Hybrid nanocomposites based on poly(3,6-dianiline-2,5-dichloro-1,4-benzoquinone) (PDACB) in salt form and graphene oxide (GO) have been obtained for the first time, and the significant influence of the preparation method on the composition and structure of nanocomposites and their functional properties has been demonstrated. Nanocomposites were prepared in three ways: via ultrasonic mixing of PDACB and GO; via in situ oxidative polymerization of 3,6-dianiline-2,5-dichloro-1,4-benzoquinone (DACB) in the presence of GO; and by heating a suspension of previously prepared PDACB and GO in DMF with the removal of the solvent. The results of the study of the composition, chemical structure, morphology, thermal stability and electrical properties of nanocomposites obtained via various methods are presented. Nanocomposites obtained by mixing the components in an ultrasonic field demonstrated strong intermolecular interactions between PDACB and GO both due to the formation of hydrogen bonds and π-stacking, as well as through electrostatic interactions. Under oxidative polymerization of DACB in the presence of GO, the latter participated in the oxidative process, being partially reduced. At the same time, a PDACB polymer film was formed on the surface of the GO. Prolonged heating for 4 h at 85 °C of a suspension of PDACB and GO in DMF led to the dedoping of PDACB with the transition of the polymer to the base non-conductive form and the reduction of GO. Regardless of the preparation method, all nanocomposites showed an increase in thermal stability compared to PDACB. All nanocomposites were characterized by a hopping mechanism of conductivity. Direct current (dc) conductivity σdc values varied within two orders of magnitude depending on the preparation conditions.

This paper addresses one class of bilevel optimization problems (BOPs) with an equilibrium at the lower level (in optimistic statement). Namely, we study BOPs with a convex quadratic optimization problem under linear constraints at the upper level and with a parametric non-normalized bimatrix game at the lower one, where we need to find a Nash equilibrium. In order to construct numerical methods for the problem in question, first, we transform the original bilevel problem into a single-level nonconvex optimization problem by replacing the lower level with its optimality conditions. Then we apply the Exact Penalization Theory and Global Search Theory (GST) to the resulting problem. According to the standard research of nonconvex problems by the GST, we construct the d.c. representations of all nonconvex functions from the original statement (into the differences of two convex functions), formulate the Global Optimality Conditions in terms of reduced penalized problem, and develop local and global search method taking into account the specific of problem in question. The main feature of the developed methods consists in the possibility of varying the penalty parameter within the methods themselves.

This work addresses the development of a hybrid approach to solving threeperson polymatrix games (hexamatrix games). On the one hand, this approach is based on the reduction of the game to a nonconvex optimization problem and the Global Search Theory proposed by A.S. Strekalovsky for solving nonconvex optimization problems with (d.c.) functions representable as a difference of two convex functions. On the other hand, to increase the efficiency of one of the key stages of the global search — constructing an approximation of the level surface of a convex function that generates the basic nonconvexity in the problem under study — operators of genetic algorithms are used. The results of the first computational experiment are presented.

New oxidative polymerization monomers—diarylaminodichlorobenzoquinones were synthesised by alkylating aniline, m-phenylenediamine and methanilic acid with chloranil. Oxidative polymerization of diarylaminodichlorobenzoquinones was studied for the first time in relation to the concentration of the monomer, acid, and oxidant/monomer ratio. It was found that the synthesized monomers are highly active in the polymerization reaction, and the oxidation rate grows with the increase in the acid concentration. Only one arylamine group is involved in the polymerization reaction. The optimal oxidant/monomer ratio is stoichiometric for one arylamine group, despite the bifunctionality of the monomers. It was shown that the type of the substituent in the aniline ring (electron donor or electron acceptor) determines the growth of the polymer chain and the structure of the resulting conjugated polymers. A mechanism for the formation of active polymerization centers for diarylaminodichlorobenzoquinones was proposed. FTIR-, NMR-, X-ray photoelectron spectroscopy, and SEM were used to identify the structure of the synthesized monomers and polymers. The obtained polymers have an amorphous structure and a loose globular morphology. The frequency dependence of the electrical conductivity was studied.

This paper addresses the optimistic statement of one class of bilevel optimization problems (BOPs) with a nonconvex lower level. Namely, we study BOPs with a convex quadratic objective function at the upper level and with a bimatrix game at the lower level. It is known that the problem of finding a Nash equilibrium point in a bimatrix game is equivalent to the special nonconvex optimization problem with a bilinear structure. Nevertheless, we can replace such a lower level with its optimality conditions and transform the original bilevel problem into a single-level nonconvex optimization problem. Then we apply the original Global Search Theory (GST) for general D.C. optimization problems and the Exact Penalization Theory to the resulting problem. After that, a special method of local search, which takes into account the structure of the problem under consideration, is developed.

This chapter addresses a new methodology for finding optimistic solutions in bilevel optimization problems (BOPs). In Introduction, we present our view of the classification for corresponding numerical methods available in the literature. Then we focus on the quadratic case and describe the reduction of BOPs with quadratic objective functions to one-level nonconvex problems and develop methods of local and global searches for the reduced problems. These methods are based on the new mathematical tools of global search in nonconvex problems: the Global Search Theory (GST). A special attention is paid to a demonstration of the efficiency of the developed methodology for numerical solution of test BOPs.

An expression is given for the spectral energy density of acoustic phonons. The basic properties of anharmonic phonons are introduced, and an expression is written for their spectral energy density.

This work addresses the optimistic statement of a bilevel optimization problem with a general d.c. optimization problem at the upper level and a convex optimization problem at the lower level. First, we use the reduction of the bilevel problem to a nonconvex mathematical optimization problem using the well-known Karush-Kuhn-Tucker approach. Then we employ the novel Global Search Theory and Exact Penalty Theory to solve the resulting nonconvex optimization problem. Following this theory, the special method of local search in this problem is constructed. This method takes into account the structure of the problem in question.

This work addresses the simplest class of the bilevel optimization problems (BOPs) with equilibrium at the lower level. We study linear BOPs with a matrix game at the lower level in their optimistic statement. First, we transform this problem to a single-level nonconvex optimization problem with the help of the optimality conditions for the lower level problem. Then we apply the special Global Search Theory (GST) for general d.c. optimization problems to the reduced problem. Following this theory, the methods of local and global searches in this problem are constructed. These methods take into account the structure of the problem in question.

In this paper, we develop new methods of local and global search for finding optimistic solutions to the hierarchical problem of optimal pricing in telecommunication networks. These methods are based on the fact that a bilevel optimization problem can be equivalently represented as a nonconvex optimization problem (with the help of the Karush–Kuhn–Tucker conditions and the penalty approach). To solve the resulting nonconvex problem, we apply the Global Search Theory (GST). Computational testing of the developed methods on a test problem demonstrated workability and efficiency of the approach proposed.

We evaluated 395 patients with acute stroke: diabetes mellitus wasdiagnosed in 19.5%, hyperglycemia was observed in 41.8% patientson day 1 and in 48.9% on day 2 after admission. Hyperglycemiaand diabetes were associated with more severe free radical imbalanceand worsened the outcome in stroke patients, decreasing rehabilitation potential. The increase of malonic dialdehyde(MDA), decrease of antiperoxide plasma activity (APA), hyperglycemiaand high leucocyte count are shown to be prognostic factorsof adverse outcome (death, severe disability), which should betaken into account during antioxidant therapy. The highest mortalityrate, which showed correlation with the size of stroke, wasobserved in patients with hyperglycemia persisting more than 3days after stroke onset, and it was 1.8-fold higher than in patientswith normoglycemia. Indications for target antioxidant therapyare: blood glucose 6.6 mmol/l, leucocyte count 9 700, APClevel 3, and MDA level 4 mol/l

This paper addresses the bilevel programming problems (BPPs) with the quadratic objective functions at the upper and the lower levels. The new solution method for such BPPs is developed. The main feature of the approach proposed is employment of the original A.S. Strekalovsky’s Global Search Theory. Numerical testing of the method on specially constructed instances demonstrated the efficiency of the approach.

This paper addresses one of the classes of bilevel optimization problems in their optimistic statement. The reduction of the bilevel problem to a series of nonconvex mathematical optimization problems, together with the specialized Global Search Theory, is used for developing methods of local and global searches to find optimistic solutions. Illustrative examples show that the approach proposed is prospective and performs well.

In this paper, we develop a global search method for finding a Nash equilibrium in a hexamatrix game (polymatrix game of three players). The method, on the one hand, is based on the equivalence theorem of the problem of finding a Nash equilibrium in the game and a special mathematical optimization problem, and, on the other hand, on the usage of Global Search Theory for solving the latter problem. The efficiency of this approach is demonstrated by the results of computational testing.

The spectrum of neutrons near the target of a portable NG-24M neutron generator is measured by the neutron activation method. The recovered neutron spectrum is represented analytically as a superposition of known physically substantiated spectra.

The problem of finding a Nash equilibrium in polymatrix game of three players (hexamatrix game) is considered. For the equivalent nonconvex optimization problem an issue of local search is investigated. First, we study the special local search method (SLSM), based on the linearization of the original problem with respect to basic nonconvexity. Then the new local search procedure is elaborated. This procedure uses the bilinear structure of the objective function and is based on the consecutive solving of auxiliary linear programs. At the end of the paper the results of comparative computational simulation for two local search methods are presented and analyzed.

The problem of numerical finding of a Nash equilibrium in a 3-player polymatrix game is considered. Such a game can be completely described by six matrices, and it turns out to be equivalent to the solving a nonconvex optimization problem with a bilinear structure in the objective function. Special methods of local and global search for the optimization problem are proposed and investigated. The results of computational solution of the test game are presented and analyzed.

Using the piecewise-linear function, consideration was given to the problem of separation of the sets whose convex hulls have nonempty intersections. For the problem of polyhedral separability, an algorithm to solve the equivalent optimization problem of seeking the family of separating hyperplanes was proposed and substantiated. Its efficiency was demonstrated by way of a numerical experiment.

The microdynamics of large-amplitude nonlinear atomic vibrations in crystals of the UO 2 , PuO 2 , and ThO 2 types with the fluorite structure has been studied using the neutron spectrometry and computer simulation methods. Investigations performed on the DIN-2PI neutron spectrometer have revealed a fine structure of the multi-resonance spectral density of vibrations in UO 2 . The temperature dependence of the coefficient of thermal conductivity of UO 2 with two maxima in the range from 500 to 3000 K and the multi-resonance density of vibrations has been interpreted according to the results of the computer simulation demonstrating the generation of single solitons and soliton beams at low and high temperatures. It has been shown that the maximum of the coefficient of thermal conductivity at a temperature of 500 K is determined by the energy transfer by solitons. A decrease in the coefficient of thermal conductivity in the range from 500 to 2000 K is determined by soliton-soliton scattering. An increase in the coefficient of thermal conductivity in the range from 2000 to 3000 K is determined by the generation of soliton beams with the formation of dynamic pores. It has been found that, in crystals of the UO 2 , PuO 2 , and ThO 2 types, there are resonances of new-type surface vibrations between the dispersion branches of optical phonons. An additional resonance between the low-frequency optical branch and the acoustic branch has been revealed at finite temperatures. This resonance has been interpreted as a nonlinear local mode, in the framework of the quantum theory, possible, a biphonon. It has also been found that, with an increase in the excitation energy, there are soliton branches between this resonance and the acoustic branch in UO 2 , which in the phase plane cross the band of a nonlinear local mode with an increasing rate.

Fundamentally new gyrosolitons with helical trajectories of motion have been revealed in UO2 and PuO2 reactor fuel materials by the computer simulation of the microdynamics of high-amplitude atomic vibrations. The phonon spectra of nanostructures, as well as of gyrotropic materials, include quasioptical branches with different-sign linear dispersion. The corresponding branches of gyrosolitons have been revealed on the phase plane in the spectral density of vibrations. The main dynamic event of the kinetic process of helical surfing diffusion of impurity atoms on gyrosolitons has been observed.