A NECESSARY AND SUFFICIENT CONDITION FOR ASYMPTOTIC STABILITY OF A FIRST ORDER DELAY EQUATION WITH TWO DELAYS

Consider the following equationwhere 6, c and τ are constants, and τ > 0, bc ≠ 0. In this paper, we establish a necessary and sufficient condition for zero solution of Eq.(*) to be asymptotically stable, which is easy to verify and apply.     

Asymptotic normality and strong consistency of maximum quasi-likelihood estimates in generalized linear models

In a generalized linear model with q x 1 responses, the bounded and fixed (or adaptive) p × q regressors Zi and the general link function, under the most general assumption on the minimum eigenvalue of ZiZ'i,the moment condition on responses as weak as possible and the other mild regular conditions, we prove that the maximum quasi-likelihood estimates for the regression parameter vector are asymptotically normal and strongly consistent.     

MULTIPLE SOLUTIONS TO AN ASYMPTOTICALLY LINEAR ROBIN BOUNDARY VALUE PROBLEM

Under some weaker conditions,we prove the existence of at least two solutions to an asymptotically linear elliptic problem with Robin boundary value condition,using truncation arguments.Our results are also valid for the case of the so-called resonance at infinity.     

The Survival Analysis of a Non-autonomous N-dimensional Volterra Mutualistic System in a Polluted Environment

In this paper,we extend the autonomous n-Dimensional Volterra Mutualistic System to a non-autonomous system.The condition of persistence and extinction is obtained for each population,and thethreshold is established for asymptotically autonomous system.     

Existence of multiple fixed points for nonlinear operators and applications

In this paper, by the fixed point index theory, the number of fixed points for sublinear and asymptotically linear operators via two coupled parallel sub-super solutions is studied. Under suitable conditions, the existence of at least nine or seven distinct fixed points for sublinear and asymptotically linear operators is proved. Finally, the theoretical results are applied to a nonlinear system of Hammerstein integral equations.     

Empirical likelihood-based dimension reduction inference for linear error-in-responses models with validation study

In this paper, linear errors-in-response models are considered in the presence of validation data on the responses. A semiparametric dimension reduction technique is employed to define an estimator of β with asymptotic normality, the estimated empirical loglikelihoods and the adjusted empirical loglikelihoods for the vector of regression coefficients and linear combinations of the regression coefficients, respectively. The estimated empirical log-likelihoods are shown to be asymptotically distributed as weighted sums of independent x12 and the adjusted empirical loglikelihoods are proved to be asymptotically distributed as standard chi-squares, respectively.     

Some properties of the psi function and evaluations of γ

In this paper, the authors show some monotonicity and concavity of the classical psi function, by which several known results are improved and some new asymptotically sharp estimates are obtained for this function. In addition, applying the new results to the psi function,the authors improve the well-known lower and upper bounds for the approximate evaluation of Euler's constant γ.     

Laws of Large Numbers for Cesàro alpha-integrable Random Variables under Dependence Condition AANA or AQSI

Both residual Cesàro alpha-integrability (RCI( α)) and strongly residual Cesàro alpha-integrability (SRCI(α)) are two special kinds of extensions to uniform integrability, and both asymp-totically almost negative association (AANA) and asymptotically quadrant sub-independence (AQSI) are two special kinds of dependence structures. By relating the RCI(α) property as well as the SRCI(α) property with dependence condition AANA or AQSI, we formulate some tail-integrability conditions under which for appropriate α the RCI(α) property yields L1-convergence results and the SRCI(α) property yields strong laws of large numbers, which is the continuation of the corresponding literature.     

TESTING THE ADEQUACY OF GARCH-TYPE MODELS IN TIME SERIES

In this article a new approach for checking the adequacy of GARCH-type models in time series was proposed. The resulted tests involve weight functions, which provide them with the flexibility in choosing scores to enhance power performance. The choice of weight functions and the power properties of the tests are studied. For a large number of alternatives, asymptotically distribution-free maximin test is constructed. The tests are asymptotically chi-squared under the null hypothesis and easy to implement. Simulation results indicate that the tests perform well.     

NONEXISTENCE AND EXISTENCE OF POSITIVE SOLUTIONS FOR 2nTH-ORDER SINGULAR SUPERLINEAR PROBLEMS WITH STRUM-LIOUVILLE BOUNDARY CONDITIONS

This paper investigates a class of 2nth-order singular superlinear problems with Strum-Liouville boundary conditions. We obtain a necessary and sufficient condition for the existence of C 2 n- 2 [0, 1] positive solutions, and a sufficient condition, a necessary condition for the existence of C 2 n-1 [0, 1] positive solutions. Relations between the positive solutions and the Green’s functions are depicted. The results are used to judge nonexistence or existence of positive solutions for given boundary value problems.     

赋范线性空间中渐近伪压缩映象的不动点迭代逼近

研究了赋范线性空间中渐近非扩张映象和渐近伪压缩映象不动点的迭代逼近问题,所得结果改进和推广了已有的一些结果.     

有限个广义渐近非扩张映射具误差的复合隐迭代过程

在一致凸Banach空间研究了一个新的有限个广义渐近非扩张映射具误差的复合隐迭代过程.利用空间满足Opial条件和算子满足半紧性条件,我们证明了这个隐迭代过程强、弱收敛于有限个广义渐近非扩张映射的公共不动点.这些结果是目前所得成果的完善和推广.     

渐近非扩张映象具误差的迭代序列的收敛性

在Banach空间中引入渐近非扩张映象和非扩张映象某些类型的具误差的迭代序列,并研究了这些迭代序列的收敛性问题.本文的结果改进、推广和完善了最新的一些结果.     

渐近伪压缩映象的Ishikawa迭代序列强收敛的充要条件

在一般的实Banach空间中,研究Lipschitz渐近伪压缩映象和渐近非扩张映象不动点的迭代逼近问题.给出Ishikawa迭代序列强收敛的充要条件,所得结果改进和推广了张石生,肖建中等人的主要结果,修正和推广了朱玲娣等人的相应结果.     

Banach空间中Ishikawa迭代序列的稳定性和收敛性问题

在Banach空间的框架下,讨论了中间意义下的渐进非扩张的渐进伪压缩的具平均误差的修正的Ishikawa和Mann迭代序列的收敛性和稳定性之间的等价性问题,改进和推广了以前的结果.     

无限族严格渐近伪压缩映象隐迭代程序的强收敛定理

在Banach空间框架下,对无限族的严格渐近伪压缩映象和无限族的非扩张映象引入了一类新的隐迭代程序,并在适当的条件下,证明了该迭代程序强收敛于这两族映象的公共不动点.结果是新的,它推广和改进了一些人的最新结果.     

渐近拟非扩张型映象的Ishikawa迭代序列的强收敛性

通过引入一新型条件,研究了渐近拟非扩张型映象不动点的具误差的修正的Ish ikaw a迭代序列的迭代逼近问题,得到新的结果.     

渐近伪压缩和渐近非扩张映像不动点的迭代逼近问题

研究了Banach空间中渐近伪压缩和渐近非扩张映像不动点的迭代逼近问题,改进和发展了张石生教授等人的相应结果.     

Iterative sequences with mixed errors for asymptotically quasi-nonexpansive type mappings in Banach spaces

The purpose of this paper is to study necessary and sufficient conditions for the Ishikawa iterative sequence with mixed errors of asymptotically quasi-nonexpansive type mappings in Banach spaces to converge to a fixed point in Banach spaces. The results presented in this paper complememt, improve and prefect the corresponding results of [1]–[4] and [7]–[9]. This revised version was published online in June 2006 with corrections to the Cover Date.     

有限个渐近伪压缩映射近迫点序列的收敛性

研究了Banach空间中有限个渐近伪压缩映射近迫点序列的收敛性问题,此结果推广了以前的结论.