Cycle and circle tests of balance in gain graphs: Forbidden minors and their groups

We examine two criteria for balance of a gain graph, one based on binary cycles and one on circles. The graphs for which each criterion is valid depend on the set of allowed gain groups. The binary cycle test is invalid, except for forests, if any possible gain group has an element of odd order. Assuming all groups are allowed, or all abelian groups, or merely the cyclic group of order 3, we characterize, both constructively and by forbidden minors, the graphs for which the circle test is valid. It turns out that these three classes of groups have the same set of forbidden minors. The exact reason for the importance of the ternary cyclic group is not clear. © 2005 Wiley Periodicals, Inc. J Graph Theory     

Achievable sets, brambles, and sparse treewidth obstructions

One consequence of the graph minor theorem is that for every k there exists a finite obstruction set Obs(TW?k). However, relatively little is known about these sets, and very few general obstructions are known. The ones that are known are the cliques, and graphs which are formed by removing a few edges from a clique. This paper gives several general constructions of minimal forbidden minors which are sparse in the sense that the ratio of the treewidth to the number of vertices n does not approach 1 as n approaches infinity. We accomplish this by a novel combination of using brambles to provide lower bounds and achievable sets to demonstrate upper bounds. Additionally, we determine the exact treewidth of other basic graph constructions which are not minimal forbidden minors.     

Counting Split Interval Orders

A poset (X,) is a split interval order (a.k.a. unit bitolerance order, proper bitolerance order) if a real interval and a distinguished point in that interval can be assigned to each xX so that xy precisely when x's distinguished point precedes y's interval, and x's interval precedes y's distinguished point. For each |X|9, we count the split interval orders and identify all posets that are minimal forbidden posets for split interval orders. The paper is a companion to Counting Split Semiorders by Fishburn and Reeds (this issue).     

Design and analysis of doped left-handed materials

We devise three sorts of doped left-handed materials （DLHMs） by introducing inductors and capacitors into the traditional left-handed material （LHM） as heterogeneous elements. Some new properties are presented through finitedifference time-domain （FDTD） simulations. On the one hand, the resonance in the traditional LHM is weakened and the original pass band is narrowed by introducing inductors. On the other hand, the original pass band of the LHM can be shifted and a new pass band can be generated by introducing capacitors. When capacitors and inductors are introduced simultaneously, the resonance of traditional LHM is somewhat weakened and the number of original pass bands as well as its bandwidth can be changed.     

直流外电场诱导的MgI高里德堡态的混合

在直流外电场存在时,观察到MgI的经双光子禁戒跃迁3s~2 ~1S→3mp ~(1P)的多光子电离和倍频效应并解释为外电场引起的里德堡(Rydberg)态之间轨道角动量的混合.实验结果与理论解释一致.     

129Xe30+轰击Ni表面激发靶原子偶极跃迁和禁戒 (M1和E2)跃迁的特征光谱线

报道了用高电荷态离子129Xe30+(150keV) 轰击金属Ni表面，激发的200—1000nm NiⅠ和NiⅡ的特征光谱线的实验结果.实验结果表明：用电荷态足够高的离子作光谱 激发源，无需很强的束流强度（nA量级），便可有效地产生原子和离子的复杂组态间跃迁所 形成的可见光波段的特征谱线，特别是NiⅠ和NiⅡ偶极禁戒的电四极跃迁E2和磁偶极跃迁M1 的特征光谱线.通过分析发现，在禁戒跃迁的谱线中，有些是电子组态相同而原子态不同的 偶极禁戒跃迁光谱线而且NiⅡ的684.84nm谱线较强. 关键词： 光谱 禁戒跃迁 电子组态 高电荷态离子     

不连续不可逆二维映象的动力学特性

总结两个保守映象不可逆地分段连续链接(称为类耗散系统)以及一个保守映象与一个耗散映象不可逆地分段连续链接(称为半耗散系统)情况下得到的五项共同动力学特征：不连续边界象集构成的随机网成为唯一的混沌轨道；由于某些相点具有两个逆象而导致的相空间塌缩(类耗散)；由于系统的不连续不可逆性质而出现的胖分形禁区网；在具有吸引子共存时占据不连续边界象集随机网和胖分形禁区网区域的点滴状吸引域以及由此导致的吸引子不可预言性；即使在传统强耗散存在的情况下点滴状吸引域仍由类耗散机制主宰.以一个累积-触发电路为例，说明这五项系统动 关键词： 随机网 禁区网 点滴状吸引域     

超高效液相色谱-串联质谱法测定白芷中51种禁用农药的残留量

将白芷药材粉碎至通过孔径为(250±9.9)μm的网筛,并称取此白芷粉末样品2.00g于聚丙烯管中与水10mL混匀,再加入含1%(体积分数)乙酸的乙腈10.0mL,涡旋1min后加入无水硫酸镁4g和乙酸钠1g,剧烈振荡3min,离心5min,取其上清液5.0mL置于已盛有无水硫酸镁900mg、N-丙基乙二胺(PSA)450mg和硅胶300mg的净化管中,剧烈振荡5min使净化完全,离心5min。移取上清液3.0mL于40℃水浴中减压蒸缩至近干。加入50μg·L^-1的磷酸三苯酯内标溶液300μL,加入乙腈定容至1.0mL,经0.20μm滤膜过滤,取其滤液,按仪器工作条件进行超高效液相色谱-串联质谱法分析。选用Eclipse Plus C18色谱柱和以不同比例的(A)含10mmol·L^-1甲酸铵的0.1%(体积分数)甲酸溶液和(B)乙腈的混合液为流动相,按梯度洗脱程序对白芷中可能残留的51种禁用农药进行色谱分离,并在电喷雾离子源正、负离子(ESI+和ESI-)电离方式和动态多反应监测(dMRM)模式条件下进行串联质谱法测定。采用基质匹配标准曲线法定量。51种农药的质量浓度在一定范围内与其对应的峰面积呈线性关系,并测得其检出限(3S/N)为0.3~5.0μg·kg^-1。标准加入法回收试验的结果显示,其中大部分农药的回收率在71%以上,测定值的相对标准偏差(n=6)均小于20%。按此方法分析了70批白芷样品,共检出16种农药,其中甲拌磷亚砜的检出率达95%,最高检出量为15.2μg·kg^-1;甲拌磷砜和毒死蜱的检出率均为10%,最高检出量依次为3.5,45.0μg·kg^-1,其余13种农药的检出率均低于5%,且检出量均较低。