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This text is an appendix to our work "On the growth of Kronecker coefficients", arXiv:1607.02887. Here, we provide some complementary theorems, remarks, and calculations that for the sake of space are not going to appear into the final…

Representation Theory · Mathematics 2016-11-23 Emmanuel Briand , Amarpreet Rattan , Mercedes Rosas

Quantum superintegrable systems are solvable eigenvalue problems. Their solvability is due to symmetry, but the symmetry is often "hidden". The symmetry generators of 2nd order superintegrable systems in 2 dimensions close under commutation…

Mathematical Physics · Physics 2015-11-02 E. Kalnins , W. Miller , E. Subag

The explicit solvability of quantum superintegrable systems is due to symmetry, but the symmetry is often "hidden". The symmetry generators of 2nd order superintegrable systems in 2 dimensions close under commutation to define quadratic…

Mathematical Physics · Physics 2016-04-20 Ernest G. Kalnins , Willard Miller , Eyal Subag

This paper has been withdrawn by the authors because it has been merged with paper arXiv:0903.3501v1 [math.DG]

General Relativity and Quantum Cosmology · Physics 2009-03-23 Erasmo Caponio , Miguel Angel Javaloyes

I provide some comments on Arithmetic Teichmuller Spaces constructed in my paper arXiv:2106.11452.

Algebraic Geometry · Mathematics 2022-01-06 Kirti Joshi

This is an appendix to our paper "An update of the Hirsch Conjecture" (arXiv:0907.1186), containing proofs of some of the results and comments that were omitted in it.

Combinatorics · Mathematics 2010-02-02 Edward D. Kim , Francisco Santos

In this note we comment on remarks about our recent effort to understand the specificities of the Boltzmann equation in the context of the alternative theories of gravity with non-minimal coupling between curvature and matter.

General Relativity and Quantum Cosmology · Physics 2020-05-11 Orfeu Bertolami , Cláudio Gomes

In this note it is worked out a new set of Laplace-Like equations for quaternions through Riemann-Cauchy hypercomplex relations otained earlier \cite{BorgesZeMarcio}. As in the theory of functions of a complex variable, it is expected that…

Complex Variables · Mathematics 2013-04-16 J A. P. F. Marão , M. F. Borges

The purpose of this article is to relate coarse cohomology of metric spaces with a more computable cohomology. We introduce a notion of boundedly supported cohomology and prove that coarse cohomology of many spaces are isomorphic to the…

Metric Geometry · Mathematics 2024-01-05 Arka Banerjee

We provide a precise statement and self contained proof of a Sobolev inequality (cf. [A, page 236 and page 237]) stated in the original paper. Higher order and fractional inequalities are treated as well.

Functional Analysis · Mathematics 2018-06-22 Mario Milman

We lay out the foundations of the theory of second-order conformal superintegrable systems. Such systems are essentially Laplace equations on a manifold with an added potential: $(\Delta_n+V({\bf x}))\Psi=0$. Distinct families of…

Mathematical Physics · Physics 2009-09-01 E. G. Kalnins , J. M. Kress , W. Miller , S. Post

This article handles in a short manner a few Laplace transform pairs and some extensions to the basic equations are developed. They can be applied to a wide variety of functions in order to find the Laplace transform or its inverse when…

General Mathematics · Mathematics 2014-02-13 Henrik Stenlund

In this supplementary appendix we provide additional results, omitted proofs and extensive simulations that complement the analysis of the main text (arXiv:1201.0224).

Statistics Theory · Mathematics 2017-10-05 Alexandre Belloni , Victor Chernozhukov , Christian Hansen

The conformal compactification is considered in a hierarchy of hypercomplex projective spaces with relevance in physics including Minkowski and Anti-de Sitter space. The geometries are expressed in terms of bicomplex Vahlen matrices and…

General Mathematics · Mathematics 2017-05-23 S. Ulrych

We obtain results on the existence and approximation of fixed points of enriched contractions in quasi-Banach spaces and thus extend the results obtained in the case of contractions defined on Banach spaces [Berinde, V.; P\u{a}curar, M.…

General Mathematics · Mathematics 2024-04-10 Vasile Berinde

This is a supplement to the article "Markov Chain Monte Carlo Based on Deterministic Transformations" available at http://arxiv.org/abs/1106.5850

Computation · Statistics 2013-07-01 Somak Dutta , Sourabh Bhattacharya

Hypercontractive inequalities are a useful tool in dealing with extremal questions in the geometry of high-dimensional discrete and continuous spaces. In this survey we trace a few connections between different manifestations of…

Discrete Mathematics · Computer Science 2011-01-18 Punyashloka Biswal

Additional supplementary material for the paper `A First-Principles Constitutive Equation for Suspension Rheology'.

Soft Condensed Matter · Physics 2008-08-12 J. M. Brader , M. E. Cates , M. Fuchs

This supplementary information contains detailed derivations, comparison to experiment, and discussion of other miscellaneous issues omitted from the main text.

Populations and Evolution · Quantitative Biology 2009-01-05 C. Scott Wylie , Cheol-Min Ghim , David A. Kessler , Herbert Levine

This supplementary part of the paper gr-qc 9312038 contains the necessary proofs of the claims stated in the main part.

General Relativity and Quantum Cosmology · Physics 2007-05-23 S. Tertychniy
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