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A decomposition approach to solving the ill-conditioned optimal estimation problems is developed using the invariance conditions. The approach allows construction of stable LSM estimators on the basis of two parallel algorithms whose dimension is substantially smaller than that of the classical LSM estimation procedure.

For the cone-beam tomographic reconstruction method, the radiation source moving trajectory consisting of two intersecting circles is studied. A circle choice algorithm for each plane intersecting the object is proposed to obtain the most accurate result of reconstruction. Computer simulation results are presented for qualitative evaluating the advantage of the circle choice algorithm. It is shown that for the trajectory under study the boundaries determination accuracy depends on the boundary location. Directions with the most accurate reconstruction are found.

An approach to distributed computer system (CS) self-diagnosis is proposed. Game-theory methods for CS dispatching in the mode of parallel task stream serving are developed. The architecture and software of a robust distributed cluster computer system are described.

Hybrid models of stochastic dependencies are considered in the presence of a priori data on their description in the incomplete space of controlled features. Asymptotic properties of the models are investigated. They are compared with results of computational experiment.

A computer model of a digital measurement system with parallel channels is developed. The system allows measuring the summarized error of a reconstructed signal in the presence of errors in individual channels. The influence of the errors of the static channel characteristic (zero offset and scaling) and the dynamic error arising as a result of channel synchronization errors is analyzed. Results of the analysis are presented in the time and frequency regions.

An approach to transformations of the definition function for geometric projection, offsetting, set-theoretic, and metamorphosis operations is considered. A characteristic of more complex operations for functionally defined objects with the use of perturbation functions: swept volume of moving solids and twisting a constructive solid, is presented. The adaptability and universality of this approach is illustrated by examples of images obtained while modeling geometric operations.

A mathematical method for modeling the adiabatic burning temperature depending on the molecular fuel structure is considered. The method was tested on experimental data in comparison with other methods.

It is proposed to solve the problem of document watermark identification by using decomposition of wavelet spectrum of a microdensitometer signal. The advantage of the proposed signal processing method over conventional methods is shown.

A composite material with an ordered periodic structure was formed as a result of spatially nonuniform photopolymerization and phase separation of a nematic liquid crystal and a polymer from the initial mixture containing a new acrylate monomer. The structure ensures refractive index modulation in the composite material volume. The obtained composite material is promising for application as electrically switchable transmission gratings.

The possibilities of applying the high-temperature superconducting quantum interferometers in measurement systems are investigated. Various designs of quantum interferometers are used: one-circuit, two-circuit, and Harvey interferometers. The following characteristics of the measurement systems are considered: the coefficient of input magnetic flux transformation to output voltage of the measurement channel, the sensitivity threshold, the frequency dependence of input noise spectral density, the amplitude frequency characteristic of magnetic flux transformation to output voltage of the measurement channel, and the upper boundary frequency of the measurement channel bandwidth. A method for investigating these characteristics is described and results are presented. It is shown that the Zimmermann type of interferometers is the most promising one. Applications of a magnetometer to finite measurement systems are illustrated.