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In this short exposition we provide a simplified proof of Buser's result for Cheeger's isoperimetric constant.

Differential Geometry · Mathematics 2022-12-29 Nelia Charalambous , Zhiqin Lu

These notes are a self-contained short proof of the stability of persistence diagrams.

Algebraic Topology · Mathematics 2021-03-22 Primoz Skraba , Katharine Turner

We obtain simple proofs of certain inequalites for bivariate means.

Classical Analysis and ODEs · Mathematics 2011-05-04 Jozsef Sandor

We propose a modular method for proving termination of general logic programs (i.e., logic programs with negation). It is based on the notion of acceptable programs, but it allows us to prove termination in a truly modular way. We consider…

Logic in Computer Science · Computer Science 2025-06-18 Annalisa Bossi , Nicoletta Cocco , Sandro Etalle , Sabina Rossi

We argue that verification of recursive programs by means of the assertional method of C.A.R. Hoare can be conceptually simplified using a modular reasoning. In this approach some properties of the program are established first and…

Logic in Computer Science · Computer Science 2009-07-27 Krzysztof R. Apt , Frank S. de Boer , Ernst-Rüdiger Olderog

We prove the `weight elimination' part of the weight part of Serre's conjecture for mod 2 Galois representations for rank two unitary groups, by modifying the results in arXiv:1203.2552 and arXiv:1309.0527.

Number Theory · Mathematics 2022-10-28 Xiyuan Wang

This is supplementary material to "Realizations of a special class of admittances with strictly lower complexity than canonical forms" [1], which presents the detailed proofs of some results. For more background information, refer to…

Optimization and Control · Mathematics 2015-01-20 Michael Z. Q. Chen , Kai Wang , Zhan Shu , Chanying Li

In this short note a new proof of the monotone con- vergence theorem of Lebesgue integral on \sigma-class is given.

Functional Analysis · Mathematics 2011-12-16 Dinh Trung Hoa

We introduce the notion of a Morse sequence, which provides a simple and effective approach to discrete Morse theory. A Morse sequence is a sequence composed solely of two elementary operations, that is, expansions (the inverse of a…

Computer Vision and Pattern Recognition · Computer Science 2024-02-13 Gilles Bertrand

The goal of this note is to give, at least for a restricted range of indices, a short proof of homogeneous commutator estimates for fractional derivatives of a product, using classical tools. Both $L^{p}$ and weighted $L^{p}$ estimates can…

Analysis of PDEs · Mathematics 2019-07-25 Piero D'Ancona

The purpose of this note is to give a self contained description of Walls finiteness obstruction.

Geometric Topology · Mathematics 2017-07-26 Erik Kjær Pedersen

We give a new proof of the existence of designs, which is much shorter and gives better bounds.

Combinatorics · Mathematics 2024-11-28 Peter Keevash

We give combinatorial proofs of several recent results due to Merca on the sum of different parts congruent to $r$ modulo $m$ in all partitions of $n$. The proofs make use of some well known involutions from the literature and some new…

Combinatorics · Mathematics 2023-03-28 Cristina Ballantine

Motivated by the problem of finding finite versions of classical incompleteness theorems, we present some conjectures that go beyond ${\bf NP\neq co NP}$. These conjectures formally connect computational complexity with the difficulty of…

Logic · Mathematics 2017-05-22 Pavel Pudlak

Let R be a commutative ring with identity, S be a multiplicatively closed subset of R, and let M be an R-module. The aim of this paper is to introduce the notion of S-secondary submodules of M as a generalization of secondary submodules of…

Commutative Algebra · Mathematics 2020-08-25 Faranak Farshadifar

This paper aims to expand and detail the notion of formal semantics of Conjectures by applying a theoretic-model approach. After a short introduction to the concepts and basics of Conjectures, we will start from the notion of Simple…

Logic in Computer Science · Computer Science 2021-10-19 Alessio Rolfini

The goal of the paper is to present two simple proofs of the Lagrange Inversion Formula for formal power series. Both proofs are non-external in the sense that they use concepts that do not go beyond the scope of formal power series…

Combinatorics · Mathematics 2026-05-07 Dominik Beck , Piotr Maćkowiak

A simple new proof of the Harish-Chandra condition, preceded by an expository part on Hermitian symmetric spaces, holomorphic induction, and on some analytic tools.

Representation Theory · Mathematics 2023-12-29 Adam Koranyi

This paper consists of two prongs. Firstly, we prove that any Specht module labelled by a 2-separated partition is semisimple and we completely determine its decomposition as a direct sum of graded simple modules. Secondly, we apply these…

Representation Theory · Mathematics 2019-04-09 C. Bessenrodt , C. Bowman , L. Sutton

In this paper we present a more transparent upgrade of our proofs and comment on Jerabek's paper [8].

Computational Complexity · Computer Science 2026-05-14 Lev Gordeev , Edward Hermann Haeusler