Asymptotic behavior of solutions of forced nonlinear neutral delay differential equations with impulses

Sufficient conditions for asymptotic behavior of the solutions of nonlinear forced neutral delay differential equations with impulses are found. The results given in [2,4,6,7] are generalized and improved.     

On the summability of the formal solutions for some PDEs with irregular singularity

In this Note, we consider some classes of nonlinear partial differential equations with regular singularity with respect to t=0 and irregular one with respect to x=0. Our purpose is to establish a result which is similar to the k-summability property, known in the case of singular ordinary differential equations. We can prove that, except at most a countable set, the formal solution is Borel summable or k-summable with respect to x in all other directions. To cite this article: Z. Luo et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

THE LIMIT SET OF A CONTINUOUS SELF-MAP OF THE TREE

Let f denote a continuous map of a tree T to itself. A point x ∈ T is called a 7-limit point of f if it is both an ω-limit point and an α-limit point. In the present paper, we show that (1) Ω-Γ is countable, (2) A -Γ and P - Γ are either empty or countably infinite, where P denotes the closure of the set of periodic points P.     

Error estimates for Hermite interpolation on spheres

In this paper, we prove convergence rates for spherical spline Hermite interpolation on the sphere S^d−1 via an error estimate given in a technical report by Luo and Levesley. The functionals in the Hermite interpolation are either point evaluations of pseudodifferential operators or rotational differential operators, the desirable feature of these operators being that they map polynomials to polynomials. Convergence rates for certain derivatives are given in terms of maximum point separation.     

The asymptotic behaviors of a stage-structured autonomous predator-prey system with time delay

In this paper, we consider an autonomous predator-prey Lotka-Volterra system in which individuals in the population may belong to one of two classes: the immatures and the matures, the age to maturity is represented by a time delay. By using eigenvalue analysis, principal term analyze method, reduction to absurdity, and iterative method, we obtain some simple conditions for global asymptotic stability of the unique positive equilibrium point. Moreover, a condition that the prey population in the system get extinction and the predator population in the system get permanence will be obtained. Meanwhile the theorems extend the corresponding conclusions in which there have no two stage structures.     

On the convergence of the affine-scaling algorithm

The affine-scaling algorithm, first proposed by Dikin, is presently enjoying great popularity as a potentially effective means of solving linear programs. An outstanding question about this algorithm concerns its convergence in the presence of degeneracy. In this paper, we give new convergence results for this algorithm that do not require any non-degeneracy assumption on the problem. In particular, we show that if the stepsize choice of either Dikin or Barnes or Vanderbei, et al. is used, then the algorithm generates iterates that converge at least linearly with a convergence ratio of , wheren is the number of variables and (0,1] is a certain stepsize ratio. For one particular stepsize choice which is an extension of that of Barnes, we show that the cost of the limit point is within O(/(1–)) of the optimal cost and, for sufficiently small (roughly, proportional to how close the cost of the nonoptimal vertices are to the optimal cost), is exactly optimal. We prove the latter result by using an unusual proof technique, that of analyzing the ergodic convergence of the corresponding dual vectors. For the special case of network flow problems with integer data, we show that it suffices to take = 1/(6mC), wherem is the number of constraints andC is the sum of the cost coefficients, to attain exact optimality.This research is partially supported by the U.S. Army Research Office, contract DAAL03-86-K-0171 (Center for Intelligent Control Systems), by the National Science Foundation, grant NSF-ECS-8519058, and by the Science and Engineering Research Board of McMaster University.     

Fuzzy集的基数

关于Fuzzy集的基数，[1]中曾对有限支集的Fuzzy集以及极苛刻条件下的无限Fuzzy集给出过一种定义。但是，正如本文将要指出的那样，该定义是不合理的。本文将从研究Fuzzy映射入手，给出Fuzzy集基数的一般性定义。基于这一定义，不但得到有关基数的大部分结论，而且有其自身的特殊性。     

GENERALIZED SIMULTANEOUS CHEBYSHEV APPROXIMATION

In this note,we develop,without assuming the Haar condition,a generalized simultaneousChebyshev approximation theory which is similar to the classical Chebyshev theory and con-rains it as a special case.Our results also contain those in[1]and[3]as a special case,and thetwo conjectures proposed by C.B.Dunham in[2]are proved to be true in the case of simulta-neous approximation.     

Studies on self-pumped phase conjugation in Cu-doped (K0.5Na0.5)0.2(Sr0.61Ba0.39)0.9Nb2O6 crystals

The use of Cu-doped (K_0.5Na_0.5)_0.2(Sr_0.61Ba_0.39)_0.9Nb₂O₆ as self-pumped phase conjugators using internal reflection is reported. Reflectivities as high as 63% at 5145.5 nm and 60% at 632.8 nm were realized. It was found that the photorefractive response changes significantly at different doping concentration. The responses of the crystals to the laser wavelength, incident angle and dopant concentration are studied.     

Variational estimates of chiral order parameter in 1+1 dimensional lattice QCD

We discuss analytically the vacuum structure and chiral-symmetry breaking in 1+1 dimensional lattice QCD with naive and Wilson fermions, using a unitary transformation and the variational method developed recently. As an example, the chiral order parameter is evaluated systematically for any coupling constant and fermion mass by including the multilink-terms in the transformation. The expected scaling behavior is observed. Our results are consistent with the continuum predictions.