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Scientific monographs

Mathematical Fundamentals of Interpretations Theory (Types of Future Science) and Fundamentally New Approach to Elementary Particles, Physics, Biology and Dynamic Programming by Pself-type and Paself-type: monograph

DOI
https://doi.org/10.36074/mfit.monograph-2026
Published
2026-01-20

Abstract

Here are given mathematical fundamentals of interpretations theory (future science) and fundamentally new approach to elementary particles, induction, energy conservation, Dynamic Programming by pself-type and paself-type. Digitization of interpretations forms allows the use of digital technologies through appropriate programming. In science, there are two approaches to studying nature beyond classical science (conditionally, the (1, 1)-interpretation): the approach through quantum mechanics (conditionally, the (1, 2)-interpretation) and dynamic mathematics (conditionally, the (2, 1)-interpretation). Both approaches have the same "root": |||, but at two opposite ends: quantum mechanics ((1, 2)-interpretation) by |||-1 by and dynamic mathematics (2, 1)-interpretation) by ||| and ((1, 2)-interpretation) by |||-1 and other interpretations with using hierarchical structures of measures, some equations.  Therefore, the conclusions are similar, but for different objects and processes. This article applies to physics, Dynamic Programming, and neural networks of the new direct-parallel and direct-accumulative types. For now, this is only an introductory article. 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. For this, some aspects are proposed for consideration of Dynamic Science. self science our theory - science here acts as a space for the application of our theory in the self-format, i.e., any place of science, in particular physics, can act as a place for the "location" of the self. It contains itself (accommodates any action C) in any place of science. 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. Objective uncertainties in any case can mean manifestations of processes and objects that are fundamentally not determined by conventional deterministic methods. Since dynamic mathematics places the primary emphasis on the dynamics of energy, rather than on objectivity, the level of approach to studying processes expands. 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. Social justice is fundamentally impossible as long as education (training) is based on achieving results, and not on the process. 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 monograph 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. SIIprt – elements and their applications
Introduction
1.1 SIIprt– elements
1.2 Dynamic SIIprt – elements
1.3 SIIprt – elements for continual sets
1.4 Dynamic continual SIIprt – elements
1.5 The usage of SIIprt-elements for networks
1.6 Variable hierarchical dynamical structures (models) for dynamic, singular, hierarchical sets
1.7 Applications Dynamic Sets Theory to physics and chemistry
1.8 PROGRAM OPERATORS SIIprt, tprSII, SII1epr, SIIeprt1
Appendix
References

Part II. Mathematical fundamentals of interpretations theory (types of future science)
Introduction
2.1 Elements of mathematical theory of interpretations
    2.1.1 Simplest operations with interpretations forms by containment
    2.1.2 Syntax of self-like formations
    2.1.3 Syntax of |||
2.2 Elements of mathematical theory of fuzzy interpretations
    2.2.1 Simplest operations with fuzzy interpretations forms by containment
    2.2.2 Syntax of fuzzy self-like formations
    2.2.3 Syntax of fuzzy |||
2.3 Fundamentally new approachs to physics
    2.3.1 Fundamentally new approach to elementary particles
    2.3.2 Induction
2.4 Elements of Dynamic Biology
References

Part III. Mathematical fundamentals of the Dynamic programming by pself-type and paself-type Introduction
3.1 Program operators Sprt and their pself-type
    3.1.1 Program operators Sprt and their pself-type
    3.1.2 The usage of Sprt-elements for networks
3.2 Program operators ffSprt and their pself-type
    3.2.1 The usage of ffSprt-elements for networks
3.3 Program operators SСprt-type and their pself-type
    3.3.1 Program operators SCprt-type and their pself-type
    3.3.2 The usage of SCprt-elements for networks
    3.3.3 The usage of SfCprt-elements for networks
3.4 FUZZY PROGRAM OPERATORS SfCprt, tprSfC, S1fCepr, SfCeprt1
3.5 Introduction to FUZZY PROGRAM OPERATORS fDprt, ftprD, fD1epr, fDeprt1
3.6 FUZZY PROGRAM OPERATORS Rprt, tprR, R1epr, Reprt1
3.7 Rprt-networks
3.8 Introduction to FUZZY PROGRAM OPERATORS SDS, tSDS, fD1epr, fDeprt1
3.9 Introduction to FUZZY PROGRAM OPERATORS SRS, tSRS, fR1epr, fReprt1
3.10 Program operators PrSprt, PrtSpr, S1e, Set1 and their pselftype
3.11 Program operators PrfSprt, PrtfSpr, fS1e, fSet1 and their pselftype
3.12 Program operators PrffSprt, PrtffSpr, S1e, Set1 and their pselftype
3.13 Program operators PrSCprt, PrtSCpr, SC1e, SCet1 and their pself-type
3.14 FSUprt and FS3Uf programming and their pselftype
3.15 The usage of FSUprt-elements for networks
3.16 RANDOM PROGRAM OPERATORS FSUprt, fftprS, FSU1epr, FSUeprt1 and their pself-type
3.17 The usage of fSAprt-elements for networks
3.18 FUZZY PROGRAM OPERATORS fSAprt, ftprSA, fS1Aepr, fSAeprt1 and their pself-type
3.19 Introduction to FUZZY PROGRAM OPERATORS Flprt,tprFL
3.20 Introduction to FUZZY PROGRAM OPERATORS FWprt, tprFW
3.21 Introduction to FUZZY PROGRAM OPERATORS FZprt, tprFZ
3.22 Zprt-networks
3.23 Introduction to FUZZY PROGRAM OPERATORS FV1prt
3.24 Interpretations forms programming by containment
3.25 Interpretations forms programming by other actions
3.26 Nth-programming
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: 336
Format: PDF (6,5 MB)
ISBN: 979-8-89898-334-5
UDC: 004:51(07)

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