Piecewise continuous partition function method in the theory of wave perturbations of inhomogeneous gas

The problem of wave disturbance propagation in rarefied gas in gravity field is explored. The system of hydrodynamic-type equations for a stratified gas in gravity field is derived from BGK equation by method of piecewise continuous partition function. The obtained system of the equations generalizes the Navier-Stokes at arbitrary density (Knudsen numbers). The verification of the model is made for a limiting case of a homogeneous medium. Results are in the good agreement with experiment and former theories at arbitrary Knudsen numbers.Comment: 12 pages, 5 figure

Piecewise continuous distribution function method: Fluid equations and wave disturbances at stratified gas

Wave disturbances of a stratified gas are studied. The description is built on a basis of the Bhatnagar -- Gross -- Krook (BGK) kinetic equation which is reduced down the level of fluid mechanics. The double momenta set is introduced inside a scheme of iterations of the equations operators, dividing the velocity space along and opposite gravity field direction. At both half-spaces the local equilibrium is supposed. As the result, the momenta system is derived. It reproduce Navier-Stokes and Barnett equations at the first and second order in high collision frequencies. The homogeneous background limit gives the known results obtained by direct kinetics applications by Loyalka and Cheng as the recent higher momentum fluid mechanics results of Chen, Rao and Spiegel. The ground state declines from exponential at the Knudsen regime. The WKB solutions for ultrasound in exponentially stratified medium are constructed in explicit form, evaluated and plotted.Comment: 20 pages, 7 figures, 14 ISNA conference, 199

Counting and computing regions of DD-decomposition: algebro-geometric approach

New methods for $D$-decomposition analysis are presented. They are based on topology of real algebraic varieties and computational real algebraic geometry. The estimate of number of root invariant regions for polynomial parametric families of polynomial and matrices is given. For the case of two parametric family more sharp estimate is proven. Theoretic results are supported by various numerical simulations that show higher precision of presented methods with respect to traditional ones. The presented methods are inherently global and could be applied for studying $D$-decomposition for the space of parameters as a whole instead of some prescribed regions. For symbolic computations the Maple v.14 software and its package RegularChains are used.Comment: 16 pages, 8 figure

Finite Automata with Generalized Acceptance Criteria

We examine the power of nondeterministic finite automata with acceptance of an input word defined by a leaf language, i.e., a condition on the sequence of leaves in the automaton's computation tree. We study leaf languages either taken from one of the classes of the Chomsky hierarchy, or taken from a time- or space-bounded complexity class. We contrast the obtained results with those known for leaf languages for Turing machines and Boolean circuits