The material in this monograph is a development of the previous monograph of the authors: «Hierarchical dynamic mathematical structures (models) theory» (USA, 2024); ISBN 979-8-89217-809-9.
We are just starting from the assumed structure of self-organization, since we are interested not so much in the numerical calculation of this as in the structure of self-organization itself, its formation (construction) for the necessary purposes and its management. Our task: to understand 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). Considering object A as the value of dynamic variable P, we can reassign P:= B at the top level and instead of A we will have object B, and also perform any other parallel dynamic operations with objects. That is, our world will be perceived as a Dynamic Programming environment. Dynamic programming is an extension of science for "working" with the top and middle levels. Here information is transformed into actions. Energy Internet: a) transmission of necessary singularities (subtle energies) (connection to necessary singularities (subtle energies)), b) transmission of necessary self-structures (subtle energies) (connection to necessary self-structures) etc. It is also necessary to construct a bioSmnsprt on living, grown elements of the central nervous system, in particular, neurons. It is also possible to construct another version of bioSmnsprt, using a viral model, on living, grown bacteriophages. We have simply outlined some aspects; it is too early to develop them without experimental study. All problems have a solution, the only question is: a) in complete identification with the problem, b) the “breadth of the field” of values that you can provide. Our mathematics is unusual for a mathematician, because here the fulcrum is the action, and not the result of an 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 advantages 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. The significance of the monograph: in a new qualitatively different approach to the study of complex processes through new mathematical hierarchical parallel dynamic structures, in particular those processes that are studied by synergetics. Our approach is not based on deterministic equations that generate self-organization, which is very difficult to study and gives very small results for a very limited class of problems and does not provide the most important thing - the structure of self-organization. We simply start from the assumed structure of self-organization, since we are interested not so much in the numerical calculation of this, but in the structure of self-organization itself, its formation (construction) for the necessary purposes and its management. Although we are also interested in numerical calculations. Laureates of the Nobel Prize in Physics 2023 Ferenc Kraus and his colleagues Pierre Agostini and Anne L'Huillier used a short-pulse laser to generate attosecond pulses of light to study the fuzzy dynamics of electrons in matter. According to our Synthesis-Type Singularity Theory, its action corresponds to a singularity, allowing the upper level of subtle energies to be reached to manipulate the lower levels. In In April 2023, we proposed to use a short-pulse laser to achieve desired goals using a directly parallel neural network. We then proposed a fundamental development of this directly parallel neural network. The significance of our monograph lies in the formation of the proposed mathematical structure of subtle energies, this is done for the first time in science, and the proposed classification of mathematical structures of subtle energies for the first time. The experiments of 2022 Nobel Prize winners Asle Allen, John Clauser, Anton Zeilinger and the chemistry experiments of Nazhipa Valitov eloquently demonstrate, that we are right and that these studies are necessary. Be that as it may, we have created classes of new mathematical structures, new fuzzy mathematical singularities, i.e. we have contributed 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. Sprt – elements and their applications
Introduction
1.1 Sprt – elements
1.2 Dynamic Sprt – elements
1.3 Sprt – elements for continual sets
1.4 Dynamic continual Sprt – elements
1.5 The usage of Sprt-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
2 Supplement: Connection Sprt – elements with usual functionals and operators
References
Part II. Fuzzy fSprt – elements and thelir applications
Introduction
2.1 Fuzzy fSprt– elements
3 2.2 Fuzzy dynamic fSprt – elements
2.3 Fuzzy Sprt – elements for continual fuzzy sets
2.4 Fuzzy dynamic continual fSprt – elements
2.5 The usage of ffSprt-elements for networks
2.6 Variable fuzzy hierarchical dynamic fuzzy structures (models, operators) for dynamic, singular, hierarchical fuzzy sets
2.7 FUZZY PROGRAM OPERATORS ffSprt, fftprS, ffS1epr, ffSeprt
Appendix
References
Part III. Classes of other structural elements
A Dprt – elements, self-type Dprt-structures and their applications
A.1 Dprt – elements, self-type Dprt-structures
A.2 fDprt – elements, self-type fDprt- structures
A.3 Elements of the theory of variables of fuzzy hierarchical dynamic fuzzy operators
A.4 Introduction to FUZZY PROGRAM OPERATORS fDprt, ftprD
B Rprt – elements, self-type Rprt-structures and their applications
B.1 Rprt – elements, self-type Rprt-structures
B.2 Variable fuzzy hierarchical dynamic fuzzy structures (models) for dynamic, singular, hierarchical fuzzy sets
B.3 FUZZY PROGRAM OPERATORS fRprt, ftprR
B.4 Rprt-networks
C Lprt – elements, self-type Lprt-structures and their applications
C.1 Lprt – elements, self-type Lprt-structures
C.2 FLprt – elements, self-type FLprt- structures
C.3 Elements of the theory of variables of fuzzy hierarchical fuzzy dynamic operators: FLprt
C.4 Introduction to FUZZY PROGRAM OPERATORS Flprt, tprFL
D SDS–elements, self-type SDS-structures and their applications
E SRS – elements, self-type SRS -structures and their applications
F Parallel Sprt – elements, self-,typ1e PrSprt-structures and their applications
F.1 Parallel Sprt – elements, self-type PrSprt-structures
F.2 PrfSprt – elements, self-type PrfSprt-structures
F.3 PrffSprt – elements, self-type PrffSprt-structures
References
Part IV. Theory of singularities of the type synthesizing. Some aspects of directly parallel operation of neural networks and their subtle energy
G Theory of singularities of the type synthesizing
H Some aspects of directly parallel operation of neural networks and their subtle energy
References
Supplement 1: S1t-elements
Supplement 2: Some aspects of dental restoration through the use of neural networks
Conclusions
References
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Year of publication: 2024
Language: English
Authors: Danilishyn I., Danilishyn O.
Translation: No
Translator: -
Type: E-book
Number of pages: 442
Format: PDF (8 MB)
ISBN: 979-8-89217-806-8
UDC: 004:51(07)