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In this paper, we will introduce charm pansystems and provide mathematical models for panweighted field‐network. Various mathematical models of pansystems will be discussed. Some traditional mathematical concepts such as topology space and rough sets theory will be analyzed within this framework.

The purpose of this paper is to present an academic programme of pansystems research with a lot of new concepts, principles, methods. Universal consideration of philosophy‐mathematics‐technology is set forth with mega‐combination. The emphasis on the transfield internet‐like investigations is developed. Many theory‐methods of pansystems get further concise optimization.

The concrete contents of the paper include: historical megawave, philosophical stratagems, meta‐mathematics, meta‐methodology, technological realistic principles, unification and differentiation of encyclopedic branches, systems science, information theory, cybernetics, biosystems, generalized vitality, computer and IT, thinking science, logic, OR, AI, PR, DM, modernization of yinyang analysis combining dialectics, sociology, economics, meta‐relativity, generalized quantification and scale theory, general process of birth‐growth‐ageing‐disease‐death, the inheritance and development of 300 scholars' researches, etc.

All of the topics concerned with are reduced to the actualizations of PVOR – pansystems variational OR: V−d(xy)=^*0^*/PRR′P′/0^**, which is an integrated synthesis of 20‐PanStemCells of PanConcepts and PanMethod, and embodies a specific pansystems summarization for the core of the true and the good. Furthermore, the formula “Pansystems Researches=^*(PVOR/0^**/Pan54787721/Everything)+^*0^*=^*Pan–netlike connections of thoughts and methods” is expanded with concrete applications.

Provides information on pansystems research.

This paper presents a new simplified text of some concepts of pansystems methodology and related applications to pedagogy, methods of teaching, study and creation, including certain principles of operations research, systems theory, cybernetics, etc.

The optimization of a panweight network is studied. A generalized concept summary of optimality is established, which unifies various related principles. This may be viewed as a sort of complement and extension of Bellman's work. Some of its applications in dynamic programming are discussed. A sufficient condition and three necessary conditions are given under which Bellman's principle holds.

Equilibrium is an important problem in mathematical economics. The paper deals with the problem by establishing pansystems models of equilibrium and introducing ε‐equilibrium solutions. Under the framework of these models, we discuss the existence of equilibrium solution and the ranges where prices, demand and supply commodities vary, respectively.

Following the study in Ref. 1 the optimization of a panweight network is further studied. A generalized fundamental equation is first defined. A sufficient condition and two necessary conditions are then supplied under which the policy obtained by the fundamental equation must be optimum. Finally, the relation between the fundamental equation and the optimum principle is discussed in detail.

To develop an overview of generalized scales based on pansystems‐relative quantification.

This is a discussion paper exploring the key issues surrounding generalized measures.

The concrete contents of the study include generalized measure views, dimension theory, concepts, logic, theories, Einstein's relativity, quality‐quantity‐degree, methodology of physics, theorems in pansystems mathematics and physics explained within the framework of pan‐scale transformations.

Provides an overview of generalized scales based on pansystems‐relative quantification.

Puts forward a new method for decomposing relational schemas by using semi‐equivalence relations based on pansystems methodology. A necessary and sufficient condition is obtained for determining whether there exists a subschema logically available in a given relational schema decomposition.

By use of equivalence operators δ_i and semiequivalence operators ε_i, studies the clustering problems of complex systems. Presents the δ (1,3) disconnection principle, dual‐transformation principle for analysing and operating complex systems and large‐scale systems. Discusses interconnectivity and disconnectivity of complex systems. Presents some related theorems. Discusses hierarchy of systems according to the pansystems clustering approach proposed.

The framework, methodology and development of pansystems cybernetics are introduced. Related contents include: the postmodernizational systems thought, the epitome of pansystems methods, hi‐tech mechanism, social cybernetics, pansystems views of value, labor, management and economics, pedagogy, history and futurology, systems mathematics, general clustering analysis, observocontrollability, generalized living systems, information metascience, regret information, general fuzzy control, generalized gray systems, entropy, large scale dynamical supercomplicated Shengke systems, function simulations, transformation theory, simplification, strengthening, forming substance of subsystems of living systems of Miller’s theory, etc.