With progress in depth, the most effective way to increase the field of application of room and pillar system is the transition to the combined support of the ore-concrete-ore or concreteore-concrete methods. With this arrangement, treatment of mine workings along the strike of the ore body enables the use of mobile equipment, which allows increasing performance indicators of stopping: performance ofsecond working, labor of face worker, labor intensity.

В статье рассматривается проблема организации оценки уровня сформированности компетенций студентов, обучающихся с использованием дистанционных образовательных технологий. Автором обосновывается математическая модель оценки уровня сформированности компетенций студентов, которая учитывает структуру существующих электронных курсов в системе дистанционного обучения ФГБОУ ВПО «Магнитогорский государственный технический университет». Раскрываются основные положения технологии проведения оценки уровня сформированности компетенций студентов.

Modern methods of diagnosing of maxillary bones in various clinical situations presume a method of computer tomography. In some cases, the treatment planning according to three-dimensional image cannot be performed and the question of creation of the biomechanical model study area arises. Various methods of computer-aided design and three-dimensional modeling are worth while using to achieve the realization of the task.
Ivanov D.V., Lepilin A.V., Smirnov D.A., Dol A.V. The possibility of different CAD systems in the construction of mathematical model of bone tissue // Saratov Journal of Medical Scientific Research, Vol. 9, Issue 3, 2013, pp. 403-405

Found that the provision of the required transmission rate of WiMAX can be achieved by solving the problem of frequency resource allocation in the downlink. As a result analyzed by the existing mechanisms of the frequency distribution of resources between subscriber stations in a downlink wireless network, operating using the technology of WiMAX. Based on the identified drawbacks of making a mathematical model the distribution of sub-channels in the network standard, IEEE 802.16, which provides a guaranteed rate subscriber stations in the downlink and submitted by a number of linear constraint equations. The novelty of the model lies in the formulation of the problem the frequency distribution of the resource allocation problem as a sub-channel with a firmly fixed number of subcarriers in each of them. The solution to the optimization problem sub-channel allocation proposed to carry out a multiple objective functions that the available frequency resources in order to allocate a minimum number of sub-channels, the distribution of the available frequency resources in order to allocate a minimum transfer speed of each the subscriber stations, the distribution of the available frequency resources to jointly minimize the number of used sub-channels and a transmission rate allocated to subscriber stations in a downlink. A comparative analysis of the solutions obtained by using different objective functions.
Al-Janabi Haider Dheyaa Kamil, Al-Dulaimi Aymen Mohammed Khodayer, Abed Ahmed Hassan Model Guaranteed Transmission Rate Providing in WiMAX Downlink // Проблеми телекомунікацій, Vol. 2013, Issue 1, 2013, pp. 3-12

In the paper the mathematical model of multipath routing with load balancing in the MPLS network is proposed. This model describes the processes of routing and distribution links resource. This model takes into account the characters of links (duplex, half-duplex or simplex links) and prevents the effect of packets looping. And criterion of load balancing in proposed model is quality service parameters.
Lemeshko O., Vavenko T., Ovchinnikov K. Design of multipath routing scheme with load balancing in MPLS-network // XIIth International Conference THE EXPERIENCE OF DESIGNING AND APPLICATION OF CAD SYSTEMS IN MICROELECTRONICS, Polyana-Svalyava-(Zakarpattya), UKRAINE 19-23 February 2013. – P. 211-213.

Action potential is considered to be one of primary responses of a plant to action of various environmental factors. Understanding of plant action potential propagation mechanisms requires experimental investigation as well as a simulation; however, a detailed mathematical model of plant electrical signal transmission is absent. Here, the mathematical model of action potential propagation in plants has been worked out. The model is a two-dimensional system of excitable cells; each of them is electrically coupled with four neighboring ones. Ion diffusion between excitable cell apoplast areas is also taken into account. The action potential generation in a single cell has been described on the basis of our previous model. The model simulates active and passive signal transmission well enough. It has been used to analyze theoretically the influence of cell to cell electrical conductivity and H+-ATPase activity on the signal transmission in plants. An increase of cell to cell electrical conductivity has been shown to stimulate an increase of the length constant, the action potential propagation velocity and the temperature threshold, while the membrane potential threshold being weakly changed. The growth of H+-ATPase activity has been found to induce to the increase of temperature and membrane potential thresholds and the reduction of the length constant and the action potential propagation velocity.
J. Theor. Biol., 2011. V. 291. P. 47–55.

Abstract—The type of mathematical model of the production function is very important for an adequate pre diction of optimal fertilizer rates and their effect on yield. In this case, easily calibrated regression models can’t be used for extrapolation, and the models proposed by Mitscherlich, Spillman, Baule, and von Bogus lawski are difficult to calibrate even in the onedimensional case. An explanation of the good approximating capacity of logarithmic transformation of the argument of the linearizing ascending branch of the production function is found on the basis of model investigations. An algorithm for simplified calibration of the von Boguslawski mathematical model is developed: (1) transform fertilizer rates into a logarithmic form after introducing a correction for the initial content of the nutrient element in soil; (2) estimate the maximum yield under experimental conditions; convert the yield data into a relative form; (3) discriminate the data based on the interval permissible for approximation; (4) find the parameters of the linear model by the leastsquares method and on their basis calculate the parameters of the von Boguslawski model, thereby correcting the form of the approximation and obtaining the possibility of its extrapolation.
DOI: 10.3103/S1068367411010162

This paper focuses on mathematical models of distribution channels in the multi-mesh-networks, the 802.11 standard by which the balancing of mesh-stations on domains conflicts with their territorial remoteness and activity that can improve the performance of multichannel mesh network as a whole.
Gogolieva M., Garkusha S., Abed A.H. A mathematical model of channel distribution in multichannel mesh networks 802.11 // 11-th International Conference THE EXPERIENCE OF DESIGNING AND APPLICATION OF CAD SYSTEMS IN MICROELECTRONICS Polyana-Svalyava-(Zakarpattya), UKRAINE 23 - 25 February 2011: Publishing House of Lviv Polytechnic, 2011. – P. 71-73.

In the paper the mathematical model of traffic management in the MPLS-TE DiffServ network is proposed. This model describes the processes of routing and distribution channel resource. In article the method of two-level traffic management in the MPLS-TE DiffServ network is offered to improve the scalability of the solutions on the basis of interactions prediction.
Lemeshko O.V., Ahmad M. Hailan, Starkova O.V. Multi-level traffic management in the MPLS-TE DiffServ network // 11-th International Conference THE EXPERIENCE OF DESIGNING AND APPLICATION OF CAD SYSTEMS IN MICROELECTRONICS Polyana-Svalyava-(Zakarpattya), UKRAINE 23 - 25 February 2011: Publishing House of Lviv Polytechnic, 2011. – P. 118-120.

Рассмотрены математические модели распространения эпидемий, предназначенные для создания эпидемиологической геоинформационной системы поддержки принятия решений. Mathematical models of epidemic spread, intended for creating an epidemiological GIS decision sup-port system, are considered.