# All Questions

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### 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
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 $G$ ...
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 (...
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 ...
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 ...
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 ...
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 ...
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?
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 ...
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 ...
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 $3$ ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 (...
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!) ...
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 ...
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 ...
176 views

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

Is there any natural group structure on the set $I_p = \{x \in \mathbb{Z}[1/p] \mid |x| < p/2\}$?
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-...
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 ...
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 ...
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 ...
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 ...
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. ...
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 \...
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 ...
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 ...
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-...
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?
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 ...