微分中值定理的几个弱逆定理

通过讨论函数凹凸性定义的等价性,得到了微分中值定理的几个弱逆定理,即微分中值定理的逆定理成立的附加条件.     

L－Fuzzy集分解与表现定理的新形式

本文从格论入手，重新讨论Ｌ—Ｆｙｚｚｙ集分解与表现定理，并给出更为广泛、具有实用价值的新形式．     

R~n上广义Riemann定理与椭圆Martin边界

设δ是R~n(n≥3)中C~2区域B内的全不连通零容紧集.借助于与方程△μ=Pμ。在Ω:=B\δ上的极小正解相关联的Martin边界,本文证明δ的椭圆维数dim P≥card δ,讨论Picard原理(即dim P=card δ)与几种广义Riemann定理之间的等价或蕴涵关系并给出在研究等值面边值问题的极限状态中应用的例子。     

关于单值映象对和集值映象对的公共不动点

本文给出了单值映象和集值映象相定和次相容的两个定义，讨论了它们与已知定义之间的关系，得到了一些单值映象和集值映象对的公共不动点定理。     

On Fixed Point Index and Fixed Point Theorems for Multivalued Semi-closed 1-set-contraction Mappings

Fitzpatrick P M and Petryshyn W V studied fixed point index and fixed point theorems of multivalued condensing mappings.The aim of this paper is to give a concept of multivalued semi-closed 1-set-contraction mapping which is a more genere.i mapping and to define its fixed point index,and then we prove some fixed point theorems to extend some Petryshyn' s results.     

P算子与积分微分方程的非线性边值问题（Ⅱ）

本文利用部分逆算子理论及线性边值问题的Ｇｒｅｅｎ函数方法,结合上、下解方法,讨论了形如ｘ”＝ｆ（ｔ,ｘ,ｘ’,Ｔｘ）ａ＜ｔ＜ｂ（ａ,ｘ（ａ）,ｘ’（ａ））＝Ａ（ｂ,ｘ（ｂ）,ｘ’（ｂ））＝Ｂ的二阶非线性积分微分方程与其非线性两点边值问题解的存在性,唯一性及求解方法。     

求解线性方程组的Jacobi和Gauss-Seidel迭代法的收敛定理

本文先描述了迭代法求解线性方程组的基本思想，然后给出三个收敛定理并分别对他们作出解释，最后说明在作题过程中这三个定理如何用和应该注意什么。     

随机过程性质的应用

应用二维 Ｂｒｏｗ ｎ 运动的常返性质、 Ｍａｒｋｏｖ 过程及二维连续局部鞅的一些性质，通过随机分析的方法，对著名的古典问题给出了一个新的证明，证明过程体现了随机分析方法的优越特点．     

横梁弯曲方程的边值问题的可解性

考虑以下横梁弯曲方程的边值问题“ｘ（４）＝ｆ（ｔ，ｘ，ｘ″），ｘ（０）＝Ａ，ｘ（１）＝Ｂ，ｘ″（０）＝ｘ″（１）＝０”．利用基于度理论的不动点定理，给出了上述边值问题有解的某些充分条件     

Einstein׳s Equations for Spin 2 Mass 0 from Noether׳s Converse Hilbertian Assertion

An overlap between the general relativist and particle physicist views of Einstein gravity is uncovered. Noether׳s 1918 paper developed Hilbert׳s and Klein׳s reflections on the conservation laws. Energy-momentum is just a term proportional to the field equations and a ‘curl’ term with identically zero divergence. Noether proved a converse “Hilbertian assertion”: such “improper” conservation laws imply a generally covariant action.Later and independently, particle physicists derived the nonlinear Einstein equations assuming the absence of negative-energy degrees of freedom (“ghosts”) for stability, along with universal coupling: all energy-momentum including gravity׳s serves as a source for gravity. Those assumptions (all but) imply (for 0 graviton mass) that the energy-momentum is only a term proportional to the field equations and a symmetric “curl,” which implies the coalescence of the flat background geometry and the gravitational potential into an effective curved geometry. The flat metric, though useful in Rosenfeld׳s stress-energy definition, disappears from the field equations. Thus the particle physics derivation uses a reinvented Noetherian converse Hilbertian assertion in Rosenfeld-tinged form.The Rosenfeld stress-energy is identically the canonical stress-energy plus a Belinfante curl and terms proportional to the field equations, so the flat metric is only a convenient mathematical trick without ontological commitment. Neither generalized relativity of motion, nor the identity of gravity and inertia, nor substantive general covariance is assumed. The more compelling criterion of lacking ghosts yields substantive general covariance as an output. Hence the particle physics derivation, though logically impressive, is neither as novel nor as ontologically laden as it has seemed.