泛系分析：数学.方法论.相对论.辩证思维

基于对广义系统、泛导、泛对称、泛箱原理、泛系相对性提出了新的分析模式与新的相对数学化的简化强化的定义，发展了泛系方法论与泛系相对论的框架与理法，具体内容涉及相对普适的数学化的泛系，200类对偶，对偶转化，泛对称转化，泛系辩证，八畴方法，泛系数学方法，广义量化，逼近转化原则，泛等价定理，供求分析，思维实验，广义灰色系统，等等     

复杂系统的泛系聚类方法

本文利用半等价算子ε_i和相等化算子δ_i研究了复杂系统的聚类问题;阐述了分析运筹复杂系统的δ(1,3)解耦原理、对偶转化原理和大系统分解原理;详细讨论了复杂系统的连通性与解耦性并提供了有关定理.最后,利用泛系聚类方法讨论了复杂系统的层次分析.     

泛系识别理论与大系统泛系运筹学的研究与应用(Ⅰ)

在泛系方法论的框架下,本工作发展一种识别理论与大系统运筹的新研究.我们给出一组关于泛系关系的定理,从事物机理中广义的系统、转化与对称的角度探讨交缘学科的一些基本问题.它们与数理系统科学、思维科学、生物生态医学以及力学基础的方法论研究有着密切的关系,本文给出100个泛系定理.     

泛系识别理论与大系统泛系运筹学的研究与应用(Ⅱ)

本文承前启后,介绍了泛系方法论新的框架以及与识别及大系统运筹有关的一些理法.     

含有锥约束的多目标变分问题的广义对称对偶性

本文研究了一类含有锥约束多目标变分问题的广义对称对偶性.利用函数的(F,ρ)-不变凸性的条件,得出了多目标变分问题关于有效解的弱对偶定理、强对偶定理和逆对偶定理,将多目标变分问题的对称对偶性理论推广到含有锥约束的广义对称对偶性上来.     

二元关系传递性泛系研究新探

本文基于泛系数学研究和一般事物机理分析的需要，讨论了二元关系对多元关系的传递性，引进一种被叫作“ｇ－传递性”的广义传递概念，考察了它的基本性质，ｇ－传递性不但是普通传递性、拟传递性、半序、拟半序等泛序概念的推广，还包容闭性、凸性、拓扑、对偶性等基本概念为其特例，从而表明这一概念的普适性。     

不动泛系定理的某些新结果*

本文讨论了复补算子的不动泛系定理,给出了泛浑沌与泛怪引子的存在条件,进而利用所得结果证明一些关于多值映射的不动点定理,后者补充与发展了Kakutani的结果.     

泛系哲学与泛系数学和应用：事理，物理，技术，医理与战理（Ⅱ）

这里从泛系观引入一种新型的哲学与数学研究，包括在泛系框架下发展哲学七论与数学和一些第二第三哲学以及对事理、物理、技理、医理与战理的某些应用。     

泛灰数在区间分析中的应用

在概述泛灰数的概念及其运算规则的基础上 ,介绍了泛灰数与区间数的转化 ,利用泛灰数的可扩展性对区间进行分析 ,它不仅具有区间分析的功能 ,而且能解决区间分析所不能解决的问题 .并给出了算例作了对比分析     

两类泛函数一致有界原理的统一与推广

本文交广义按范γ－拟次加算子族的一致有界原理与凸泛函数的一致有界面原理作了统一与推广。     

泛系关系族的泛对称与不动泛系定理

本文在泛系方法论的框架下,将泛对称与不动泛系定理的一些结果推广到了二元关系族的情形.具体地讨论了对于有限论域上的一族二元关系何时存在公共的不动子集的问题,得到了几个确定二元关系族是否存在公共的不动子集的简括的判别定理.其结果推广了传统的不动点理论中有关映射族是否存在公共的不动点的主要判别定理——Markov-Kakutani定理.     

Index theory, nontrivial solutions, and asymptotically linear second-order Hamiltonian systems

In this paper, we consider the existence and multiplicity of solutions of second-order Hamiltonian systems. We propose a generalized asymptotically linear condition on the gradient of Hamiltonian function, classify the linear Hamiltonian systems, prove the monotonicity of the index function, and obtain some new conditions on the existence and multiplicity for generalized asymptotically linear Hamiltonian systems by global analysis methods such as the Leray-Schauder degree theory, the Morse theory, the Ljusternik-Schnirelman theory, etc.     

Modification of special relativity and local structures of gravity-free space and time

Besides two fundamental postulates, (i) the principle of relativity and (ii) the constancy of the one-way speed of light in all inertial frames of reference, the special theory of relativity uses the assumption about the Euclidean structure of gravity-free space and the homogeneity of gravity-free time in the usual inertial coordinate system. Introducing the so-called primed inertial coordinate system, in addition to the usual inertial coordinate system, for each inertial frame of reference, we assume the flat structures of gravity-free space and time in the primed inertial coordinate system and their generalized Finslerian structures in the usual inertial coordinate system. We combine this assumption with the two postulates (i) and (ii) to modify the special theory of relativity. The modified special relativity theory involves two versions of the light speed, infinite speed c^′ in the primed inertial coordinate system and finite speed c in the usual inertial coordinate system. It also involves the c^′-type Galilean transformation between any two primed inertial coordinate systems and the localized Lorentz transformation between any two usual inertial coordinate systems. The physical principle is: the c^′-type Galilean invariance in the primed inertial coordinate system plus the transformation from the primed to the usual inertial coordinate systems. Evidently, the modified special relativity theory and the quantum mechanics theory together found a convergent and invariant quantum field theory.     

不动泛系定理的新研究:泛浑沌和泛怪引子

关于浑沌、引子、怪引子等的研究是非线性分析中的重要课题.文[1]在泛系方法论的框架下,讨论了这些问题,提出了泛浑沌、泛引子和泛怪引子的概念,这些概念去掉了诸如连续性、紧性等条件,突出反映了一集合上的二元关系的性质.已有的研究结果指出,泛浑沌、泛引子和泛怪引子分别对应于某个特定的泛系算子作用下的不动子集.本文继续文[1、2]的工作,探讨了存在这类泛系不动子集的条件以及它们的构造和相互间的联系.     

Modification of special relativity and formulation of convergent and invariant quantum field theory

Besides two fundamental postulates, (i) the principle of relativity and (ii) the constancy of the speed of light in all inertial frames of reference, the special theory of relativity uses another assumption. This other assumption concerns the Euclidean structure of gravity-free space and the homogeneity of gravity-free time in the usual inertial coordinate system. Introducing the primed inertial coordinate system, in addition to the usual inertial coordinate system, for each inertial frame of reference, we assume the Euclidean structures of gravity-free space and time in the primed inertial coordinate system and their generalized Finslerian structures in the usual inertial coordinate system. We combine the alternative assumption with the two postulates (i) and (ii) to modify the special theory of relativity. The modified special relativity theory involves two versions of the light speed, infinite c′ in the primed inertial coordinate system and finite c in the usual inertial coordinate system. It also involves the c′-type Galilean transformation between any two primed inertial coordinate systems and the localized Lorentz transformation between two corresponding usual inertial coordinate systems. Since all our experimental data are collected and expressed in the usual inertial coordinate system, the physical principle is: the c′-type Galilean invariance in the primed inertial coordinate system plus the transformation from the primed inertial coordinate system to the usual inertial coordinate system. This principle is applied to a reformulation of mechanics, field theory and quantum field theory. Relativistic mechanics in the usual inertial coordinate system is unchanged, while field theory is developed and divergence-free. Any c′-type Galilean-invariant field system can be quantized by using the canonical quantization method in the primed inertial coordinate system. We establish a transformation law for quantized field systems as they are transformed from the primed to the usual inertial coordinate system. It is shown that the modified special relativity theory, together with quantum mechanics, leads to a convergent and invariant quantum field theory, in full agreement with experimental facts. The formulation of this quantum field theory does not demand departures from the concepts such as local Lorentz invariance in the usual inertial coordinate system, locality of interactions, and local or global gauge symmetries.     

浑沌与怪引子的某些泛系研究

文[1]讨论了泛浑沌及泛怪引子与泛系算子ε₇(g)之间的联系。文[2]讨论了不动泛系定理在这些典型的非线性问题研究中的应用。本文首先给出了增关系、极大泛浑沌等几个概念,讨论了它们之间的关系;本文还讨论了g的泛浑沌与它的传递包的泛浑沌的关系以及在一定条件下两个增关系的泛浑沌相同的条件。     

泛系哲学与泛系数学和应用：事理，物理，技理，医理与战理（Ⅰ）

这里从泛系观引入一种的哲学与数学研究，包括在乏系框架下 发展哲学七论与数学和一些第二第三哲学以及对事理、物理、技理、医理与战理的某些应用。