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Image formation in gamma-ray cameras is made by defining scintillation coordinates, produced by the absorption of gamma-quanta. By the present time different methods for scintillation coordinates defining have been developed based on previously measured and calculated amplitude-spatial features of a photodetector. The paper gives a method for estimating scintillation coordinates without any prior information. The method is based on approximation of the photodetecor response surface, located at the output window of permanent scintillation detector, on the scintillation light distribution function. For the approximation bicubic smoothing splines were used, which weight coefficients are set based on statistical features of measurement results. The paper proposes the approximation algorithm, taking into account geometry of photodetectors distribution at the output window of detector in the points of trigonal lattice. The algorithm can be applied in gamma cameras and other systems of gamma-rays imaging when using detectors such as gamma cameras. Relatively high computational intensiveness as compared to the Anger's method makes the proposed method more appropriate for off-line processing of accumulated data aimed at improving the image quality. [ABSTRACT FROM AUTHOR]

Despite the wide spread of computing devices and mathematical optimization methods in various fields of knowledge, little attention is paid to optimization of solving the problems of labor safety. In the author's opinion the promising solution is developing the methods of sound-absorbing cover optimization based on non-linear programming, one of which has been the objective of the work. The method for estimation of the optimal cover in premises with multi-tone noise conditions is proposed in the paper. Different noise tones can be absorbed by different materials with the most suitable properties. The method is based on random selection of surface area values of different materials, with further selection of the optimal cover. The paper gives the estimation algorithm and the obtained results using the Mathcad computer program. The estimation results indicate the regularities of achieving the optimum and a significant economic effect. The proposed estimation method and algorithm can be used for taking labor safety measures for noise reduction, namely, sound-absorbing covers design for production facilities. The paper has a scientific novelty, based on random selection of materials surface area values, and practical significance based on economic effect and working conditions improvement. [ABSTRACT FROM AUTHOR]

Recently we have seen the active penetration of computer algebra systems to the educational process because it allows to form an innovative learning technologies. Almost every branch of mathematics the Maple developed the separate specialized package commands. However, currently these technologies, despite its effectiveness and visibility, for various reasons, are still not common in the classroom. The purpose of this article is to review basic information about the capabilities of computer algebra to solve some common problems of the elementary number theory, and which can be used to solve educational problems. The paper describes the package description commands NumberTheory of the computer algebra system Maple. The methods of solving some common problems in the number theory in Maple. Using discussed the team package Maple a teacher can illustrate the problem solving in the classroom for the subject of the elementary number theory [ABSTRACT FROM AUTHOR]

The paper substantiates the conditions of seismic stability in the rock mass with cavities, on which protected objects are located, under constant seismic effects of mass explosions in quarries. Based on the ray-tracing method, a mathematical model of the interaction between longitudinal and transverse waves with a spherical cavity has been developed. An algorithm has been elaborated for determining the total static and dynamic loads along the spherical cavity perimeter from seismic explosion waves falling on the interface. The regularities of joint action of static loads have been determined, when located above the objects cavity, with allowance for the effect of the mass of cavity ceiling, the mass of the protected object above it and dynamic loads in the rock mass, and under the plane wave front fall on the cavity from different directions. The dependences of the change of total stresses referred to the incident wave stress at the interface of the rock mass and the cavity depending on the coordinate on its surface have been set. It has been established that the most dangerous points of cavity surface, in which destruction is likely to occur, are the cases when the seismic wave front falls on the cavity from the bottom directions typical for blasting operations in deep quarries. Under the arbitrary angles of the wave incidence on the cavity the stresses rearrange along the perimeter, which under different circumstances might lead to the mass breach and the fall of the protected objects, located above it, under the ground. [ABSTRACT FROM AUTHOR]