The minimum forcing number of perfect matchings in the hypercube

Let $M$ be a perfect matching in a graph. A subset $S$ of $M$ is said to be a forcing set of $M$, if $M$ is the only perfect matching in the graph that contains $S$. The minimum size of a forcing set of $M$ is called the forcing number of $M$. Pachter and Kim (1998) conjectured that the forcing number of every perfect matching in the $n$-dimensional hypercube is $2^{n?2}$, for all $n\ge 2$. This was revised by Riddle (2002), who conjectured that it is at least $2^{n?2}$, and proved it for all even $n$. We show that the revised conjecture holds for all $n\ge 2$. The proof is based on simple linear algebra.     

Perfect matchings extend to two or more hamiltonian cycles in hypercubes

Kreweras conjectured that every perfect matching of a hypercube $Q_n$ for $n\ge 2$ can be extended to a hamiltonian cycle of $Q_n$. Fink confirmed the conjecture to be true. It is more general to ask whether every perfect matching of $Q_n$ for $n\ge 2$ can be extended to two or more hamiltonian cycles of $Q_n$. In this paper, we prove that every perfect matching of $Q_n$ for $n\ge 4$ can be extended to at least $2^{2^{n?4}}$ different hamiltonian cycles of $Q_n$.     

Operation principle of self-phase compensated optical waveguide isolator

A theory is developed for the self-phase compensated optical waveguide isolator recently reported in the literature. The operation principle of such device is explained in terms of synchronization of phase and power conversion. The effect of balancing phase mismatches of the two convertors on achieving a proper percentage of mode conversion is revealed. The way to make use of the phase mismatches of different sections to accommodate the different requirements in phase relationship for the reciprocal and nonreciprocal mode convertors is discussed. The theory is extended to the case where phase compensator is used. It is demonstrated that the introduction of phase compensator separates the adjustment of phase from the adjustment of power for the mode convertors so that relaxes fabrication tolerances of such devices. An isolator consists of three phase mismatched waveguide sections is designed and simulated. The simulation results confirm the self-phase compensation theory.     

2型糖尿病患者尿液的代谢组学研究

目的 从代谢组学角度分析并寻找2型糖尿病（T2DM）患者可能的代谢标记物。方法 选取30例初诊、或有糖尿病史经药物治疗控制不理想且无并发症的T2DM 患者,另选取30例性别、年龄匹配的健康者为正常对照。收集清晨空腹中段尿,以气相色谱- 质谱联用（GC-MS）技术对尿液样本进行代谢图谱分析,正交偏最小二乘法判别研究尿液内源性化合物在两组间的差异。结果 T2DM 组和正常对照组尿液代谢谱明显分离。与正常对照组比较,T2DM 组尿液2,3,4- 三羟基丁酸、肌醇、D- 葡萄糖、D- 葡萄糖酸及尿素含量升高（P＜0.05 或0.01）,马尿酸含量减少（P＜0.01）。结论 代谢组学检查提示T2DM 患者尿液中代谢标志物为2,3,4- 三羟基丁酸、肌醇、马尿酸、D-葡萄糖、D- 葡萄糖酸及尿素,观察这些标志物含量的变化有助于T2DM 的临床诊断及发病机制研究。     

宽离子能量检测范围垂直引入反射式飞行时间质谱仪的研制

本实验室研制了国内首台宽离子能量检测范围飞行时间质谱仪。仪器采用紧凑式电子轰击源设计,配合离子透镜系统有效的调制离子流,飞行时间质量分析器采用了离子垂直引入式,双场加速和双场反射以及大尺寸MCP检测装置设计。仪器单离子信号半峰宽约2 ns,仪器分辨率优于1600FWHM,检测实际样品质量范围为1~127 amu(仪器理论质量检测上限优于800 amu),可检测离子能量范围优于2个数量级(3~140 eV)。若该TOF质量分析器与短瞬高压脉冲放电离子源耦合联用,可广泛应用于高能离子束的快速检测,如真空阴极放电对制备薄膜、离子注入材料的表征,导电材料的离子电荷态分布以及离子扩散速度的测定等。     

径向电场对纳米管中水分子通量的影响

水分子在纳米通道中的运动对于生命活动、纳米器件的设计等都有着重要的意义. 现在已经证实, 在(6,6)的碳纳米管中, 水分子会以单分子水链的形式协同通过碳纳米管. 但是如何控制水分子的流量仍然是一个困难的课题. 本文研究了在径向电场作用下, 碳纳米管中水分子通量的变化趋势和碳纳米管的开关行为.发现在碳纳米管两端存在200 MPa的压力差时, 电场强度从1 V·nm^-1增加到3 V·nm^-1, 水分子通量线性减小. 当径向电场强度增加到3 V·nm^-1时, 碳纳米管处于关闭状态, 水分子无法通过碳纳米管. 进一步, 我们发现水偶极与碳纳米管管轴夹角的平均值的概率分布和翻转频率都与水分子在纳米管中的个数有很大关系.     

基于图像处理的闸机口跳闸事件检测算法

文中提出了一种基于图像处理的闸机口跳闸事件检测方法。首先,利用模板匹配的方法进行预处理,得到闸门图像匹配率;其次,根据跳闸事件的连贯性特点,提取一段连续时间序列的匹配率作为分类特征;最后,采取基于最小错误率的贝叶斯分类方法对这段时间序列特征向量进行分类。实验表明,该算法可以有效的检测出闸机口的跳闸事件,具有实时性好、不需要额外的传感器、成本低的优点,具有较好的工程应用前景。     

Matching energy of unicyclic and bicyclic graphs with a given diameter

Gutman and Wagner proposed the concept of matching energy (ME) and pointed out that the chemical applications of ME go back to the 1970s. Let G be a simple graph of order n and be the roots of its matching polynomial. The ME of G is defined to be the sum of the absolute values of . In this article, we characterize the graphs with minimal ME among all unicyclic and bicyclic graphs with a given diameter d. © 2014 Wiley Periodicals, Inc. Complexity 21: 224–238, 2015     

Effect of hybrid fillers on the mechanical behavior of polypropylene based hybrid composites

The present study investigates the effect of hybrid fillers such as graphene nanoplatelets (GnPs) and Titanium di-oxide (TiO₂) in polypropylene (PP) composites on the mechanical properties. The compatibilizing agent of Maleic anhydride grafted polypropylene (MAPP) are used in the polypropylene based composites to increase the interfacial adhesion between matrix and fillers. The experiments are designed according to L₁₆ orthogonal array (OA) based design of experiments (DOE). The parameters selected for this study are GnPs, TiO₂ and MAPP with four different levels are used.By using Orthogonal array and Taguchi based experimental design, the performance characteristics of tensile modulus, tensile strength, elongation at break and toughness can be analyzed with more objective through a small set of experiments.Taguchi based analysis are used to find out the optimal parameters to maximize the tensile properties for the GnPs and TiO₂ reinforced PP hybrid composites. Further, analysis of variance (ANOVA) is investigated to identify the most significant parameters which influence the mechanical properties.From the analysis it was found that the optimal parameters of 3 ?wt% GnPs, 2 ?wt% TiO₂ and 6 ?wt% MAPP for maximum tensile modulus and tensile strength. The most significant parameter for tensile modulus and tensile strength is GnPs followed by TiO₂ and MAPP according to ANOVA analysis.