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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.

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.

The purpose of this paper is the coupled nonlinear fractal Schrödinger system is defined by using fractal derivative, and its variational principle is constructed by the fractal semi-inverse method. The approximate analytical solution of the coupled nonlinear fractal Schrödinger system is obtained by the fractal variational iteration transform method based on the proposed variational theory and fractal two-scales transform method. Finally, an example illustrates the proposed method is efficient to deal with complex nonlinear fractal systems.

The coupled nonlinear fractal Schrödinger system is described by using the fractal derivative, and its fractal variational principle is obtained by the fractal semi-inverse method. A novel approach is proposed to solve the fractal model based on the variational theory.

The fractal variational iteration transform method is an excellent method to solve the fractal differential equation system.

The author first presents the fractal variational iteration transform method to find the approximate analytical solution for fractal differential equation system. The example illustrates the accuracy and efficiency of the proposed approach.

The variational principle views a complex problem in an energy way, it gives good physical understanding of an iteration method, and the variational-based numerical methods always have a conservation scheme with a fast convergent rate. The purpose of this paper is to establish a variational principle for a fractal nano/microelectromechanical (N/MEMS) system.

This paper begins with an approximate variational principle in literature for the studied problem, and a genuine variational principle is obtained by the semi-inverse method.

The semi-inverse method is a good mathematical tool to the search for a genuine fractal variational formulation for the N/MEMS system.

The established variational principle can be used for both analytical and numerical analyses of the N/MEMS systems, and it can be extended to some more complex cases.

The variational principle can be used for variational-based finite element methods and energy-based analytical methods.

The new and genuine variational principle is obtained. This paper discovers the missing piece of the puzzle for the establishment of a variational principle from governing equations for a complex problem by the semi-inverse method. The new variational theory opens a new direction in fractal MEMS systems.

A three-dimensional (3D) unsteady potential flow might admit a variational principle. The purpose of this paper is to adopt a semi-inverse method to search for the variational formulation from the governing equations.

A suitable trial functional with a possible unknown function is constructed, and the identification of the unknown function is given in detail. The Lagrange multiplier method is used to establish a generalized variational principle, but in vain.

Some new variational principles are obtained, and the semi-inverse method can easily overcome the Lagrange crisis.

The semi-inverse method sheds a promising light on variational theory, and it can replace the Lagrange multiplier method for the establishment of a generalized variational principle. It can be used for the establishment of a variational principle for fractal and fractional calculus.

This paper establishes some new variational principles for the 3D unsteady flow and suggests an effective method to eliminate the Lagrange crisis.

The purpose of this paper is to point out a paradox in variational theory for viscous flows. Chien (1984) claimed that a variational principle of maximum power loses for viscous fluids was established, however, it violated the well-known Helmholtz’s principle.

Restricted variables are introduced in the derivation, the first order and the second order of variation of the restricted variables are zero.

An approximate variational principle of minimum power loses is established, which agrees with the Helmholtz’s principle, and the paradox is solved.

This paper focusses on incompressible viscose flows, and the theory can be extended to compressible one and other viscose flows. It is still difficult to obtain a variational formulation for Navier-Stokes equations.

The variational principle of minimum power loses can be directly used for numerical methods and analytical analysis.

It is proved that Chien’s variational principle is a minimum principle.

A generalized variational principle of 2D unsteady compressible flow around oscillating airfoils is established directly from the governing equations and boundary/initial conditions via the semi‐inverse method proposed by He. In this method, an energy integral with an unknown F is used as a trial‐functional. The identification of the unknown F is similar to the identification of the Lagrange multiplier. Based on the variational theory with variable domain, a variational principle for the inverse problem (given as the time‐averaged pressure over the airfoil contour, while the corresponding airfoil shape is unknown) is constructed, and all the boundary/initial conditions are converted into natural ones, leading to well‐posedness and the unique solution of the inverse problems.