PANSYMMETRY AND FIXED PANSYSTEMS THEOREMS OF A CLASS OF PANSYSTEMS RELATIONS

In this paper. some results of pansymmetry and fixed pansystems theorems areextended to the case of a class of binary relations under the framework of pansystemsmethodology It is concretely discussed when a class of binary relations has a common fixedsubset on a finite universal set. Several simple but comprehensive decisive theorems areobtained which can be determined if a class of binary relations has a common fixed subset.Asaresult the main decisive theorem-Markov-Kakutani Theorem-is extended whichis in traditionally fixed point theory and can be determined if a class of mappings has acommon fixed point.     

INVESTIGATION AND APPLICATIONS OF PANSYSTEMS RECOGNITION THEORY AND PANSYSTEMS-OPERATIONS RESEARCH OF LARGE-SCALE SYSTEMS(Ⅰ)

In this work, a sort of recognition theory and operations research of large scale systems are developed within the framework of pansystems methodology. We establish a series of theorems concerning pansystems relations, which discuss some fundamental problems of interdisciplines from the viewpoint of generalized system-transformation-symmetry in things mechanism, and are connected closely with mathematical physics systems thinking science bioecological sciences and the methodological investigation of mechanical foundation. This paper offers 100 pansystems theorems.     

The description of the characteristics of the structure and the quantity in fixed pansystems theorems

Pansymmetry is the abstract of symetry, stability and other concepts in physics and so on. Fixed pansystems theorems portray a typical pansymmetry of systemic structure. The present paper complements and extends the Work in concerned in fixed pansystems theorems. It gives in finite case the structural character of fixed subsets; the criterion of existence of the least fixed subset, and the numbering formula of fixed subsets and minimal fixed subsets.     

Pansymmetry and fixed pansystems theorems

In this paper, we continue the research of fixed pansystems theorems presented in ref [1], and discuss the existence, the structure and the number of fixed subsets.     

Some pansystems studies on panchaos and strange panattractor

Paper [1] discussed the relations among panchaos and strange panattractor and pansystems operators. Paper [2] gave the applications of the fixed-point pansystems theorems to these typical nonlinear problems. In this paper, we firstly present several concepts: increasing relation, maximal panchaos, etc., and discuss the relations among them. We also discuss the problems when two increasing relations have the same panchaos and when panchaos of g is panchaos of g^t as well.     

An approach on fixed pansystems theorems: Panchaos and strange panattractor

The investigations about chaos, attractor and strange attractor are main subjects in nonlinear analysis. Under the framework of pansystems methodology, reference [1] discussed these problems and introduced the concepts of panchaos, panattractor and strange panattractor. These concepts omitted the condition of continuity, compactness, etc. and put stress on the properties of binary relations on a set. A certain obtained result indicates that panchaos, panattractor and strange panattractor correspond respectively to fixed subsets of certain pansystems operators. This paper continues the investigation of [1,2], discusses the existence of these pansystems fixed subsets, their construction and interrelations.The authors appreciate Associate Research Fellow Qin Guo-guang for his discussion on related problems.     

Fixed pansystems theorems and eigen-fuzzy sets

In this paper, we apply fixed pansystems theorems to study when a fuzzy transformation has a nonzero eigen-fuzzy set. Many necessary conditions and sufficient conditions are obtained. Furthermore, the properties of nonzero eigen-fuzzy sets are investigated, and the results presented in Ref. [4] are extended.     

Pansystems Analysis: Mathematics, Methodology, Relativity and Dialectical Thinking

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Fixed pansystems theorems and pansystems logic conservation of chaos

The study of nonlinear problems was developed in works ^[1,2] by means of the pansystems methodology (PM) which does not need the condition related to differential manifolds and linear space. In work [2], within the framework of PM, we proved that study of panchaos, panattractor and strange panattractor can be transformed conditionally into some forms of fixed subsets. As a continuation of work [2], we now research the pansystems logic conservation of panchaos, panattractor, strange panattractor and some other fixed subsets.     

Variation transforming analysis (II)

This paper introduces some related concepts of pansystems analysis (such as pansystem, pansystem space, pansystem logic space, pometric pansystem, etc), and develops the convex set theory, Banach's theorem of completeness, Lax equivalence theory, theorems of Kuhn-Tucker type and Dubovitsky-Milutin type into the pometric (partial ordered metric) pansystem forms, they are different from traditional results. Furthermore, the general stability of operator equations and MSP transforming principles of approximation are investigated.     

INVESTIGATION AND APPLICATIONS OF PANSYSTEMS RECOGNITION THEORY AND PANSYSTEMS-OPERATIONS RESEARCH OF LARGE-SCALE SYSTEMS(Ⅱ)

Forming a connecting link between what goes before and comes after,this papersummarizes the general framework of pansystems methodology and related mathematicalmodelling of fundamental concepts including generalized systems,structure,function,entirety principle of system,pansystems relations,pantransformations,panderivatives,pansymmetries,generalized quantization,etc.     

PANSYSTEMS PHILOSOPHY,PANSYSTEMS MATHEMATICS(PPPM)AND APPLICATIONS TO APTMS:AFFAIROLOGY,PHYSICS,TECHNOLOGY,MEDICIEN AND STRATEGICS(Ⅱ)

A new type of philosophy and mathematics from the pansystems view is introduced here, including the 7 philosophy theories (7PT) and related mathematizing researches. Many second/third philosophies are developed within pansystems framework and related applications to APTMS.     

Pansystems clustering analysis of complex systems

In this paper, by use of equivalence operators δ_i and semi-equivalence operators ε_i we study the clustering problems of complex systems, present δ_i(1,3) disconnection principle,dual transformation principle and large-scale systems decomposition principle for analizing and operating complex systems, discuss interconnectivity and disconnectivity of complex systems in detail and present some related theorems. Finally, we discuss the levels of systems according to pansystems, clustering approach proposed in this paper.     

PANSYSTEMS PHILOSOPHY,PANSYSTEMS MATHEMATICS(PPPM)AND APPLICATIONS TO APTMS:AFFAIROLOGY,PHYSICS,TECHNOLOGY,MEDICIEN AND STRATEGICS(Ⅱ)

A new type of philosophy and mathematics from the pansystems view is introduced here,including the7 philosophy theories(7PT)and related mathematizing researches.Many second/third philosophies are developed within pansystems framework and related applications to APTMS.     

Pansystems logic conservation of bifurcation,catastrophe, chaos and stability

It is in references[4,5]that the combination of the relative researches of pansystems methodology and the researches of bifurcation,catastrophe,chaos and stability in nonlinear mechanics was put forward and the concepts were redefined from the point of view of pansystems methodology.The present paper studies the logic conservation law of these nonlinear mechanics phenomena under the framework of pansystems methodology.     

Minimal and maximal fixed point theorems and iterative technique for nonlinear operators in product spaces

In this paper, we study minimal and maximal fixed point theorems and iterative technique for nonlinear operators in product spaces. As a corollary of our result, some coupled fixed point theorems are obtained, which generalize the coupled fixed point theorems obtained by Guo Da-jun and Lankshmikanthamt and the results obtained by Lan in, and.     

FIXED POINT THEOREMS FOR FUZZY MAPPINGS IN PROBABILISTIC METRIC SPACES

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Caristi type hybrid fixed point theorems in menger probabilistic metric space

I.IntroductionandPreliminariesInl976,CaristiprovedtheCaristi'sfixedpointtheoreminIll.Becausethistheoremdoesnotrequirethecontinuityofthemapping.ittindsapplicationsinmanyfields.Inl99l,S.S.Changetal.l'l,broughtforwardCaristi'sfixedpointtheoremandEkeland'svar…     

Existence and stability of common fixed points for systems of mappings

In this paper,we establish some common fixed point theorems and stability theorems of the sets of common fixed points for the systems of set-valued and single-valued nonlinear contractive type mappings in a finite Cartesian product of metric spaces.     

Ritz向量法与Lanczos方法的关系

本文通过对计算结构固有振动的Ritz向量法与Lanczos方法进行分析比较后,证明了关于两者之间关系的几个定理,指出在算法上Lanczos方法要比Ritz向量法更优越。