In this paper, we modify the algorithm in [1] and prove that the modified algorithm is globally convergent without regular condtions. Comparing with the results in [1], (SBSQ) constaint qualification is not needed. Then the results in this paper strengthen and generalize the results in[1].

Combining the wavelet smoothing method and random weighting method, we obtain that the rates of random weighting approximation of wavelet estimates for parametric components in the semiparametric regression model can attain the accuracy of o(n~{-1/2}) under suitable conditions.

Using information theoretic criterion, the problem of change points is considered. In the framework of model selection, procedures are developed to estimate the locations and the number of change points. These procedures are shown to be strongly consistent in estimating the number and locations of change points in the mean vector when the covariances are different.

In this paper, using for the most pare geometric methods, authors study centers around mang periodic solutions to the two-dimensional differential difference equations as follows Then the equations (E) has periodic solutions.

A production-inventory system is studied in which an unreliable machine is susceptible to failure following which they must be repaired to make it operative again and the demands for the product are superposition of k Poisson demand arrival processes,demand sizes are independent and identically distributed randmom variables.A rwo-critical-number policy is used to control a machines setups and shutdowns.The sufficient conditions to ensure the existence of the stationary distribution of inventory level and explicit expression of this steady-state condition are also obtained.

Let {Xn} be a standardized nonstationary Gaussian sequence, rij = cov (Xi, Xj), and Nn be the point process formed by the exceedances of level un = x/an + bn by {Xn}. If rij log (j - i) -r (0, ) (j - i +00), n - o, then the point process Nn converges indistribution to Cox-process.

Consider a bivariate exponential distribution due to Gumbel, whose reliability function is We call this distribution (X1,X2) - GBVE ( ). Based on the properties of mixed moments for (LnX1,LnX2), this article proposes two moment-type estimators δ1 and δ2 of δ,prones that both δ1 and δ2 have stromg consistency and asymptotic normality,obtains asymptotic variances σδ12 and σδ22 of δ1 and δ2 respectively,and compares σδ12 with σδ22.Some simulation results are also given.

In this paper, the author prove the existence of solutions of two and three point boundary value problems for the equation with the boundary conditions (2) and (3) where , and di is indepandent of each other, thus we deal with 2n-2 different types of boundary conditions.

In this paper, the transformable conditions and the transformation matrices of two arbitrary B-spline bases are studied, and the theoretical results about the representation and properties of the elements of the transformation matrices are given.In addition,two recurrent formulas are derived which pronide a mathematical approach to the calculations of the elements of the transformation matrices. The applications of the transformation matrices of B-spline bases in CAGD are also discussed,includeing the problems about the paper provide a uniform mathematical mode and approach to the basic operations of B-spline curves such as knot insertion,degree elevation,decomposition etc.

In this paper, the following Lotka-Volterra system is considered:\[\frac{d_{X_i}}{dt}=x_i\quad(b-\sum_{j=1}^n a_{ij}\quad x_j),x_i(0)>0,i=1,2,3.] The necessary and sufficient conditions are given for the existence of periodic orbits in the system.

In this paper, the existence of positive solutions of the fourth-order boundary value problem \[u^{(4)}(t)=\phi(t)\quad f(u(t),u^"（t）, t\in (0.1),\\u(0)=u(1)=u^"(0)=u^"(1)=0).\] is discussed. The auther obtains the existence and multiplicity results of positive solutions by employing the fixed-point theorem of cone expansion or compression type.

In this paper, a singular nonlinear boundary value problem of second order three-point is considered, and we obtain the existence and uniqueness of the positive solution by use of the perturbation technique and comparison principle.

By establishing some probability exponential inequalities of maximal partial sum, we obtain some results on the bounded law of the iterated logarithm for negatively associated random variables with different distributions, which extend the Wittmanns results for independent random variables to the case of negative association.

Let G be a graph, the isolated toughness of G is defined as I(G) = min if is not complete. Otherwise, set I(G)=o. A variation of isolated toughness is defined as, I'(G) = min if G is not complete. Otherwise, I'(G) = o; In this paper, the relationship between the isolater toughness,the variation of isolated toughness and fractional factors of graphs is discussed;Sufficient conditions for guaphs to have fractonal 1-factors and 2-factors with some consreaints are given.Some newproblems are presented.

In this paper, nonlinear integrodifferential equations with infinite delay of the form. are considered, where the n x n matrix function A(t, x) and the n- vectors f(t,x),g(t,x) are continuous in (t,x) R x .Rn, C(t,s) C(R x R). By combinning the theory of exponential dichotomies of linear system and ficed point theorem,some sufficient coditionthat guarantee the existence and uniqueness of periodic solution of the systen(1)and(2)are obtained.Somenew results are obtained.

A environment mathematical model with delays: is discussed. By using Hale-Watlman's Theorem on uniform persistence, it is proved that the system is uniformly persistent if it has a positive equilibrium. It is also shown that the positive equilibrium of the model is globally asymptotically stable.

In this paper, we study the asymptotic behavior of solutions for a class of delay artifical neural networks model of two neurons with two thresholds. In a given space of initial functions, the anvergence of salutions is proved for such a model. Furthermore,the basin of attraction is given for every equilibrium point.

Let fif be a domain on the complex plan obtained by moving from a disc of radius a a totally disconnected compact set 3 of zero capacity. Consider a stationary Schrodinger equation (-A + p,)u = 0 on fi, where the potential j, < 0 is a signed Rado measure of Kato class.We Denote by_uH^+ the class of all distributional solution of the equation which are nonnegative and continuous on Ωαβ vanishing on its boundary Ωαβ={z||z|=a}.For any ζ\inβ,ad an ideal boundary point in the Stoilows sense,an operator \pi^ζ=H+→μH+ is introduced.It is showm that_uH^+=H_β\oplusP_α.

In this paper, with W-correspondence, the variational inequality proved by Kok Keong Tan is improved and a generalized variational inequality is established.

By application of fixed point theorem and using approximation method, the author investigates the existence of positive solutions for nonlinear singular second order initial value problem: y"(t)-(t)f(t,y(t),y'(t)), 0<1; y(0)=y'(0)=0, and obtains new results.

This paper considers the very weak solutions of a class of quasilinear elliptic equation. The local regularity result is obtained by using the method of Hodge decomposition.

Using segmented periodograms we studied the model estimation in hidden periodicity model with frequency change points. We gave strongly consistent estimates for the change points and the hidden frequencies. Simulation results show that estimates are not sensible to naise.

In general, there are three methods to deal with the continuous inspection problem. One is the well-known Shewhart chart proposed by [3]?Shewhart (1924). Many authors pointed out that when the shift in mean is small (i.e. n ?u0 is small) then the Shewhart chart is mot effective.the other two methods are the CUSUM(Cumulative Sum) chart proposed by Page~[1] and the EWMA (exponential weighted movving average)chart proposed by Roberts~[2].Lots of authors compared the CUSUM with EWMA.Generally speaking,the optimal CUSUM and the optimal EWMA both act well in detecting the small shift in mean.Since the CUSUM is most comparable in practice. The CUSUM text statistic was proposed by Page~[1] basedon the likelihood ratio.Wepointed out that we can inprone the CUSUM intwo ways and then we ginetwo new CUSUM test statistics and their decision principle.One is the P_n named by PCUSUM,and the other is the S_n named by DCUSUM. To judge a inspection method,one ususlly compute its ARL(average run lengeh).A good test should has the smallest out-of-control ARL with the same in-control ARL.We established the formula to compute the ARL of the PCUSUM and the DCUSUM。The results of ARL show that the PCUSUM and the DCUSUM both impromved the ususal CUSUM.

In this paper, we study the polarity of nondegenerate diffusion processes X(t). Several sufficient conditions for P(X(E) F 0) =0 and P(X-1(F)0) = 0 is obtained which are better than the results in [1]. Furthermore, we study the intersection for two independent nondegenerate diffusion processes and obtain seneral interesting results.

The study of sign stability of a real square matrix has important applications in various areas such as economics, ecology, and so on. In this paper, the sign stability problem for matrices is turned into an equivalent graph theoretical problem,namely,the stability problem for the vertex subsets of tress.We introduce the concept of stable vertex subsets of tress and give a recursive method for recognizing them.We also introduce for trees a new parameter,stable index,which is the smallest cardinality among all the stable nertex subsets of the tree.We prove a min-max type theorem for stable index,give a sharp upper bound for the stable indices of tress of order n,and gine a complete characterization for the extreme tress whose stable indices attaining this upper bound.

Through blending MMOCAA difference method with UNO interplation, the UNO-MMOCAA difference method is constructed for covection diffusion equation in the paper, which is free from oscillation of MMOCAA difference method based on high order (>2) Lagrange interplation at the sharp front.The methods of ancillary interpolating operater etc.are introduced to get error estimates of UNO-MMOCAAdifference scheme.The numerical examples shoe that the new scheme is free from the oscillation.

The existence of positive solutions has been discussed for the nonlinear boundary value problem y"(t) + g(t,y) = 0, y'(0) = 0 and y(l) = b > 0, where g is locally Lipschitz continuous, g(t, 0) > 0 and may change sign. The main result as follows:If g(t,y) satisfies a superlinear condition at y=+∞ and there exists a nonnegative supersolution βwith β(1)>0,then there exists a positive number B shuch that this problem has at least two positive solutions for 0B.Our approach is based on the Leray-Schauder degree arguments and the method of sub-and supersolutions.

This paper discusses the problem of periodic solution of singular differential equation with delay. Particularly, we give the problem of existence of periodic solution of two-dimensional singular differential equation with delay, and give an example to illustrate the main results of this paper.

An efficient subset for portfolio selection means that it may replace the original security set to generate the Markowitz portfolio efficient frontier. This paper gives a necessary and sufficient condition for a subset to be efficient without short subset.

The present paper based on solving method of Copson investigated, made an improvement and generalization, is used solving complex dual integral equations of more general form. Firstly via introduced function are transformed equations, and then by introduced integual transformation of unknown function it is decoupled.Using Able anti-transformation,the equations are further reduced to regularized Fredholm integral equations of the second kind Thus are given general solutions of dual integal equations.The given theoretical solutions and solving method in this paper provides Chice and reference on problems of the solving mixed boundary valre of complex mathematics,physics,mechanics.At the time the anthor useful method of solving complex sual integral equations is furnished.

In this paper, a simple method for determining all roots of a complex polynomial are inside the unit circle is presented. The method is used to determine stability of discrete control system and find all roots of a polynomial.

The miscible displacement of one incompressible fluid by another in a porous medium is modeled by a nonlinear system of two partial differential equations. The pressure equation is elliptic, while the concentration is parabolic but normally convection-dominated.In this papper,a finite-different streamline diffusion with mixed finite element method is defind=ed,and the quasi-optimal convergence rates in the norm L~∞(L~2) is derived.

In this paper, we consider the oscillation of solutions for the first order superlin-ear delay differential equations x'(t) + p(t)[x(t -r)]a = 0 (a > 1), and obtain some "almost sharp" oscillation criteria. In the final, by applying the obtained results in this paper,we also obtain some oscillation conditions for the mixed type delay differential equations $$x′(t)+\sum_{i=1}^n p_i(t)[x(t-r_i)]^{α_i}=0$$

A kind of refined optimality necessary and sufficient conditions for constrained vector optimization of set-valued maps with Benson proper efficient solutions is established without the assumption that the partial order cone's interior is nonempt

In this article, we studied uniform dimension and uniform measure of image set of N-parameter d-dimension generalized Wiener process. We obtained uniform Hausdorff dimension and uniform Packing dimension of its image set.

Using the matching condition, the shock solutions for a class of nonlinear singularly perturbed problems are discussed. The relation of the shock solution and its boundary condition is considered.

In this paper, the authors improve the disk theorem and give a new estimation of eigenvalues of the matrix. And a sufficient condition is obtained for the nonsingularity of diagonally dominant matrix.