THE BOUNDS OF THE GENERAL M AND J SETS AND THE ESTIMATIONS FOR THE HAUSDORFF''''S DIMENSION OF THE GENERAL J SET

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎ 1 975,Ｂ .Ｍａｎｄｅｌｂｒｏｔａｄｖａｎｃｅｄｔｈｅｃｏｎｃｅｐｔｉｏｎ“ｆｒａｃｔａｌ”ａｎｄｅｓｔａｂｌｉｓｈｅｄｈｉｓｆｒａｃｔａｌｇｅｏｍｅｔｒｙｔｈｅｏｒｙ .Ｎｏｗａｄａｙｓ,ｔｈｅｆｒａｃｔａｌｇｅｏｍｅｔｒｙｉｓｒｅｇａｒｄｅｄａｓｏｎｅｏｆｔｈｅｂｅｓｔｔｏｏｌｓｔｏｄｅｓｃｒｉｂｅｔｈｅｎｏｎｌｉｎｅａｒｐｒｏｂｌｅｍｓ.Ｉｔａｌｓｏｉｍｐｒｏｖｅｄｔｈｅｄｅｖｅｌｏｐｍｅｎｔｏｆｍａｎｙｒｅｌａｔｅｄｆｉｅｌｄｓ,ｓｕｃｈａｓｄｙｎａｍｉｃｓｓｙｓｔ…     

SPLITTING OF THE SPECTRAL DOMAIN ELECTRICAL DYADIC GREEN’S FUNCTION IN CHIRAL MEDIA

A new method of formulating dyadic Green‘s functions in lossless , reciprocal and unbounded chiral medium was presented. Based on Helmholtz theorem and the nondivergence and irrotational splitting of dyadic Dirac delta-function was this method, the electrical vector dyadic Green‘s function equation was first decomposed into the nondivergence electrical vector dyadic Green‘s function equation and irrotational electrical vector dyadic Green‘s function equation, and then Fourier‘s transformation was used to derive the expressions of the non-divergence and irrotational component of the spectral domain electrical dyadic Green‘s function in chiral media. It can avoid having to use the wavefield decomposition method and dyadic Green‘s function eigenfunction expansion technique that this method is used to derive the dyadic Green‘s functions in chiral media.     

IMPULSIVE CONTROL FOR THE STABILIZATION AND SYNCHRONIZATION OF LUR＇ E SYSTEMS

An impulsive control scheme of the Lur‘e system and several theorems on stability of impulsive control systems was presented, these theorems were then used to find the conditions under which the Lur‘e system can be stabilized by using impulsive control with varying impulsive intervals. The parameters of Lur‘e system and impulsive control law are given, a theory of impulsive synchronization of two Lur‘e system is also presented. A numerical example is used to verify the theoretical result.     

Lie symmetries and conserved quantities of nonconservative nonholonomic systems in phase space

The invariance and conserved quantities of the nonconservative nonholonomic systems are studied by introducing the infinitesimal transformations in phase space.The Lie’s symmetrical determining equations are establish ed.The Lie’s symmetrical structure equation is obtained.An example to illustrate the application of the result is given.     

STUDY FOR THE BIFURCATION TOPOLOGICAL STRUCTURE AND THE GLOBAL COMPLICATED CHARACTER OF A KIND OF NONLINEAR FINANCE SYSTEM (Ⅰ)

Based on the mathematical model of a kind of complicated financial system, all possible things that the model shows in the operation of our country’s macro-financial system were analyzed, such as balance, stable periodic, fractal, Hopf-bifurcation, the relationship between parameters and Hopf-bifurcations,and chaotic motion etc. By the changes of parameters of all economic meanings, the conditions on which the complicated behaviors occur in such a financial system, and the influence of the adjustment of the macro-economic policies and adjustment of some parameter on the whole financial system behavior were analyzed. This study will deepen people’s understanding of the lever function of all kinds of financial policies.     

An improved level-set re-initialization solver

Re-initialization procedure in level-set interface capturing method were investigated. The algorithm accomplishes the re-initialization step through locking the interface positions. Better accuracy was obtained both on the interface positions and the total fluid volume keeping. Though one mare step of the interpolations is added in the procedure, there is no significant increase in total machine time spent.     

A CLASS OF ALTERNATING GROUP METHODOF BURGERS＇ EQUATION

Some new Saul‘ yev type asymmetric difference schemes for Burgers’ equation isgiven, by the use of the schemes, a kind of alternating group four points method for solvingnonlinear Burgers‘ equation is constructed here. The basic idea of the method is that thegrid points on the same time level is divided into a number of groups, the differenceequations of each group can be solved independently, hence the method with intrinsicparallelism can be used directly on parallel computer. The method is unconditionally stableby analysis of linearization procedure. The numerical experiments show that the method has good stability and accuracy.     

Global existence and blow-up phenomena of classical solutions for the system of compressible adiabatic flow through porous media

By means of maximum principle for nonlinear hyperbolic systems, the results given by HSIAO Ling and D. Serre was improved for Cauchy problem of compressible adiabatic flow through porous media, and a complete result on the global existence and the blowup phenomena of classical solutions of these systems. These results show that the dissipation is strong enough to preserve the smoothness of ‘ small ‘ solution.     

ASYMPTOTIC ANALYSIS OF MODE Ⅱ STATIONARY GROWTHCRACK ON ELASTIC-ELASTIC POWER LAWCREEPING BIMATERIAL INTERFACE

A mechanical model was established for mode Ⅱ interfacial crack static growingalong an elastic-elastic power law creeping bimaterial interface. For two kinds of boundaryconditions on crack faces, traction free and frictional contact, asymptotic solutions of thestress and strain near tip-crack were given. Results derived indicate that the stress andstrain have the same singularity, there is not the oscillatory singularity in the field; thecreep power-hardening index n and the ratio of Young‘s module notably influence the crack-tip field in region of elastic power law creeping material and n only influences distribution ofstresses and strains in region of elastic material. When n is bigger, the creepingdeformation is dominant and stress fields become steady, which does not change with n.Poisson‘s ratio does not affect the distributing of the crack-tip field.     

Switched processes generalized mandelbrot sets for complex index number

IntroductionTheMsetgeneratedfromthecomplexmapzz2 +cinthecomplexC_planehasbeenwidelystudiedintherecenttwentyyearsandtheintricateregularstructurehiddeninithasbeenfound ,whichenrichesgreatlythefractaltheory[1].In 1 987and 1 991 ,LakhtakiaandGujar,etal.,respectively ,discussedthegeneralizedMsetsfromthecomplexmappingzza +c(α∈R1)andpresentedseveralconjecturesaboutthevisualstructurecharacteristicsofthegeneralizedMsets[2 ,3].Onthebasisoftheabovefindings,theauthorhastheoreticallyanalyzedthestr…     

NONLINEAR SATURATION OF BAROCLINIC INSTABILITY IN THE GENERALIZED PHILLIPS MODEL (Ⅰ) -THE UPPER BOUND ON THE EVOLUTION OF DISTURBANCE TO THE NONLINEARLY UNSTABLE BASIC FLOW

On the basis of the nonlinear stability theorem in the context of Arnol’s second theorem for the generalized Phillips model, nonlinear saturation of baroclinic instability in the generalized Phillips model is investigated. By choosing appropriate artificial stable basic flows, the upper bounds on the disturbance energy and potential enstrophy to the nonlinearly unstable basic flow in the generalized Phillips model are obtained, which are analytic completely and without the limitation of infinitesimal initial disturbance.     

RESEARCH OF REGULARITY OF THROWING MOVEMENT FOR SOLID PARTICLE ON THE SHAKER’S SCREEN

By means of Delta-function & unit step function to express the force of solid particle on plane inertial shaker’s screen, an mathematical model of the differential equation type was set up and solved. According to analysis of the solution, the relation is given between the throw period & displacement with the parameters of shaker design & solid particle. The method of numerical value calculation & analysis for the relation is given too.     

Investigation on gradient-dependent nonlocal constitutive models for elasto-plasticity coupled with damage

IntroductionIntheframeworkofconventionalplasticity ,materialinstabilityisoneoftheprincipalfactorsthatresultinginthestrainlocalizationphenomenon .Byusingtheterminology‘homogenized’ ,itisreferredtothefactthatinitialflawsandboundaryconditionsnecessarilyinduceanon_homogeneousstressstateinaspecimenduringtesting .Inparticularintheprocessofprogressivefailure ,theflawsandlocalstressconcentrationwillcausestronglyinhomogeneousdeformationofthespecimen[1,2 ].Asthedeformation_inducedfracture/damagephenom…     

CONTROLLABILITY OF A CLASS OF HYBRID DYNAMIC SYSTEMS (Ⅱ)—SINGLE TIME-DELAY CASE

The controllability for switched linear systems with time-delay in controls is first investigated. The whole work contains three parts. This is the second part. The definition and determination of controllability of switched linear systems with single time-delay in control functions is mainly investigated. The sufficient and necessary conditions for the oneperiodic, multiple-periodic controllability of periodic-type systems and controllability of periodic systems are presented, respectively. Contributed by YE Qing-kai Foundation items: the National Natural Science Foundation of China (69925307, 60274001); the National Key Basic Research and Development Program (2002CB312200); the Postdoctoral Program Foundation of China Biography: XIE Guang-ming (1972 ∼), Doctor (E-mail: xiegming@mech.pku.edu.cn)     

Stability and strict positive realness of convex polytopes of interval polynomials

For an uncertain system described by convex combination of interval polynomials, its Hurwitz-stability can be guaranteed by certain subset composed of vertices and edges. Furthermore, the testing set does not increase when the order of given system increases. Foundation item: the National Natural Science Foundation of China (69925307) Biography: WANG Zhi-zhen (1974-)     

CONTROLLABILITY OF A CLASS OF HYBRID DYNAMIC SYSTEMS (Ⅲ)—MULTIPLE TIME-DELAY CASE

The controllability for switched linear systems with time-delay in controls is first investigated. The whole work contains three parts. This is the third part. The definition and determination of controllability of switched linear systems with multiple time-delay in control functions is mainly investigated. The sufficient and necessary conditions for the one-periodic, multiple-periodic controllability of periodic-type systems and controllability of aperiodic systems are presented, respectively. Finally, the case of distinct delays is discussed, it is shown that the controllability is independent of the size of delays. Contributed by YE Qing-kai Foundation items: the National Natural Science Foundation of China (69925307, 60274001); the National Key Basic Research and Development Program (2002CB312200); the Postdoctoral Program Foundation of China Biography: XIE Guang-ming (1972≈), Doctor (E-mail:xiegming@mech.pku.edu.cn)     

On the existence of common fixed points for a pair of lipschitzian mappings in banach spaces

ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔＫｂｅａｎｏｎｅｍｐｔｙｓｕｂｓｅｔｏｆａＢａｎａｃｈｓｐａｃｅＸ .ＴｈｅｎａｍａｐｐｉｎｇＴ :Ｋ→ＫｉｓｓａｉｄｔｏｂｅａＬｉｐｓｃｈｉｔｚｉａｎｍａｐｐｉｎｇｉｆ,ｆｏｒｅａｃｈｉｎｔｅｇｅｒｎ≥ 1 ,ｔｈｅｒｅｅｘｉｓｔｓａｃｏｎｓｔａｎｔｋｎ >0ｓｕｃｈｔｈａｔ‖Ｔｎｘ-Ｔｎｙ‖ ≤ｋｎ‖ｘ-ｙ‖　ｆｏｒａｌｌｘ ,ｙ∈Ｋ .ＡＬｉｐｓｃｈｉｔｚｉａｎｍａｐｐｉｎｇＴｉｓｓａｉｄｔｏｂｅｕｎｉｆｏｒｍｌｙｋ＿Ｌｉｐｓｃｈｉｔｚｉａｎｉｆｋｎ =ｋｆｏｒａｌｌｎ ≥ 1 ;ｎｏ…