# Tagged Questions

This tag is used if a reference is needed in a paper or textbook on a specific result.

**3**

votes

**3**answers

311 views

### Reference request: a guide through quantum probability

Could you point out a comprehensive reference book (or more than one, if it is the case) on Quantum Probability that introduces the subject and then gradually builds up to the edges of contemporary ...

**1**

vote

**0**answers

99 views

### Explicit description/calculation of norm group of ideles of characteristic $p$ global field

I posted the same question earlier in stack exchange,
(http://math.stackexchange.com/questions/1130391/algebraic-proof-of-2nd-inequality-of-global-class-field)
thinking it is most definitely not a ...

**1**

vote

**1**answer

167 views

### Heegner points on elliptic curves

I want to know about Heegner point computations for a CM elliptic curve. What is the best reference book/paper for reading?

**11**

votes

**1**answer

341 views

### Schemes over topological rings

I have recently been interested in studying an extension of 'usual' algebraic geometry to take into account the topology of $R$ in the definition of the affine scheme $\mathrm{Spec}\, (R)$ when the ...

**9**

votes

**0**answers

205 views

### Proving regularity properties from forcing axioms

It's well known that PFA implies projective determinacy. It's also well known that PD implies that all projective sets are Lebesgue measurable, have the Baire property, etc.
Is there a direct proof ...

**0**

votes

**1**answer

146 views

### Totally non hereditary $C^{*}$-subalgebras

Assume that $B$ is a $C^{*}$ subalgebra of $A$. We say $B$ is totally non hereditary subalgebra of $A$ if not only $B$ is not a hereditary subalgebra but also it is not isomorphic to any ...

**5**

votes

**0**answers

190 views

### Legendre polynomials and formal groups

Let $P_n(x)$ be Legendre polynomials:
$$\frac{1}{\sqrt{1-2tx+t^2}}=\sum\limits_{n=0}^{\infty}P_n(x)t^n.$$
Usual arguments from the theory of formal groups allow to
prove that for any $n$
...

**3**

votes

**1**answer

111 views

### Lower bound for the $p$-th absolute moment of a sum of random variables

Suppose that $X_1,\ldots,X_n$ are independent random variables with $\operatorname E X_k=0$ and $\operatorname E |X_k|^p<\infty$ with $1<p<2$ for each $1\le k\le n$. I am interested in the ...

**8**

votes

**0**answers

106 views

### Comparing a Chevalley basis with the canonical basis of the adjoint module?

First some background: Given a simple Lie algebra $\mathfrak{g}$ over an algebraically closed field of characteristic 0 such as $\mathbb{C}$, fix a Cartan decomposition $\mathfrak{g} = \mathfrak{h} ...

**3**

votes

**0**answers

56 views

### Are all $k$th-longest-tour problems equally hard?

It is well known, that determining the shortest and, the longest Hamilton Cycle of a complete graph with real edge weights are algorithmically two sides of the same medal: one transforms to the other ...

**14**

votes

**0**answers

365 views

### Can there be arbitrarily many cubic fields unramified outside $\{p,\infty\}$?

Observe, trivially, that since quadratic fields correspond to rational integers modulo squares (viz. discriminants), there are (roughly about, but certainly at most) $2^{|S|+1}$ quadratic fields ...

**0**

votes

**1**answer

128 views

### Ambient isotopy of the diagonal submanifold in product space

Given a closed manifold $M^n$ and its $k$-fold product space $M^n\times\cdots\times M^n$,Can the diagonal submanifold $\Delta:=\{(m,\cdots,m)\in (M^n)^k\mid m\in M\}$ be isotopied to the submanifold
...

**17**

votes

**1**answer

723 views

+50

### On Grothendieck's idea on his Standard Conjecture B

Let me recall the Standard Conjecture B (see [1,2] below):
The $\Lambda$-operation of Hodge theory is algebraic.
It more or less says that the partial inverse to “cupping with the class of a ...

**5**

votes

**0**answers

100 views

### What's the variance in the Six Degrees model?

Recall the six degrees of Kevin Bacon game. You can even play the game at The Oracle of Bacon, and their search works via Breadth First Search.
I interpret the punchline as saying that if I start ...

**1**

vote

**0**answers

122 views

### Intuition for hereditary torsion theories

I'm looking for intuition and references for the definition of a hereditary torsion theory and two facts found here. First, the definition and facts:
Definition. A torsion theory $(\mathcal ...

**6**

votes

**2**answers

154 views

### Geometric dominating set: NP-complete?

Let $G=(V,E)$ be a geometric graph, a graph embedded in the plane whose edge lengths are
the Euclidean distance between its endpoint vertices.
Say that a set of vertices $D \subseteq V$ is a geometric ...

**3**

votes

**1**answer

225 views

### book about string theory a la Von Neumann [duplicate]

Can we summarize string theory (in its actual state) in some principles and fundamental equations like electromagnetism, general relativity, quantum mechanics and classical mechanics ?
I am looking ...

**0**

votes

**0**answers

47 views

### Shuffle multiplication and generalized Leibniz rule in tensor calculus

The headline already says it: Is anybody (except me) aware of this formula for higher total covariant derivatives of tensor products?
It is the simplest application of the commutative shuffle product ...

**2**

votes

**0**answers

103 views

### Does this symmetrization operator have a name? Any theory?

Consider a function $f(x_1,\ldots,x_n)$ of $n$ complex variables. Define
$$f_{\mathrm{symm}}(x_1,\ldots,x_n) =
2^{-n}\sum_{\varepsilon_1,\ldots,\varepsilon_n=\pm 1}
...

**4**

votes

**1**answer

141 views

### reference for higher spin - not gravitational nor stringy

Other than the papers of Berends, Burgers and van Dam, are there any papers that study the general case of deforming a free field theory with higher spin fields to be interactive?

**7**

votes

**2**answers

801 views

### Surveys of the items of Erdős' “toolbox”

Could you point out some survey papers and monographs that highlight the kernel of tricks, techniques, and tools that Paul Erdős employed the most in his research work (in particular in graph theory, ...

**6**

votes

**1**answer

95 views

### What is the original reference for disorientations on tangle diagrams?

There are several invariants whose "natural" domain is a category of disoriented tangles, that is tangles which are piecewise-oriented, but which contain points called `disorientations' at which the ...

**11**

votes

**1**answer

230 views

### Papers about decentralized search and cluster

I just start an independent study about small world network and clusters and I try to find papers about decentralized search and clusters.
Can anyone give me some references? Thanks!
EDIT (David ...

**4**

votes

**1**answer

226 views

### Besse p134 Riemann tensor in dimension 4

Does someone have a reference for the proof of 4.72 page 134 of Einstein Manifolds? It is said that
$$\check{R}-\vert R\vert^2g/4=S/3 (Ric-S/4) +2\mathring{W}(Ric -S/4) $$
because we are in dimension ...

**2**

votes

**0**answers

42 views

### Decidability of first order theory of subclasses of posets

Is the first order theory of finite posets known to be undecidable?
Does anyone know a survey about such results?

**3**

votes

**3**answers

317 views

### Find an integrable, positive, unbounded, analytic function

Is there a standard example of a function $f \in L^1( \mathbb R)$ which is analytic, positive, integrable but not bounded?
An example which comes immediately to mind is to take the series of narrower ...

**1**

vote

**0**answers

127 views

### Help in understanding “Local well-posedness for the Maxwell-Schrodinger system”

Is there someone who knows the following paper
"Local well-posedness for the Maxwell-Schrodinger system" by M.Nakamura and T.Wada.
I'm trying to study it but I've some doubts. In particular I'm not ...

**4**

votes

**1**answer

147 views

### Tiling with restricted overlap

Non-overlapping tilings of regions is a well-studied topic.
I wonder if the following variant has been considered:
A tile can be partitioned into several regions, where such regions from different ...

**3**

votes

**1**answer

247 views

### Reference request for the relation of Ext groups and bar construction

I need a reference for the description of Ext groups in mixed categories (i.e. abelian categories with a weight filtration and semisimple graded quotients) by using the bar complex, as mentioned in ...

**2**

votes

**1**answer

133 views

### Legendre transform and Lipschitz approximation

Let $(X,d)$ be a compact metric space and $f:X \to \mathbb{R}$ a real valued continuous function. Let us agree that a modulus of continuity means concave, nondecreasing, uniformly continuous function ...

**0**

votes

**0**answers

26 views

### Interesting properties of complex Gateaux derivatives

The complex Gateaux derivatives are for $\psi=\psi_{1}+i\psi_{2}$ and functional F
$dF(\psi,\xi)=d_{\psi_{1}}F(\psi_{1},\xi_{1}-id_{\psi_{2}}F(\psi_{2},\xi_{2}$ and ...

**3**

votes

**1**answer

92 views

### Reference for exercises with solutions for affine Lie algebras

I am doing self-study of affine Lie algebras, and while I have all recommended reference material, I find it hard to prepare for the exam.
It was quite easy to study finite-dimensional simple Lie ...

**14**

votes

**2**answers

866 views

### Open problems in Berkovich geometry

I would like to know if there is a state of the art recent reference on non-archimedean analytic spaces mentioning/listing open problems, conjectures, unresolved questions in the theory (*). I have ...

**2**

votes

**1**answer

79 views

### Is a matrix element of a norm continuous representation always a trigonometric polynomial?

I asked a similar question for the case of compact groups not long ago in math.stackexchange. Now I understand that the answer was "yes", and I want to modify that question. This is also related to my ...

**6**

votes

**1**answer

129 views

### Trigonometric polynomials on non-compact and non-abelian groups

I asked this initially in math.stackexchange, but it disappeared almost immediately, so I hope it will be proper to aks this here.
Hewitt and Ross define trigonometric polynomial on a locally compact ...

**7**

votes

**2**answers

204 views

### Recent trends in effective analysis

The references listed at http://en.wikipedia.org/wiki/Computable_analysis have all been published 30-15 years ago. Are the approaches which these references expose still up-to-date and relevant to the ...

**3**

votes

**0**answers

174 views

### Is $\mathcal{K}(H)$ injective $\mathcal{B}(H)$-module?

Does anyone know if the right Banach $\mathcal{B}(H)$-module $\mathcal{K}(H)$ is injective?
The same question for $\ell_\infty$-module $c_0$. Both these modules are not dual, so standard arguments ...

**3**

votes

**3**answers

262 views

### Survey papers of results (relevant to mathematics) produced during research on the relationship between mathematics and music theory

It is well-known that there is a relationship between music and mathematics, and there are many references that explore this topic (for example, Benson's book).
However, I would like to ask if there ...

**7**

votes

**1**answer

168 views

### A question on the twistor space of a manifold

Let $M$ be either (a) self-dual conformal 4-manifold, or (b) hypercomplex $4n$-manifold.
In either case one can construct the twistor space $Z$ (in the case (b) $Z=\mathbb{C}\mathbb{P}^1\times M$ as a ...

**2**

votes

**0**answers

93 views

### Isomorphic subcategories of directed graphs and presets

For the purposes of this post, a digraph (directed graph) has neither loops nor multiple parallel edges, and a preset is an ordered pair consisting of a set $S$ and a preorder (viz., a reflexive and ...

**1**

vote

**1**answer

64 views

### Are Carnot groups (as Carnot Caratheodory metric spaces) doubling?

I need to use the Lebesgue differentiation theorem for doubling metric measure spaces and was wondering if Carnot groups are doubling. If yes, is there any reference you can point me to? Thank you.

**11**

votes

**2**answers

738 views

### nonstandard models and mathematical theorems

Is there a first order statement about the natural numbers (not nonstandard analysis) such that the truth of the statement is easier to see in a nonstandard model? In other words, do nonstandard ...

**3**

votes

**1**answer

177 views

### Special linear groups over function fields

Let $p$ be a prime number, and let $q$ be a finite power of $p$. Denote by $F_q$ the unique field with $q$ elements.
What is known about the structure and properties of $\mathrm{SL}_2(F_q[t])$ as ...

**5**

votes

**0**answers

123 views

### Characterizations of an exotic measure on the open sets in the circle $S^{1}$

Suppose that $U\subseteq S^{1}$ is open where $S^{1}=\{z\in\mathbb{Z}:|z|=1\}$. Then define $\mu_{n}(U)=\max_{t\in S^{1}}\frac{1}{n}\cdot|\{k\in\{1,...,n\}|t\cdot e^{\frac{2\pi ik}{n}}\in U\}|$. ...

**7**

votes

**0**answers

93 views

### Approximate singular value decomposition in Banach spaces

I am interested in generalisations to Banach spaces of the following construction, which relates to the singular value decomposition of a finite-dimensional linear map. If $V$, $W$ are ...

**3**

votes

**1**answer

371 views

### Do hom-sets really live in the category Set?

This isn't really a research-level question (sorry!), but I asked on
math.se (link), and though the question was upvoted a few times, I didn't
get any answers. So since there may well be more ...

**1**

vote

**0**answers

55 views

### Invariance of the Noether charge

The paper http://epubs.siam.org/doi/abs/10.1137/1023098 (Generalizations of Noether’s Theorem in Classical Mechanics, by Willy Sarlet and Frans Cantrijn) mentions "an interesting property of the ...

**5**

votes

**1**answer

432 views

### Consequences of ZF+“all subsets of reals are Lebesgue measurable”

(I'm not sure if this is entirely suitable here so feel free to close it if it's not.) The statement "there is a Lebesgue measure on $\mathbb{R}$($2^\omega$)" means: there is a total $\sigma$-additive ...

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vote

**2**answers

252 views

### A question on the Lebesgue differentiation theorem

In the paper [Jessen, B., Marcinkiewicz, J., and Zygmund, A. Note on the differentiability of multiple integrals. Fundamenta Mathematicae 25.1 (1935): 217-234] it is considered the limit
$$
...

**0**

votes

**0**answers

36 views

### Regularity of solutions of strongly elliptic system: how smooth must the boundary be?

Let $\Omega \subset \mathbb{R}^d$ be a bounded domain with the boundary of class $C^{1,1}$.
Let $A$ be a selfadjoint operator acting in $L^2(\Omega;\mathbb{C}^n)$.
The operator $A$ is given by the ...