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The purpose of this paper is to explore the quantitative properties of systemic yoyos both with and without their internal structures.

This entire paper is based on the idea of the infinitesimals so that some of the well‐developed concepts and methods of calculus can be adequately employed to address some of the local properties of spinning yoyos.

The concepts of potential energies and yoyo potentials of both particle yoyos and general systemic yoyos are introduced and investigated.

This work is expected to pave the necessary ground for further deepened studies along the idea of rotational kinetic energies and rotational momentums.

The purpose of this paper is to establish quantitative properties for the general systemic yoyo model so that this model can be readily employed to study problems from various disciplines of knowledge, be they from natural science or social science.

Figurative analysis combined with calculus‐based methods is applied in this research, in order to achieve the goal that whatever is obtained theoretically, here can be practically used in various applications.

The paper introduces the concepts of gravitation, potential energy, and yoyo potentials for general spinning yoyos and look at the structure of yoyo fields with relevant quantitative representations developed for practical computation purposes. The paper shows how the spin field of a yoyo can be decomposed into eddy and meridian fields and why spinning yoyos have the tendency to line up in such a way that their axes of spin are parallel to each other and their like polarities face the same direction. When looking at yoyo flows and resistances, the Kirchhoff Junction and Loop Laws are generalized to the most general case of systemic yoyos. By considering the concept of yoyo fluxes, it is possible to rewrite the Gauss's law in the relevant most general language.

This work is the first of its kind to develop quantitative methods for studying various properties of systems on a unified footing: the general systemic yoyo model. As shown in this special issue, the results of this work have been and will continue to be applied to address many difficult problems that have been encountering scholars in the areas of modern science and humanities.

The purpose of this paper is to introduce the necessary background information and literature in order to make this special issue self‐contained.

The paper comprises: an Introduction; Section 2 outlines the origin of the yoyo structure by presenting a brief historical account and the concept of whole evolution of systems; Section 3 introduces the literature on applications of the systemic yoyo model in areas of natural science, social science, epistemology, and practical disastrous weather forecasts; and Section 4 outlines what is contained in this special issue.

A personal account of aspects of a career in systems research and description of a personal ambition to introduce laws for social science and laws that make both natural and social sciences exact at the same time.

With regard to the systemic yoyo model, this paper presents an introduction to what has been accomplished by using this model and what will be presented in this special issue in order to provide all interested colleagues with an overall picture in terms of where the paper stands in the relevant research activities.

The purpose of this paper is to investigate such fundamental concepts as mass, charge, and quark structure of the general systemic yoyo model so that this model could be more widely applied in studies of various scientific disciplines.

Laboratory experiments well documented in quantum mechanics and particle physics are employed as supporting evidence.

A yoyo model explanation for Stern‐Gerlach experiment is provided. The yoyo structures of an electron and a positron are established. Other than illustrating how a radioactive element is decayed, the paper provides an argument for why n‐quark yoyos can theoretically exist in the physical world, for any natural number n.

The paper shows how some properties of the general systemic yoyo model can be established and how some of these very properties can be employed to deepen the understanding of the elementary particles studied in particle physics.

The purpose of this paper is to establish the relevant quantitative methods for the investigation of the eddy and meridian fields of the general systemic yoyo model.

On the basis of established systemic yoyo models for electrons and positrons, flows of negative yoyo charges are naturally identified with electric currents so that use of the well‐developed quantitative methods can be made in electromagnetic theory to investigate the relationship between eddy and meridian fields of the general systemic yoyo model.

A general method is established on how to compute the intensity of the magnetic yoyo fields accompanying a moving yoyo charge or a canal of yoyo flow. A quantitative representation for magnetic yoyo fields is provided. And, the well‐known Ampere's law of electricity is generalized to the case of general yoyo flows.

By establishing an adequate quantitative method for the general systemic yoyo model, it should be possible to know more about the yoyo model and gain additional potential to successfully employ this model in various areas of learning, as proposed by Lin.

The purpose of this paper is to investigate the structure of the fields of the general systemic yoyo model and how these fields interact with each other.

Qualitative analysis and figurative reasoning, combined with calculus‐based methods, are employed to enrich the analysis of how spinning yoyos interact with each other. Known laboratory observations in relevant studies, such as those in electromagnetic theory, are employed as the basis of the investigation, while brand new understandings of these observations are derived.

Some well‐known facts of magnetism are shown to hold true with the general systemic yoyo model.

It is shown that general systems also satisfy such important properties of magnets and electricity as the following: like poles attract and opposite poles repel; field intensities can be superpositioned over each other; systems can potentially become yoyo dipoles when influenced by external systems; etc.

The purpose of this paper is to reach two goals: one is to generalize the well‐studied theories of electricity and magnetism to the enrichment of deepened understanding of the general systemic yoyo model, and the other is to employ the established yoyo model to provide more refined explanations for some of the known experimental observations in physics.

The general structure and the field characteristics of the general systemic yoyo model are employed as the basis of our exploration in this paper. Then, methods of quantitative analysis are introduced to address some of the problems encountered.

Among several new results, many important concepts, such as ring‐shaped electric fields, cylinders of equal potential intensities, yoyo resistances, yoyo capacitors, etc. are introduced and studied in some detail. Several important Laws in electromagnetic theory, such as Ohm's law, Kirchhoff's laws, etc. are generalized to the case of the general systemic yoyo model. The refined theory is applied to provide theoretical explanations for some laboratory‐observed phenomena that cannot be well illustrated by either Faraday's theory of electromagnetic induction or Lenz's law.

Phenomena related to electricity and magnetism are explained the first time in history by using a unified model: the systemic yoyo model. At the same time, some well established Laws in physics are generalized to scenarios of this general mode with the hope that these new Laws can be applied equally well to natural and social sciences in the coming years.

The purpose of this paper is to use the general systemic yoyo model to illustrate why electric fields and magnetic fields can manifest each other and interact with each other.

The coordinated interaction of eddy and meridian fields of spinning yoyos is employed as our methodology for the investigation in this paper. At the end, the First Law on State of Motion is beautifully utilized.

Among many new theoretical discoveries, systemic yoyo models are provided to understand electric currents and the induced magnetic fields, which lead to a distinction between the yoyo structures of permanent magnets and those of the magnetic field induced by electric currents. It is theoretically shown why all fields in nature, such as electric, magnetic, universal, gravitational, and nuclear fields, have to exist in pairs of opposite polarities, even though one polarity might not be visible or recognizable with the current technology. Using the quark structures of spinning yoyos, an explanation is provided for why protons carry positive electric fields, while neutrons are electrically neutral.

One of the originalities of this paper is about its unified theory underlying many observed phenomena of electric and magnetic fields.

The purpose of this paper is to investigate how networks of canals with various parts, such as a battery, yoyo capacitor, inductor, and yoyo resistor, of yoyo flows could practically function.

The characteristics of spin of the general systemic yoyo model, combined with the traditional analytic tools, are employed as the method and thinking logic for this work of quantitative representations.

Formulae are developed for calculating the inductance, intensity of the magnetic field, the total magnetic yoyo flux, and induced magnetomotive force of a coil. For LC networks of canals of electric yoyos, by analyzing the relationship between the electric yoyo charge Q of the capacitor and the induced electric yoyo current I in the network, the following problem is addressed: when the switch of the network is turned on, what will be the reaction of the network? For LR networks of canals of electric yoyo flows, the problem considered is: when the switch is turned off, how would the electric yoyo current evolve? Analysis shows that at the moment of the time constant, the electric yoyo current drops to the level of about 37 percent of its initial strength.

It is expected that some properties of the general systemic yoyo model can be reasonably expressed by using numbers and quantities so that good amount of the traditional quantitative analysis will become useful in the study of this general and intuitive systemic model. This end will become useful when this model is applied to investigate problems and phenomena considered in social science and humanities.

The purpose of this paper is to establish a systemic yoyo model‐based explanation for the internal structure of atoms, which is totally different of the conventional ones.

The spin fields of systemic yoyos are used to explain the interactions between electric and magnetic fields and between elementary particles.

The concepts of potential pits (traps) and ramparts for electrons and those of nuclear, atomic, and molecular bonds are introduced. These concepts are employed successfully to describe the topological structure of atoms.

Other than providing a brand new model for the internal structure of atoms, this paper establishes a deeper understanding of the general systemic yoyo mode.