On Toughness and Hamiltonicity of 2K2‐Free Graphs

The toughness of a (noncomplete) graph G is the minimum value of t for which there is a vertex cut A whose removal yields components. Determining toughness is an NP‐hard problem for general input graphs. The toughness conjecture of Chvátal, which states that there exists a constant t such that every graph on at least three vertices with toughness at least t is hamiltonian, is still open for general graphs. We extend some known toughness results for split graphs to the more general class of 2K₂‐free graphs, that is, graphs that do not contain two vertex‐disjoint edges as an induced subgraph. We prove that the problem of determining toughness is polynomially solvable and that Chvátal's toughness conjecture is true for 2K₂‐free graphs.     

森田六元组的几乎分裂序列

令ΛA_1,Λ_2为两个环,M是(A_2-Λ_1)-双模,且N是(Λ_1-Λ_2)-双模.六元组Γ=(Λ_1,Λ_2,N,M,ψ,φ)是一个森田六元组.对于Γ的表示,确定其几乎分裂序列(也称AR-序列)是非常重要的.通过modΛ_1和modΛ_2的右(左)几乎分裂同态、既约同态构造Γ上的相应同态,并进一步确定它的几乎分裂序列.     

The role of ion-pairing in peak deformations in overloaded reversed-phase chromatography of peptides

The paper reports a study on the role of ion-pairing behind peak deformations, e.g. peak splitting and even peak disappearance, during the elution of a peptide at highly overloaded conditions in reversed-phase chromatography. Deformation of component peaks is not uncommon in chromatography. There are reports which discuss their occurrence, but mostly at analytical scale, while their occurrence is quite common also in the preparative scale, as in the case discussed in this work. This paper first describes the conditions leading to peak splitting and peak disappearance of an industrial peptide, then explains the plausible reasons behind such behaviour, and finally with experimental analysis demonstrates the role of ion-pairing in causing such behaviour.     

Dynamic Scheduling on a Single Batch Processing Machine with Split Compatibility Graphs

We consider the problem of minimizing the makespan on a batch processing machine, in which jobs are not all compatible. Only compatible jobs can be included into the same batch. This relation of compatibility is represented by a split graph. Jobs have release dates. The capacity of the batch processing machine is finite or infinite. The processing time of a batch is given by the processing time of the longest job in the batch. We establish the NP-hardness of the general problem and present polynomial algorithms for several special cases. Relating scheduling theory and graph theory appears to be an interesting and important concept.     

黏性不可压流体的自适应网格技术和基本特性方程分离算法的联合分析

组合基本特性方程分离算法和自适应网格技术,分析二维黏性不可压流体.该方法使用3节点三角单元,对速度分量和压力等变量分析,使用等阶次的插值函数.组合解法的主要优点在于,在自适应网格技术中,对解梯度变化大的区域,通过耦合误差估计生成小的单元,利于提高解的精度,在其它区域生成大单元,可以节省时间.最后,通过对一个黏性流体圆柱体绕流问题的瞬态和稳态特性分析,给出了组合解法性能的评价.     

Finite separable metacyclic 2-groups

A finite separable metacyclic 2-group G can be written as the semidirect product of a cyclic group with another cyclic group. Necessary and sufficient conditions are given for when all other split decompositions of G result in, up to isomorphism, this same semidirect product representation for G.     

Perturbed projections and subgradient projections for the multiple-sets split feasibility problem

We study the multiple-sets split feasibility problem that requires to find a point closest to a family of closed convex sets in one space such that its image under a linear transformation will be closest to another family of closed convex sets in the image space. By casting the problem into an equivalent problem in a suitable product space we are able to present a simultaneous subgradients projections algorithm that generates convergent sequences of iterates in the feasible case. We further derive and analyze a perturbed projection method for the multiple-sets split feasibility problem and, additionally, furnish alternative proofs to two known results.     

非对称开口六边形谐振单环的微波透射特性

受自然界树型结构的启发，设计了分叉树型微结构单元，用电路板刻蚀技术制作了非对称开口六边形谐振单环及其组合结构.采用计算机模拟和实验研究了单个和多个谐振环在微波段(7—12 GHz)的电磁响应行为.研究结果表明：该结构具有负磁导率特性，开口谐振环几何尺寸影响环的磁谐振频率；两环环间距较小时出现二次谐振；带高级分支的辐射状环列相对于不带分支环列透射峰向低频移动.实验和模拟结果相符. 关键词： 负磁导率 开口谐振环 透射率     

色散补偿和色散位移光纤实现光脉冲压缩

根据超短光脉冲在光纤中传输的非线性薛定谔方程，模拟了不同色散参量情况下色散补偿和色散位移光纤对增益开关半导体激光器产生的光脉冲的压缩，给出了光脉冲在经过色散补偿光纤前后的啁啾曲线。结果表明，使用色散参量D分别为-150，-180和-20ps/(nm·km)的色散补偿光纤可以实现其他脉冲压缩方法的压缩效果，最大压缩因子达到6.09，但色散参量越大，所需光纤长度就越短。此外，脉冲经过色散补偿光纤后线性啁啾几乎为零。还利用色散位移光纤对脉冲进行孤子压缩，脉冲宽度由最初的45ps减小到1.23ps。指出采用这2种光纤相结合的方法可以对光脉冲实现高效压缩。