# Questions tagged [reference-request]

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

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### Complex factorization of the angular part of the Laplacian

Some time ago some research led me to the following equality: \begin{equation} \frac{1}{\sin^2 \phi }\frac{\partial^2 }{\partial \theta^2} +\frac{\partial^2 }{\partial \phi^2} +\cot \phi \frac{\...
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### Adequate equivalence relations and algebraic $K$-theory

I have a somewhat vague question. We know that Adams operation gives a filtration on $K_i(X)\otimes \mathbb{Q}$ for the scheme $X$ such that the weight $j$ elements are isomorphic to higher Bloch Chow ...
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### Further study of “Elementary geometry” in the sense of Tarski

Tarski in the article "WHAT IS ELEMENTARY GEOMETRY" describes four candidates ($\mathscr{E}_2,\mathscr{E}'_2,\mathscr{E}''_2,\mathscr{E}'''_2$) to be called "Elementary geometry". Here the name "...
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### Representation of iterated generic embedding

I'm looking for a reference (if there is one) for a representation theorem for iterated generic embeddings. What I mean by representation is a generalization of the following: If $U$ is an ...
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### Correlated tree interval and existence of unary subtree

We have a collection of random intervals $\{I_{k}:=(X_{k},Y_{k})\}_{k=1}^{\infty}\subset [0,1]$ s.t. For deterministic $l_{k}\to 0$ we have $0<l_{k}^{a_{1}}\leq Y_{k}-X_{k}\leq l_{k}^{a_{2}}$. The ...
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### Are proper subspaces of Banach spaces which are isomorphic to the ambient Banach space necessarily complemented?

I had the following little question pop up, but I cannot seem to find any reference to it. Let $X$ be a Banach space and $E\subseteq X$ a proper subspace with $E$ isomorphic to $X$ itself. Is the ...
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### $G$-analogues of symmetric functions (reference request)

Let $G$ be a simple graph with vertex set $V$. Stanley defined the $G$-analogs of the symmetric function as follows: For $i \ge 0$, define $$e^G_i = \sum_S \big(\prod_{v \in S}v\big)$$ where the sum ...
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### Finitistic dimension conjecture for quadratic algebras

The finitistic dimension of a finite dimensional algebra is defined as the supremum of all projective dimensions of modules having finite projective dimension. The finitistic dimension conjecture says ...
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### Verbal description, or terminology, for the ${\mathcal L}_p$-spaces of Lindenstrauss and Pelczynski

This question is intended for Banach-space specialists and so I will not repeat all the definitions here. My aim is to find out how the Banach space community refers to such spaces in discussions, and ...
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### Correspondence between matrix multiplication and a graph operation of Lovasz

In his book "Large networks and graph limits" (available online here: http://web.cs.elte.hu/~lovasz/bookxx/hombook-almost.final.pdf), Lovasz describes a multiplication operation (he calls it ...
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### Filling $1..mn$ into a $m×n$ rectangle such that every number $<mn$ is dominated

This is a problem from my professor, who claimed that it's open: Combinatorial problem. Fill $1,2,...,mn$ into a rectangle of size $m\times n$, such that for every number other than $mn$, ...
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### What do absolute neighborhood retracts look like?

In the course of filling in my map of non-pathological topology, I'd like to understand the class of ANRs (Absolute Neighborhood Retracts) as a sort of "neighborhood" of the class of CW complexes. ...
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### Open problems about Morita and derived invariants

Are there properties of rings of which one does not know whether they are Morita or derived invariances? For a recent such example for Morita invariance, see https://www.sciencedirect.com/science/...
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### Continuity of a differential of a Banach-valued holomorphic map

Originally posted on MSE. Let $U$ be an open set in $\mathbb{C}^{n}$ let $F$ be a Banach space (in my case even a dual Banach space), and let $\varphi:U\to F$ be a holomorphic map. I seem to be able ...
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### Kaczorowski's Paper on Distribution of Primes

I am looking for a digital copy of the following paper by Jerzy Kaczorowski: ON THE DISTRIBUTION OF PRIMES (mod4) https://www.degruyter.com/view/j/anly.1995.15.issue-2/anly.1995.15.2.159/anly.1995.15....
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### Exponential Deconvolution Using the First Derivative

There is an interesting observation using the first derivative to deconvolve an exponentially modified Gaussian: The animation is here, https://terpconnect.umd.edu/~toh/spectrum/...
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### Research Request for a Paper of A.M. Leontovich

I am looking for a digital copy of a the English version of the paper "The Number of Mappings of Graphs, Ordering of Graphs, and Muirhead's Theorem" by A.M. Leontovich. The math.ru link to the paper ...
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### Continuous embedding between parabolic Sobolev spaces

I was wondering whether the following continuous embedding theorem for parabolic Sobolev space is correct? Let $I=[0,T]$ and $\Omega$ be a sufficiently smooth domain in $\mathbb{R}^n$, we consider ...
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### Shortest path on graphs

I would like to now if there has been any work on related problems, that is, shortest path problem in dynamically evolving graphs.
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### What system suffices to show the strength of PRA is $\omega^\omega$?

Russell O'Connor wrote in 2009 (link): PRA has consistency strength equivalent to the well-foundness of $\omega^\omega$, which can be stated again as the termination of some other program on all ...
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### Jensen's Formula for Arbitrary Neighborhoods

The Jensen's formula says the following: Let $f$ be analytic on the disc $D$ of radius $R$ centered at the origin such that $f(0)\neq 0$, then \begin{align} \log(|f(0)|)+ \sum_{i=1}^n \log \left(\...
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### Weak enrichment and bicategories

I'm trying to find examples where the following perspective on bicategories is developed. We can define a 2-category as being enriched in Cat, where Cat is treated as a monoidal category using the ...
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### Extensive survey of computations of equivariant stable stems

Where can I find a comprehensive survey of computations of equivariant stems? To my knowledge, the status is: Classical Work of Araki and Iriye, Osaka J. Math. 19 (1982). ...
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### Picard group of the moduli space of semistable rank 2 parabolic vector bundles over smooth complex projective curves with trivial determinant

I am looking for the Picard group of the moduli space of semistable rank 2 parabolic vector bundles over smooth complex projective curves with trivial determinant. Having determinant trivial, I ...
What is the/a main reference book for spaces with curvature bounded from below (CBB spaces/spaces with curvature $\geq \kappa$ in the sense of Alexandrov)? Looking for an up to date reference.