# All Questions

116,202
questions

**0**

votes

**2**answers

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

**3**answers

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

**4**answers

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

**1**answer

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

**2**answers

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

**3**answers

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

**3**answers

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

**3**answers

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

**1**answer

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

**2**answers

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

**6**answers

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

**2**answers

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

**3**answers

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

**3**answers

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

**3**answers

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

**1**answer

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

**2**answers

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

**1**answer

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

**8**answers

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

**6**answers

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

**1**answer

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

**0**answers

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

**4**answers

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

**15**answers

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

**1**answer

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

**1**answer

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

**3**answers

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

**1**answer

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

**1**answer

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

**5**answers

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

**5**answers

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

**1**answer

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

**2**answers

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

**33**answers

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

**1**answer

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

**1**answer

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

**1**answer

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

**1**answer

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

**2**answers

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

**2**answers

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

**11**answers

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

**3**answers

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

**1**answer

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

**1**answer

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

**4**answers

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

**3**answers

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

**7**answers

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

**2**answers

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

**3**answers

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

**1**answer

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 ...