On Group Connectivity of Graphs

Tutte conjectured that every 4-edge-connected graph admits a nowhere-zero Z ₃-flow and Jaeger et al. [Group connectivity of graphs–a nonhomogeneous analogue of nowhere-zero flow properties, J. Combin. Theory Ser. B 56 (1992) 165-182] further conjectured that every 5-edge-connected graph is Z ₃-connected. These two conjectures are in general open and few results are known so far. A weaker version of Tutte’s conjecture states that every 4-edge-connected graph with each edge contained in a circuit of length at most 3 admits a nowhere-zero Z ₃-flow. Devos proposed a stronger version problem by asking if every such graph is Z ₃-connected. In this paper, we first answer this later question in negative and get an infinite family of such graphs which are not Z ₃-connected. Moreover, motivated by these graphs, we prove that every 6-edge-connected graph whose edge set is an edge disjoint union of circuits of length at most 3 is Z ₃-connected. It is a partial result to Jaeger’s Z ₃-connectivity conjecture. Received: May 23, 2006. Final version received: January 13, 2008     

Synthesis,Crystal Structure and Luminescent Property of a Novel Pt（Ⅱ） Complex with Weak Metal-metal Interaction

The title complex cis-bis（tetrahydrothiophene）-bis（nitrate） platinum（H）, （tht）2Pt（NO3）2, was the reducing product from potassium hexachloroplatinate（IV） K2PtC16 where the platinum is tetra-valenced. Crystal data for CsH16N206PtS2： monoclinic, space group P21/c, a = 9.8833（5）, b = 8.6744（4）, c = 18.6407（9）A,β = 114.401（3）°, V = 1455.35（12）A3 Z = 4, Mr = 495.44, Dc = 2.261 g/cm3, F（000） = 944,μ = 9.950 mm-1, 2（MoKa） = 0.71073 A, T= 293（2） K, 2θmax = 54.96°, GOOF = 1.033, R = 0.0350 and wR = 0.0785 for 2572 observed reflections with I 〉 2σ（I）. X-ray diffraction studies reveal that the title complex has interesting weak metal-metal interactions and two molecules linked by metal-metal interaction exist as a group. Luminescent spectrum illuminates red emission of the complex at room temperature.     

Highly sensitive and interference-free determination of bismuth in environmental samples by electrothermal vaporization atomic fluorescence spectrometry after hydride trapping on iridium-coated tungsten coil

Bismuthine was on-line trapped on tungsten coil and subsequently electrothermally vaporized for the determination by atomic fluorescence spectrometry (AFS). Several noble metals, including Pd, Rh, Pt, and Ir, were explored as permanent chemical modifier for tungsten coil on-line trapping. Investigation showed that Ir gave the best performance, in which bismuthine was on-line trapped on Ir-coated tungsten coil at 560 °C, and then released at 1550 °C for subsequent transfer to AFS by a mixture of Ar and H₂. Under optimum instrumental conditions, the trapping efficiency was found to be 73 ± 3%. With 120 s (12 mL sample volume) trapping time, a limit of detection (LOD) of 4 ng L^− 1 was obtained, compared to conventional hydride generation AFS (0.09 μg L^− 1); the LOD can be lowered down to 1 ng L^− 1 by increasing the trapping time to 480 s. The LOD was found to be better or at least comparable to literature levels involving on-line trapping and some other sophisticated instrumental methods such as ICP-MS and GF-AAS. A comprehensive interference study involving conventional hydride-forming elements and some transition metals was carried out, and the result showed that the gas phase interference from other hydride-forming elements was largely reduced, thanks to the use of on-line tungsten coil trapping. Finally, the proposed method was applied to the determination of bismuth in several biological and environmental standard reference materials, and a t-test shows that the analytical results by the proposed method have no significant difference from the certified values at the confidence level of 95%.     

Linearization of Poisson Brackets

We review the linearization of Poisson brackets and related problems, in the formal, analytic and smooth categories.     

First-principles electronic structure calculations with molecular dynamics made easy

The technique of quantum molecular dynamics is reviewed, and a simplified approach based on a first-principles tight-binding implementation of local density theory is discussed. Several illustrations and applications of the theory are presented. Applying it to amorphous materials, we have developed a procedure for producing amorphous Si networks with small defect concentrations. Benchmark checks are made for atomic geometries at Si(111)-(2×1) and Si(001)-(2×1), p(2×2), and c(4×2) reconstructed surfaces. A simulation of a Scanning Tunneling Microscope tip interacting with a reconstructed surface is performed, and it is shown how the tip can alter the reconstruction of the surface. Simulation of a kinked Si(001) surface step and comparison to an unkinked step are also presented.     

GLOBAL ATTRACTIVITY IN A PERIODIC COMPETITION SYSTEM WITH FEEDBACK CONTROLS

ＷＥＮＧＰＥＩＸＵＡＮ（翁佩萱）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＳｏｕｔｈＣｈｉｎａＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｇｕａｎｇｚｈｏｕ５１０６３１，Ｃｈｉｎａ）ＧＬＯＢＡＬＡＴＴＲＡＣＴＩＶＩＴＹＩＮＡＰＥＲＩＯＤＩＣＣＯＭＰＥＴ...     

LM-g splines

As an extension of the notion of an L-g spline, three mathematical structures called LM-g splines of types I, II, and III are introduced. Each is defined in terms of two differential operators the coefficients a_j, J = 0,…, n − 1, and b_i, I = 0,…, m, are sufficiently smooth; and b_m is bounded away from zero on [0, T]. Each of the above types of splines is the solution of an optimization problem more general than the one used in the definition of the L-g spline and hence it is recognized as an entity which is distinct from and more general mathematically than the L-g spline. The LM-g splines introduced here reduce to an L-g spline in the special case in which m = 0 and b₀ = constant ≠ 0. After the existence and uniqueness conditions, characterization, and best approximation properties for the proposed splines are obtained in an appropriate reproducing kernel Hilbert space framework, their usefulness in extending the range of applicability of spline theory to problems in estimation, optimal control, and digital signal processing are indicated. Also, as an extension of recent results in the generalized spline literature, state variable models for the LM-g splines introduced here are exhibited, based on which existing least squares algorithms can be used for the recursive calculation of these splines from the data.     

Determination of hydrogen peroxide concentration in THOR coolant during reactor operation

The concentrations of hydrogen peroxide formed in the coolant due to radiolysis were studied during THOR operation at 1 MW. The relation between doses and hydrogen peroxide formation in a neutron-gamma mixed field was investigated. The initial concentration was 2.3×10^–5 g/ml at the beginning of reactor operation, and then it was increased rather rapidly at the first 9 h. The increasing rate was slowed down till the end of 30 h operation. The maximum concentration of hydrogen peroxide was found to be 4.7×10^–5 g/ml, and its decrease followed the exponential curve.