STRONGLY CONVERGENT ITERATIVE METHODS FOR SPLIT EQUALITY VARIATIONAL INCLUSION PROBLEMS IN BANACH SPACES

The purpose of this paper is to introduce and study the split equality variational inclusion problems in the setting of Banach spaces. For solving this kind of problems, some new iterative algorithms are proposed. Under suitable conditions, some strong convergence theorems for the sequences generated by the proposed algorithm are proved. As applications, we shall utilize the results presented in the paper to study the split equality feasibility prob- lems in Banach spaces and the split equality equilibrium problem in Banach spaces. The results presented in the paper are new.

Generalized Strongly Nonlinear Quasi-Complementarity Problems

Using the algorithm in this paper, we prove the existence of solutions to the gene-ralized strongly nonlinear quasi-complementarity problems and the convergence of theiterative sequences generated by the algorithm. Our results improve and extend thecorresponding results of Noor and Chang-Huang. Moreover, a more general iterativealgorithm for finding the approximate solution of generalized strongly nonlinear quasi-complementarity problems is also given. It is shown that the approximate solution ob-tained by the iterative scheme converges to the exact solution of this quasi-com-plementarity problem.

UNIQUENESS FOR THE SOLUTIONS OF ELASTIC THIN PLATES AND SHALLOW SHELLS AS WELL AS THEIR CONTACT PROBLEM WITH HALF SPACE

The uniqueness for the solutions mentioned in the subject is proved by using the uniqueness of the solution for the internal boundary problem of Laplace and bi-Laplace equations of the first kind as well as of the second.

ANALYTICAL SOLUTION OF AXIAL SYMMETRICAL WALL TEMPERATURE DISTRIBUTION FOR HOLLOW CYLINDER

Using the variable transformation method,the formulae of the axial symmetrical wall temperature distribution during steady heat conduction of a hollow cylinder are derived in this paper.The wall temperature distribution and the wall heat flux distribution in both axial and radial direction can be calculated by the temperature distribution of the liquid medium both inside and outside the cylinder with temperature changing in axial direction.The calculation results are almost consistent with the experience results.The applicative condition of the formulae in this paper consists with most of practice.They can be applied to the engineering calculation of the steady heat conduction.The calculation is simple and accurate.

NON-UNIFORM DEPENDENCE ON INITIAL DATA FOR THE MODIFIED CAMASSA-HOLM EQUATION ON THE LINE

In this paper, we study the Cauchy problem for the modified Camassa-Holm equation mt ＋ umx ＋ 2ux m = 0, m =（1- δx^2）^2u,u（x, 0） = u0（x） ∈ H^s（R）, x ∈ R, t 〉 0,and show that the solution map is not uniformly continuous in Sobolev spaces H^s（R） for s 〉 7/2. Compared with the periodic problem, the non-periodic problem is more difficult,e.g., it depends on the conservation law. Our proof is based on the estimates for the actual solutions and the approximate solutions, which consist of a low frequency and a high frequency part.

Hybrid Meta-Model Based Design Space Differentiation Method for Expensive Problems

In this work,a hybrid meta-model based design space differentiation（HMDSD）method is proposed for practical problems.In the proposed method,an iteratively reduced promising region is constructed using the expensive points,with two different search strategies respectively applied inside and outside the promising region.Besides,the hybrid meta-model strategy applied in the search process makes it possible to solve the complex practical problems.Tested upon a serial of benchmark math functions,the HMDSD method shows great efficiency and search accuracy.On top of that,a practical lightweight design demonstrates its superior performance.

Representation of measures of noncompactness and its applications related to an initial value problem in Banach spaces

This paper is devoted to studying the representation of measures of non-generalized compactness,in particular,measures of noncompactness,of non-weak compactness and of non-super weak compactness,defined on Banach spaces and its applications.With the aid of a three-time order-preserving embedding theorem,we show that for every Banach space X,there exist a Banach function space C(K)for some compact Hausdorff space K and an order-preserving affine mapping T from the super space B of all the nonempty bounded subsets of X endowed with the Hausdorff metric to the positive cone C(K)^(+) of C(K),such that for every convex measure,in particular,the regular measure,the homogeneous measure and the sublinear measure of non-generalized compactnessμon X,there is a convex function F on the cone V=T(B)which is Lipschitzian on each bounded set of V such that F(T(B))=μ(B),■B∈B.As its applications,we show a class of basic integral inequalities related to an initial value problem in Banach spaces,and prove a solvability result of the initial value problem,which is an extension of some classical results due to Bana′s and Goebel(1980),Goebel and Rzymowski(1970)and Rzymowski(1971).

A STABILITY STUDY OF NAVIER-STOKES EQUATIONS (Ⅲ)

In this paper, the necessary conditions of the existence of C￣2 solution. in someinitial problems of Navier-Stokes equations are given. and examples of instability ofinitial value (at t=0) problems are also given. The initial value problem ofNavier-Stokes equation is one of the most fundamental problem for this equationvarious authors studies this problem and contributed a number of results .J.Leray .aFrench professor, proved the existence of Navier-Stokes equation under certain definedinitial and boundary value conditions .In this paper,with certain rigorously definedkey.concepts,based upon the basic theory of J.Hadmard partial differentialequanous￣[1], gives a fundamental theory of instability of Navier-Stokes equations.Finally,many examples are given,proofs referring to Ref.[4] .

Optimal two-impulse space interception with multiple constraints

We consider optimal two-impulse space interception problems with multiple constraints.The multiple constraints are imposed on the terminal position of a space interceptor,impulse and impact instants,and the component-wise magnitudes of velocity impulses.These optimization problems are formulated as multi-point boundary value problems and solved by the calculus of variations.Slackness variable methods are used to convert all inequality constraints into equality constraints so that the Lagrange multiplier method can be used.A new dynamic slackness variable method is presented.As a result,an indirect optimization method is developed.Subsequently,our method is used to solve the two-impulse space interception problems of free-flight ballistic missiles.A number of conclusions for local optimal solutions have been drawn based on highly accurate numerical solutions.Specifically,by numerical examples,we show that when time and velocity impulse constraints are imposed,optimal two-impulse solutions may occur;if two-impulse instants are free,then a two-impulse space interception problem with velocity impulse constraints may degenerate to a one-impulse case.

Improving Strategies Based on Problem Space Analysis in Line with Critical Thinking:Re-flections on the Planning Theory Study in Contemporary China

In the age of algorithms,planning theory study has gradually deviated from its original purpose under the influence of information technology,resulting in the problems of dogmatic thinking and passive cognition.Based on the concept of problem space,this paper tries to sort out the main procedure of theoretical planning studies and trace the roots of the above problems through the suspicion and introspection of criticism.In line with the philosophical speculations on the primacy of cognition and the primacy of ethics from the perspectives of epistemology and ideology,it discusses the cores and the values of planning theory study and concludes that humanistic philosophy,utilitarianism,arithmetic operation,and professional context would reorient planning theory study back to its original track.

Reducing problem of multiplication operators on Bergman space

THE L_a^2(D) refers to Bergman space on D, where D is the unit disk on the complex plane. Using the super-isometric dilation technique, we obtain the following results. Proposition 1. The multiplication operator M_φ on Bergman space L_a^2 (D) is unitarily equivalent to the compression of the direct sum of 2N-1 copies of Bergman shift, where φ is a Blaschke product of order N (【∞).

Hangzhou Parking Problem and Underground Space Usage

The author analyses the possibility,feasibility and scheme of solving the parking problem in the city ofHangzhou by using the underground space.

Pathwise no-arbitrage in a class of Delta hedging strategies

We consider a strictly pathwise setting for Delta hedging exotic options,based on Follmer’s pathwise It¨o calculus.Price trajectories areˆd-dimensional continuous functions whose pathwise quadratic variations and covariations are determined by a given local volatility matrix.The existence of Delta hedging strategies in this pathwise setting is established via existence results for recursive schemes of parabolic Cauchy problems and via the existence of functional Cauchy problems on path space.Our main results establish the nonexistence of pathwise arbitrage opportunities in classes of strategies containing these Delta hedging strategies and under relatively mild conditions on the local volatility matrix.