The optimal exchange algorithm and comparisons with the generalized remes algorithm † ‡

This paper is concerned with the general problem of the determination of the best uniform approximation of a given function. A special case is the calculation of the minimax solution of an overdetermined linear system. Single point exchange algorithms produce successive approximate solutions for such problems. An example is furnished by the generalized Remes algorithm, which includes both the original Remes algorithm and the Stiefel algorithm as special cases. The optimal exchange algorithm is similar, but it has the important feature that every exchange is optimal in a certain desirable sense. It is proved that eventually the optimal exchange and generalized Remes algorithms coincide. However, early exchanges in the latter algorithm can be far from optimal and quite inefficient. A combination of the optimal exchange and generalized Remes algorithms is suggested as a reasonable strategy.     

On a new type of distance Fibonacci numbers

In this paper, we define a new kind of Fibonacci numbers generalized in the distance sense. This generalization is related to distance Fibonacci numbers and distance Lucas numbers, introduced quite recently. We also study distinct properties of these numbers for negative integers. Their representations and interpretations in graphs are also studied.     

The Gauss Theorem for Domain Decompositions in Sobolev Spaces

This paper belongs to a broad line of research leaded by Herrera, which encompasses a good number of numerical methods such as Localized Adjoint Method (LAM), Eulerian-Lagrangian LAM (ELAM) and Trefftz-Herrera Method. The results presented in this paper are required in order to incorporate Herrera's general theory in a Sobolev-space setting. In particular, this article introduces a class of partitions (or domain decompositions) whose internal boundaries belong to a category of manifolds with corners, here also presented. Then a version of Gauss (or divergence) theorem, in a wider sense, is established and an explicit integral formula is associated for any given linear partial differential operator L, its adjoint and concomitant. The structure of the bilinear concomitant induced by L is first determined. Then the required formula is given over that class of domain decompositions. Finally, an integral formula well on the way of the Green-Herrera formula is settled.     

Low degree GW invariants of surfaces Ⅱ

We prove a conjectural formula of Maulik-Pandharipande on the degree one and two GW invariants of a surface with a smooth canonical divisor.We use the method of degeneration and the localized GW invariants introduced by the authors.     

全概率公式的推广与应用

认为全概率公式成立的条件＂事件组须为样本空间的划分＂可以减弱,给出全概率公式在有限事件组情形和无限可列事件组情形下的两种推广形式,由此对贝叶斯公式进行两种相应推广,并通过实例展示全概率公式在敏感性调查中的应用.     

Rate of convergence by Chlodowsky-Taylor polynomials

Approximation on an unbounded interval is studied in this work by means of a newly-defined two-parameter polynomial operator based on Chlodowsky polynomials. The operator’s properties including convergence rate are investigated using the weighted modulus of continuity. An example is given to illustrate the effect of the parameters. Some basic results are presented.     

Calculation of the light intensity distribution reflected by a planar corner-cube retroreflector array with the size of centimeter and above

The light intensity distribution (LID) reflected by a planar corner-cube retroreflector array with the size of centimeter and above (PCCRA) is calculated based on the Collins formula, coordinate transformation matrixes and vector algebra. The expression can be used for the PCCRAs with different parameters and different complex optical systems described by ABCD matrix. The expression indicates that the LID of a PCCRA is much different from a single corner-cube retroreflector (CCR) with equivalent aperture. Computer simulations are applied to explain the expression clearly. The results show that the LID of the PCCRA is more homogeneous than the single CCR with equivalent aperture under circumstances of both normal incident light and oblique incident light. In addition, the expression is proved by comparing the simulation result of the PCCRA only comprising a single CCR and the previous experimental result.     

推广的梯形公式中间点的渐近性质

得到梯形公式和推广的梯形公式中间点的渐近性质的主要结果是limx→aξ-a/x-a=6/(n+3)(n+2)~(1/n).     

一类具有随机扰动竞争系统生存分析的研究

通过引入白噪声,提出了一类具有随机扰动的经典竞争系统,并对其生存分析进行了研究.不仅给出了保证灭绝性和弱持久性的充分条件,还得到了弱持久性和灭绝性之间的阀值.最后,给出数值模拟验证了理论分析结果.