相关论文: Banach Couples. I. Elementary Theory

We compare the results of our two papers with the results of the paper Aratyn H., Gomes J.F., Zimerman A.H., Higher order Painlev\'e equations and their symmetries via reductions of a class of integrable models, J. Phys. A: Math. Theor., V.…

We present new proofs to four versions of Peano's Existence Theorem for ordinary differential equations and systems. We hope to have gained readability with respect to other usual proofs. We also intend to highlight some ideas due to Peano…

The purpose of this article is to motivate the study of invariant, and especially conformally invariant, differential pairings. Since a general theory is lacking, this work merely presents some interesting examples of these pairings,…

In the papers from Chui and Parnes (1971) and Luh (1972), as well on the paper from V.Nestoridis (1996) on the Universal Taylor series, it is used, without proof, that the union of two compact sets in $\mathbb{R} ^2$ with connected…

The aim of the present text is to provide some basics around Reshetnyak's theory of subharmonic distances, together with an overview of the main results. This text is intended to be a complement to the English translation of \cite{R1954},…

In this paper we give a new proof, relying on Banach's contraction mapping principle, of a celebrated theorem of Andr\'e Bloch. Also, via the same contraction mapping principle, we give a proof of a Bloch type theorem for normalised Wu…

We show that the phase tropical pair-of-pants is (ambient) isotopic to the complex pair-of-pants. This paper can serve as an addendum to the author's joint paper with Ruddat arXiv:2001.08267 where an isotopy between complex and…

Considering the class of almost periodic functions in the Stepanov sense we extend and generalize the results of the first author [4]. as well as the results of L. Leindler [3] and P. Chandra [1,2].

In this paper we both review the famous article "Eine fur die Valenztheorie geeignete Basis der binaren Vektorinvarianten" of G. Rumer, E. Teller, and H. Weyl on Rumer diagrams and use a powerful old result from algebraic geometry to…

In this note a far extension of the Banach fixed point theorem is proved.

We present some extensions of classical results that involve elements of the dual of Banach spaces, such as Bishop-Phelp's theorem and James' compactness theorem, but restricting to sets of functionals determined by geometrical properties.…

A Comment on the Letter by Atsushi Ikeda and Kunimasa Miyazaki, [arXiv:1003.5472v2, Phys. Rev. Lett. 104, 255704 (2010)].

We recover a recent result of A. Alekseev et E. Meinrenken (arXiv: math. RT/0308135) by using our theory of generalized Harish-Chandra homomorphism for symmetric pair.

In this paper, we prove the Noether theorem with the multiplicities described by PD operators. Despite the known analogue versions in this case the provided conditions are necessary and sufficient. We also prove the Cayley-Bacharach theorem…

This is a technical report, containing all the theorem proofs and additional evaluations in paper "Network Capability in Localizing Node Failures via End-to-end Path Measurements" by Liang Ma, Ting He, Ananthram Swami, Don Towsley, and Kin…

We point out how the "Fundamental Theorem of Stability Theory", namely the equivalence between the "non order property" and definability of types, proved by Shelah in the 1970s, is in fact an immediate consequence of Grothendieck's…

This is a survey article with a limited list of references (as required by the publisher) which appears in the Encyclopedia of Mathematical Physics, eds. J.-P. Francoise, G.L. Naber and Tsou S.T. Oxford: Elsevier, 2006. vol.4, pp.94--104.

The theory of one-relator groups is now almost a century old. The authors therefore feel that a comprehensive survey of this fascinating subject is in order, and this document is an attempt at precisely such a survey. This article is…

The well known theorems of Khintchine and Jarn\'ik in metric Diophantine approximation provide comprehensive description of the measure theoretic properties of real numbers approximable by rational numbers with a given error. Various…

In this note we prove new cases of the Mumford-Tate conjecture by extending a theorem of Richard Pink for abelian varieties without nontrivial endomorphisms and with bad semistable reduction. We use quadratic pairs introduced by…