THE CONTEMPORARY DRIVE TO PRESERVE AND DEVELOP TRADITIONAL TIBETAN CUL TURE

Preserving and carrying on the finerpoints of traditional Tibetan culture as well as promoting further advancement and innovation in order to satisfy the growing expectations regarding the spiritual and cultural lives of those living in today's modern society are not only publicly recognized as relevant world values,but are valid points in effectively upholding and shouldering the principle of governance.

Event-Triggered Bipartite Consensus Tracking and Vibration Control of Flexible Timoshenko Manipulators Under Time-Varying Actuator Faults

For bipartite angle consensus tracking and vibration suppression of multiple Timoshenko manipulator systems with time-varying actuator faults,parameter and modeling uncertainties,and unknown disturbances,a novel distributed boundary event-triggered control strategy is proposed in this work.In contrast to the earlier findings,time-varying consensus tracking and actuator defects are taken into account simultaneously.In addition,the constructed event-triggered control mechanism can achieve a more flexible design because it is not required to satisfy the input-to-state condition.To achieve the control objectives,some new integral control variables are given by using back-stepping technique and boundary control.Moreover,adaptive neural networks are applied to estimate system uncertainties.With the proposed event-triggered scheme,control inputs can reduce unnecessary updates.Besides,tracking errors and vibration states of the closed-looped network can be exponentially convergent into some small fields,and Zeno behaviors can be excluded.At last,some simulation examples are given to state the effectiveness of the control algorithms.

Lyapunov Conditions for Finite-Time Input-to-State Stability of Impulsive Switched Systems

Dear Editor,This letter studies finite-time input-to-state stability(FTISS)for impulsive switched systems.A set of Lyapunov-based conditions are established for guaranteeing FTISS property.When constituent modes governing continuous dynamics are FTISS and discrete dynamics involving impulses are destabilizing,the FTISS can be retained if impulsive-switching signals satisfy an average dwell-time(ADT)condition.

Theoretical Calculation of Dielectronic-Recombination Cross Section for Hydrogen-Like Argon

Dielectronic-recombination cross sections of hydrogen-like argon are calculated conveniently by our simplified relativistic configuration-interaction method.The results for the KLL,KLM,KLN,and KLO resonances are in good agreement with experimental measurement within a few percent.Our methods can provide various dielectronic-recombination rates which can satisfy the need for relevant applications.

FURTHER INVESTIGATION ON REFLECTION AND REFRACTION OF FINITE AMPLITUDE SOUND WAVE

Based on the authors'former work,a study on reflection and refraction of finite-amplitude sound wave was carried out.A solution completely satisfying the continuity conditions was obtained by means of the method of making the inhomogeneous terms of the wave equation to be determined.

The Cover Layer Phenomenon of Solution for Singularly Perturbed Problem for Third Order Nonlinear Equation

Now we point out the "cover layer" phenomenon of solution. Namely, the solution of problem has a non-uniformly thin layer region, in which there exists a smaller thin layer. It is formed a "layer-in-layer". Mo studied the second order singularly perturbed problem. In many nonlinear mechanical problems there exist singular perturbations of nonlinear

THE FREDHOLM THEOREM FOR SYSTEMS OF INTEGRO-FUNCTIONAL EQUATIONS

Some problems of hyperbolic systems of partial differential equations can be turned into systems of in-tegro-functional equations of the following form[1]here F（x） = （f1（x）,…,fm（x））T and H（x）=（h1（x）,…,tm（x））T both belong to （C∞[-R,R]）m, are theunknown and know vector functions respectively; λis a parameter, 0【R≤+∞, T is an integral func-tional operator, such thathere s is a positive integer, A; and B1 are square matrices of order m, αi and βi are constants satisfying |αi|【1, |βi|≤1.

A KIND OF BOUNDARY VALUE PROBLEMS FOR THE REGULAR FUNCTIONS WITH VALUES IN A REAL CLIFFORD ALGEBRA

Let A. （R） be a real Clifford algebra and Gan open connected set in Rn . By [1], the function with val-ues in An （R） may be written aswhere B ={r1,r2,…,rh} {1,2,…,n}represent that from the sum for’lst and 2nd indi-sates respectively, and we have the following result.Theorem A Function f （x） with values in A. （R） is regular in G if and only ifLet G be the unit hyperball and L the unit hypersphere. Cutting G by the plane: x3= a3, …,xn = an（n3） , we obtain a section domain Ga in the x1x2 plane. Let La be the boundary of Ga, and its center is writ-ten as 0 = （0,0,α3,...,αn） .

THE BOUNDARY VALUE PROBLEM OF DEGENERATE ELLIPTIC EQUATION IN FOUR-DIMENSION SPACE

If G is a bounded domain in the plane R^2, Its boundary consists of a line segment [0,1] in x-axis anda smooth curve which lies upper half plane. Tian Maoying studied the following non-linear degenerate ellip-tic equation of second orderand proved that some boundary value problems of equation (1) and (2) have a unique solution.Wen Guochun discussed some boundary value problem for elliptic system of first order equations in thedomainThis paper makes a deeper study about the degenerate elliptic equation. Utilizing the qualities of four-

REPRESENTATION THEOREM AND ONE-ITERATION THEOREM FOR FREDHOLM INTEGRAL EQUATION OF THE FIRST KIND Ax=y

In this paper, two theorems are presented. The representation theorem stales: ij theFredholm integral equation of the first kindAx=y, with bounded L2 kernel, has a uniquesolutionThe one-iteration theorem states: x can be achieved in one iteration byiffone of the following conditions is satisfied.

Hierarchical satisfying optimal algorithm with different importance and priorities

A hierarchical satisfying optimal algorithm incorporating different importance and preemptive priorities is formulated. With the priority structure given by the decision-maker in the constrained multi-objective multi-degree-of-freedom optimization (CMMO) problem, the commonly used quadratic programming model is converted into a two-level optimization problem solved by the tolerant lexicographic method and the varying-domain optimization method. In contrast to previous works, the proposed approach allows the decision-maker to determine a desirable achievement degree for each goal to reflect explicitly the relative importance of these goals. The resulting solutions satisfy both the preemptive priority structure and have the maximum achievement degrees in sum. The power of the proposed approach is demonstrated with an example.

THE COMPLEX FORM AND EXISTENCE THEOREM OF GENERALIZED SOLUTION FOR NONLINEAR ELLIPTIC SYSTEMS OF THIRD ORDER

Let G be a simply connected bounded domain, we consider the system of partial differential equationsof third order in Gφj(x,y,u,v,u10,v10,u01,v01,...,u03,v03) = 0, （j = 1,2）,（1）where uik = Uxiyk, vik = Vxiyk（0≤i, k≤3）, φj （j = 1, 2） are continuous real functions of the variablesx,y[（x,y） ∈G] and uik, vik（0≤i, k≤3, i+k≤3） , and continuously differentiable for uik ,vik（0≤i,k≤3, i+k=3）Definition 1 If the system （1） satisfy the following conditions in G respectively|A30λ3 + A21λ2+ A12λ+ A02|≠0,λ∈R.（2）3A30+ 21 + A12+ 3 03|≠0.（3）then （1） will be called π-elliptic type and π-strong elliptic type equation system respectively,

NONLINEAR GENERALIZED HASEMAN BOUNDARY VALUE PROBLEMS FOR FIRST ORDER QUASILINEAR ELLIPTIC SYSTEMS IN THE PLANE

1 Problems and ConditionsA class of the lst order quasilinear elliptic systems in the plane, on the basis of Douglis algebra, can bewritten in the simple form Dw=F（z. w） , here D = / x+ / y+e（a / x+ / y） be the Douglis opearator[1], F be a hypercomplex function.Let be a simple and smooth closed curve in the complex plane C,D+ be the simple connected domainbounded by and D-=C- （D+ ∪ ）. Out problem is to find piecewise regular solutions w（z） for Dw=F（z,w） with jump curve in the whole plane that have fixed integer order at infinity and satisfy the condi-tion on ; w+ （τ） = G1（τ）w- （a（τ）） + G2（τ）w+ （β（τ）） +g（τ,w+ （τ）,w- （τ））, which be calledthe nonlinear generalized Haseman boundary value problems. By suitable transformations the problem

THE DIRICHLET PROBLEMS FOR NONLINEAR ELLIPTIC SYSTEMS OF 2n ORDER COMPLEX EQUATIONS

In this paper, the Dirichlet boundary value problems for the 2n order nonlinear elliptic systems of sev-eral complex equations are considered,where z = x+iy, U = （U1（z）,...,Un（z））’, Qj = （Q m）n×n,Ajk= （A mk）n×n, A= （A1,...,An）’, Q m=Q m(z,U,U2,...,Uzn zn-1.Uz2n…Uzn+1 n+1,A mk =A k(z,U,U2z,...,Uzn n-1),Am=Am(z,U,Uz,...,Uzn n-1),j,k≥0,j+k≤2n-1, l,m=.1,2,...,n,Tj（z）=（T （z）,...,Tj（z））′D={|z|【1}, ={{|z| =1}is the boundary of D , γis the outer normal vector of . Suppse that （1） , （2） satisfy the condition C in D :（i） For arbitrary vector of real value functions with 2n - 1 order continuous partial derivative: U（z）

NONHOMOGENEOUS PROBLEM E FOR THE SYSTEMS OF PARTIAL DIFFERENTIAL EQUATIONS OF COMPOSITE TYPE

In this paper, we first consider the following problem;Problem Ewhere G is a simple connected domain, L0 is an elliptic operator, a1、1（z）and b2,0（z） are real functions, u is required to satisfy the following conditions;S = {（t,z） |t】 O,z ∈ G}. We suppose that the coefficient functions are all differentiable and integrable(belong to w22（ ） ).First, let f* （t,z） ≠0, g1（t,z） = g2（t,z） 0. Assume that {vk}, {wk} are the system of eigenfunc-

THE GENERALIZED RIEMANN-HILBERT PROBLEM WITH CARLEMAN'S SHIFT AND HIGHER-ORDER DERIVATIVES FOR GENERALIZED CAUCHY-RIEMANN EQUATIONS

This paper deals with the Noether theory of the generalized Riemann-Hilbert problem with Carleman’sshift and higher-order derivatives for generalized Cauchy-Riemann equations.Let D be a (m + 1) -connected domain with the boundary0,1,……,N) are simple closed curves, z = 0 D.In this paper, the following problem A for generalized Cauchy-Rirmann equtions is donsideredFind the sectionally regular solution of the equationson the domain D, and the boundary values of which satisfy the condition;

ON THE COMPOUND BOUNDARY PROBLEM FOR DOUBLY-PERIOD WITH SHIFT

In this paper, we will discuss a kind of the compound boundary problem for doubly-period-Haseman-Carleman boundary Problem Rm with doubly-period （simply called H-C Problem Rm） :To find a doubly-periodic function φ（z） analytic in S+ and S- except z=0 （including the union of z= 0 with periods 2ω1, 2ω2） and φ（z） may have m order of singularity at z= 0, which satisfies the follow-ing boundary condition:where a（t） is sense-preserving homeomorphic mapping on L1 and α′（t）≠0,α′（t）∈H（L1）, α(t+2n1ω1

THE DIRCHLET PROBLEM FOR A CERTAIN DEGENERATE ELLIPTIC EQUATION AND POTENTIAL METHOD

In this paper we consider the Dirichlet problem for the equation uxx+yuyy= 0 （y】0） on the domainDlocated in upper half-plane, which is bounded by the suitable smooth curve T with the ends A; （-α, 0）and B; （α, 0） and the segment AB. By means of the potential method, the uniqueness and existence of the so-lution of the problem,having a representation of potential, are proved.0 A Special Solution With An Logarithmic SingularityLet two points in upper half-plane, P; （x, y） and M; （ζ,η）, be given. We may construct a special so-lution of the equation above as follows;

ELASTIC ANALYSIS OF THE DEEP FOUNDATION-SOIL INTERACTION

In the past, the problem of the deep foundation-soil interaction was commonly analysed by Mindlin so-lution[1]. It had an error as compared with the practice foundation engineering because it can not be con-sulted the effect of the groove produced by the deep foundation Fuly Man[2] tried the problem by way ofsimplifying the deep foundation-soil interaction to the plane problem of semi-infinite elastic solid subjectedto a concentrated force at the midpoint of bottom of a groove, but it failed because there were some mis-takes.In this paper, the problem of the stress distribution of the grooveis solved by way of Mushelisvili’ s complex stress function. To simpli-

Kaluza-Klein Corrections to the μ Anomalous Magnetic Moment in the Appelquist-Cheng-Dobrescu Model

Applying the effective Lagrangian method,we analyze the radiative contributions of the Kaluza–Klein(KK)modes to the muon magnetic dipole moments in the Appelquist–Cheng–Dobrescu model.Summing over the infinite series composed by the KK towers,we verify the final results satisfying the decoupling theorem in the limit R^(-1)→∞.For the compactification scale R^(-1)=300 GeV,we obtain the electroweak radiative corrections from the KK modes to the muon MDM amount to 6.72×10^(-12) at one loop level.