Search results

A model is constructed describing the interaction of systems of carbohydrate and fatty‐lipoid metabolism. The model equations can be presented in the form of a system of linear differential equations which combines 36 velocities of different metabolic and hormonal variances in different tissues into a system of combined feedback loops. A simplified variant is given of the model of a system of regulating sugar in blood. The mathematical model being available, it is possible to choose proper dosage. Mathematical models are used for practical medical applications.

The system of integrated equations was simplified for the stationary conditions of ion movement velocity. Several values of the synapse diameters have been chosen for the calculation. For each synapse diameter several values of exciting and inhibiting potentials have been taken. Graphic dependences of a change of the monosynaptic potential with respect to the length of the membrane are constructed. Calculation results enable one to coordinate on a sound basis the known experimental electrophysiological data of values of monosynaptic potentials with structural parameters of the membrane and synapses.

The equations take into account structural and geometrical parameters (sizes and a configuration of the synapse, geometrical properties of the neuron membrane, local changes of concentrations and potential) and determine changes of concentrations and the potential on the membrane and in hemispheres for discrete areas of the cytoplasm and the adjacent membrane part. Their investigation demonstrated that the equations may form the basis of sufficiently complete neuron description with due allowance for the fundamental physico‐chemical laws of motion and for the structural properties of separate parts of the nerve‐cell.

The purpose of this paper is to establish the nature of mathematical modeling of systems within the framework of the object-semantic methodology.

The initial methodological position of the object-semantic approach is the principle of constructing concepts of informatics proceeding from fundamental categories and laws. As the appropriate foundation, this paper accepts the system-physical meta-ontology is being developed in this paper.

The genesis of system modeling is considered in the aspect of the evolution of language tools in the direction of objectification. A new conception of formalized knowledge is being put forward as the mathematical form of fixing time-invariant relations of the universe, reflecting regularity of the dynamics of natural or anthropogenic organization. Object knowledge is considered as a key component of the mathematical model, and the solving of system information problems with its use is characterized as “work of knowledge.” The establishment of the meta-ontological essence of modern mathematical modeling allows us to formulate its fundamental limitations.

The establishment of system-physical limitations of modern mathematical modeling outlines the boundaries from which it is necessary to proceed in the development of future paradigms of cognition of the surrounding world, which presuppose convergence, synthesis of causal (physicalism) and target (elevationism) determination.