In the present work the problems of correctness of a linear inverse problem for the mixed type equation of the second kind of the second order in three-dimensional space are considered. For this problem, the theorems on existence and uniqueness of the solution are proved in certain class by «ε-regularization», Galerkin’s and of successive approximations methods.
In the study of problems of mathematical physics, the methods of differential and integral equations are used. This paper is an example of the application of these methods to the solution of a single boundary-value problem for a third-order parabolic-hyperbolic equation in a concave hexagonal domain.
The existence and the uniqueness of solution of local problem for degenerating mixed type equation is investigated. Considering parabolic-hyperbolic equation involve the Caputo fractional derivative. The uniqueness of solution is proved using the method of the extremume principle and integral energy, the existence is proved by the method of integral equations.
A mathematical model of the propagation of the nervous pulse of FitzHugh-Nagumo is proposed, which takes into account the effect of heredity. This hereditary model is described by an integro-differential equation with a power kernel — a function of memory. The algorithm for the numerical solution of this model is implemented in a computer program in the environment of symbolic mathematics Maple. With the help of this program, calculated curves — oscillograms, and also phase trajectories were constructed depending on various values of control parameters.
We consider the Riccati differential equation with a fractional derivative of variable order. The introduction of a derivative of a fractional variable order into the initial equation determines the property of the medium — the memory effect or the heredity, which consists in the dependence of the current state of the dynamic system on its previous states.
On the basis of theoretical-probabilistic approach to the Kamchatka earthquakes catalog the subset of random events was specified and their probabilities were calculated. The received probabilities of random events considered as predictors of strong earthquakes with energy class KS 14. Their effectiveness V, reliability R and prediction efficiency (informative) J were calculated for periods of seismic activity and seismic calm.
The article discusses methods for solving optimization problems with the use of table processor tools — «Solution search»and «Script manager». Solutions of several examples of linear and integer optimization are presented. The tasks of optimization are widely used in science, economics, engineering and are used when it is necessary to obtain the best results under certain conditions.
The article shows the methodology for conducting a lesson on the topic «Account to three, number and figure three»with presentation as presentation. The main stages of training have been elaborated in detail: preparation for learning new material, studying new material, fixing, repeating. The abstract can be used in the second younger group of the kindergarten.