Hamiltonian N2‐locally connected claw‐free graphs

A graph G is N₂‐locally connected if for every vertex ν in G, the edges not incident with ν but having at least one end adjacent to ν in G induce a connected graph. In 1990, Ryjá?ek conjectured that every 3‐connected N₂‐locally connected claw‐free graph is Hamiltonian. This conjecture is proved in this note. © 2004 Wiley Periodicals, Inc. J Graph Theory 48: 142–146, 2005     

Analysis of queueing policies in QoS switches

It is widely accepted that next-generation networks will provide guaranteed services, in contrast to the “best effort” approach today. We study and analyze queueing policies for network switches that support the QoS (Quality of Service) feature. One realization of the QoS feature is that packets are not necessarily all equal, with some having higher priorities than the others. We model this situation by assigning an intrinsic value to each packet. In this paper we are concerned with three different queueing policies: the nonpreemptive model, the FIFO preemptive model, and the bounded delay model. We concentrate on the situation where the incoming traffic overloads the queue, resulting in packet loss. The objective is to maximize the total value of packets transmitted by the queueing policy. The difficulty lies in the unpredictable nature of the future packet arrivals. We analyze the performance of the online queueing policies via competitive analysis, providing upper and lower bounds for the competitive ratios. We develop practical yet sophisticated online algorithms (queueing policies) for the three queueing models. The algorithms in many cases have provably optimal worst-case bounds. For the nonpreemptive model, we devise an optimal online algorithm for the common 2-value model. We provide a tight logarithmic bound for the general nonpreemptive model. For the FIFO preemptive model, we improve the general lower bound to 1.414, while showing a tight bound of 1.434 for the special case of queue size 2. We prove that the bounded delay model with uniform delay 2 is equivalent to a modified FIFO preemptive model with queue size 2. We then give improved upper and lower bounds on the 2-uniform bounded delay model. We also show an improved lower bound of 1.618 for the 2-variable bounded delay model, matching the previously known upper bound.     

A theoretical study of the ion pair SN2 reaction between lithium isocyanates with methyl fluoride with inversion and retention mechanism

This paper is devoted to a detailed theoretical study of an ion pair S_N2 reaction LiNCO+CH₃F in the gas phase and in solution at the level of MP2(full)/6-31+G**//HF/6-31+G**. Two possible reaction mechanisms, inversion and retention, are discussed. There are eight possible reaction pathways. The inversion mechanism is more favorable no matter in the gas phase or in solution based on analyses of the transition structures. Methyl isocyanate should form preferentially in the gas phase and more stable methyl cyanate is the main product in solution. The retardation of the reaction in solvents was attributed to the difference in solvation in the separated reactants and in the transition state.     

A Promising MoO_x-based Catalyst for n-Heptane Isomerization

The increasing demand for higher-octane gasoline and the regulations limiting the amount of aromatics in the fuel motivate the interest in catalytic isomerization of n-alkanes. In the last ten years, transition metal oxides or oxycarbides based on molybdenum or tungstate have attracted much attention due to their high activity and isomerization selectivity compared to the conventional bifunctional supported platinum catalyst and high resistance to sulphur and nitrogen catalyst poisons1-5. Ma…     

凹整数规划的分枝定界解法

凹整数规划是一类重要的非线性整数规划问题，也是在经济和管理中有着广泛应用的最优化问题．本文主要研究用分枝定界方法求解凹整数规划问题，这一方法的基本思想是对目标函数进行线性下逼近，然后用乘子搜索法求解连续松弛问题．数值结果表明，用这种分枝定界方法求解凹整数规划是有效的．     

Circular perfect graphs

For 1 ≤ d ≤ k, let K_k/d be the graph with vertices 0, 1, …, k ? 1, in which i ～j if d ≤ |i ? j| ≤ k ? d. The circular chromatic number χ_c(G) of a graph G is the minimum of those k/d for which G admits a homomorphism to K_k/d. The circular clique number ω_c(G) of G is the maximum of those k/d for which K_k/d admits a homomorphism to G. A graph G is circular perfect if for every induced subgraph H of G, we have χ_c(H) = ω_c(H). In this paper, we prove that if G is circular perfect then for every vertex x of G, N_G[x] is a perfect graph. Conversely, we prove that if for every vertex x of G, N_G[x] is a perfect graph and G ? N[x] is a bipartite graph with no induced P₅ (the path with five vertices), then G is a circular perfect graph. In a companion paper, we apply the main result of this paper to prove an analog of Haj?os theorem for circular chromatic number for k/d ≥ 3. Namely, we shall design a few graph operations and prove that for any k/d ≥ 3, starting from the graph K_k/d, one can construct all graphs of circular chromatic number at least k/d by repeatedly applying these graph operations. © 2005 Wiley Periodicals, Inc. J Graph Theory 48: 186–209, 2005     

A lithium ethyl­ene­diphos­phon­ate containing lithium chains and symmetric hydrogen bonds

In the title compound, catena‐poly[lithium‐μ₃‐ethyl­ene­diphos­phon­ato], [Li(C₂H₇O₆P₂)]_n, the supra­molecular monoclinic (C2/c) structure consists of one‐dimensional lithium chains [Li⋯Li = 2.7036 (8) Å] that are embedded within ethyl­ene­diphosphon­ate anions linked by strong symmetric hydrogen bonds [O⋯O = 2.473 (3) Å]. The Li atoms and the H atom in the symmetric hydrogen bond reside on twofold rotation axes and there is an inversion center at the mid‐point of the C—C bond of the ethylenediphosphonate ligand.     

Elliptic equations with BMO coefficients in Reifenberg domains

The inhomogeneous Dirichlet problems concerning divergence form elliptic equations are studied. Optimal regularity requirements on the coefficients and domains for the W^1,p theory, 1 < p < ∞, are obtained. The principal coefficients are supposed to be in the John‐Nirenberg space with small BMO seminorms. The domain is a Reifenberg domain. These conditions for the W^1,p theory not only weaken the requirements on the coefficients but also lead to a more general geometric condition on the domains. In fact, these domains might have fractal dimensions. © 2004 Wiley Periodicals, Inc.     

Crystallographic report: Bis{[diacetyl‐bis(2,6‐isopropylphenylimine)]nickel(I)(µ‐chloro)}

The first α‐diimine nickel(I) complex having a chloro bridge is reported. The centrosymmetric dinuclear structure of {[ArN?C(Me)C(Me)?NAr]NiCl}₂[Ar?2,6?C₆H₃(i‐Pr)₂] features two chelating α‐diimine ligands and two bridged chlorine atoms, so that a distorted tetrahedral N₂Cl₂ coordination geometry for nickel results. Copyright © 2004 John Wiley & Sons, Ltd.