p = P \cap A$. Then ...
1
vote
2answers
257 views

For which integers u,v does au=bv *approximately*? [closed]

Given two positive integers a,b what is the minimal integer n, so that there exist two positive integers ...
0
votes
1answer
387 views

Estimating probability of set membership

I have a number of discrete finite sets, $A_0$ through $A_n$. I do not actually know their contents, but I know the size of each set and the size of the intersection between $A_0$ and each of the ...
39
votes
8answers
4k views

What is a metric space?

According to categorical lore, objects in a category are just a way of separating morphisms. The objects themselves are considered slightly disparagingly. In particular, if I can't distinguish ...
14
votes
6answers
3k views

Definition of a strange attractor.

May be it's not the right place for this, but I don't know the right definition of a strange attractor. Wikipedia states that "An attractor is informally described as strange if it has non-integer ...
49
votes
1answer
5k views

Is it best to run or walk in the rain? [closed]

According to the Norwegian meterological institute, the answer is that it is best to run. According to Mythbusters (quoted in the comments to that article), the answer is that it is best to walk. My ...
7
votes
0answers
279 views

What morphisms / Morita equivalences induce the 2-periodicity isomorphisms of $KK$-theory?

In Kasparov's paper, the canonical isomorphisms $KK_* \rightarrow KK_{*+2k}$ are defined rather implicitely (by tensoring and stabilization). Are there morphisms of $C^*$-algebras which induce them (...
7
votes
4answers
5k views

Beamer hints and tips [closed]

I deleted a rant from this question because I felt it detracted from the given answer to the specific question. However, beamer is the "new kid on the block" in terms of giving talks (not that new!) ...
40
votes
15answers
11k views

What's so great about blackboards? [closed]

Many mathematicians seem to think that the only way to give a mathematics talk is by using chalk on a blackboard. To some, even using a whiteboard is heresy. And we Don't Talk About Computers. I'd ...
4
votes
1answer
330 views

correspondence between invariant forms and Lie groups

In Lie theory, one often asks about alternating forms on $\mathbb{R}^n$ which are invariant under some particular subgroup $G\subseteq GL_n(\mathbb{R})$, and there is always some algebra of invariant ...
1
vote
1answer
176 views

Group structure on an interval in Z[1/p]

Is there any natural group structure on the set $I_p = \{x \in \mathbb{Z}[1/p] \mid |x| < p/2\}$?
16
votes
3answers
856 views

A rigid type of structure that can be put on every set?

Call a type of structure rigid if any automorphism of such a structure is an identity. (This is a bit different from some other uses of the word, but hopefully I'll be forgiven.) For example, well-...
8
votes
1answer
540 views

Cohomology map induced by the group actions on homogeneous vector bundles

Here is a topological question which seems quite elementary. The answer to this question may be useful e.g. in estimating the orders of the automorphism groups of some algebraic varieties and in ...
4
votes
1answer
433 views

Is there a name for this topology?

Let $X$ be a set and let $f: X\longrightarrow X$ be a function on $X$. Introduce a topology on $X$ by the following basis of open sets: for any subset $S$ of $X$, let $B_S$ be the set of forward ...
28
votes
5answers
2k views

Do the signs in Puppe sequences matter?

A basic construction in homotopy is Puppe sequences. Given a map $A \stackrel{f}{\to} X$, its homotopy cofiber is the map $X\to X/A=X \cup_f CA$ from $X$ to the mapping cone of $f$. If we then take ...
7
votes
5answers
2k views

Why the rank of a locally free sheaf is well defined?

In Hartshorne p. 109 he defines a sheaf $\mathcal{F}$ of $O_X$-modules to be locally free if there is an open cover of $X$, s.t. on each $U$, $\mathcal{F}|U$ is a free $O_X|U$ module of rank $I$. Then ...
10
votes
1answer
3k views

What are tame and wild hereditary algebras?

What are tame and wild hereditary algebras? Are they related to hereditary rings? (Those are rings for which every left (resp. right) ideal is projective, equivalently, for which every left (resp. ...
10
votes
2answers
16k views

Beamer printout [closed]

I have just created a presentation using beamer, and I want the "one" command at the top of the file that creates a printable version. It is true that I can recompile having searched for all the \...
160
votes
33answers
61k views

What is convolution intuitively?

If random variable $X$ has a probability distribution of $f(x)$ and random variable $Y$ has a probability distribution $g(x)$ then $(f*g)(x)$, the convolution of $f$ and $g$, is the probability ...
2
votes
1answer
299 views

Is there an agreed name for partial ordering based on Pareto Dominance relation?

What's the correct mathematical name for the partial ordering on vectors based on what is sometimes called "Pareto Dominance"? Does Pareto Dominance have an alternative name in fields other than ...
4
votes
1answer
341 views

Does the non-commutative Chern class depend on the choice of connection?

In classical geometry the calculation of the Chern classes of a vector bundle using a connection is independent of the choice of connection. Does any such result hold for projective modules in non-...
3
votes
1answer
374 views

(n+1,r+1)-Theta space of (n,r)-Theta spaces?

I started writing nLab:Theta space. Not done yet, but while I am working on it: is there a good proposal for what the "$(n+1,r+1)$-$\Theta$-space of all $(n,r)$-$\Theta$-spaces" would be?
2
votes
1answer
133 views

Classical Calculi as Universal Quotients

As is well known, every differential calculus $(\Omega,d)$ over an algebra $A$ is a quotient of the universal calculus $(\Omega_A,d)$, by some ideal $I$. In the classical case, when $A$ is the ...
16
votes
2answers
543 views

Which quadratic forms on $\Lambda^2 V$ come from quadratic forms on $V$?

Let $V$ be a finite dimensional vector space, say over $\mathbf R$. Let $g \in S^2 V^*$ be a quadratic form on $V$. Then $g$ induces a quadratic form $\Lambda^2 g \in S^2 \Lambda^2 V^*$ on $\Lambda^...
5
votes
2answers
428 views

Quantum Frobenius II

In a previous question, I asked how Lusztig's quantum Frobenius generalizes the classical Frobenius map on a variety over a finite field. I was directed to a very interesting paper by Kumar and ...
37
votes
11answers
13k views

Blackboard rendering of math fonts

I learned most of my math font rendering from watching others (for example, I draw ζ terribly). In most cases it is passable, but I'm often uncomfortable using fonts like Fraktur on the board. ...
9
votes
3answers
1k views

Is there a Faa di Bruno-like formula for composition of three functions?

Faa di Bruno's formula (MathWorld, Wikipedia) gives the kth derivative of f(g(t)) as a sum over set partitions. (I'm not sure how well-known the combinatorial interpretation is; for example see a ...
2
votes
1answer
319 views

Basis for Universal Calculus

Can anyone give an explicit basis of the universal (noncommutative) differential calculus over an algebra $A$ with basis ${e_i}$. (The universal calculus over $A$ is the kernel of the multiplication ...
2
votes
1answer
220 views

Spectra of rings that are projective module over a subring

This question is motivated from my last question here. I wonder if one has a ring A and an over-ring of this ring say B, and if we know that B is a projective A-module can we have a particular idea of ...
4
votes
4answers
918 views

Deconvolution of gamma distributions

If the sum of two independent random variables is gamma distributed does this imply that the individual random variables are also gamma distributed. I suspect that the answer is no, but I do not know ...
7
votes
3answers
733 views

Symmetric Powers, Tableau and Wreath Products

Let V and W be irreducible representations of $S_n$ and $S_m$ over a field of characteristic 0. Then the Littlewood-Richardson coefficients allow us to compute the isomorphism type of the induced $S_{...
6
votes
7answers
1k views

CLT for stationary sequences with infinte variance

There is a well-known central limit theorem for as a stationary sequences. If $( X_n )_n$ is a sationary sequence and $E X_n=0$ then under suitable mixing conditions the sequence $S_n := n^{-1/2}\...
2
votes
2answers
5k views

Examples of random variables

I'm looking for a list of examples of random variables to use in teaching a measure-theoretic probability course. For example, the Rademacher functions are an explicit construction of independent ...
8
votes
3answers
803 views

Is there any Grothendieck Riemman Roch theorem for general stack ?

It seems that there is no g.r.r for stack yet according to dejong. Does anyone know anything about it? But as you might know, there are some complex manifold which is not scheme having atiyah singer ...
5
votes
1answer
599 views

Local Joyal-simplicial presheaves?

It is well known that left Bousfield localizations of the global functor model category $Func(C^{op}, SSet_{standard})$ of functors with values in simplicial sets equipped with the standard model ...

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