The surface structure of silicon single crystals grown in the [111] direction using the floating zone technique and the distribution of electric parameters of these crystals over the crystal length are investigated. Geometrical parameters of the morphological characteristics of deltoidal icositetrahedral habit are determined. It is demonstrated that, similarly to ridgelike protrusions, bulges are morphological elements of the ingot surface that characterize the rhombododecahedral and deltoidal icositetrahedral growth habits. It is established that, in the region of bulges, the nonequilibrium charge carriers lifetime distribution is more inhomogeneous due to instability of the crystallization rate.

The localized inverse problem of electrocardiography is formulated and a solution method is proposed. The method allows determining the potential of the cardiac electric field on one of the heart sections.

Introduction: A long-term priority of contemporary biomedicine is the problem of ischemic heart disease. The aim of our investigation was to study, with the use of mathematical and computer models, the tendencies of variation of the morphological characteristics of the T wave of the ECG following a change of parameters of the transmembrane action potential in an “ischemic” zone with evaluation of the possible use of the results in computer based diagnostic algorithms. Methods: Computer experiments were executed on a system for 3D-modeling of the cardiac electrical activity with the aid of our earlier developed model of ECG genesis (cellular automaton of about a million elements of the Myocardium-His-Purkinje type), the parameters of which are electrophysiological, anatomical, and biophysical characteristics of heart muscle. Processing of the model ECG was carried out with our special program. Results: Methods of segmentation of the model hearts on separate compartments (segments), as well as calculation and visualization of the partial contribution of any segment into the potential of the chosen lead against a background of the summary ECG have been developed and were used in the given work. For the modeled cardiosignals, some «medical» evaluation in terms of the Minnesota Code has been carried out and a set of characteristics, similar to parameters of the real ECG, has been measured and calculated. The most sensitive parameters of “ECG” for ischemia have been selected and analysed. Conclusion: Systematic comparative investigations on the basis of modeling ischemia of various localization, extensiveness and degree of intensity are necessary. In conclusion, it should also be noted that the method of phase space is far from having exhausted itself and, as a preliminary consideration, may be developed into an n-dimensional area during a search for a complex of informative parameters for new diagnostic algorithms.

We consider the three-dimensional Dirichlet problem for equations of elliptic type in inhomogeneous media. The problem can be reduced to a system of loaded Fredholm integral equations of the second kind over the volume. We prove the uniqueness of a classical solution of the problem. We suggest a numerical solution algorithm of iterative type. An example of the numerical solution of the problem is considered, and the convergence of the iterative procedure is demonstrated numerically.

The problem of determining the point on the heart surface (projection) nearest to the arrhythmogenic focus, which is located inside the heart, is considered. Localization of this point is crucial for a successful cardiac ablation procedure. The sought projection is calculated on the basis of solving the inverse electrocardiography problem, which is a generalization of the Cauchy problem for the Laplace equation. The inverse electrocardiography problem is solved by the boundary integral equation and Tikhonov regularization methods. Examples of test computations are demonstrated, and the results of processing real electrophysiological data are presented and compared with the medical observation data.

Methods of assessing the electrophysiological state of the heart by solving the inverse problem of electrocardiography in potential form are actively used in clinical practice. Some results suggest, however, that on its own the electric potential of the heart may not be sufficient for diagnosing complex cases of cardiac arrhythmia. Studies have shown that the absolute value of the potential gradient is an important characteristic that produces a more precise assessment of the electrophysiological state of the heart. In this article we propose an algorithm for numerical reconstruction of the potential gradients from the solution of the inverse problem of electrocardiography.

The article presents a modification of the algorithm for the inverse problem of electrocardiography originally proposed in [ 6 ]. The modification is intended to improve the computation accuracy and to reduce the computing time.

A numerical method is proposed for solving an inverse electrocardiography problem for a medium with a piecewise constant electrical conductivity. The method is based on the method of boundary integral equations and Tikhonov regularization.

The inverse problem for mathematical models of heart excitation is stated; this problem is to determine the initial condition in the initial-boundary value problem for an evolutionary system of partial differential equations given the volume potential whose density is determined by the solution to the evolutionary system. It is proved that the solution of the inverse problem in the generic statement is not unique.

Aspects are considered of providing safe oxidative conversion of acid gases directed in plant handling ethanolaminar purification of petroleum fetching gases in a fluidized bed of spherical catalyst. Details are established of an automated machine system for controlling the process in accordance with the current transformation from hazardous production objects. A unified approach is provided for analog and digital regulators with contours for maintaining the control by reference to perturbation in the reverse-coupling contour, which allows one to use a model to realize automatic regulation in a control computer. The basis is given for regulating the optimal relationship between volume flow rates for oxygen and hydrogen sulfide.

We consider numerical methods for solving inverse problems that arise in heart electrophysiology. The first inverse problem is the Cauchy problem for the Laplace equation. Its solution algorithm is based on the Tikhonov regularization method and the method of boundary integral equations. The second inverse problem is the problem of finding the discontinuity surface of the coefficient of conductivity of a medium on the basis of the potential and its normal derivative given on the exterior surface. For its numerical solution, we suggest a method based on the method of boundary integral equations and the assumption on a special representation of the unknown surface.

Boundary integral equation methods are considered for computing dc fields in three-dimensional regions filled with a piecewise-homogeneous medium. The problem is formulated and a system of Fredholm boundary integral equations of first kind is constructed, following directly from Green’s formula. The numerical solution stages are considered in detail, including construction and triangulation of the numerical surfaces, evaluation of surface integrals, and solution of a system of block-matrix equations.

The advantages and drawbacks of methods used to produce inert gases at oil and gas refineries are analyzed. The promising nature of the development of units for the production of inert gases based on treatment of flue gases released by these refineries is demonstrated in connection with trends established for the reconstruction and construction of sulfur-producing plants. Principal approaches to the development of a procedure for producing inert gases are outlined. Primary among these approaches is process and equipment integration for the cleaning of flue gases in a Klaus plant with a unit for tertiary treatment of the flue gases and the production of nitrogen and carbon dioxide.

This is the first of two articles devoted to a detailed description of studies on measurements of the electric conductivity of aqueous electrolytes. A theoretical analysis of the problem is presented and the methods and techniques for independently measuring the active (real part) and reactive (imaginary part) complex resistance are developed. The errors in the values measured are also analyzed.

CEA is involved in the design of the cooling scheme of the future ITER tokamak. Pulsed operation of ITER will result in heat load variations (which refrigerators have difficulties to cope with). A load smoothing device has been proposed by the ITER team which needs to be validated. To do this, a scaled-down experiment (hereafter also called model) has been proposed and studied in the framework of an EFDA sub-task. This paper presents the test loop dimensioning and the preliminary design for constructing the model. The choice of the relevant design criteria had to be defined so as to obtain in fine a geometric ratio between the ITER system and the model. It is shown that this ratio is then applicable for the mass flow rates as well as the different volumes (heat exchanger, pipes,…) existing on ITER and on the proposed experimental model. Details of the scaling, model design and 3D views corresponding to this preliminary study are presented in this paper.

The inverse electrocardiography problem related to medical diagnostics is considered in terms of potentials. Within the framework of the quasi-stationary model of the electric field of the heart, the solution of the problem is reduced to the solution of the Cauchy problem for the Laplace equation in R 3 . A numerical algorithm based on the Tikhonov regularization method is proposed for the solution of this problem. The Cauchy problem for the Laplace equation is reduced to an operator equation of the first kind, which is solved via minimization of the Tikhonov functional with the regularization parameter chosen according to the discrepancy principle. In addition, an algorithm based on numerical solution of the corresponding Euler equation is proposed for minimization of the Tikhonov functional. The Euler equation is solved using an iteration method that involves solution of mixed boundary value problems for the Laplace equation. An individual mixed problem is solved by means of the method of boundary integral equations of the potential theory. In the study, the inverse electrocardiography problem is solved in region Ω close to the real geometry of the torso and heart.

This is the second paper containing a detailed description of electroconductivity measurements of an aqueous electrolyte. The results of laboratory experiments measuring the active and reactive resistance of a NaCl-aqueous solution are presented. The accuracy of the measured values is estimated. An analysis of factors strongly influencing the determination of the real and virtual parts of the complex resistance of an aqueous electrolyte is presented.