On Least Common Multiples of Polynomials in Z/n Z[x]

Let 𝒫(n, D) be the set of all monic polynomials in ?/n?[x] of degree D. A least common multiple for 𝒫(n, D) is a monic polynomial L ∈ ?/n?[x] of minimal degree such that f divides L for all f ∈ 𝒫(n, D). A least common multiple for 𝒫(n, D) always exists, but need not be unique; however, its degree is always unique. In this article, we establish some bounds for the degree of a least common multiple for 𝒫(n, D), present constructions for common multiples in ?/n?[x], and describe a connection to rings of integer-valued polynomials over matrix rings.     

Coupled fixed point results for nonlinear integral equations

In this paper, we prove some coupled coincidence point theorems for such nonlinear contraction mappings having a mixed monotone property in partially ordered metric spaces by dropping the condition of commutative. We also prove coupled common fixed point theorem for w-compatible mappings. An example of a nonlinear contraction mapping which is not applied by Lakshmikantham and ?iri?’s theorem [1] but applied by our result is given. Further, we apply our results to the existence theorem for solution of nonlinear integral equations.     

关于多元多项式分解的必要条件

类似于一元多项式因式分解的相关结论,利用多元多项式函数与其偏导函数的关系,介绍多元多项式能够因式分解的必要条件,即若 f′xi （x1,x2,…,xn ）与 f （x1,…,xi-1,0,xi＋1,…,xn ）有公因式,则 f （x1,x2,…,xn ）可以分解。     

Photoinjector beam quality improvement by shaping the wavefront of a drive laser with oblique incidence

To increase the quantum efficiency (QE) of a copper photocathode and reduce the thermal emittance of an electron beam, a drive laser with oblique incidence was adopted in a BNL type photocathode rf gun. The disadvantageous effects on the beam quality caused by oblique incidence were analyzed qualitatively. A simple way to solve the problems through wavefront shaping was introduced and the beam quality was improved.     

Drive-based recording analyses at >800 Gfc/in using shingled recording

Since the introduction of perpendicular recording, conventional perpendicular scaling has enabled the hard disk drive industry to deliver products ranging from ∼130 to well over 500 Gb/in² in a little over 4 years. The incredible areal density growth spurt enabled by perpendicular recording is now endangered by an inability to effectively balance writeability with erasure effects at the system level. Shingled magnetic recording (SMR) offers an effective means to continue perpendicular areal density growth using conventional heads and tuned media designs. The use of specially designed edge-write head structures (also known as ‘corner writers’) should further increase the AD gain potential for shingled recording. In this paper, we will demonstrate the drive-based recording performance characteristics of a shingled recording system at areal densities in excess of 800 Gb/in² using a conventional head.Using a production drive base, developmental heads/media and a number of sophisticated analytical routines, we have studied the recording performance of a shingled magnetic recording subsystem. Our observations confirm excellent writeability in excess of 400 ktpi and a perpendicular system with acceptable noise balance, especially at extreme ID and OD skews where the benefits of SMR are quite pronounced. We believe that this demonstration illustrates that SMR is not only capable of productization, but is likely the path of least resistance toward production drive areal density closer to 1 Tb/in² and beyond.     

行波管中多级降压收集极效率评估的研究

在行波管中,多级降压收集极(MDC)效率由于其与总效率的关系密切而显得非常重要. 而在设计MDC之前对其效率和行波管的总效率进行准确的评估可以把握管子的整体性能, 并为相关软件的开发提供理论指导,因而对MDC的优化和行波管总效率的提高具有十分重要的意义. 虽然Kosmahl在1980年就给出了MDC的效率评估公式,但其预测值比实测值偏高较多, 因而需要更为准确的评估公式.本文首先引入耗散公差的概念, 然后建立作用完电子注等差三角能量分布模型推导了MDC效率评估的公式,与Kosmahl给出的预测相比, 新公式的估计结果更接近实测值.最后根据MDC效率最高和各个电极上耗散能量最低这两个极值条件, 给出了MDC最佳电极级数的选取公式,其预测结果合理而且准确.     

集合族交运算的上半连续性和公共元的通有稳定性

建立了全新的集合族空间, 讨论了公共元的通有稳定性, 得到了闭集族空间上的交运算在Hausdorff拓扑下的上半连续性, 从而证明了有关集合族空间上的公共元的通有稳定性.     

采用改进最长公共子序列的人名消歧

将名词、形容词、动名词和命名实体作为文本特征,考虑词序与词频,结合特征项的语义,提出一种基于改进最长公共子序列的文本聚类(LCSC)方法.实验结果表明:相对于传统的余弦值聚类方法,LCSC方法在人名消歧的P-IP指标上,F平均值由74.2%提高到了84.9%;相对于最长公共子序列方法,总体性能也提高了3.7%.     

集族交运算的连续性和不动点、Fan Ky点的通有稳定性

建立集合族空间,讨论了公共元的通有稳定性,得到了闭集族空间上的交运算在Hausdorff拓扑下的上半连续性,并研究了不动点、 Fan Ky点的通有稳定性.