Generalizations of self-type and │││-type structures, elements of s- morphology and others: monograph

Abstract

The monograph first task: to understand hierarchy of energies in the Universe and the principles of functioning of living energy (s-morphology) (living organism, in particular, human, subtle energies), and then using these principles to "construct" artificial living energies (let's call them pseudo-living energies). It is possible to significantly expand the horizons of science, in particular physics, by studying the subtle energies in the Universe. On the basis of mathematical uncertainties, new mathematical structures are formed, allowing us to describe processes and objects that are fundamentally not determined by conventional deterministic methods.  Here is considered new mathematical uncertainties. Objective uncertainties in any case can mean manifestations of processes and objects that are fundamentally not determined by conventional deterministic methods. Many energies are indeterminate because they are based on uncertainties from the perspective of traditional science—large concentrations of specific energy in a chaotic state. The foundation of dynamic mathematics lies in working with uncertainties, which makes it possible to manipulate these indeterminate energies using direct-accumulative direct-parallel neural networks. The second task of the monograph is to construct a new mathematical apparatus for neural networks of a fundamentally new type: generalization of paradoxical singularities (singularities of disintegration&synthesis), self-type singularities, self-type structures, direct-parallel and direct-accumulative action. We construct models of singularities for singular work with them through neural networks - analogues of the human CNS. Ordinary regular work with them in ordinary science is fundamentally unable to realize their capabilities. Therefore, singular science realized on a neural network - an analogue of the human CNS - will be much more natural. Unfortunately, we do not have funding to perform the necessary experiments and the practical creation of a technical model of such a neural network. There is a need to develop an instrumental mathematical base for new technologies. The task of the work is to create new approaches for this by introducing new concepts and methods. Our mathematics is unusual for a mathematician, because here the fulcrum is the action, and not the result of the action as in classical mathematics. Therefore, our mathematics is adapted not only to obtain results, but also to directly control actions, which will certainly show its benefits on a fundamentally new type of neural networks with directly parallel calculations, for which it was created. Any action has much greater potential than its result. It is time for physicists to begin studying not only the manifestations of living energies, but also the living energies themselves, which are by no means expressed through objectivity and ordinary energies, although they are capable of manifesting themselves through a lower level - objectivity and ordinary energies. We, as mathematicians, offer a new corresponding apparatus for understanding nature and studying living energies. Significance of the article: in a new qualitatively different approach to the study of complex processes through new mathematical, hierarchical, dynamic structures, in particular those processes that are dealt with by Synergetics. The significance of our article is in the formation of the presumptive mathematical structure of subtle energies, this is being done for the first time in science, and the presumptive classification of the mathematical structures of subtle energies for the first time. The experiments of the 2022 Nobel laureates Asle Ahlen, John Clauser, Anton Zeilinger and the experiments in chemistry Nazhipa Valitov, experiments of prof. Be that as it may, we created classes of new mathematical structures, new mathematical singularities, i.e., made a contribution to the development of mathematics.

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^REVIEWER:

^{Volodymyr PASYNKOV - PhD of physic-mathematical science, assistant professor of applied mathematics and calculated techniques department of «National Metallurgical Academy», Ukraine.}

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CONTENTS:

Introduction

Part I. Generalizations of self-type and |||-type structures
Introduction
1.1 Elements of self-type and |||-type actions
1.1.1 Designations and definitions
1.1.2 Simplest equations
1.1.3 Syntax of |||-like actions
1.1.4 Generalizations of |||-like actions
1.1.5 Syntax of self-like formations
1.2 Inorganic beings
1.3 Some applications to physics
1.4 Elements of s-chemistry
1.5 S-arithmetics
1.6 Self-operators
1.7 Some remarks to Singular analysis
1.8 Matrix Interpretations
1.8.1 Interpretations with the observer
References

Part II. Elements of s-morphology
2.1 Energy of a non-living organism
2.2 Elements of s-morphology for living organism
2.3 Energy of a living organism of a person
2.4 Elements of s-morphology for bacteriums
2.5 Elements of s-morphology for viruses
References

Part III. GrSprt – elements and Their Applications
B.1 GrSprt – elements, self-type GrSprt – structures
Introduction
B.1.1 GrSprt – elements, self-type GrSprt- structures
B.1.2 Dynamic GrSprt – elements
B.1.3 GrSprt – elements for continual sets
B.1.4 Dynamic continual GrSprt – elements
B.1.5 The usage of GrSprt -elements for networks
B.1.6 Variable hierarchical dynamical structures (models) for dynamic, singular, hierarchical sets
B.1.7 PROGRAM OPERATORS GrSprt, tprGrSt
Appendix
References

Part IV. GrfSprt – elements and Their Applications
Introduction
F.3.1 Fuzzy GrSprt – elements (GrfSprt), self-type fuzzy GrSprt – structures
F.3.2 Dynamic GrfSprt – elements
F.3.3 GrfSprt – elements for continual sets
F.3.4 Dynamic continual GrfSprt – elements
F.3.5 The usage of GrfSprt -elements for networks
F.3.6 Variable hierarchical dynamical structures (models) for dynamic, singular, hierarchical sets
F.3.7 PROGRAM OPERATORS GrfSprt, tprGrfS
Appendix
References

References

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^{Year of publication: 2026
Language: English
Authors: Danilishyn I., Danilishyn O.
Translation: No
Translator: -}

^{Type: E-book
Number of pages: 222
Format: PDF (5,2 MB)
ISBN: 979-8-89898-335-2
UDC: 004:51(07)}