Numerical modeling of electronic state evolution due to non-uniform external electric field in the structure metal-insulator-semiconductor with solitary donor center is carried out. Considering a nanometer disc-shaped gate as a source of the electric field, the problem for the Laplace equation in multilayered medium is solved numerically to determine the distribution of the gate potential. The energy spectrum of a bound electron is calculated from the problem for the stationary Schrödinger equation. Finite difference schemes are constructed to solve both the problems. Difference scheme for the Schrödinger equation takes into account cusp condition for the wave function at the donor location. To solve the problem for the Laplace equation, asymptotic boundary conditions for approximating the external field potential at large distances from the gate in different layers are suggested. These conditions allow to reduce the calculation domain for the electrostatic problem essentially. The effect of the boundary conditions on the accuracy of calculating the potential and energies is investigated. Using the developed difference schemes, the dependences of the energy spectrum of the bound electron on the gate potential are calculated, and the values of critical potential at which the wave function of the electron is relocated are determined. It has been found on the basis of calculation results, that governing parameter for the description of electronic behavior is the potential difference between the donor and semiconductor surface. It has been shown that critical potential difference does not depend on dielectric thickness and permittivity.

Modeling of movement of objects without stops in a network of crossing routes is studied. The problem is formulated in terms of disjunctive linear programming, mixed integer linear programming and graph theory. Several variants for representing constraints on convergence of objects are considered. NP-completeness of the problem in the strong sense is proved.

The mathematical substantiation of the algorithm for synthesis of the proper transformation and finding the eigenvalue formulae of a persymmetric matrix of dimension N = 2 ^k ( k =1, 4 ) based on orthogonal rotation operators is given. The proposed algorithm made it possible to improve the author's approach to calculating eigenvalues based on numerical examples for the maximal dimension of matrices 64×64, resulting the possibility to obtain analytical relations for calculating the eigenvalues of the persymmetric matrix. It is shown that the proper transformation has a factorized structure in the form of a product of rotation operators, each of which is a direct sum of elementary Givens and Jacobian rotation matrices.

 

The article gives the basic approaches to updating the systems of combat operations modeling in the part of enemy missile attack simulation taking into account the possibility of tactical ballistic missile maneuvering during the flight. The results of simulation of combat tactical missile defense operations are given.

 

For nonlinear random sequences filtering the extended least-square method is proposed. The received suboptimal filter equations include linearization for nonlinear measurement function only. The filter gain coefficient can be calculated by formulas without solving additional equations as in extended Kalman filter. In comparison with the extended Kalman filter, the implementation of the proposed filter has less computational complexity. Examples of a comparative accuracy evaluation of the proposed filter with the extended Kalman filter are given.

 

A mathematical model is proposed for the analysis of text documents and short messages based on verbal associations, that is, the semantic links between words and word-combinations corresponding to associative relations between the entities they designate. The aim of the analysis is to create for each analyzed text a tuple of verbal-associative networks of all sentences of the text, as well as constructing a verbal-associative network of the text itself. The verbal-associative supply network is a graph whose vertices are all communicative fragments of the sentence (stable word combinations), and the edges correspond to verbal-associative connections between them. In the case of the text as a whole, the vertices of its verbalassociative network are all communicative fragments of the text.

 

Transformation of a digital radar image with a wide dynamic range of luminance values (up to 2¹⁶ tones) for visualization on a standard monitor is considered. The monitor has 2⁸ gray value range or any of three basic colors in the RGB system. Linear quantization of the luminance values of the original image generates a nearly black image with small light blobs, since most of the original values are less than 255–512 and are reduced by 256 times. To solve the problem, it is proposed to use a nonlinear logarithmic transformation with a parameter calculated from the original images. On real data received from the TerraSAR-X satellite in the geoTIFF format, comparative studies with other compression algorithms for a wide dynamic range of image brightness are performed. It is shown that the proposed solution allows creating a visually better image in comparison with the known algorithms.

 

The method of determination of the dynamic characteristics like the vessel diameter change, the linear and volume blood velocities in the vessels of the eye fundus is considered. Such characteristics allow to determine blood flow changes in the microvasculature affecting the blood flow in the brain, kidneys and coronary vessels. Developed algorithm includes four stages: the video sequence stabilization, the vessels segmentation with the help of a neural network, the determination of the instantaneous velocity in the vessels based on the optical flow and the analysis of the results.

The description and the operability analysis of the implemented instrumental software system «PlagiarismControl» has been done. The system affords to automatize solving the task of the identification of the adopted fragments in the given text document both from the local full-text user’s database and from the Internet. The system affords solving the task taking in account explicit as well as implicit adoptions with precision up to lexical units paradigms and both lexical and grammatical synonymy relations, according to the structural-functional schematic diagram of the system of the automatic recognition of reproduced fragments of the text documents. «PlagiarismControl» is able to work in different modes, to automatize the work of the expert and to speed up significantly the procedure of the analysis of the documents, with the purpose of recognition of the adoptions (plagiarism) from other text documents.

Methods for modern memory devices are analyzed. The validity of using pseudo-exhaustive tests to detect complex memory faults is shown. A necessary condition for generating a pseudo-exhaustive test for a given number of memory cells is formulated. It is shown that the problem of generating a pseudo-exhaustive test based on multiple memory tests with a variable background is reduced to the combinatorial task of the coupon collector. Estimates of the mean, minimum, and maximum multiplicity of a multiple test are given to provide an exhaustive set of combinations for a given number of cells of a memory device. The validity of analytical estimates is shown experimentally and the possibility of pseudo-exhaustive memory testing is confirmed.