the milne and kramers problems for the boltzmann equation of a hard sphere gas existence uniqueness and properties of asymptotic behavior are proved for solutions of the milne and kramers problems for the linearized boltzmann equation for a gas of hard spheres the proof uses energy like estimates and follows the analysis of bardos santos and sentis for the equations of neutron transport

morphisms of f isocrystals and the finite monodromy theorem for unit root f isocrystals we discuss tate type problems for f isocrystals that is the full faithfulness of the natural restriction functors between categories of overconvergent f isocrystals on schemes of positive characteristic we prove it in the cases of unit root f isocrystals using this result we prove that an overconvergent unit root f isocrystal has a finite monodromy

t s fuzzy based sliding mode controller design for discrete time nonlinear model and its applications abstract this paper investigates the takagi sugeno t s fuzzy based sliding mode control smc design of the discrete time nonlinear model by constructing a suitable fuzzy membership functions fmfs dependent lyapunov function the sufficient conditions are derived such that the resultant discrete time t s fuzzy model can achieve strictly q s r dissipative where q s and r are known matrices with compatible dimensions satisfying q 0 and r r t and is a positive constant then the desired control gain can be obtained by solving a set of linear matrix inequalities lmis besides that a fuzzy smc is designed to assure reaching condition a modified fuzzy sliding mode controller is also constructed to adapt input saturation finally simulation results are presented to demonstrate the applicability and effectiveness of the proposed approaches

fuzzy model based admissibility analysis and output feedback control for nonlinear discrete time systems with time varying delay abstract this paper is concerned with the admissibility analysis and stabilization problems for singular fuzzy discrete time systems with time varying delay the novelty of this paper comes from the consideration of a new summation inequality which is less conservative than the usual jensen inequality the abel lemma based inequality and the seuret inequality based on the inequality sufficient conditions are established to ensure the systems to be admissible moreover the corresponding conditions for the existence of desired static output feedback controller gains are derived to guarantee that the closed loop system is admissible the conditions can be solved by a modified cone complementarity linearization ccl algorithm examples are given to show the effectiveness of the proposed method

decay estimates of solutions for the equations of motion of compressible viscous and heat conductive gases in an exterior domain in ℝ3 we consider the equations of motion of compressible viscous and heat conductive gases in an exterior domain in 3 we give the l q l p estimates for solutions to the linearized equations and show an optimal decay estimate for solutions to the nonlinear problem

decay of the navier stokes poisson equations we establish the time decay rates of the solution to the cauchy problem for the compressible navier stokes poisson system via a refined pure energy method in particular the optimal decay rates of the higher order spatial derivatives of the solution are obtained the h s 0 s 3 2 negative sobolev norms are shown to be preserved along time evolution and enhance the decay rates as a corollary we also obtain the usual lp l2 1 p 2 type of the optimal decay rates compared to the compressible navier stokes system and the compressible irrotational euler poisson system our results imply that both the dispersion effect of the electric field and the viscous dissipation contribute to enhance the decay rate of the density our proof is based on a family of scaled energy estimates with minimum derivative counts and interpolations among them without linear decay analysis

empirical study on learning in fuzzy systems by rice taste analysis abstract the aim of this paper is to examine the ability of trainable fuzzy systems as approximators of non linear mappings by computer simulations on real life data fuzzy if then rules with non fuzzy singletons in the consequent part are adjusted by a gradient descent method in fuzzy systems after examining the ability of fuzzy systems for numerical examples we apply them to the modelling of the relation among six factors in the sensory test on rice taste by computer simulations based on a random subsampling technique it is shown that the performance of fuzzy systems is comparable to that of neural networks it is also shown that pre specified conditions such as a fuzzy partition initial fuzzy if then rules and the number of iterations have a significant effect on the performance of trained fuzzy systems

thermal non equilibrium flows in three space dimensions we study the equations describing the motion of a thermal non equilibrium gas in three space dimensions it is a hyperbolic system of six equations with a relaxation term the dissipation mechanism induced by the relaxation is weak in the sense that the shizuta kawashima criterion is violated this implies that a perturbation of a constant equilibrium state consists of two parts one decays in time while the other stays in fact the entropy wave grows weakly along the particle path as the process is irreversible we study thermal properties related to the well posedness of the nonlinear system we also obtain a detailed pointwise estimate on the green s function for the cauchy problem when the system is linearized around an equilibrium constant state the green s function provides a complete picture of the wave pattern with an exact and explicit leading term comparing with existing results for one dimensional flows our results reveal a new feature of three dimensional flows not only does the entropy wave not decay but the velocity also contains a non decaying part strongly coupled with its decaying one the new feature is supported by the second order approximation via the chapman enskog expansions which are the navier stokes equations with vanished shear viscosity and heat conductivity

overholonomicity of overconvergent f isocrystals over smooth varieties we prove the overholonomicity of overconvergent f isocrystals over smooth varieties this implies that the notions of overholonomicity and devissability in overconvergent f isocrystals are equivalent then the overholonomicity is stable under tensor products so the overholonomicity gives a p adic cohomology stable under grothendieck s cohomological operations

robust fuzzy control of nonlinear systems with parametric uncertainties addresses the robust fuzzy control problem for nonlinear systems in the presence of parametric uncertainties the takagi sugeno t s fuzzy model is adopted for fuzzy modeling of the nonlinear system two cases of the t s fuzzy system with parametric uncertainties both continuous time and discrete time cases are considered in both continuous time and discrete time cases sufficient conditions are derived for robust stabilization in the sense of lyapunov asymptotic stability for the t s fuzzy system with parametric uncertainties the sufficient conditions are formulated in the format of linear matrix inequalities the t s fuzzy model of the chaotic lorenz system which has complex nonlinearity is developed as a test bed the effectiveness of the proposed controller design methodology is finally demonstrated through numerical simulations on the chaotic lorenz system

the pointwise estimates of diffusion wave for the navier stokes systems in odd multi dimensions we study the dissipation of solutions of the isentropic navier stokes equations in odd multi dimensions pointwise estimates of the time asymptotic shape of the solutions are obtained and shown to exhibit the generalized huygen s principle our approach is based on the detailed analysis of the green function of the linearized system this is used to study the coupling of nonlinear diffusion waves

nonlinear boundary layers of the boltzmann equation i existence we study the half space problem of the nonlinear boltzmann equation assigning the dirichlet data for outgoing particles at the boundary and a maxwellian as the far field we will show that the solvability of the problem changes with the mach number of the far maxwellian if 1 respectively we also show that the same is true for the linearized problem at the far maxwellian and the manifold is then a hyperplane the proof is essentially based on the macro micro or hydrodynamics kinetic decomposition of solutions combined with an artificial damping term and a spatially exponential decay weight

a fuzzy logic based approach to qualitative modeling this paper discusses a general approach to quali tative modeling based on fuzzy logic the method of qualitative modeling is divided into two parts fuzzy modeling and linguistic approximation it proposes to use a fuzzy clustering method fuzzy c means method to identify the structure of a fuzzy model to clarify the advantages of the proposed method it also shows some examples of modeling among them a model of a dynamical process and a model of a human operator s control action

optimal lp lq convergence rates for the compressible navier stokes equations with potential force in this paper we are concerned with the optimal lp lq convergence rates for the compressible navier stokes equations with a potential external force in the whole space under the smallness assumption on both the initial perturbation and the external force in some sobolev spaces the optimal convergence rates of the solution in lq norm with 2 q 6 and its first order derivative in l2 norm are obtained when the initial perturbation is bounded in lp with 1 p 6 5 the proof is based on the energy estimates on the solution to the nonlinear problem and some lp lq estimates on the semigroup generated by the corresponding linearized operator

l1 asymptotic behavior of compressible isentropic viscous 1 d flow we study the large time behavior in l1 of the compressible isentropic viscous 1 d flow under the assumption that the initial data are smooth and small we show that the solutions are approximated by the solutions of a parabolic system and in turn by diffusion waves which are solutions of burgers equations decay rates in l1 are obtained our method is based on the study of pointwise properties in the physical space of the fundamental solution to the linearized system 1994 john wiley sons inc

f isocristaux surconvergents et surcoherence differentielle soient mathcal v un anneau de valuation discrete complet d inegales caracteristiques de corps residuel parfait k mathcal p un mathcal v schema formel propre et lisse t un diviseur de la fibre speciale p de mathcal p u l ouvert de p complementaire de t y un sous k schema ferme lisse de u nous prouvons que la categorie des f isocristaux surconvergents sur y est equivalente a celle des f isocristaux surcoherents sur y voir car 6 2 1 et 6 4 3 a plus generalement nous etablissons par recollement une telle equivalence pour tout k schema separe lisse y nous verifions de plus que les f complexes de mathcal d dag mathcal p phantom dag t mathbb q modules a cohomologie bornee et mathcal d dag mathcal p phantom dag t mathbb q surcoherente se devissent en f isocristaux surconvergents

nonlinear stability of rarefaction waves for compressible navier stokes equations it is shown that expansion waves for the compressible navier stokes equations are nonlinearly stable the expansion waves are constructed for the compressible euler equations based on the inviscid burgers equation our result shows that navier stokes equations and euler equations are time asymptotically equivalent on the level of expansion waves the result is proved using the energy method making essential use of the expansion of the underlining nonlinear waves and the specific form of the constitutive eqution for a polytropic gas

solving the non isentropic navier stokes equations in odd space dimensions the green function method in this paper we investigate the wave structure of the solution for the compressible navier stokes equations in both one space dimension and three space dimensions first we give the pointwise estimate on the green function for the linearized system by dividing the physical domain into two parts which are the finite mach number region and outside finite mach number region we use long wave short wave decomposition and a weighted energy estimate method in each region separately the green function provides a complete picture of the wave pattern with explicit leading terms then with the help of the duhamel principle we give the pointwise estimate of the solution for the nonlinear problems 1 1 and 1 2 specially we find that the decay rate in lp r3 2 p for the energy is faster than those for the density and the momentum m

decentralized sampled data fuzzy observer design for nonlinear interconnected systems this paper presents the decentralized sampled data fuzzy observer design techniques for nonlinear interconnected systems which are assumed to be composed of fuzzy subsystems and unknown interconnections to design the decentralized fuzzy observer the estimation error dynamics is obtained and the performance function is defined based on the estimation error dynamics and the performance function the continuous time decentralized fuzzy observer is first proposed to minimize the interconnection bound to attenuation degree ratio in addition the decentralized sampled data fuzzy observers are designed by using the approximate discretization and the exact discrete time design approaches respectively each proposed observer design technique is formulated into the optimal problems with the linear matrix inequalities finally several simulation examples show the validity and superiority of the proposed observer design techniques by comparing with the conventional techniques

pointwise estimates of solution for the navier stokes poisson equations in multi dimensions abstract the cauchy problem of the navier stokes poisson equations in multi dimensions n 3 is considered we obtain the pointwise estimates of the solution when it is a perturbation of the constant state then we have the optimal l p r n p 1 convergence rate of the solution

boundary layers for compressible navier stokes equations with outflow boundary condition abstract in this paper we study the asymptotic relation between the solutions to the initial boundary value problem of the one dimensional compressible full navier stokes equations with outflow boundary condition and the associated euler equations we assume all the three characteristics to the corresponding euler equations are all negative up to some small time then we prove the existence and the stability of the boundary layers as long as the strength of the boundary layers is suitably small

stability of contact discontinuities for the 1 d compressible navier stokes equations in this paper we study the large time asymptotic behavior of solutions of the one dimensional compressible navier stokes system toward a contact discontinuity which is one of the basic wave patterns for the compressible euler equations it is proved that such a weak contact discontinuity is a metastable wave pattern in the sense introduced in 24 for the 1 d compressible navier stokes system for polytropic fluid by showing that a viscous contact wave which approximates the contact discontinuity on any finite time interval for small heat conduction and then runs away from it for large time is nonlinearly stable with a uniform convergence rate provided that the initial excess mass is zero this result is proved by an elaborate combination of elementary energy estimates with a weighted characteristic energy estimate which makes full use of the underlying structure of the viscous contact wave

asymptotic stability of traveling wave solutions of systems for one dimensional gas motion the asymptotic stability of traveling wave solutions with shock profile is investigated for several systems in gas dynamics 1 the solution of a scalar conservation law with viscosity approaches the traveling wave solution at the ratet for some 0 ast provided that the initial disturbance is small and of integral zero and in addition decays at an algebraic rate for x 2 the traveling wave solution with nishida and smoller s condition of the system of a viscous heat conductive ideal gas is asymptotically stable provided the initial disturbance is small and of integral zero 3 the traveling wave solution with weak shock profile of the broadwell model system of the boltzmann equation is asymptotically stable provided the initial disturbance is small and its hydrodynamical moments are of integral zero each proof is given by applying an elementary energy method to the integrated system of the conservation form of the original one the property of integral zero of the initial disturbance plays a crucial role in this procedure

the pointwise estimates of solutions for euler equations with damping in multi dimensions we study the time asymptotic behavior of solutions for the isentropic euler equations with damping in multi dimensions the global existence and pointwise estimates of the solutions are obtained furthermore we obtain the optimal lp 1 p convergence rate of the solution when it is a perturbation of a constant state our approach is based on a detailed analysis of the green function of the linearized system and some energy estimates

dissipativity based sliding mode control of switched stochastic systems this technical brief is concerned with dissipativity analysis and dissipativity based sliding mode control smc of continuous time switched stochastic systems firstly a sufficient condition is proposed to guarantee the mean square exponential stability and strict dissipativity for the switched stochastic system then an integral type sliding surface function is designed for establishing a sliding mode dynamics which can be formulated by a switched stochastic system with an external disturbance uncertainty dissipativity analysis and synthesis are both investigated for the sliding mode dynamics and consequently sufficient conditions are derived which pave the way for solving the dissipativity analysis and control problems moreover a smc law is synthesized to drive the system trajectories onto the predefined sliding surface in a finite time finally the efficiency of the theoretical findings is demonstrated by an illustrative example

initial boundary value problem for one dimensional wave solutions of the boltzmann equation tai ping liu and his collaborator shih hsien yu solve the initial boundary value problem for the boltzmann equation because of the inclusion of microscopic velocity in the kinetic theory the boltzmann equation can model richer and physically more realistic boundary effects more so than the fluid equations such as the navier stokes this motivates our study the reflection of fluid waves off the boundary is indicated in the figure for the case only one of the euler wave velocities is positive

optimal guaranteed cost sliding mode control of interval type 2 fuzzy time delay systems this paper is concerned with the optimal guaranteed cost sliding mode control problem for interval type 2 it2 takagi sugeno fuzzy systems with time varying delays and exogenous disturbances in the presence of the uncertain parameters hidden in membership functions an adaptive method is presented to handle the time varying weight coefficients reflecting the change of the uncertain parameters a new integral sliding surface is presented based on the system output by designing a novel adaptive sliding mode controller system perturbation or modeling error can be compensated and the reachability of the sliding surface can be guaranteed with the ultimate uniform boundedness of the closed loop system optimal conditions of an mathcal h 2 guaranteed cost function and an mathcal h infty performance index are established for the resulting time delay control system finally an inverted pendulum system represented by the it2 fuzzy model is applied to illustrate the advantages and effectiveness of the proposed control scheme

on sampled data models for nonlinear systems models for deterministic continuous time nonlinear systems typically take the form of ordinary differential equations to utilize these models in practice invariably requires discretization in this paper we show how an approximate sampled data model can be obtained for deterministic nonlinear systems such that the local truncation error between the output of this model and the true system is of order spl delta sup r 1 where spl delta is the sampling period and r is the system relative degree the resulting model includes extra zero dynamics which have no counterpart in the underlying continuous time system the ideas presented here generalize well known results for the linear case we also explore the implications of these results in nonlinear system identification

theory of weights in p adic cohomology let k be a finite field of characteristic p 0 we construct a theory of weights for overholonomic complexes of arithmetic d modules with frobenius structure on varieties over k the notion of weight behave like deligne s one in the adic framework first the six operations preserve weights and secondly the intermediate extension of an immersion preserves pure complexes and weights this is joint work with tomoyuki abe

a new discrete time robust stability condition a new robust stability condition for uncertain discrete time systems with convex polytopic uncertainty is given it enables to check stability using parameter dependent lyapunov functions which are derived from lmi conditions it is shown that this new condition provides better results than the classical quadratic stability besides the use of a parameter dependent lyapunov function this condition exhibits a kind of decoupling between the lyapunov and the system matrices which may be explored for control synthesis purposes a numerical example illustrates the results

universal fuzzy integral sliding mode controllers based on t s fuzzy models this paper addresses the universal fuzzy integral sliding mode controllers problem for continuous time multi input multi output nonlinear systems based on takagi sugeno t s fuzzy models by using the approximation capability of t s fuzzy models the nonlinear systems are expressed by uncertain t s fuzzy models with norm bounded approximation errors a novel fuzzy dynamic integral sliding mode control dismc scheme is then developed for the nonlinear systems based on their t s fuzzy approximation models one of the key features of the new dismc scheme is that the restrictive assumption that all local linear systems share a common input matrix which is required in most existing fuzzy integral sliding mode control ismc approaches is removed furthermore the results of universal fuzzy ismcs for two classes of nonlinear systems along with constructive procedures to obtain the universal fuzzy ismcs are provided respectively finally the advantages and effectiveness of the proposed approaches are illustrated via a numerical example

dissipativity based fuzzy integral sliding mode control of continuous time t s fuzzy systems this paper is concerned with dissipativity based fuzzy integral sliding mode control fismc of continuous time takagi sugeno t s fuzzy systems with matched unmatched uncertainties and external disturbance to better accommodate the characteristics of t s fuzzy models an appropriate integral type fuzzy switching surface is put forward by taking the state dependent input matrix into account which is the key contribution of the paper based on the utilization of lyapunov function and property of the transition matrix for unmatched uncertainties sufficient conditions are presented to guarantee the asymptotic stability of corresponding sliding mode dynamics with a strictly dissipative performance a fismc law is synthesized to drive system trajectories onto the fuzzy switching surface despite matched unmatched uncertainties and external disturbance a modified adaptive fismc law is further designed for adapting the unknown upper bound of matched uncertainty two practical examples are provided to illustrate the effectiveness and advantages of developed fismc scheme

pleine fidelite sans structure de frobenius et isocristaux partiellement surconvergents soit mathcal v un anneau de valuation discrete complet d inegales caracteristiques 0 p de corps residuel parfait k de corps des fractions k soient x une variete sur k y un ouvert de x nous prolongeons le theoreme de pleine fidelite de kedlaya de la maniere suivante en effet nous ne supposons pas y lisse le foncteur canonique f text mathrm isoc dag y x k to f text mathrm isoc dag y y k est pleinement fidele supposons a present y lisse nous construisons la categorie mathrm isoc dag dag y x k des isocristaux partiellement surcoherents sur y x dont les objets sont certains mathcal d modules arithmetiques de plus nous verifions l equivalence de categories rm sp y x mathrm isoc dag y x k cong mathrm isoc dag dag y x k

asymptotic stability of combination of viscous contact wave with rarefaction waves for one dimensional compressible navier stokes system we are concerned with the large time behavior of solutions of the cauchy problem to the one dimensional compressible navier stokes system for ideal polytropic fluids where the far field states are prescribed when the corresponding riemann problem for the compressible euler system admits the solution consisting of contact discontinuity and rarefaction waves it is proved that for the one dimensional compressible navier stokes system the combination wave of a viscous contact wave which corresponds to the contact discontinuity with rarefaction waves is asymptotically stable provided the strength of the combination wave is suitably small this result is proved by using elementary energy methods