In this paper we prove that both the pseudo orbit tracing property and expansibility are invariant under lifting or projecting a continuous flow on a compact metric space.Then we give the characterization of C_r flows with the pseudo orbit tracing property on nonorientable closed surfaces.

In this paper,we have discussed a plane vector field whose linear part has two zera olgenvalues with a Jordan block at the bifurcation point,tend the nonlinear item is five powers.The whole orbit bifurcation graphs are obtined.The method with which we studied the judgement function is general,it will be useful in the research for the more degenerate vector field.

First,the concepts and computational methods of inverse variable decomposition and composition (IVD and IVC) for a real polynomial are introduced in this paper,and then,the decomposition and composition methods of generalized ARIMA Series as will as the unique decomposition conditions are given for a general case.

Let P_n and Q_n be the Rudin-Shapiro polynomials and let ψ be the associated Rudin-Shapiro function.We study first the arithmetic and analytic properties of ψ by studing two auxiliary functions △ and ψ.To discuss the fractal structure of ψ,we determine the Hlder exponent of △ and ψ.Then by using interpolating technique,we prove that the Boul.gand dimension and the Packing dimension of the graph of ψ are 3/2.The result shows that we can simulate one dimensional Brown Movement by the Rudin-Shapiro function.

Hopfield neural network model and multi-layered network model have led to many mathematical problems,of which the most important one is the capacity,that is,the number of stable states.In previous work,probability models were considered at most.In this paper we advance some problems in the light of combinatorics,and get some basic results for them.We hope that these problems would induce some interest in this field.

The paper discusses the repairable queueing system with a general arrival,where the lifetime of server and the service time are also exponential random variables,the repair time is PH variable.First,We show that this queueing system can be transformed into the classical model ,then we derive various performances in the stable case.

This paper gives a definition of Bahadur asymptotic efficiency for estimates in general truncated distribution family,proves the efficiency of ordinary important estimates,and compares this ei$ciency with Takeuchi efficiency.

In this paer,using the Bott-Duffin inverse we derive expressions and more condensed determinantal formulas for the unique solution or the general solution of a restricted matrix equation,and give those for solutions of special kinds of matrix equation and restricted linear equations and for several important generalized inverses of matrices.Our results improved and extended those obtained in References [2-11,14,15].

Based on [1-4],this paper establishes the first-order sufficient optimality conditions for the efficient and the strong efficient solutions,and the first-order necessary optimality conditions for the weak efficient solutions of multiobjective programming with set functions,by introducing several new concepts such as pseudoconvex,strictly pseudoconvex,quasiconvex and strictly quasiconvex for set functions.

In this paper,the behaviour of solutions of the Equation:
x'(t)=(x²(t)-μ)x(x(t))μ≤0(1)
are studied.Some new results as well se similar ones to Eder^[1],Wang^[2] and the suthor^[3] are obtained as μ<0.The existence of strictly monotone maximal strong solutions which can not be continuated to ∞ in the two ends are proved as μ=0,i.e.,μ=0 is a bifurcation value of the above Equation.

In this paper we have discussed the confidence limits in the case of no failure data.The general formulae for computing optimal lower confidence limits of some reliability parameters are derived and the concrete results for exponential,weibull and lognormal distribution cases are given respectively.

In this paper.the authors discuss a group of parabolic partial differential equations with contour boundary condition,which is closely related to well testing.The heat kernel with contour boundary condition is discussed,and the gradient of the solution is estimated.The authors also provide a Harnack-type inequality,a comparison theorem of the heat equation and a set of nonlinear parabolic partial differential equations.In addition,an example of application in well testing analysis is presented.

In this paper a general form of acceptability stepsize selection rule of linesearch in algorithms for unconstrained optimization is introduced,which summarizes a lot of known stepsize selection rules as its special cases,and some foundamental properties of this new stepsize selection rule are proved.Finally,we prove the global convergence of BFGS algorithm associated with this general form of linesearch.

In this paper,the stability of a nonlinear gray discrete system is studied,and some criteria for the stability of trivial solutions are obtained by using interval matrices and Lyapunov's second method.We will see that the main results in [5] are generalized from linear systems to nonlinear gray systems.Finally,some concrete examples are given.

In this paper,first we show that the Baska.kov operator is unbounded with usual weighted norm; then we give a new norm,and with this new norm,Baskakov operators have the property of contraction; and lastly,we discuss mainly the direct and inverse results for Baskakov operators with Jacobi-weights.

In this paper,the concepts of the strongly' quasiconvexity in infinite dimensional spaces is introduced.Under the condition that the constraint set is compact and convex while the objective function is continuous and strongly^* quasiconvex,we get the connectedness of the efficient solution sets to multiobjective optimization problems.

In this paper, the authors study a type of transcendental equation which is the characteristic equation of a population model with gap-distribution delay. The variational situation of stability with the change of delay has been investigated completely by means of the character of a spiral. Comparing the results of our equation with the results of the equation P(λ)+Q(λ)e^-λT=0, some essential differences have been noticed.

In this paper, we consider two dimensional time-dependent predator-prey model with prey supplement. By using the differential inequality we discuss the existence and attractiveness of a periodic solution, and existence of an almost periodic solution and its stability under disturbances from the hull.

This note shows that the problem of justifying if a graph has a 3-regular subgraph is still NP-complete even for a planar graph with valency not greater than four. The result is of course in the best possible case for the valent restriction.

In this paper, the used condition for Hotelling T²-test of a two-sample n₁>m, n₂>m is extended to n₁+n₂-m-1>0, and the backround for general application is provided. An example is given.

Abstract Considering the problems of scheduling n independent unit-execution-time jobs in a two-machine open shop, we discuss two problems, one is to minimize the total weighted completion times (O₂/UET/Σ_wici) and the other is to minimize the maximum leteness (O₂/UET/L_max). A polynomial optimal solution algorithm is designed here for each of the problems respectively.

In this paper, we present a kind of iterative correction method for a kind of the second kind non-smooth Fredholm integral equations so that we can raise the convergent order of the collocation approximations some times with less additional computations and apply the method to the approximations of both boundary integral equations of polygonal domains on the plane and the differential equations respectively to show that. This is not only a high order method but also an adaptive one.

In this paper the necessary and sufficient condition for the unique existence of the best L₂ local approximation is obtained. Let f∈L₂[0,δ],S-n=span{u₀,u₁,…,u_n-1}⊂C^n-1[0,δ],and det W_n(u₀,u₁,…,u_n-1;0)≠0.Then the net {P_x(f,S_n)}converges,as x→0,to an element P₀(f,S_n) of S_n if and only if f=P^n-1+h,where P^n-1(t)=, as x→0.Furthermore,P₀(f,S_n)=uW_n^-1A.

In this paper, the performance of some kind of Bayes estimates for the maximum range of a missile is analysed in terms of the quality factor of the prior data and their mean square error. For the different quality factor, some approximation to the best volume of the prior bata are given. In view of the rash advance of this kind of Bayes estimates, an improvement is made for them and some new kinds of estimates are obtained. Furthermore, a comparision of their mean square error is reported by the Monte Carlo, and shows the good performance of the new estimates.

In this paper, the asymptotic error expansion for numerical solution of two-dimmsional Fredholm integral equation is considered. We show that the Nyström solution admits an error expansion in even powers of the step-size h and the step-size k, beginning with terms in h² and k². Thus Richardson's extrapolation can be performed on the solution; and this will increase the accuracy of numerical solution greatly.

Suppose 1,r₁,r₂,…,r_m is positive definite series, existence x,1,r₁,r₂,…,r_m,x,y is positive definite series ⇔ y∈(a,b),a,b-function of r₁,r₂…,r_m.

In this paper the eigenstructure problem of linear regulators is discussed, by using that the frequency conditions are neccjsary and sufficient conditions for o linear regulator. Furthermore, a new approach is suggested to find out the optimal feedbsck matrices.

In this paper, the notion of random conditional entropy of finite nonhomogeneous markov chains is introduced, and the relation between this notion and the relative entropy density is studied. The condition of existence of the entropy rate of nonhomogeneous markov chains{X_n} and the conditions in which the relative frequency, the relative entropy density and the average random conditional entropy density and the average random conditional entropy of {X_n} are a.e. convergence to a constant are given by using the notion of absolute convergence in mean of the sequence.

In this paper we construct a hierarchy of generalized Hamiltonian equations and prove that it is generalized integrable by means of an r-matrix. Afterwards we discuss the relation between it and a new Liouville integrable hierarchy of genetalized Hamiltonian equations in [4].

Let X be a reflexive Banach space, A a maximal monotone mapping defined on X and J:X-X^* a normal dual mapping. This paper considers the composite mapping B=JA^-IJ. The Yosida approximate summation resolvent operator of the mapping B is defined and its asymptotic properties are analyzed. It is pointed out, as applications, that the constructive solvability problem of Browder monotone operator can be simplified and that the convergence results of Rockafellar, Kassay's proximal point algorithms can be extended.

In this paper we study the blow-up problems of solutions for the initial boundary value problem and initial value problem of the pseudohyperbolic equations of nerve conduction type

not only for arbitrary nonnegative initial value, but also for sufficiently large initial value by using an improved eigenfunction method.

Let {X_n, n≥1} be i.i.d. random variables and X_n,1≤X_n,2≤…≤X_n,n be order statistics of X₁,X₂,…,X_n. Let S_n (k,r)=Σ_t=k+1^n-r X_n,i, where k,r are fixed. In this paper we study convergence rates of the law of large numbers for S_n(k,r) and prove the comlete cenvergence theorems, which generalize the results of independent sums.

In this paper,through some direct studies of the spectral problem ψx=U(u,λ)ψ,an approach for obtaining the hierarchy of soliton equations is presented by the use of spectral gradient. Moreover, a general structure of commutator representations for the soliton hierarchy is constructed. Meanwhile, it is revealed that the same spectral problem can produce two different hierarchies of soliton evolution equations.

In CAGD, free-form curves and surfaces are main object of study, their shapes frequently need to be modified. A class of 4-order rational alternate spline curves with a parameter ε and weights {w_i} is presented in this paper. They have continuous second derivatives vectors. By varying the parameter ε or weights {w_i},the curves can entirely or locally approximate their control polygon. Therefore, they provide a convenient and flexibly way for modifying shape.