Mathematical uncertainties and their applications: monograph

Abstract

The monograph first task: to understand hierarchy of energies in the Universe and the principles of functioning of living energy (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: 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 eloquently demonstrate that we are right and that these studies are necessary. 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. Mathematical uncertainties and their applications
Introduction
1.1 Mathematical uncertainties
1.2 Regular uncertainties
1.3 Singular uncertainties
1.4 Algebra of Singular Transformations
1.5 Beginnings of Mathematical uncertainties
Calculations
1.6 Beginnings of uncertain dynamic geometry
1.7 Dynamic interpretation of uncertainties such as random events
1.8 Self-type structures of probability
1.9 |||-type structures of probability
Supplement: Types of dynamic concepts
References

Part II. Dynamic interpretation of uncertainties such as random events
Introduction
2.1 SUprt– elements
2.2 Dynamic SUprt – elements
2.3 SUprt – elements for continual random sets
2.4 The dynamic continual random SUprt – elements
2.5 The usage of SUprt-elements for networks
2.6 Variable random hierarchical dynamic random structures (models, operators) for dynamic, singular, hierarchical random sets
2.7 RANDOM PROGRAM OPERATORS SUprt,fftprSU, SU1epr, SUeprt1
References

Part III. Dynamic interpretation of uncertainties such as random events with fuzzy probabilities
3.1 Fuzzy SUprt – elements
3.2 Random dynamic fuzzy SUprt – elements
3.3 FSUprt – elements for continual fuzzy sets
3.4 The dynamic random continual fuzzy Sprt – elements
3.5 The usage of FSUprt-elements for networks
3.6 Variable random hierarchical dynamic fuzzy structures (models, operators) for dynamic, singular, hierarchical fuzzy sets
3.7 RANDOM PROGRAM OPERATORS FSUprt, fftprS, FSU1epr, FSUeprt1 their applications
References

Part IV. SAprt – elements and their applications
4.1 Fuzzy SAprt – elements
4.2 The dynamic fSAprt – elements
4.3 fSAprt – elements for continual fuzzy sets
4.4 The dynamic continual fuzzy SAprt – elements
4.5 The usage of fSAprt-elements for networks
4.6 Variable fuzzy hierarchical dynamic fuzzy structures (models, operators) for dynamic, singular, hierarchical fuzzy sets
4.7 FUZZY PROGRAM OPERATORS fSAprt, ftprSA, fS1Aepr, fSAeprt1
References

Part V. Uprt-elements and Their Applications
A Uprt – elements, self-type Uprt-structures
A.1 Uprt – elements, self-type Uprt-structures
A.2 Dynamic Uprt – elements, self-type dynamic Uprtstructures
A.3 FUprt – elements, self-type FUprt-structures
A.4 Dynamic FUprt – elements, self-type dynamic FUprt-structures
A.5 Elements of the theory of variables of fuzzy hierarchical fuzzy dynamic operators: FUprt
A.6 Introduction to FUZZY PROGRAM OPERATORS FUprt, tprFU, FU1epr, FUeprt1
A.7 Paradoxical singularities (singularities of disintegration&synthesis)
A.8 Singularities algebra
A.9 Types, forms internal and external, structures of self and |||
A.10 Types, forms internal and external, structures of potential self, potential ||| and others potential singularities
A.11 Some available types of "pseudo-living energy"
A.12 Uprt-networks
A.13 Some aspects of directly parallel operation of neural networks
References

Part VI. Applications for Physics
References

References

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^{Year of publication: 2025
Language: English
Authors: Danilishyn I., Danilishyn O.
Translation: No
Translator: -}

^{Type: E-book
Number of pages: 612
Format: PDF (14,0 MB)
ISBN: 979-8-89660-284-2
UDC: 004:51(07)}