Stochastic integrals with respect to the compensations of point processes are pure-discontinuous martingales.This fao,t suggests that them: exists some relationship between S.M.(O) and such kind of stochastic integrals.Ln this paper,we discuss what kind of point processes can generate some S.M.(O) so,that the above stochastic integrals can be regarded as S.I.with respect to the corresponding S.M.(O).We found the sufficient and necessary condition.called it "Class (L) property".Applying it to the jump point process of a pure-discontinuous martingale."Class (L) property" is equivalent to the quasi-left continuity of the martingale.

According to Ms.J.Durbin's a two-step least-squares estimate method for regression models with AR noise,we get the estimates for the autoregressive and regressive parameters by the linear method.A eonveraence property of the estimates for the autoregressive and regressive parameters is proved.We also introduce a version of.Akaike's model selection procedure for the regression model with AR noise.A consistency property of the estimate for the autoregressive order is proved,a simple algorithm is described,and an exaatple is given to illusrate out result computated.

A restricted 3+1 Toda lattice equation is studied.Its Backlund transformation,nonlinear superposition formula,Lax representation,Miura transformation,Darboux transformation and 1-soliton solution are obtained.

A stochastic series {X_t} is generated by a doubly stochastic serves model
X_t=θX_t-1+e_t,
where {e_t} is a i.i.d Series,{θ_t} also is a stochastics Series.We discuss that case: when {θ_t} is a MA(2),Series,the necessary and sufficient condition of that {X_t} have stationary of solution; and when {logθ_t²}is a ARMA(p,q) Series,the necessary and sufficient condition of that {X_t} have stationary of solution.

In this paper,the asymptotic behaviour of nonoscillatory solutions of a second order non-linear NFDE has been studied.Sufficient and necessary conditions for non-oscillatory solutions of a second order linear NFDE have been obtained also.

In theis paper,we give a sufficient condition of harmonic oscillation for an interval matrir and discuss the problem of harmonic oscillation for a large scale system when the subsystem has the property of harmonic oscillation for an interval matrix.In the end,we give some criteria on the existence of a unique stable periodic solution for a type of linear system with variable coefficients and compound system.

In this paper,we prove the existence of general random solutions for several kinds of continuous random set-valued (single-valued) operator equations and systems of continuous random set-valued (single-valued) operator equations in Cartesian space.As a result,we enlarge the class of random operators which make the equations corresponding to them have random solutions.

A nonlinear parabolic system is derived to describe compressible nuclear waste-disposal contamination in porous modia.The model was developed for use by the Nuclear Regulatory Commission in the analysis of deep geologic nuclear waste-disposal facilities.Two numerical methods(Mixed finite element-characteristics-finite difference methods) are introduced.The brine,radionuclide and heat are treated by an implicit finite difference method that applies a form of the method of characteristics to the transport terms.The pressure is treated by a parabolic mixed finite element method.Optimal order estimates are derived for the errors in approximate solutions.

Consider a growth curve model as follows:
Y=X₁BX₂+UJ
where has a quasi-normal distribution,Es-0,,and Σ≥0 is an unknown covariance matrix.This paper gives the n.s.condition for Uniformly Minimum Variance Nonnegative Quadratic Unbiased Estimator (UMVNNQUE) of tr (CΣ) to be existenr,and gives UMVNNQUE of tr(CΣ) when it exists,where C≥0(≠0) is an arbitrarily given matrix.As corollaries,this paper also gives the n.s.condition for tr (CΣ^*) to be UMVNNQUE of tr (CΣ),where Σ^* is Σ"s LSE in a certain sense.

In this paper we use Ekeland's Variational Principle and Fattorini's lemma,to treat optimal control problems of infinite-dimentional nonlinear generalized systems with constraints on the control variable.The maximum principle is given.

In the beginning of this paper the oscillation behavior of solutions of first order differential equations with forced term and deviatsng arguments have been considered.Some new oscillation criteria have been estiblished.Next the asymptotic behavior of solutions of a class of first order nonlinear delay differential equations have been investigated.Some sufficient conditions for the global attractivity have been obtained.

In this paper,a new algorithm for the reverse convex programming with linear object function is proposed,which convert the problem into a series of minimization of a concave function on a polyhedron.

In this paper,we discuss the existence,uniqueness and regularity of the solution to a quasiIinear elliptic variational inequality with arbitrary polynomial growth.We obtain the existence,uniqueness and regularity theorems of the so lotion,under some nature assumpttona.

In this paper,we offer a procedure for estimating weight functions of the mixed density esttmates,and reach the strong convergence of the weight function estimates.From it,we obtain the strong consistent rates of the mixed density estimates with respect to true density functions.

In this paper we obtain the discrinimanting rules for the oscillation of the solutions of an even order nonlinear differential equation with deviating arguments.

In this paper, some general results on the relations between nonsingular perturbations and {2} generalized inverses of matrices are obtained. These results extend th ose in [2].Moreover, several applications are gwen.

This paper gives a simple description that a convex polytope of d-dimension is represened only by its d-1-faces, d-2-faces and vertices. This greatly reduces the space complexities of the existing algorithms. Futhermore, a new and very fast real-time algorithm is developed for ineremently constructing convex hulls of finite points in higher dimensions.

In this paper we consider the covering mapping of a compact manifold M, and prove that if the closure of the α-limit set of f denoted by L^-1(f), is hyperbolic and does not admit of cycles, then f statisfies Axiom A and has no cycles, and therefore f is orbit shiftΩ-stable.

In this paper we study the oscillation of solutions of a nonlinear second order damped differential equation
(r(t)x'(t))'+p(t)x'(t)+q(t)f(x(t))=0.
Some new criteria are established, and they improve all the results of [21].

In this paper we obtain a necessary and sufficient condition for the existence of Eelliptic separatrix cycles in a quadratic system, and describe the phase-portrait of the whole quadratic system with elliptic separatrix cycles. Furthermore, we obtain an accurate parameter interval for a certain Ⅲ-type quadratic system to have limit cycles. This paper shows that a new method for finding the bifurcation value of a limit cycle for a quadratic system is very effective.

This paper presenrs some criteria for the stability, uniform stability and asymptotic stability of Volterra integral and differential equations. The criteria are of simple forms, easily checked and applicable.

A branch and bound algorithm is presented for the problem of sequencing njobs on a single machine to mmtmize the weighted number of tardy jobs, which is NP-complete. An optimal sequence in which jobs completed on time are is EDD order is found. We propose and consider precedence relationship bPrween jobs so that we may reduce branches and pick up the speed searching. Born Moore-Hodgson's algorithm for non-weighted jobs and Lawler's algorithm fos agreeable jobs are special cases of our algorithm.

In this paper, we prove that for any martingale or non-negative order submartingale M={M_t}_t∈t with right continuous trajectories(or more weakly, separable),insexed by T=[0,1]^*, if we let M^*=, 1=(1,1,…1)∈T, Ψ_a=x(log⁺x)^a, and || ||Ψ_n denote the Orlicz norm determined by Ψ_n, then
||M^*||₁≤C_n||M₁||Ψ_n
holds for some positive constent C_n.

To find the maximum distribution of second-order Volterra response due to a stationary Gaussian excitation is very important and useful nor only in mathematical statistical theory but also in its application to engineering structure reliability. Two new methods are given in this paper. They are established by rigorous mathematical theory. At the same time, a numerical example of ocean engineering is given. Obviously these results and methods can be extended to n-order Volterra system easily, and they are not only applicable in ocean engineering.

In this paper, we study the existence, uniqueness, regularity, asympatotic property and continuous dependence on the initial-boundary values of the generalized solution to the problem of natural convection in an annular cavity.

In this paper,by means of constructing a kind of Lyapunov functional which is different from the one in [1],we not only obtain results of stability of the zero solution to convolution and nonconvolution type equations, but also obtain the uniform boundedness of solutions to nonhomogeneous equations. At the same time, we also weaken and delete some reasonless conditions of the related theorem in [1].

This paper deals with the single-level connnunus sampling plan CSP-1-P in which probability sampling is used during sampling inspection. Theoretic formula and strict calculating method are obtained by introducing transition probability flow braph, transition probability generaung function and probability generating function.

For the principal chiral model, we construct two Hamiltonian operators, their related Poisson manifolds, recursion operator and infinitesimal symmetry transformations with their Le algebraic properties:Associated with both Poisson structures, we also give the r-matrices which satisfy the generalized Yang-Baxter equation.For the principal chiral model, we construct two Hamiltonian operators, their related Poisson manifolds, recursion operator and infinitesimal symmetry transformations with their Le algebraic properties:Associated with both Poisson structures, we also give the r-matrices which satisfy the generalized Yang-Baxter equation.

We consider the large-time behaviour of solutions of the Cauchy problem and the Cauchy-Dirichlet problem for the nonlinear degenerate parabolic equation
u₁=(Ψ(u))_xx-(g(u))_xx
We prove that the large-time behaviour of solutions depends strongly upon the shape of g(convex or concave) as well as upon the values u^-=₀(-∞) and a+=u⁺(+∞).Furthermore, we give sufficient conditions under which the solution converges to a travelling wave and converges to a rarefaction wave respectively; moreover, the rate of convergence to a rarefaction wave is stimated.

In this paper, we firat present a necessary and sufficient condition for a polynomial equation of degree n with real coefficients to have a pair of pure imaginary roots and the remaining n-2 roots with negative real parts. Then we obtain an algebraic criterion for Hopf Bifurcation which enables us to know the existence of bifurcating periodic solutians of an autonomous nonlinear ordinary differential system by directly using the coefficients of the characteristic equation of the linearized system.This result generalizes. Theorem 1 and Theorem 2 in [1].

A two-dimensional, multicomponent, multiphase, composite reservoir simulator has been developed and applied to micellar/polymer flooding. The mathematical model of the two dimensional boosted oil recovery simulation can be described by a system of nonlinear partial differential equations. We put forward the continuous time finite element and discrete time finite element methods. Optimal order estimates are derived for the errors in the approximate solutions.

In this paper,the problem of periodic contact of an elastic half-plane bonded by a strip and a half-plane with different isotropic materials is solved by means of method of analytic functions and singular integral equations,and we obtain the solutions in closed form.

In this paper,we prove a comparison theorem concerned with the existence of periodic solutions for functional differential equations with Iead and delay argumants of type
.

For a class of generalized Radon transform,we suppose density function μ belongs to the sobolev speace H^α of order α>1/2 and n curves Radon integeral with a root mean squre error and ν the minimizer of Tikhoaov-Phillips method,then one have error estimate of estimate of estimate of ‖μ+η-ν‖_L²≤C(g^α(α+1/2)+n^{-α/2)‖u‖_Hα,where η∈N(F)(Null space of F),η∈C∞ F is a Fourier integral operator derived from Radon transform when N(F)={0},η=0,N(F)={0} for some generalized Radon transform.This estimate is optimal to some case.Finally we consider the Attenuated Radon transform as the result obtained.The work of [16] is generalized in this paper.}

In this paper,SP-solution concept for(m,n)-person games is defined.Its basic properties are discussed.And the existenr conditions of the solution are green.

Let {x_n} be a sequence of independent random elements in a separable Banach space B, and {t_n} a nondecreasing sequence of positive real numbers such that t_n→∞ as n→∞.

We prove an upper bound of Dulmage-Mendelsohn type and an upper bound of Lewin-Vitek type for the indices of convergence of irreducible Boolean matrices,then use these upper bounds to obtain explicit formulas for the largest index of convergence M(n,p) of all the n×n nearly reducible Boolean matrices with period p.

Grey model can be applied to describe dy namic characteristics of complex systems.However,it is difficult to get some useful physical interpretation by this model,because its description is indirect.According to the method to build the grey model,a method called relative sustitution is proposed in this paper.Consequently a model called direct grey model,by which the dynamic system characteristics can be directly described,is derived.On this basis,two properties of a kind of direct grey model under a linear transformation are derived.One of them may be applied to the estimation of step inteference signals in adaptive control.

In this paper we extend a class of stationary singular control prohlems and give the construction of the optimal control.It acts only when the state reaches the boundaries of some interval and reflects the state into the interval at its boundaries,in order not to exit from the interval.