Journal•ISSN: 1439-7617
Acta Mathematica Sinica
Springer Science+Business Media
About: Acta Mathematica Sinica is an academic journal published by Springer Science+Business Media. The journal publishes majorly in the area(s): Bounded function & Banach space. It has an ISSN identifier of 1439-7617. Over the lifetime, 4332 publications have been published receiving 30405 citations. The journal is also known as: Acta mathematica Sinica. English series.
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TL;DR: In this article, the Banach contractive mapping theorem for partially ordered sets is extended to nonincreasing mappings as well as non-monotone mappings, and the existence of a unique solution admitting a lower solution is proved.
Abstract: We prove some fixed point theorems in partially ordered sets, providing an extension of the
Banach contractive mapping theorem. Having studied previously the nondecreasing case, we consider
in this paper nonincreasing mappings as well as non monotone mappings. We also present some
applications to first–order ordinary differential equations with periodic boundary conditions, proving
the existence of a unique solution admitting the existence of a lower solution.
578 citations
TL;DR: In this article, a twisted version of the Alexander polynomial associated with a matrix representation of the knot group is presented, and examples of two knots with the same Alexander module but different twisted Alexander poynomials are given.
Abstract: We present a twisted version of the Alexander polynomial associated with a matrix representation of the knot group. Examples of two knots with the same Alexander module but different twisted Alexander polynomials are given.
263 citations
TL;DR: The boundary layer theory has become a standard tool in addressing these questions as mentioned in this paper, but there is still a lack of fundamental understanding of these questions and the validity of the boundary layer theories.
Abstract: A central problem in the mathematical analysis of fluid dynamics is the asymptotic limit of the fluid flow as viscosity goes to zero. This is particularly important when boundaries are present since vorticity is typically generated at the boundary as a result of boundary layer separation. The boundary layer theory, developed by Prandtl about a hundred years ago, has become a standard tool in addressing these questions. Yet at the mathematical level, there is still a lack of fundamental understanding of these questions and the validity of the boundary layer theory. In this article, we review recent progresses on the analysis of Prandtl's equation and the related issue of the zero-viscosity limit for the solutions of the Navier-Stokes equation. We also discuss some directions where progress is expected in the near future.
203 citations
TL;DR: In this paper, the authors give a natural definition of Morrey spaces for Radon measures which may be non-doubling but satisfy a certain growth condition, and investigate the boundedness in these spaces of some classical operators in harmonic analysis and their vector-valued extension.
Abstract: The authors give a natural definition of Morrey spaces for Radon measures which may be non–doubling but satisfy certain growth condition, and investigate the boundedness in these spaces of some classical operators in harmonic analysis and their vector–valued extension.
178 citations
TL;DR: In this article, the generalized I-contraction or I-none-expansive type conditions for non-commuting selfmaps were established and applied to obtain several invariant approximation results which unify, extend and complement the well-known results.
Abstract: Common fixed point results for new classes of noncommuting selfmaps satisfying generalized I-contraction or I-nonexpansive type conditions are established. We apply them to obtain several invariant approximation results which unify, extend, and complement the well-known results.
169 citations