# Tag Info

1 vote

### Has anyone attempted to generalize the notion of a higher differential of $A$ and the sheaf of differentials $\Omega_{A/k}$?

I have this strange feeling I have commented on this or an identical question recently, but can't place it. Here is one solution which may not be what you are looking for and you have mentioned it in ...
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### Reference request: “A random integral and Orlicz spaces”

I could not find it on the internet so I uploaded it here: https://www.transfernow.net/dl/20221126nnUfCto7
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1 vote
Accepted

### First visit of intervals for an irrational rotation

No, it is not possible. In the following I will use $I_n=(a_n,b_n)$ instead of $[a_n,b_n)$ (this is not a problem, you can just increase $a_n$ a bit so that the statement with $I_n=(a_n,b_n)$ is ...
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### Results on Boolean matrices

We can try to produce some of the basic theory of Boolean matrices here to see what makes sense and what does not. For this post, we do not lose much by generalizing to the Boolean algebras of the ...
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### Mathematical analysis of Lewisian concepts, esp. natural properties

I have engaged with the Lewis-style set-theoretic mereology in a few papers, undertaken jointly with Makoto Kikuchi. My interest in this topic was inspired originally by a MathOverflow question, Why ...
Accepted

### Reference for Calderon-Zygmund $L^p$ inequalities on the sphere

I don't know of an exact reference, and in general this sort of result (transfering a "classical" result from the analysis of PDE in $\mathbb{R}^n$ to Riemannian manifolds) is often quite ...
• 5,792

### Sum of three squares as class numbers and Waldspurger's formula

This is not an answer, but I found a work that seems to be related to my question. There's a paper by Ting-Yi Pei on the Eisenstein series of weight 3/2. Author defines a weight 3/2 Eisenstein series (...
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### Differentiability of the fixed points of a family of contraction maps

I found the answer myself: One can simply apply the Banach space version of the implicit function theorem to the function $G(t,x) = x-F_t(x)$. The implicit function theorem shows that, given $G$ is in ...
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### A question on a result of Colin de Verdière

Vedrin Šahović in his unpublished thesis [Approximations of Riemannian manifolds with linear curvature constraints, 2009] proved that any compact metric space can be appoximated by hyperbolic ...
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### Reference request for "Tangent relation" for functions between metric spaces

I don't know whether there are "good" references to what you are actually asking but at least in some kind of implicit sense this kind of "tangency" was already considered by ...
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### Mutual information in large deviation theory

There's a few results. First of all there is the classical Sanov's Theorem. One other result is about Gaussian measures. For a centered Gaussian measure $\mu_0$ on Banach space $\mathcal B$ we can ...
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### Catalogue of groups with short finite presentations

I would very much like to have such a database and would like to contribute to its development. Prompted by this question, we talked about what such a database could look like (e.g. in terms of groups ...
• 1,956
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### Is $L_p(X, \mu, E)$ uniformly convex for $p \in (1, \infty)$ if $E$ is a uniformly convex Banach space?

A reference for this result would be Some more uniformly convex spaces by Mahlon M. Day, Bull. Amer. Math. Soc. 47(6): 504-507 (June 1941). (Alternative link at Project Euclid)
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1 vote

### Attaching an ideal whose square is zero: does this operation have a name and a notation?

I have recently been enlightened by colleagues in the Mathematics Dept. here at HWU on this very question: this construction (in various guises, inessential variations for the purposes of the ...
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### Applications of equivariant homotopy theory to representation theory

There are decades and decades of algebraic results that use techniques from equivariant homotopy theory. Some examples ... (1) Quillen's work on ring theoretic aspects of the cohomology of finite ...
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1 vote
Accepted

### Explicit formula for Fibonacci numbers; compositions of $n$

Yes, this identity is well known. According to Singh's The so-called Fibonacci numbers in ancient and medieval India, the $s=1$ case has been known since at least the the 14th century. Since ...
• 3,256
1 vote

### Axioms for the category of groups

The category of groups is the universal example of a cocomplete category equipped with a cogroup object. A similar statement holds for other types of algebraic structures. This is due to Freyd. See ...
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### Are any embeddings $[0,1]\to\mathbb{R}^3$ topologically equivalent?

As igorf pointed out in the comment, the answer to the first question is 'no'. A quick counterexample is by looking into the complement of Fox-Artin arc, which is not simply connected. See figure ...
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### When are filtered colimits of (trivial) cofibrations still (trivial) cofibrations?

If both cofibrations and weak equivalences are stable under filtered colimits, then so are trivial cofibrations. This happens for instance if $\mathcal{M}$ is a presheaf category on an elegant Reedy ...
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### A simple proof of the fundamental theorem of Galois theory

At a first glance your approach reminds me of Meinolf Geck's American Mathematical Monthly article, see also the arxiv version of his article.
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### Making a submanifold transverse to a vector field by an isotopy

The simplest case is when $M$ is a compact manifold with connected boundary $N$. If $N$ is nowhere tangent to $X$ then, by replacing $X$ by $-X$ if necessary, we can assume $X$ points outwards at ...
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### Coordinate principal bundle over a curve

The standard reference for where this comes from originally is I. Gelfand and D. Kazhdan, Some problems of differential geometry and the calculation of cohomologies of Lie algebras of vector fields, ...
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### General form of bounded linear functionals on Banach spaces

For example: For the real Banach space $L^p(\mathbb R)$, with $1 < p < \infty$, the "conjugate space" is $L^q(\mathbb R)$ where $\frac{1}{p}+\frac{1}{q}=1$. For general linear ...
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### Discontinuous functions without removable discontinuities

I claim that one can always get rid of all removable discontinuities of a function to obtain a function without removable discontinuities. For generality, we shall work in the framework of general ...
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It is not true even for $\mathbb{P}^n$. For instance, the tangent bundle $T_{\mathbb{P}^n}$ restricts to each line as  T_{\mathbb{P}^n}\vert_L \cong \mathcal{O}_L(2) \oplus \mathcal{O}_L(1)^{\oplus (...