Applied Mathematics and Control Sciences

The paper discusses a method which permits obtain effective conditions of the solvability for one class of singular at the independent variable differential and functional differential equations. The proposed method is based on the application of the Shur test to the integral operators which are generalizations of Cesaro operator. Also the generalizations of Cesaro operator norms estimates are obtained.

Diseases of the temporomandibular joint is subject to 40 % of people in the world aged 20-40. Currently, the etymology of diseases of the temporomandibular joint is poorly studied, there is only an approximate their medical classification. A study of the literature shows that, as a rule, virtually none of the components of the joint disease is not without its mechanical damage. The disc of the temporomandibular joint plays a key role in the performance of the joint and the dentoalveolar complex. The main factor influencing the use of the disc - the magnitude of the mechanical stresses caused by different loads. Typically, treatment of diseases of this kind are non-invasive, but in complex cases surgical methods are used. To avoid surgical intervention and prevention of diseases at an early stage, it is necessary to conduct mathematical modeling of biomechanical disc of the temporomandibular joint. The study of the histology and physiology of the disc shows that the optimal model for the mechanical behavior of the disc under load - isotropic poroelastic model proposed by M.A. Bio. It allows to estimate the stress state of the disk and explain the role of the synovial fluid inside it in terms of the mechanics. In the formulation of the problem based on the theory of linear isotropic poroelasticity a model of behavior of the disc of the temporomandibular joint under load is constructed. The solution is reduced to an initial boundary value problem for the non-stationary parabolic equation. Analysis of results shows that the distribution of the fluid pressure in the disc by applying a constant force allows to reduce the amount of stress in elastic cartilage skeleton, protecting it from damage. The dependence of the pressure of the synovial fluid from the hydraulic permeability coefficient is investigated, which analyzed the results of the decision model with different values of this coefficient.

The model of planning in large industrial enterprise subject to order priority, work-in-progress, reservation remains for order is considered.

A numerical model of stereolithography (SLA) for the manufacture of photopolymer prototypes implemented in ANSYS is presented. A method for reducing defects by modifying the shape of the original geometry is offered. A comparative analysis of deviations of the form after two stages of analysis (the original and modified geometry) for three variants of design of a prototype of the simplest detail is done. It is shown that the presented method allows to reduce shape defects by more than 5 times.