A class of the generalized product-limit estimators is introduced for regression analysis in the presence of both left-truncation and right-censoring on the response variable. The weak convergence of the generalized product-limit estimators is established. These generalized product-limit estimators are used to define some minimum distance estimator of the parameter vector in the regression analysis. The consistent and asymptotic normality of the minimum distance estimators are obtained under certain assumptions.

In the paper, a new interval method is given for a kind of global optimization problem using the feature of interval expansion, and it can solve global optimization problems with several variables. Numerical experiments show that the proposed method is feasible and effective.

Influence analysis played a key role in regression problems. For inequality constrained regression problems, influence analysis will be as important as in unconstrained regression. Here we have to consider two types of influential points and have to define several different kinds of distance. In this paper, we will derive a method to check two types of influential points.

In this paper, we first obtained the criterion for determining the stability of a semi-stable multiple limit cycle by computing the successor function. Then by generalizing the criterion, we obtained the criterion for determining the stability of a homoclinic cycle for the second critical case. Appling the criterion we determined the stability of a homoclinic cycle with the second critical case. The method used in this paper can give a unified treatment for the results given in the past. Finally, we study the number of limit cycles by bifurcation from a multiple limit cycle or a homoclinic cycle for the second critical case.

In this paper, we study the complex nonlinear phenomena in a fundamental power system provided by paper, We analyze local stability and bifurcation of equilibriumin the dynamics systems. When $0\frac{V^2_s(X_d-X_d')}{2X_{d\Sigma'}X_{d\Sigma}}$ and withcontrol$u_f>E_{fdsc} +u_{fc}-E_{fds}$ , there are two fixed points, one is stable, the other is always unstable. $E_{fds}+u_f=E_{fdsc}+u_{fc}$is saddle-node bifurcation value corresponding to collapse of the power system. As$E_{fds}+u_f

In this paper, higher dimentional periodic system with delays of the form $$ x' (t)=A (t,x(t))x(t)+\int_{-r}^{0} f(t,s,x(t+s))\, \d s +\sum\limits_{i=1}^{p}f_i (t,x(t-\tau_i(t))) $$ is considered. By using the coincidence degree theory and constructing suitable Lyapunov functional, some sufficient conditions which guarantee the existence and global attractivity of periodic solution of above system are obtained. The results are effctive and easily testified.

The purpose of this paper is to study the existence and algorithms of solution for multivalued nonlinear mixed variational inclusions. The results presented in this paper extend and improve the previously known results.

In this paper, a linear varying-coefficients structural EV model is given. The estimators of parameters of linear coefficient at $t = t_0$ are constructed by using the weighted orthogonal regression least square method. The weak and strong consistency of estimators are also obtained.

The circular chromatic number(also called the star chromatic number)$\ssize \chi_c(G)$ of a graph G is a natural generalization of the chromatic number of a graph which was introduced by Vince in 1988. In this paper, we construct a family of planar graphs with circular chromatic number just between 2 and 3 based on odd wheels, thus we filled the space of this field.

The existence of traveling wavefronts in systems of spatially discrete reaction diffusion equations with delay on higher dimensional lattices is established by Schauder fixed point theorem and upper-lower solutions technique. The cases of quasimonotonicity nonlinear terms, weaken exponential quasimonotonicity one, partial quasimonotonicity one and partial weaken exponential quasimonotonicity one are considered.

We present an affine-scaling interior-point trust-region algorithm for simple constrained optimization in this paper. The global convergence of the algorithm is discussed. Moreover, we also analyze its local convergence when the strict complementarity condition does not hold.

By using the coincidence degree theory of Mawhin, we study the existence of periodic solutions for Duffing equation with impulses and delays. Even if the equation has no impulses, our results are new.

In this paper, by use of energy integral and some estimates of analytic semigroup, the existence of the exponential attractors of The Generalized 2D Ginzburg-Landau equations in Banach subspaces X-αof Lp(Ω) is proved.

The number of clear two-factor interactions in a $2_{\rm IV}^{m-p}$ design is an important measure for design selection. We prove that some $\ssize 2_{\rm IV}^{m-p}$ designs with minimum aberration have the maximum number of clear two-factor interactions. And we provide a class of $2_{\rm IV}^{m-p}$ designs with minimum aberration and the maximum number of clear two-factor interactions at the end of this paper.

In the paper the robust M-estimates of the unknown function and the unknown parameter of the partial linear models are discussed. The robust M-estimate of the unknown function is proposed by local linear method, and the robust M-estimate of the unknown parameter by tow step method. The weak consistence and the asymptotic normality of the robust M-estimate of the unknown function are given, and the weak consistence of the robust M-estimate of the unknown parameter is established.

For two species and three species competitive Lotka-Volterra systems, it is known that as axial fixed points are asymptotically stable, almost all the orbits tend to the axial fixed points. That is, the measure of solutions that do not tend to the axial fixed points, is equal to aero. Motivated from this result, van den Driessche and Zeeman raised a conjecture in 1998: for n(n > 3) species competitive Lotka-Volterra systems, almost all the orbits tend to axial fixed points as the axial fixed points are asymptotieally stable．That is ,in n dimensional space，the measure of solutions that do not eonverge to the axial fixed points，is equal to aero .In this paper，we prove the conjecture under the condition that the of n dimensional competitive Lotka-Volterra systems can be projected to one dimensional Lotka-Volterra systems.we give the algebraic criteria under which the systems can be projected and our result includes those in previous works.

Strong Partical Balance Design can be used to construct Optimal Authentication Code and Key Predistribution Scheme. In this paper, we provide a construction of Strong Partical Balance Design, and achieve some resault from this method.

In this paper, we, at first, considered a sort of method constructed high accurate finite difference scheme for linear Schrodinger equation and get dissipation term of the equation. Next, we proposed a conservative finite difference scheme with precision $\ssize O\, (\tau^2+h^2)$ for the nonlinear Schrodinger equation. It is proved that the scheme preserves two conservative quantities and is convergent and stable. The numerical results show that the scheme has higher precision than the other implicit schemes.

A α-joint efficient mapping from individual preferences to group preferences is constructed in this paper by means of group α-joint efficient numbers of alternatives. Meanwhile its essential properties for the Arrow, Sen and May are proved.

By using the continuation theorem of Mawhin's coincidence degree theory, Lyapunov functional, and combining with Yang's inequality and some analysis techniques, some sufficient conditions are obtained ensuring existence and global exponential stability of periodic solution to the BAM neural networks with periodic coefficients and delays. These results are helpful to design globally exponentially stable BAM networks and periodic oscillatory BAM neural networks.

In this paper, the authors provide conditions on nonlinear functions $f\,(t,x_1,x_2$, $\cdots, x_{n-1})$ and $g(t,y_1,y_2,\cdots,y_{n-1})$ such that the higher-order coupled boundary value problem has at least one positive solution. Moreover, they shall apply this result to establish several existence theorems which guarantee the existence of multiple positive solutions.

In this paper, we study the two-plied oriented percolation on the square lattice ${\Bbb Z}^2$. We prove that the corresponding critical probability function is monotone, symmetrical and continuous. In addition, we point out that the related Grimmett's conjecture follows from the strict concavity of this critical probability function.

In this paper, we obtain the Hajek-Renyi type inequality under second mement conditions, some applications for the PA, NA sequences and the $L^r$-mixingale sequences are given. It generalizes the Prakasa Rao's results for positively associated sequences.

In this paper,we discuss the bifurcation problem in solving nonlinear operator equation $ f(x,\lambda)=0,$ where $f$ is a differentiable mapping from $X\times R\rightarrow Y$and $X,Y$ are Banach spaces.By means of the generalized inverse $A^{+}$ of the partial derivatire operator $A=f_{x}(x_{0}, \lambda _{0}),$ a class of bifucation problems from non-simple eigenvalue has been investigaed, and we obtain a bifurcation theorem on the degenerate solutions, which extend a bifuration theorem from simple eigenvalue by Crandall and Robinowitz.

A directed graph $D$ is called primitive if there exists a positive integer $k$ such that for each ordered pair of vertices $x$ and $y$ (not necessarily distinct), there is a walk of length $k$ from $x$ to $y$. The smallest such $k$ is called the exponent of $D.$ As a generalization of exponent, R. A. Brualdi and Bolian Liu introduced the new concept of generalized exponent for primitive digraphs in 1990. In this paper, we give some qualities of the set exponent of symmetric primitive digraphs, and characterize completely the extremal graphs of the $k$th upper generalized exponent for primitive simple graphs.

In this paper, law of large numbers and complete convergence for pairwise NQD random sequences are investigated. As a result, we extend law of large numbers and complete convergence for independent random variable sequences.

The relation between the global attractors ${\cal A}^\varepsilon$ for $$ \partial _t u_\epsilon -\mbox{div}\, A(x/\varepsilon, \nabla u_\varepsilon)- \kappa u_\varepsilon =f $$ and the global attractor ${\cal A}^0$ for the homogenized equation is discussed, and an {\it explicit} error estimate between ${\cal A}^\varepsilon$ and ${\cal A}^0$ is given.

A reaction-diffusion model with fast reaction in multi-dimensional space is studied in this article. The model describes the relation between the antibody and virus in certain anti-tumour therapies which is reduced to a system of parabolic equations with certain degeneracy. The authors proved the existence and uniqueness results by using the bootstrap method and discussed the behavior of the solutions to the system in the limit of fast reaction.

We prove that for all problems of Ky Fan's Lemma in normed vector space there exists at least one essential component of the set of solutions of Ky Fan's Lemma. As a consequence, we deduce that for any general $n$-person game with some convexity and continuity conditions, there exists at least one essential component of the set of Nash equilibrium points.

The existence of solution with $p$-Laplacian operator of $m$-piont boundary value problem about resonance is studied by using coincidence degree continuation theorem and strict upper and lower solutions theory.

In this paper, A kind of semiparametric errors-in-variables functional relationship model is studied. The estimators of unknown parameters and unknown functions is derived by wavelet method and total least square method. Under some weaker conditions, it is shown that these estimators are strongly consistent, and the strong convergence rate of the estimator of $\sigma^2$ is obtained.

Tikhonov regularization is one of the most important regularization methods for the study of ill-posed problems. But because of the saturation effect of this method, it is impossible to improve the convergence rate of the approximate solution with increasing smoothness assumption of solutions, i.e., the error estimate between the exact and approximate solutions can not be order optimal for sharp smoothness assumption. A general Tikhonov regularization has been given by Schr\"oter T and Tautenhahn U, and the optimal error estimates have been considered. In this paper the further research shows that this regularization method can prevent the saturation effect and the numerical experiment works well.

In this paper, a new contained region for eigenvalue of matrix is obtained and this improves the disc theorem in paper [1]. By this, a sufficient condition is given for the nonsingularity of diagonally dominant matrix.

The maximum likelihood stimator and the approximate maximum likelihood estimator discussed by Harter H.L., Balakrishnan N. and others for the logistic population. After then, Ogawa J., Lloyd E.H., Kulldorff G., Gupta S.S., Chan L.K. and others discussed the best linear unbiased estimator for the logistic population. Unfortunately, it is very trouble to solve them. So, we discuss the asymptotically best linear unbiased estimator for the logistic population based on the selected order statistics, give the properties of the estimator, the variance and the covariance of the estimator in limit in this paper. And then, give the optimum chosen of spacings with the maximum asymptotic relative fficiency based on the order statistics when the selected order statistics number less than 10, and obtain its the maximum asymptotic relative efficiency.

The problem on the construction of positive Jacobian matrix from three eigenpairs is considered. Necessary and sufficient conditions for the existence of a unique solution of this problem ,as well as the analytic formula of this solution are derived. A numerical algorithm for computing the solution is presented.

In this paper, we study the global behavior of the time-depent drift-diffusion model for semiconductor devices. We have proved the estimates of global upper and lower bounds of solutions by using Stampacchia estimates method.

No Claim Discount System (briefly denoted by NCD System) is an experience rating method which is widely accepted in the automobile insurance markets all over the world. we try to formulate its rigorous mathematical theory. Mainly, the mathemaical modeling and equilibrium analysis of NCD system will be shown in some details. As a necessary mathematical prerequisite for such discussions, in the second section, we first explore some properties of stochastic dominance order defined between stochastic matrices, and then apply the conclusions obtained to the researches of homogeneous, irreducible and ergodic Markov chain. Those contents have also their own mathematical interests too.

By exploring the relationship between orthogonal arrays and orthogonal decompositions of projection matrices, we present a method for constructing a class of mixed-level orthogonal arrays. As an application of this method, we construct some new mixed-level orthogonal arrays having 144 runs and factors with a large non-prime power number of levels. Also, these arrays have high percent saturations.