关于强有界算子

本文讨论了强有界算子范数间的关系及强有界算子空间的各种完备性,得出了强有界算子的一致有界原理。     

关于部分K值逻辑中Sheffer函数判定的一些结果(Ⅰ)

根据部分多值逻辑的完备性理论,证明了ｍ＝２时的一类完满对称函数集在Ｐ*Ｋ中极大封闭集之最小覆盖中必需出现．     

Hilbert's axiomatic method and Carnap's general axiomatics

This paper compares the axiomatic method of David Hilbert and his school with Rudolf Carnap's general axiomatics that was developed in the late 1920s, and that influenced his understanding of logic of science throughout the 1930s, when his logical pluralism developed. The distinct perspectives become visible most clearly in how Richard Baldus, along the lines of Hilbert, and Carnap and Friedrich Bachmann analyzed the axiom system of Hilbert's Foundations of Geometry—the paradigmatic example for the axiomatization of science. Whereas Hilbert's axiomatic method started from a local analysis of individual axiom systems in which the foundations of mathematics as a whole entered only when establishing the system's consistency, Carnap and his Vienna Circle colleague Hans Hahn instead advocated a global analysis of axiom systems in general. A primary goal was to evade, or formalize ex post, mathematicians' ‘material’ talk about axiom systems for such talk was held to be error-prone and susceptible to metaphysics.     

压缩映象不动总定理与空间的完备性表征

Borwein[11]中研究了赋范空间中Banach压缩映象原理与空间的完备性等价这一事实,张石生与作者在度量空间进一步讨论了这一问题[7]1,本文是这一工作的继续。     

Metrics on Noncompact Fuzzy Number Space E^~n

Introduction Thetheoryofmetricspacesoffuzzynumbers (normal,uppersemicontinuousfuzzyconvexfuzzysetswithcompactsupportset)hasbeenestablishedbyDiamondandKloeden[1,2],GoetschelandVoxman[3],Klement, PuirandRelescu[4～6],Kaleva[7],ect..Thistheoryhas beenfoundveryconvenientinmanyresearchfieldson fuzzyanalysissuchasfuzzyintegralsanddifferentials, fuzzydifferentialequations(e.g.see[8～11]),fuzzyrandomvariablesandfuzzystochasticprocesses(e.g.see[4 ～6,12～14]),etc.. However,alargepartofthistheory…     

Hamilton体系下的辛-Fourier展开法及其应用

采用无穷维Hamilton理论和广义Fourier方法对四阶梁横向振动问题进行求解，获得了解析解．同时证明了相应的无穷维Hamilton算子特征函数系的完备性．     

弹性力学通解的构造和完备性

对任意向量本文构造了两种分解形式,从而构造性地给出了Boussinesq-Galerkin解和Papkovich-Neuber解中的势函数,由此直接证明了它们的完备性。文中也讨论了这两种通解之间的关系。