NEW CONCATENATION SCHEMES BASED ON THE MULTITHRESHOLD DECODERS OF CONVOLUTIONAL SELF-ORTHOGONAL CODES FOR GAUSSIAN CHANNELS

New serial concatenation schemes based on the multithreshold decoders and di- vergent principle for the convolutional self-orthogonal codes under Gaussian channels are proposed. Using both binary and symbolic decoders on the second decoding stage of the convolutional codes are considered. Simulation results are indicated the higher performance characteristics of the proposed cascade schemes on majority decoders in comparison with clas- sical schemes based on the Viterbi algorithm and Reed-Solomon codes. A moderate increase in decoding delay during concatenation is revealed. It is determined by the absence of the need to use traditional two-dimensional concatenated structures.

A MODIFIED METHOD OF SOLVING THE PRESSURE–RATE DECONVOLUTION PROBLEM FOR IDENTIFICATION OF WELLBORE–RESERVOIR SYSTEM

In the paper, the method suggested in [5] for solving the pressure–rate deconvo- lution problem was modified with implementation for the synthetic (quasi-real) oil and gas data. Modification of the method is based on using the additional a priori information on the function v(t) = tg(t) in the logarithmic scale. On the initial time interval, the function is concave and its final interval is monotone. Here, g(t) is the solution of the basis equation (1). To take into account these properties in the Tikhonov algorithm, the penalty function method is used. It allowed one to increase the precision of the numerical solution and to improve quality of identification of the wellbore–reservoir system. Numerical experiments are provided.

COMPARISON OF ALGORITHMS FOR DETERMINING THE THICKNESS OF OPTICAL COATING LAYERS BASED ON THE MONOCHROMATIC MONITORING DATA

The reverse engineering problem of determining the layer thicknesses of deposited optical coatings from on-line monochromatic measurements is considered. To solve this inverse problem, non-local algorithms are proposed that use all the data accumulated during the deposition process. For the proposed algorithms, the accuracy of solving the inverse problem is compared in the presence of random and systematic errors. It is shown that in the case when the measured data contains only random errors, the best accuracy is provided by the algorithm based on minimizing the discrepancy functional. In the case of systematic errors, the advantage of one the algorithms based on minimizing the variance functionals is demonstrated. Key words: inverse problems, reverse engineering, optical coatings, thin films.

THE BOUNDARY VALUE PROBLEM OF FINDING A RIGHT-HAND SIDE FOR MIXED TYPE EQUATION WITH CHAPLYGIN’S TYPE OPERATOR

In this paper, we study the inverse problem for a mixed-type equation with power degeneracy on a transition line by definition of its right-hand side, depending on the spatial coordinate. The theory of identity has been proved. In the case of degree degeneracy, the uniqueness criterion for the solution of the problem is proved, and the solution itself is con- structed in the form of a sum of orthogonal series. The consistency of series in the class of solutions of the given equation is justified and the validity of the solution with respect to the boundary conditions is proved.

OBSERVER’S TRAJECTORY TRACKING OBJECT BYPASSING OBSTACLE ON THE SHORTEST CURVE

Motion of some object is considered. The object t moves from the initial point t∗ to the final one t ∗ . But since absent of the direct path, he should bypass an obstacle a connected bodily set G. It is supposed that t moves by the most short trajectory T = Tt , and the trajectory T is a convex curve. The observer’s f task is to find the trajectory Tf that provides tracking the object on the most part of the object’s motion and, if possible, the lesser object’s stealth of motion along the trajectory T . The latency is defined by the distance that the observer must pass to see the object in the field of vision. The object and observer start at the same initial instant, and their velocities are equal. In the paper, examples of the trajectories Tf in R 2 are presented, on which the observer can see the object’s trajectory T ; also, the value of the object’s latency is shown for the invisible parts of the trajectory T . The variant of Tf in R 3 is shown.

FINITE ELEMENT ANALYSIS OF THE DIFFUSION MODEL OF THE BIOCLOGGING OF THE GEOBARRIER

The distribution of an organic chemical and the filtration process in the soil which contains a thin geochemical barrier are considered. Microorganism colonies develop in the presence of organic chemicals in the soil which leads to the so-called phenomenon of bioclogging of the pore space. As a result, the conductivity characteristics of both the soil as a whole and the geochemical barrier change. Conjugation conditions as a component of the mathematical model of chemical filtration in the case of inhomogeneity of porous media and the presence of fine inclusions were modified for the case of bioclogging. The numerical solution of the corresponding nonlinear boundary value problem with modified conjugation conditions was found by the finite element method. The conditions of the existence of a generalized solution of the corresponding boundary value problem are indicated. The results on the theoretical accuracy of finite element solutions are presented. Differences in the value of pressure jumps at a thin geochemical barrier were analyzed for the case considered in the article and the classical case on a model example of filtration consolidation of the soil in the base of solid waste storage. The excess pressure in 600 days after the start of the process reaches 25 % of the initial value when taking into account the effect of bioclogging, while is only 6 % for the test case disregarding the specified effect.

TRANSMISSION EIGENVALUES FOR MULTIPOINT SCATTERERS

We study the transmission eigenvalues for the multipoint scatterers of the Bethe- Peierls-Fermi-Zeldovich-Beresin-Faddeev type in dimensions d = 2 and d = 3. We show that for these scatterers: 1) each positive energy E is a transmission eigenvalue (in the strong sense) of infinite multiplicity; 2) each complex E is an interior transmission eigenvalue of infinite multiplicity. The case of dimension d = 1 is also discussed.

MODIFIED METHOD OF SEPARATION OF VARIABLES FOR SOLVING DIFFRACTION PROBLEMS ON MULTILAYER DIELECTRIC GRATINGS

A modified method of separation of variables is proposed for solving the direct problem of diffraction of electromagnetic wave by multilayer dielectric gratings (MDG). To apply this method, it is necessary to solve a one-dimensional eigenvalue problem for a 2nd- order differential equation on a segment with piecewise constant coefficients. The accuracy of the method is verified by comparison with the results obtained by the commercially available RCWA method. It is demonstrated that the method can be applied not only to commonly used MDG elements with one line in a grating period but also to potentially promising MDG elements with several different lines in a grating period.

AN EFFICIENT IDENTIFICATION OF RED BLOOD CELL EQUILIBRIUM SHAPE USING NEURAL NETWORKS

This work of applied mathematics with interfaces in bio-physics focuses on the shape identification and numerical modelisation of a single red blood cell shape. The purpose of this work is to provide a quantitative method for interpreting experimental observations of the red blood cell shape under microscopy. In this paper we give a new formulation based on classical theory of geometric shape minimization which assumes that the curvature energy with additional constraints controls the shape of the red blood cell. To minimize this energy under volume and area constraints, we propose a new hybrid algorithm which combines Particle Swarm Optimization (PSO), Gravitational Search (GSA) and Neural Network Algorithm (NNA). The results obtained using this new algorithm agree well with the experimental results given by Evans et al. (8) especially for sphered and biconcave shapes.

THE MODIFIED TIKHONOV REGULARIZATION METHOD WITH THE SMOOTHED TOTAL VARIATION FOR SOLVING THE LINEAR ILL-POSED PROBLEMS

We investigate a linear operator equation of the first kind that is ill-posed in the Hadamard sence. It is assumed that its solution is representable as a sum of smooth and discontinuous components. To construct a stable approximate solutions, we use the modified Tikhonov method with the stabilizing functional as a sum of the Lebesgue norm for the smooth component and a smoothed BV-norm for the discontinuous component. Theorems of exis- tence, uniqueness, and convergence both the regularized solutions and its finite-dimentional approximations are proved. Also, results of numerical experiments are presented.