Auslander–Reiten components with bounded short cycles

We study Auslander–Reiten components of an artin algebra with bounded short cycles, namely, there exists a bound for the depths of maps appearing on short cycles of non-zero non-invertible maps between modules in the given component. First, we give a number of combinatorial characterizations of almost acyclic Auslander–Reiten components. Then, we shall show that an Auslander–Reiten component with bounded short cycles is obtained, roughly speaking, by gluing the connecting components of finitely many tilted quotient algebras. In particular, the number of such components is finite and each of them is almost acyclic with only finitely many DTr-orbits. As an application, we show that an artin algebra is representation-finite if and only if its module category has bounded short cycles. This includes a well known result of Ringel’s, saying that a representation-directed algebra is representation-finite.     

考虑背景风险的高阶矩三角模糊随机投资组合模型

在已有的大部分投资组合模型中,证券的收益服从随机分布或者模糊分布。然而,在实际的市场中存在大量的不确定性,市场不仅具有内在的风险,也存在由投资者个体差异产生的背景风险。本文推导随机模糊数的高阶矩性质,构建一个考虑背景风险的高矩三角模糊随机投资组合风险模型,采用沪深股市的数据分析背景风险对投资组合的影响。     

Optimal cyclic quaternary constant‐weight codes of weight three

A cyclic code is a cyclic q‐ary code of length n, constant weight w and minimum distance d. Let denote the largest possible size of a cyclic code. The pure and mixed difference method plays an important role in the determination of upper bound on . By analyzing the distribution of odd mixed and pure differences, an improved upper bound on is obtained for . A new construction based on special sequences is provided and the exact value of is almost completely determined for all d and n except when and . Our constructions reveal intimate connections between cyclic constant weight codes and special sequences, particularly Skolem‐type sequences.     

空间目标材料偏振光学特性研究

基于二向反射模型,对碳纤维、渗碳膜、F46和OSR四种典型的空间目标样本的偏振光谱数据进行测量;通过测算样本Stokes参量获取样品多角度下的线偏振度与偏振角信息,并对其进行统计.结果表明,样本线偏振度和线偏振角的均值、方差之间存在较大差异,对比分析样本均值和方差之间的关系能有效提高目标的探测和识别性能,可以解决传统光谱技术上产生的"同物异谱"和"同谱异物"问题;所获取的偏振特性可为偏振遥感提供更多的光学信息.     

Orthonormal bases associated with multi-knot piecewise linear function sequences on [0, 1)<Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>

We investigate two classes of orthonormal bases for L^2（[0, 1）^n）. The exponential parts of those bases are multi-knot piecewise linear functions which are called spectral sequences. We characterize the multi-knot piecewise linear spectral sequences and give an application of the first class of piecewise linear spectral sequences.     

Sturm Sequences and Random Eigenvalue Distributions

This paper proposes that the study of Sturm sequences is invaluable in the numerical computation and theoretical derivation of eigenvalue distributions of random matrix ensembles. We first explore the use of Sturm sequences to efficiently compute histograms of eigenvalues for symmetric tridiagonal matrices and apply these ideas to random matrix ensembles such as the β-Hermite ensemble. Using our techniques, we reduce the time to compute a histogram of the eigenvalues of such a matrix from O(n ²+m) to O(mn) time where n is the dimension of the matrix and m is the number of bins (with arbitrary bin centers and widths) desired in the histogram (m is usually much smaller than n). Second, we derive analytic formulas in terms of iterated multivariate integrals for the eigenvalue distribution and the largest eigenvalue distribution for arbitrary symmetric tridiagonal random matrix models. As an example of the utility of this approach, we give a derivation of both distributions for the β-Hermite random matrix ensemble (for general β). Third, we explore the relationship between the Sturm sequence of a random matrix and its shooting eigenvectors. We show using Sturm sequences that assuming the eigenvector contains no zeros, the number of sign changes in a shooting eigenvector of parameter λ is equal to the number of eigenvalues greater than λ. Finally, we use the techniques presented in the first section to experimentally demonstrate a O(log n) growth relationship between the variance of histogram bin values and the order of the β-Hermite matrix ensemble. This research was supported by NSF Grant DMS–0411962.     

混合胶束中Gemini阳离子表面活性剂14-s-14与常规表面活性剂的协同作用:连接臂及反离子效应(英文)

The mixed micelle formation of binary cationic 14-s-14 gemini with conventional single chain surfactants was studied by conductivity measurements.The critical micelle concentration(cmc) and the degree of counterion binding values(g) of the binary systems were determined.The results were analyzed by applying regular solution theory(RST) to calculate micellar compositions(X),activity coefficients(f1,f2),and the interaction parameters(β).The synergistic interactions of all the investigated cationic gemini+conventional surfactant combinations were found to be dependent upon the length of hydrophobic spacer of the gemini surfactant.The excess Gibbs free energy of mixing was evaluated,and it indicated relatively more stable mixed micelles for the binary combinations.     

逼近一致凸Banach空间中渐近非扩张映象的不动点

借助于B ruck′s不等式,研究了一致凸Banach空间中渐近非扩张映象不动点的具误差的Ish ikaw a迭代序列的强收敛定理.所得的结果推广和改进了Schu,Rhoades,周海云,王绍荣等作者的相应结果.     

Long arithmetic progressions in sumsets: Thresholds and bounds

For a set of integers, the sumset consists of those numbers which can be represented as a sum of elements of :

Closely related and equally interesting notion is that of , which is the collection of numbers which can be represented as a sum of different elements of :

The goal of this paper is to investigate the structure of and , where is a subset of . As application, we solve two conjectures by Erdös and Folkman, posed in 1960s.