In this paper, we discuss the locally topological structures of nonlinear homogeneous systems with one zero characteristic root, and give a criteria by the right-hand polynomial coefficients.

At first, H_∞ control problems for homogeneous systems are studied in this paper,then the robust stabilization of nonlinear discrete switched systems have been explored and robust stabilization of non-linear discrete-time systems with uncertain parameters are studied. Furthermore ,the problem of H_∞ control for symmetric Systems with time-delay via asynchronous controller switching is studied . Finally,we study the robust and adaptive control of H_∞ almost disturbance decoupling problem with stability for uncertain nonlinear systems.

Based on a property of the homogeneous systems of Volterra series,homo- geneity,the block diagrams of formulating the second order and the third order transfer functions are derived in cooperation with the block diagrams of nonlinear elements des- cribed above,and then the transfer functions can be obtained from them.

As an application of the generalized result, and under more weak conditions we obtain a result of Furta [8] about local first integrals of semi-quasi-homogeneous systems.

Three-dimensional (3-D) computer simulations of the coarsening have been performed for elastically homogeneous systems with tetragonal misfit strain and elastically heterogeneous systems with dilatational misfit strain.

Heterogeneous systems have the potential to achieve enhanced performance as well as cost-effectiveness over homogeneous systems when the application domain is known since they can match the problem structure more closely.

To allow direct comparisons with algorithms from the applied mathematics and computer vision communities, we consider both inhomogeneous and homogeneous systems.

First, those derived from supported carbonylate clusters-nanocatalysts and second, those produced from the heterogenization of known chiral homogeneous systems.

The dependence of the entropy of a homogeneous system on the composition is investigated with the help of a reversible adiabatic process which allows the change of composition by means of a semipermeable wall. The conditions of equilibrinm for phase transition and for homogeneous chemical reaction are derived in a new way. Next the criterion of minimum energy for constant entropy and volume is derived from the principle of increase of entropy. This criterion is then applied to obtain the conditions...

The dependence of the entropy of a homogeneous system on the composition is investigated with the help of a reversible adiabatic process which allows the change of composition by means of a semipermeable wall. The conditions of equilibrinm for phase transition and for homogeneous chemical reaction are derived in a new way. Next the criterion of minimum energy for constant entropy and volume is derived from the principle of increase of entropy. This criterion is then applied to obtain the conditions of equilibrium and stability with the help of Lagrange's multipliers. The conditions of stability are expressed in several alternative forms. Next the equilibrium properties of a binary system arc considered, and some types of phase diagram are explained by means of equations. The theory is extended to the general heterogeneous equilibrium of a system consisting of any number of independent components. A system of equations for the change of temperature, pressure, and composition are obtained and are solved by means of determinants. Next Planck's theory of a binary solution is extended to a solution consisting of several solnte components, with the same conclusion regarding the lowering of freezing point as for a binary solution. Finally Planck's theory on the number of coexisting phases for aone-component system is extended to a system consisting of k components with the result that a state with, σ coexisting phases is more stable than one with σ-1 phases: where σ is an integer not greater than k + 2.

On the basis of the Oregonator model, we took the rate constant k6, the stoichio-metric coefficient f and the wave number k as the parameters to study the stability of the BZ reaction system. The expressions of the following physical quantities were obtained, they included: the critical rate constant k6c of the space periodic structure, its short-wavelength critical wave number ksc and long-wavelength critical wave number kLc; the critical rate constant k 6c of time-space periodic structure and its critical...

On the basis of the Oregonator model, we took the rate constant k6, the stoichio-metric coefficient f and the wave number k as the parameters to study the stability of the BZ reaction system. The expressions of the following physical quantities were obtained, they included: the critical rate constant k6c of the space periodic structure, its short-wavelength critical wave number ksc and long-wavelength critical wave number kLc; the critical rate constant k 6c of time-space periodic structure and its critical wave number kc (kc = kLc ). Then we worked out the critical frequency λc of BZ reaction system and analyzed the near-by critical state behavior of the system, whereby we obtained the trigger wave velocity ur and phave wave velocity up. We came to the conclusion that, under certain conditions, the near-by critical state of unstirred BZ reaction system may exhibit a stable wave group, or, a wave packet.. The trigger wave is a wave packet in the homogeneous system and the phase wave is a wave packet in the inhomogeneous one with a slight gradient. We have got that (uT=2ηDkc, where D is the diffusion coefficient of HBr02,η changes slowly with [H+] (to the extent of experimental observation, η≈ 0.1), and UP = v, where v is the phase velocity.