This tag is for questions where the poster seeks references (books, articles, etc.) about a particular subject. Please do not use this as the only tag for a question.
2
votes
0answers
42 views
smoothness structure on a set
I'm reading Milnor's 'characteristic classes', and in the first chapter he defines smoothness structure on a set M, which is confusing for me, as what follows:(these are not Milnor's words so please ...
2
votes
0answers
126 views
Quotation and reference requested
I am looking for a quotation I once read, and I think it was by a famous mathematician. It is in the context of the balance between reading and writing mathematics, and said something like "I enjoy ...
2
votes
0answers
33 views
Combinatorics: Selecting non-adjacent subsets or objects arranged in a circle
Lets say you have a circular table that seats $n$ people and $b\lt n -1$ identitcal boys. If you were to divide the boys into $k$ teams of size $\geq 1$, how many ways are there to seat the boys so ...
2
votes
0answers
12 views
Linearly compact module
I must prove some results which relative to linearly compact module, but it is difficult to find all references. Two of them are :
1) T. Onodera, Linearly compact modules and cogenerators. J. Fac. ...
2
votes
0answers
52 views
Classification of Bieberbach groups
Does anybody know if there exists a list of the four dimensional Bieberbach groups presented by generators and relations on the web?. I know there exists the book Crystallographic Groups of ...
2
votes
0answers
36 views
Crossing number of simple undirected graph
There's a well-established result which provides a lower bound for the crossing number of any simple undirected graph.
However, is there any known result for an upper bound in this setting?
2
votes
0answers
55 views
Reference Request: Regge Symmetry “Angle-Edge” Duality
A tetrahedron in hyperbolic 3-space can be defined (up to isometry) by the measures of its dihedral angles, $(a, b, c, a^\prime, b^\prime, c^\prime)$, with $a$, $b$, $c$ along edges that meet at a ...
2
votes
0answers
64 views
Pullbacks as manifolds versus ones as topological spaces
Let $Y_1\overset{f}{\longrightarrow}X\overset{f_2}{\longleftarrow} Y_2$ be smooth maps with a common target. Suppose that we have a pullback $Z$ of the diagram in (Mfd).
Questions:
Suppose that we ...
2
votes
0answers
122 views
Boundedness of expected reward Markov chain (may be related to discret $M/M/\infty$ queue)
[EDIT]:
I read a bit on $M/M/\infty$ queue and it may not be the right comparison and my notation may be confusing (I'm in discrete time and $\lambda,\mu$ look likes rates when they are probability). ...
2
votes
0answers
17 views
Semilattice of functions with meet as “common restriction”
Is there an established name for the operator $\bigwedge$ which takes a nonempty family $F$ of functions and returns their "common restriction":
$$
\bigwedge F = f|_{\bigcap_{f_0, f_1 \in ...
2
votes
0answers
35 views
Set of Morse-Smale Functions is Dense in Euclidean Space
In much of the Morse Theory literature, it seems that we always assume $M$ is a smooth closed (or compact) manifold so that we get theorems like:
The set of Morse-Smale gradient vector fields on ...
2
votes
0answers
39 views
Uniform integrability, book
I search about this theme, in the books is as exercise. But I want some more theory.
What book recommend?
2
votes
0answers
50 views
Survey papers in real analysis
Can somebody recommend a good survey paper (or something similar to it) for real analysis?
I'm looking for something much shorter than a $200$ page text-book, but should still tell what the main ...
2
votes
0answers
88 views
suggestion for video lectures on algebraic topology
can anyone suggest me any good video lecture series forr algebraic topology other than N.J.wildberger video.If it is equivalent to munkres topology(algebraic topology section)
it should be great.
...
2
votes
0answers
102 views
Existence of solution of PDE using Galerkin method
I wonder if anyone can give me a reference to a paper/book that rigorously addresses how to use the Galerkin method to show existence/uniqueness of a PDE. The usual suspects (Evans, Renardy, ...) do ...
2
votes
0answers
107 views
A book suggestion on algebraic number theory
I'm looking for a book on Algebraic Number Theory, which is somewhat in Analytic spirit.
In particular, I want to see the precise connection between
$$\delta_{f}(p)=\{a\pmod p : f(a) \equiv 0 ...
2
votes
0answers
64 views
What is the correct technical term for this generalization of an integer partition?
Given a vector $v$ with non-negative integer coordinates, is there a technical term for an unordered tuple of vectors $(v_1,\dots, v_k)$ with non-negative integer coordinates such that
$v_1+\dots+v_k ...
2
votes
0answers
41 views
Global sections of covering spaces
Let $p:C\to X$ be a covering space having a global section $s:X\to C$. I can show that this implies that $s(X)$ is disconnected from the rest of $C$.
Is there any reference where this is explicitly ...
2
votes
0answers
67 views
Double sequences and series double.
I would like a good reference devoted exclusively to double sequences and series double. At the moment I have only this reference in google.
Thanks in advance.
2
votes
0answers
51 views
Resolutions over finite dimensional algebra
Let $A$ be a finite dimensional algebra over a field $k$ and global dimension of $A$ is finite. I want to study $A$ as a bimodule i.e. as $A^e=A \otimes A^{op}$-module. It is easy to see that ...
2
votes
0answers
72 views
Solved problems book in Mathematical statistics
Are there some solved problems book in Mathematical statistics?
Or some set of solutions for qualifying exams preparation?
Say to the level of
Casella, Berger, Statistical Inference, or,
Hogg et ...
2
votes
0answers
40 views
Tight bounds for harmonic measure
I recently came across a question concerning harmonic measure here, and was wondering if there is a good reference summarizing different methods of estimating harmonic measure?
Specifically, I would ...
2
votes
0answers
46 views
tangents of infinite sums — reference request
This section of Wikipedia's List of trigonometric identities was, as far as I know, written entirely by me. For a time, it dealt only with finite sums, and said something like this:
$$
...
2
votes
0answers
45 views
Terminology: is there a term for one order being on a geodesic between two others in the Cayley graph?
Think about the graph whose nodes are total orders on a finite set, and whose edges connect orders that only differ on two elements. This is actually a Cayley graph of $S_n$, but I don't want to fix ...
2
votes
0answers
54 views
good books on measures and integration theory in infinite-dimensional spaces
I am looking for good books on measures and integration in infinite-dimensional spaces, covering generalizations of Wiener measure and their properties.
2
votes
0answers
68 views
How to express, say, the Hausdorff property of a topological space using categories. (And a request for general advise in such practices)
I am new to Category theory and for the sake of the practice, I am interested in revisiting and expressing those concepts that I am familiar with --however basic--, in the language of categories. ...
2
votes
0answers
55 views
$\sum_p z^p$ where $p$ is prime
I've started reading Shakarchi's Complex Analysis, and I thought about something interesting.
If I haven't mistaken, for any subsequence $A\subset \mathbb{Z}^+$, $\sum_{n\in A} z^n$ has radius of ...
2
votes
0answers
67 views
Multiplicativity of the Euler characteristic
One can find all over the internet that it is well-known (and obvious) that given a fiber bundle $F \to E \to B$, the equality $\chi(E) = \chi(F)\chi(B)$ holds ($\chi$ is the Euler characteristic). ...
2
votes
0answers
48 views
What is a good resource for functional derivatives and functional determinants?
What is a good resource for functional derivatives, functional determinants, etc.? What is the branch of mathematics dealing with those things? It is not in my functional analysis book. What is a ...
2
votes
0answers
62 views
Where read recent developments in Math presented in a way that is easy to understand?
I posted a similar question a few months ago, but I don't think people understood my question. I often find articles such as this which discuss exciting developments in science. I have a great ...
2
votes
0answers
42 views
The effect op graph operations on the chromatic number (Papers/Books)
Can anyone please direct me to a paper or even a textbook which would provide a good read on how graph operations influence the chromatic number of a graph?
Thanks.
2
votes
0answers
31 views
Quotients of the CAR algebra
Recently, I heard about the following theorem: each nuclear separable operator space is a completely bounded quotient of the CAR algebra. Yet, I have no idea who and where proved this theorem ...
2
votes
0answers
56 views
Standard parabolic Lie subalgebras and conjugacy
Let $\mathfrak g$ be a given semisimple Lie algebra with corresponding adjoint Lie group $G$. A parabolic subalgebra is any subalgebra containing a Borel subalgebra.
We can pick a Borel ...
2
votes
0answers
34 views
Fibered Product of Subcategories
Is there a general construction or existence theorem for the fibered product of two subcategories of some ambient category? What sort of problems might one run into? Does this require a 2-categorical ...
2
votes
0answers
163 views
Explanation/reference for method of steepest descent (integration method, not gradient descent)
I am wondering if someone could point me to a resource where I could learn the method of steepest descent. Unfortunately, my knowledge of calculus is limited to a college multivariable calculus ...
2
votes
0answers
116 views
Birthday paradox for non-uniform distributions
The classic birthday paradox considers all $n$ possible choices to be equally likely (i.e. every day is chosen with probability $1/n$) and once $\Omega(\sqrt{n})$ days are chosen, the probability of ...
2
votes
0answers
63 views
Kolmogorov's unit interval probability space
Somewhere I've heard that Kolmogorov proved that for all practical purposes, the probability space $$(\Omega,\mathcal F,\mathbb P)$$ that he invented could be taken without loss of generality to be ...
2
votes
0answers
44 views
Subgroups of semi-direct products arising from fixed-point-free actions
I am interested in subgroups of semidirect products arising from fixed-points-free actions. Suppose you have a group $A$ acting fixed-point-freely on a group $N$. Can we describe completely the ...
2
votes
0answers
39 views
Bijection between $\operatorname{GL}_n(F)/\operatorname{GL}_n(O)$ and lattices in $F^n$
I've come across mention of a bijection between lattices in $F^n$ ($F$ a field, in my case $\mathbb{C}(\!(t)\!)$) and elements of $\operatorname{GL}_n(F)/\operatorname{GL}_n(O)$, where $O$ is the ring ...
2
votes
0answers
49 views
a certain property of flatness
This question is related to this post.
Let $X$ sit in some affine space. Suppose $f: X\rightarrow \mathbb{C}$ is a flat family and the fiber over some nonzero point is a complete intersection. ...
2
votes
0answers
41 views
Wiener's Lemma on Locally Compact Abelian Groups
The version of Wiener's lemma that I know, from Katznelson's Introduction to Harmonic Analysis, is $\lim_{N\to\infty}\frac{1}{2N}\sum_{-N}^{N} |\hat{\mu}(n)|^2 =\sum_{t\in\mathbb{T}}|\mu(\{t\})|^2$.
...
2
votes
0answers
35 views
References needed for gradient flow
Can anyone recommend lecture notes or (not too obscure) books that teaches me about gradient flow and what it has to do with PDEs? I did search but usually the material talks about dynamical systems ...
2
votes
0answers
64 views
Classifying continuous characters $\epsilon:\mathbf{C}^\times\to \mathbf{C}^\times$.
I recently saw the following claim: Let $\mathbf{C}$ denote the field of complex numbers together with its usual topology. If $\epsilon:\mathbf{C}^\times\to \mathbf{C}^\times$ is a continuous ...
2
votes
0answers
146 views
Equivalence books for Bourbaki's Element of Mathematics
I find that the arrangement of basic topics in Bourbaki's book is quite elegant, I want to learn mathematics following this order. But one problem is the books is too old and sometimes too complex for ...
2
votes
0answers
39 views
Finite-dimensional representations of the Lie algebra of vector fields on a circle
I have just began to study infinite-dimensional Lie algebras and I am curious whether the Lie algebra $L$ spanned by the vector fields $z^n \partial/\partial z$, $n=0,1,2,3,\dots$ admits any ...
2
votes
0answers
41 views
JSJ-decompositions of groups and 3-manifolds: a reference request
I am, for whatever reason, interested in learning about the JSJ-decomposition of groups. Having asked around a bit, it was suggested I first learn about what is happening in the manifolds and then ...
2
votes
0answers
87 views
Integral Geometry Reference Request
I am looking for a good introductory reference (book, lecture notes, survey article) on integral geometry. I am especially interested in the Crofton formula in $\mathbb{R}^n$ and its extensions to ...
2
votes
0answers
99 views
Can anybody suggest me references for functional analysis? My main concern is to do examples as much as i can.
Can anybody suggest me references for functional analysis? My main concern is to workout examples as much as i can do. Also if there is any web resources to help mein this regard ?
Thanks for giving ...
2
votes
0answers
51 views
Sufficient condition for surjectivity of a morphism of group schemes
Let $G$ be a group scheme over a field $F$, and let $f:G\to G$ be a homomorphism. Written in my notes, I have the following statement:
To check surjectivity (on $F$-rational points), it suffices ...
2
votes
0answers
125 views
Poincaré-Hopf theorem using Stokes
The wiki entry on the Poincaré-Hopf theorem claims that it "relies heavily on integral, and, in particular, Stokes' theorem". However, in the sketch of proof given there which is more or less the one ...
