Inverse problems for the Sturm-Liouville equation with the discontinuous coefficient

In this study we derive the Gelfand-Levitan-Marchenko type main integral equation of the inverse problem for the boundary value problem $L$ and prove the uniquely solvability of the main integral equation. Further, we give the solution of the inverse problem by the spectral data and by two spectrum.     

Existence, non-existence and asymptotic behavior of global solutions to the Cauchy problem for systems of semilinear hyperbolic equations with damping terms

We consider the Cauchy problem for systems of semilinear hyperbolic equations. Using the L_p→L_q type estimation for the corresponding linear parts, the existence and uniqueness of weak global solutions are investigated. We also established the behavior of solutions and their derivatives as t→+∞. Using the method of test functions developed in the works (Mitidieri and Pokhozhaev, 2001 [11], Veron and Pohozaev, 2001 [12] and Caristi, 2000 [23]) we obtain the analogue of the Fujita-Hayakawa type criterion for the absence of global solutions to some system of semilinear hyperbolic inequalities with damping. It follows that the conditions of existence theorem imposed on the growth of nonlinear parts are exact in some sense.     

Dilepton and strangeness production probed with HADES

With the High Acceptance Di-Electron Spectrometer (HADES) at GSI we have studied dilepton production in the few-GeV energy regime in various collisions systems, from elementary NN, over pA, up to the medium-heavy Ar + KCl system. We have thus confirmed the puzzling results of the former DLS Collaboration at the Bevalac. While we have traced the origin of the excess pair yield in CC collisions to elementary pp and pn processes, in our Ar + KCl data a contribution from the dense phase of the collision has been identified. Together with the e ⁺ e ^? pairs, we have also obtained in the Ar + KCl system at 1.76 A GeV a high-statistics data set on open and hidden strangeness, i.e. K ^±, K _s ⁰ , ??, ?, and ??^?, allowing for a comprehensive discussion of strangeness production in this system.     

Hydrolysis of polyacrylonitrile in aqueous solution of sodium carbonate

The kinetics of homogeneous hydrolysis of polyacrylonitrile in an aqueous solution of sodium carbonate and the chemical structure of the resulting copolymer are studied by FTIR spectroscopy, ¹³C NMR analysis, and titration methods. It is found that hydrolysis in the presence of sodium carbonate does not include the stage of amidine formation and does not result in the complete exhaustion of nitrile groups in a polymer. The designed partial-hydrolysis method permits the use of polyacrylonitrile for the synthesis of the copolymer with a predominant unit alternation; this copolymer is identical in terms of chemical structure to the Rohacell copolymer obtained through block copolymerization of acrylonitrile and methacrylic acid.     

Effect of the composition of polyacrylimide-forming copolymers on their processing

Thermomechanical studies of thermosetting copolymers of acrylonitrile with methacrylic acid and acrylamide with acrylic acid that form similar polyacrylimide foam plastics during curing have been performed. The dependence of the glass-transition temperatures of the copolymers on the degrees of intramolecular imidization has been calculated and confirmed experimentally. Procedures to control the curing rate have been proposed. The influence of plasticizing additives on the glass-transition temperatures, imidization, and foaming of foam-forming compositions has been studied. Plasticized powdered foam-forming compositions with delayed imidization have been developed, and temperature conditions for their processing have been determined.     

Surface bundles with non-zero signature

In this paper we develop a new technique that yields infinitely many surface bundles with non-zero signature.     

Study of phenol and carbon dioxide adsorption by the sorbents based on montomorillonite and diatomite

The nature, concentration and strength of the basic sites on the outer and inner surfaces of diatomite and bentonite toward adsorption of carbon dioxide and phenol was studied by derivatographic methods in respect of the conditions of processing the samples.     

Magnetic-field-controlled polarized luminescence of Y3Al5O12-Tb and Y3Al5O12-Ho garnets

The circularly polarized luminescence spectra of Y₃Al₅O₁₂-Tb and Y₃Al₅O₁₂-Ho garnets are analyzed in the wavelength ranges of the ⁵ D ₄ → ⁷ F ₅ transition in the Tb³⁺ ion and the ⁵ S ₂ → ⁵ I ₈ transition in the Ho³⁺ ion. It is found that the intensities of the orthogonal circularly polarized components of the series of luminescence lines attributed to the studied garnets differ substantially. The results obtained are interpreted in terms of the mixing of the Tb³⁺ and Ho³⁺ electronic states in an external magnetic field.     

Dynamical algebra of invariants of integra-differential equations of quantum theory

The Heisenberg-Weyl dynamical algebra of invariants for the special type of integro-difierential equations of quantum theory is developed.