Solution Transformations and Their Effects on the Systems with Open Boundary Conditions

The solution transformations and properties of the R-matrices for two-component systems under these transformations are analyzed in details.Not all transformed R-matrices can be put into the Skalyanin‘s formalism.For those R-matrices with all required properties,the effects of solution transformations to the six-and eight-vertex systems with open boundary conditions are discussed.these effects can be one of the following types:the Hamiltonian is invariant or transposition-invariant or made in a similarity transformation,or its coupling coefficients are multiplied by an overall factor,or the spin of the system is rotated around the z axis or/and reflected with respect to some plane.In these cases,the transformed systems remain to be integrable.     

极低频高压脉冲电场对萌发玉米种子超弱发光的影响

生物超弱发光是来自细胞的电磁信号,在揭示电磁生物学效应的机理研究中具有重要作用.为了研究极低频脉冲电场生物学效应及其机理,采用基于玉米细胞电位波动频率的1 Hz极低频高压脉冲电场处理萌发玉米种子,结果发现玉米种子的萌发过程明显加快,根长和芽长均有显著增长.对萌发种子的自发发光和延迟发光的测量结果显示,1 Hz极低频高压脉冲电场对萌发过程中玉米种子的自发发光和延迟发光积分强度都有明显的促进作用,表明1 Hz极低频高压脉冲电场加速了玉米种子萌发过程中的DNA合成和细胞代谢.     

Parafermion vertex operator algebras

This paper reviews some recent results on the parafermion vertex operator algebra associated to the integrable highest weight module L(k, 0) of positive integer level k for any affine Kac-Moody Lie algebra ĝ, where g is a finite dimensional simple Lie algebra. In particular, the generators and the C ₂-cofiniteness of the parafermion vertex operator algebras are discussed. A proof of the well-known fact that the parafermion vertex operator algebra can be realized as the commutant of a lattice vertex operator algebra in L(k, 0) is also given.     

On the imaginary simple roots of the Borcherds algebra II9,1

In a recent paper [O. Bärwald, R.W. Gebert, M. Günaydin and H. Nicolai, preprint KCL-MTH-97-22, IASSNS-HEP-97/20, PSU-TH-178, AEI-029, hep-th/9703084, to appear in Commun. Math. Phys.] it was conjectured that the imaginary simple roots of the Borcherds algebra _II9,1 at level 1 are its only ones. We here propose an independent test of this conjecture, establishing its validity for all roots of norm − 8. However, the conjecture fails for roots of norm −10 and beyond, as we show by computing the simple multiplicities down to norm −24, which turn out to be remarkably small in comparison with the corresponding E₁₀ multiplicities. Our derivation is based on a modified denominator formula combining the denominator formulas for E₁₀ and _II9,1, and provides an efficient method for determining the imaginary simple roots. In addition, we compute the E₁₀ multiplicities of all roots up to height 231, including levels up to l = 6 and norms −42.     

Two‐sided Group Digraphs and Graphs

We study a family of digraphs (directed graphs) that generalises the class of Cayley digraphs. For nonempty subsets of a group G, we define the two‐sided group digraph to have vertex set G, and an arc from x to y if and only if for some and . In common with Cayley graphs and digraphs, two‐sided group digraphs may be useful to model networks as the same routing and communication scheme can be implemented at each vertex. We determine necessary and sufficient conditions on L and R under which may be viewed as a simple graph of valency , and we call such graphs two‐sided group graphs. We also give sufficient conditions for two‐sided group digraphs to be connected, vertex‐transitive, or Cayley graphs. Several open problems are posed. Many examples are given, including one on 12 vertices with connected components of sizes 4 and 8.     

Effects of ultrasound on Microcystis aeruginosa cell destruction and release of intracellular organic matter

Harmful algal blooms negatively impact ecosystems and threaten drinking water sources. One potential method to effectively counteract algal blooms is ultrasonication. However, ultrasonication can easily lead to the release of intracellular organic matter (IOM). The purpose of this study was to investigate the relationship between the destruction of algal cells and IOM release at different ultrasound frequencies. Microcystis aeruginosa cells were ultrasonicated at 20 kHz with an intensity of 0.038 W/mL, 740 kHz with an intensity of 0.113 W/mL, and 1120 kHz with an intensity of 0.108 W/mL. The IOM release was detected by fluorescence spectroscopy in addition to the more commonly used haemocytometry and optical density. After ultrasonication for 15 min, the removal rate of algal cells reached 10.5% at 20 kHz, 9.46% at 740 kHz, and 35.4% at 1120 kHz. The 20 kHz and 740 kHz ultrasound caused local damage to algal cells and then disrupted them, whereas the 1120 kHz ultrasound directly disrupted most algal cells. The extracellular organic matter (EOM), which was increased by ultrasonication, mainly consisted of protein-like compounds, chlorophyll, and a small amount of humic-like substances. Gas vacuoles had been destructed before the cells were broken, as indicated by the decrease of cell size and the wrinkles on the cell surface. Moreover, the removal of algae cells while upholding integrity is more conducive to the safety of the water environment.     

On cubic non‐Cayley vertex‐transitive graphs

In 1983, the second author [D. Maru?i?, Ars Combinatoria 16B (1983), 297–302] asked for which positive integers n there exists a non‐Cayley vertex‐transitive graph on n vertices. (The term non‐Cayley numbers has later been given to such integers.) Motivated by this problem, Feng [Discrete Math 248 (2002), 265–269] asked to determine the smallest valency ?(n) among valencies of non‐Cayley vertex‐transitive graphs of order n. As cycles are clearly Cayley graphs, ?(n)?3 for any non‐Cayley number n. In this paper a goal is set to determine those non‐Cayley numbers n for which ?(n) = 3, and among the latter to determine those for which the generalized Petersen graphs are the only non‐Cayley vertex‐transitive graphs of order n. It is known that for a prime p every vertex‐transitive graph of order p, p² or p³ is a Cayley graph, and that, with the exception of the Coxeter graph, every cubic non‐Cayley vertex‐transitive graph of order 2p, 4p or 2p² is a generalized Petersen graph. In this paper the next natural step is taken by proving that every cubic non‐Cayley vertex‐transitive graph of order 4p², p>7 a prime, is a generalized Petersen graph. In addition, cubic non‐Cayley vertex‐transitive graphs of order 2p^k, where p>7 is a prime and k?p, are characterized. © 2011 Wiley Periodicals, Inc. J Graph Theory 69: 77–95, 2012     

Improved estimation of duality gap in binary quadratic programming using a weighted distance measure

We present in this paper an improved estimation of duality gap between binary quadratic program and its Lagrangian dual. More specifically, we obtain this improved estimation using a weighted distance measure between the binary set and certain affine subspace. We show that the optimal weights can be computed by solving a semidefinite programming problem. We further establish a necessary and sufficient condition under which the weighted distance measure gives a strictly tighter estimation of the duality gap than the existing estimations.     

A cell-based study on pedestrian acceleration and overtaking in a transfer station corridor

Pedestrian speed in a transfer station corridor is faster than usual and sometimes running can be found among some of them. In this paper, pedestrians are divided into two categories. The first one is aggressive, and the other is conservative. Aggressive pedestrians weaving their way through crowd in the corridor are the study object of this paper. During recent decades, much attention has been paid to the pedestrians’ behavior, such as overtaking (also deceleration) and collision avoidance, and that continues in this paper. After sufficiently analyzing the characteristics of pedestrian flow in transfer station corridor, a cell-based model is presented in this paper, including the acceleration (also deceleration) and overtaking analysis. Acceleration (also deceleration) in a corridor is fixed according to Newton’s Law and then speed calculated with a kinematic formula is discretized into cells based on the fuzzy logic. After the speed is updated, overtaking is analyzed based on updated speed and force explicitly, compared to rule-based models, which herein we call implicit ones. During the analysis of overtaking, a threshold value to determine the overtaking direction is introduced. Actually, model in this paper is a two-step one. The first step is to update speed, which is the cells the pedestrian can move in one time interval and the other is to analyze the overtaking. Finally, a comparison between the rule-based cellular automata, the model in this paper and data in HCM 2000 is made to demonstrate our model can be used to achieve reasonable simulation of acceleration (also deceleration) and overtaking among pedestrians.     

NaN_3对玉米萌发过程中超弱光子辐射的影响

为了解读植物种子萌发过程中超弱光子辐射信息的生物学意义,采用呼吸抑制剂NaN3处理萌发玉米种子,跟踪测量和分析了玉米种子萌发过程中超弱光子辐射中自发光子辐射和外界光诱导的延迟光子辐射的变化规律,同时研究了萌发玉米种子鲜质量的变化.结果发现,NaN3同步抑制了萌发玉米自发光子辐射和鲜质量的增长,造成萌发玉米延迟光子辐射的初始光子数和延迟光子辐射积分强度大幅度降低,相干时间减小.机理分析表明,NaN3对呼吸代谢电子传递链的抑制造成的自由基反应减弱是萌发玉米自发光子辐射减小的原因,自发光子辐射强度可以作为玉米萌发状态的信号,延迟光子辐射动力学参数的大小可以表征萌发玉米呼吸代谢的强弱,相干时间是种子细胞组织序性的量度,通过对萌发种子超弱光子辐射的采集和分析可以实现对萌发种子细胞代谢和功能状态变化的灵敏和无损检测.