Introduction to Dynamic Mathematics: dynamic sets, dynamic operators and their applications
Authors: Danilishyn Illia , Danilishyn Oleksandr 
Published: December 2024

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.