[reference-request] tag is for questions that the poster wants to seek for references (books, articles, etc) in a subject. Please do not use this as the only tag for a question.
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0answers
20 views
How should I study complex (ordinary) differential equations (reference-request related)?
I'm currently studying complex analysis at a university (undergraduate) but my lecturer is doing a little bit of ordinary differential equation theory too, inclduing hypergeometric functions.
As I ...
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0answers
29 views
conditions for a finite group with order $p^aq^b$ to have a sylow normal subgroup
It is well-known that Burnside has proved that a finite group $G$ with order $p^aq^b$, where $p, q$ are distinct primes and $a, b\in \mathbb{N}$, is solvable.
So I want to know whether there are some ...
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0answers
28 views
Modern differo-integral equations analysis
What are modern techniques for analyzing diffeo-integral equations?
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3answers
76 views
Is $A$ a Borel set?
Let be $X$ a metric compact space and $(G,+)$ a topological compact abelian group. Let be $\mathcal{A}$ the Borel $\sigma$-algebra of $X$ and $\mathcal{B}$ the Borel $\sigma$-algebra of $G$. ...
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0answers
15 views
Name for maximum transition probability
Let $p(x,y)$ denote the transition probability of a markov chain. Similarly, let $p^n(x,y)$ be the n-step transition probability. My question is, is there a formal name for $S(x,y):=\sup_n p^n(x,y)$. ...
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0answers
27 views
Extension of Choi's theorem on extreme completely positive maps
In this paper Man-Duen Choi gave a criteria for a completely positive map to be extreme. For convenience I am writing it below.
Let $\phi:\mathcal{M}_n\rightarrow\mathcal{M}_m$. Then $\phi$ is
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2answers
36 views
Number of prime divisors of element orders from character table.
From wikipedia:
It follows, using some results of Richard Brauer from modular representation theory, that the prime divisors of the orders of the elements of each conjugacy class of a finite group ...
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0answers
8 views
Reference Request: Geometric figures where each dimension is dependent on a vertex.
I have an oddly specific reference request.
I keep encountering a class of problems where, loosely speaking, I have a geometric figure in $\mathbb{R}^n$ where each dimension is "supported" by a ...
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1answer
82 views
Where do Chern classes live? $c_1(L)\in \textrm{?}$
If $X$ is a complex manifold, one can define the first Chern class of $L\in \textrm{Pic}\,X$ to be its image in $H^2(X,\textbf Z)$, by using the exponential sequence. So one can write something like ...
2
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0answers
45 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
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2answers
84 views
Prerequisites to category theory
I am trying to delve into category theory but my math background is quite limited.
What books would be recommended to get me up to speed with what is needed to grasp the concepts?
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0answers
19 views
Which graphs satisfy this property?
I am currently looking into a conjecture in graph theory, known as the Jackson conjecture (1992). It says the following, in an equivalent formulation to its equivalent statement:
*Conjecture*Every ...
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0answers
24 views
Reference Request: Background/Extention on Bill Thurston's Lecture 'The Mystery of Three-Manifolds'
I found Thurston's lecture The Mystery of Three- Manifolds fascinating but, well, mystifying. For those with insufficient time to watch the video, he establishes correspondence (in his very intuitive ...
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1answer
91 views
$C_0(X)$ is not the dual of a complete normed space
Let $X$ be any locally compact Hausdorff space and assume that it is not compact.
I've heard that the Banach space $(C_0(X),\|\!\cdot\!\|_\infty)$ is not isometrically isomorphic to the (norm) dual of ...
3
votes
1answer
46 views
On the converse of Sard's theorem
Let $f: M \rightarrow N$ be a smooth map between two submanifolds of $\mathbb{R}^{m}$, $\mathbb{R}^{n}$ respectively. Sard's famous theorem asserts that the set of critical values $C$ of $f$ has ...
