Annotation. This article shows a method for solving two periodic solutions of second order differential equations with piecewise continuous constant arguments in the form x''(t)+px''(t-1)=qx([t])+f(t ), where [.]denotes the function of the largest integer, p and q are non-zero real numbers, and f(t) is a real-valued periodic function. In the article, firstly, the conditions for the existence of 2-periodic solutions of second-order differential equations are given, and then the solution of the problem is represented as a linear system of algebraic equations
The derivation of kinetic equations for the oxidation processes by the free-radical nonbranched-chain mechanism is shown. This derivation is based on the proposed reaction scheme for the initiated addition of free radicals to the multiple bond of the molecular oxygen includes the addition reaction of the peroxyl free radical to the oxygen molecule to form the tetraoxyl free radical. This reaction competes with chain propagation reactions through a reactive free radical. The chain evolution stage in this scheme involves a few of free radicals, one of which – alkyl(or hydro)tetraoxyl – is relatively low-reactive and inhibits the chain process by shortening of the kinetic chain length. The rate equations (containing one to three parameters to be determined directly) are deduced using the quasi-steady-state treatment. These kinetic equations were used to describe the γ-induced nonbranched-chain processes of free-radical oxidation of liquid o-xylene at 373 K and hydrogen dissolved in water containing various amounts of oxygen at 296 K. The ratios of rate constants of competing reactions and rate constants of addition reactions to the molecular oxygen are defined. In these processes the oxygen with the increase of its concentration begins to act as an oxidation autoinhibitor (or an antioxidant), and the rate of peroxide formation as a function of the dissolved oxygen concentration has a maximum. It is shown that a maximum in these curves arises from the competition between hydrocarbon (or hydrogen) molecules and dioxygen for reacting with the emerging peroxyl 1:1 adduct radical. From the energetic standpoint possible nonchain pathways of the free-radical oxidation of hydrogen and the routes of ozone decay via the reaction with the hydroxyl free radical in the upper atmosphere (including the addition yielding the hydrotetraoxyl free radical, which can be an intermediate in the sequence of conversions of biologically hazardous UV radiation energy) were examined. The energetics of the key radical-molecule gas-phase reactions is considered.
An algorithm for calculating multi-span continuous beams is developed on the basis of the integral deformation modulus method. This takes into account the nonlinear and nonequilibrium properties of concrete deformation, the rheological equations of the mechanical state.
The article discusses the possibilities of using nonlinear control systems in production processes. An analysis of synergetic control systems is presented as a science based on a unified concept for the self-organization of dynamic systems of production processes, the main properties of nonlinear control systems having the structure of various stationary states. Based on a three-dimensional system of nonlinear autonomous Lorentz differential equations of the first order, results of stability preservation for synergetic systems are obtained, which allows the design of a special three-dimensional subspace
The article presents opinions about the method and sequence of explanation using Maxwell's equations in the explanation of laws and regulations in the department of electromagnetism to students. In the educational process organized on the basis of the proposed sequence, students will understand all the laws of electromagnetism and will be able to apply them to natural phenomena and processes.
The article is devoted to the development of a mathematical model of the process of geometric nonlinear deformation of thin magnetoelastic plates of a complex structural shape based on the Hamilton-Ostrogradsky variational principle, and conducting computational experiments. In this case, the three-dimensional mathematical model was transferred to a two-dimensional view using the Kirchhoff-Liav hypothesis. Cauchy's relationship, Hooke's law, Lawrence's force and Maxwell's electromagnetic tensor were used to determine kinetic and potential energy and work done by external forces. The effects of the electromagnetic field on the deformation stress state of the magnetoelastic plate were observed, as a result, a mathematical model was created in the form of a system of differential differential equations with initial and boundary conditions for displacement. To solve the equation, a calculation algorithm was developed using the R-function, Bubnov-Galerkin, Newmark, Gaussian, Gaussian squares, and Iteration number methods. Calculation experiments were carried out in various mechanical states of the magneto-elastic plate, its borders were tightly fixed, one side was hinged and the other side was free, and numerical results were obtained. A comparative analysis of the results of the calculations was presented.
Asynchronous motors require its study not only in stationary modes, but also in dynamic ones. At the same time, this makes it possible to formulate the corresponding requirements for automatic control devices of a regulated IM, the implementation of which will ensure the optimal course of transient processes in the electric drive system; it requires its study not only in stationary modes, but also in dynamic ones. This simultaneously makes it possible to formulate the corresponding requirements for automatic control devices of variable IM, the implementation of which will ensure the optimal course of transient processes in the electric drive system.
The study of electromechanical transient modes requires a joint consideration and solution of the equations of equilibrium of electrical quantities in the windings of the machine and the equations of motion of an electric drive.
In this work, an initial boundary value problem is posed for the fractional order diffusion equation, and the posed problem is approximately reduced to a system of algebraic equations using the finite difference method. Using the Python software package, an approximate solution to the problem was found