Solution bundle for a class of impulsive differential inclusions on Banach spaces

In this paper a class of impulsive differential inclusions is investigated. The existence of solution bundle is proved. And we also construct a nonlinear semigroup of operators on cb(E) (closed-bounded subset of E) to describe the set of attainable states.     

On the theory of isentropic solutions of quasilinear conservation laws

This paper studies isentropic solutions of quasilinear first-order equations with two independent variables and a flux function that is only continuous. The isentropic solutions are characterized by the requirement that the S. N. Kruzhkov entropy conditions hold for these solution with the equality sign. It turns out that the existence of a nonconstant isentropic solution imposes rather strong restrictions on the nonlinearity. In particular, it is shown that on the minimal interval containing the essential image of the isentropic solution, the flux function satisfies the local Lipschitz condition, and its generalized derivative is a function of locally bounded variation. Also, it is proved that when the flux function is nonlinear, any isentropic solution is continuous on nondegenerate intervals. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 33, Suzdal Conference-2004, Part 1, 2005.     

Systems of generalized quasivariational inclusions problems with applications to variational analysis and optimization problems

In this paper, we study an existence theorem of systems of generalized quasivariational inclusions problem. By this result, we establish the existence theorems of solutions of systems of generalized equations, systems of generalized vector quasiequilibrium problem, collective variational fixed point, systems of generalized quasiloose saddle point, systems of minimax theorem, mathematical program with systems of variational inclusions constraints, mathematical program with systems of equilibrium constraints and systems of bilevel problem and semi-infinite problem with systems of equilibrium problem constraints. This research was supported by the National Science Council of the Republic of China.     

Periodic solutions for a quasilinear non-autonomous second-order system

In this paper, a quasilinear second-order system with periodic boundary conditions is studied. By the least action principle and classical theorems of variational calculus, existence results of periodic solutions are obtained.     

Revealing the common sources of commercial explosive-containing articles

A method for identification of explosive-containing commercial articles is suggested. The method is based on chromatographic analysis of petroleum products present in the articles as process admixtures and structural components.     

Chemical compositions of extracts of organic matter of schungite rock form Zazhogino Deposit of Karelian Transonega region

The organic matter of schungite rock from the Zazhogino Deposit of Karelian Transonega region was extracted in the sequential mode. The extract composition was determined by several modern physicochemical methods.     

Case of a Boltzmann gas leading to the Smoluchowski coagulation equation

A special model of a rarefied hard-sphere gas is considered. The hard-sphere particles undergo absolutely elastic collisions. It is assumed that particles can collide only if their nonzero velocities are orthogonal to each other. The model makes it possible to proceed from the Boltzmann equation to the Smoluchowski coagulation equation, where coagulation means that the kinetic energies of the colliding particles are added. A Monte Carlo scheme for simulation of the phenomenon is described, and the convergence of the simulation algorithm is proved. The convergence of numerical results to exact solutions of the Smoluchowski equation and to finite-difference solutions is tested.