Super Narrow Bandpass Filter Using Fractal Cantor Structures

In this paper, we present a new photonic crystal structure, which is composed of fractal Cantor multilayer with a defect embedded in its middle. Optical transmission matrix method is used to calculating the transmittance and reflectance. Compared with general Cantor multilayer, we find the new structure has wider stopband and shows a super narrow band in the middle of wider stopband. It can be served as a super narrow bandpass filter. The pass band obtained can be less than 0.6nm near the infrared 1530 nm. The optical transmission is the center wavelength is higher than 99 %. This means a very low insert loss. It is more superior to other kind narrow band filters. This kind of photonic crystal super narrow band optical filter may find applications in super dense wavelength division multiplexing for optical communications and precise optical measurement.     

Analyse de complexité pour un théorème de Hall sur les fractions continues

We give a polynomial time controlled version of a theorem of M. Hall: every real number can be written as the sum of two irrational numbers whose developments into a continued fraction contain only 1, 2, 3 or 4. Mathematics Subject Classification: 03D15, 03F60, 11A55, 68Q25.     

不协调目标信息系统知识约简的比较研究

研究不协调目标信息系统的各种知识约简之间的关系。证明分布约简既是β上分布约简，也是β下分布约简，并且在一定条件下,β上、下分布约简与不协调目标信息系统的分配约简和最大分布约简等价。     

带核集分划问题的一个线性1／7近似算法

设有整数集Ｓ＝｛ｒ１，ｒ２；ｐ１，ｐ２，…，ｐｎ｝，这里ｒｉ≥０，ｐｊ＞０（ｉ＝１，２；ｊ＝１，２，…，ｎ），寻找一个Ｓ的最优分划Ｐ＝（Ｓ＊１，Ｓ＊２）使得：（１）ｒｉ属于不同子集，（２）Ｓ＊１与Ｓ＊２中元素总和较大者尽可能地小．这是一个ＮＰ－完备问题，本文给出一个线性时间近似算法，它的近似界为８７．     

Iterations of transformations on the unit interval: Approach to a periodic attractor

We consider a transformation of the unit interval which exhibits a stable periodic attractor and whose topological entropy is positive. We show that the dynamics leading to this attractor has a statistical character.     

An example of cycling in a feasible point algorithm

An example shows that, if in Rosen's [4] algorithm for calculating a point that satisfies linear constraints a natural criterion is used to select constraints to delete from active sets, then the algorithm may cycle instead of converging. There are no degeneracies in the example.     

实Banach空间中锥上的随机逼近和随机不动点定理

本文在实Ｂａｎａｃｈ空间的锥上证明了集值映射的随机逼近定理．作为应用，讨论了几个随机的不动点定理．我们的工作推广了Ｌｉｎ，Ｓｅｈｇａｌ和Ｓｉｎｇｈ的结果．     

实函数的相对处处不连续性

经典实函数理论指出：Ｒ１的一个子集合，要成为某个Ｒ１上实函数之不连续点的全体，当且仅当该集合为Ｒ１上可数个闭集的并。本文将给出进一步精细的刻画：考虑相对连续性，即指定Ｒ１的子集合Ａ，及实函数ｆ，对于Ａ之导集Ａ＇中一点ｘ０，考察ｆ（ｘ）是否存在，及极限是否等于ｆ（ｘ０），具体地，有着下述结果。设Ｅ为可数个闭集的并，Ｒ分为３个子集的不交并：Ｒ１＝（Ｅ∩Ｅ＇）∪（Ｅ－Ｅ＇）∪（Ｒ－Ｅ）。那么存在Ｒ１上的有界实函数，使得１：ｆ之不连续点的全体恰为Ｅ（与经典结果一致），２：当时，ｆ（ｘ）不存在，３：当时，不存在。     

A localization inequality for set functions

We prove the following theorem, which is an analog for discrete set functions of a geometric result of Lovász and Simonovits. Given two real-valued set functions f₁,f₂ defined on the subsets of a finite set S, satisfying for i∈{1,2}, there exists a positive multiplicative set function μ over S and two subsets A,B⊆S such that for i∈{1,2}μ(A)f_i(A)+μ(B)f_i(B)+μ(A∪B)f_i(A∪B)+μ(A∩B)f_i(A∩B)?0. The Ahlswede-Daykin four function theorem can be deduced easily from this.