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。     

On geometric interpretations of split quaternions

Quaternions are an important tool that provides a convenient and effective mathematical method for representing reflections and rotations in three-dimensional space. A unit timelike split quaternion represents a rotation in the Lorentzian space. In this paper, we give some geometric interpretations of split quaternions for lines and planes in the Minkowski 3-space with the help of mutual pseudo orthogonal planes. We classified mutual planes with respect to the casual character of the normals of the plane as follows; if the normal is timelike, then the mutual plane is isomorphic to the complex plane; if the normal is spacelike, then the plane is isomorphic to the hyperbolic number plane (Lorentzian plane); if the normal is lightlike, then the plane is isomorphic to the dual number plane (Galilean plane).     

Fullerene Black Modified Screen Printed Electrodes for the Quantification of Acetaminophen and Guanine

Fullerene Black (FB) and Extracted Fullerene Black (EFB) were used in modified screen‐printed electrodes producing electrochemical transducers (FB‐SPEs and EFB‐SPEs). A complete electrochemical study was performed and the best results are obtained working with FB‐SPEs, especially in terms of: 1. improved electron‐transfer kinetic mechanisms and 2. sensitivity and selectivity toward Acetaminophen (Ac) and Guanine (G). These latter represent two important electro‐active targets to quantify in medicine field application, because: Ac is a preferred alternative (as analgesic‐antipyretic agent) to aspirin, particularly for patients who cannot tolerate aspirin; the oxidation signal of G is useful for the fabrication of emerging analytical tools, such as DNA chipsand user‐friendly diagnostic devices. Ac and G are quantify by using FB‐SPEs electrochemical devices, with an extended linearity (1–300 μM for Ac; 0.1–300 μM for G), an excellent sensitivity (2.82 μA μM⁻¹ cm⁻² in the case of Ac; and 0.183 μA μM⁻¹ cm⁻² in the case of G), a low detection limit (0.01 μM for Ac; 0.005 μM for G), a very good reproducibility (both: intra‐; inter‐electrodes reproducibility RSD % ranging from 0.3–0.5 for Ac; and 0.50–0.85 for G) and a very fast response time (6 s for Ac; 5 s in the case of G). In addition, high selectivity is obtained at FB‐SPEs, meaning that the FB‐SPEs electrochemical transducers are suitable to simultaneously quantify Ac and G in real samples, having several different (highly concentrated) interference.