Hamiltonian cycles in 7-tough (P3 ∪ 2P1)-free graphs

The toughness of a noncomplete graph G is the maximum real number t such that the ratio of $|S|$ to the number of components of $G?S$ is at least t for every cutset S of G. Determining the toughness for a given graph is NP-hard. Chvátal's toughness conjecture, stating that there exists a constant $t_0$ such that every graph with toughness at least $t_0$ is hamiltonian, is still open for general graphs. A graph is called $(P_3\cup 2P_1)$-free if it does not contain any induced subgraph isomorphic to $P_3\cup 2P_1$, the disjoint union of $P_3$ and two isolated vertices. In this paper, we confirm Chvátal's toughness conjecture for $(P_3\cup 2P_1)$-free graphs by showing that every 7-tough $(P_3\cup 2P_1)$-free graph on at least three vertices is hamiltonian.     

Synthesis,cytotoxicity, apoptosis and cell cycle arrest of a monoruthenium(II)-substituted Dawson polyoxotungstate

By 5-h reaction of cis-[Ru^IICl₂(DMSO)₄] (M2) with K₁₀[α₂-P₂W₁₇O₆₁] (M3) in ice-cooled, HCl-acidic aqueous solution, a water-soluble 1:2-type diamagnetic ruthenium(II) complex of formula K₁₈[Ru^II(DMSO)₂(P₂W₁₇O₆₁)₂]·35H₂O (M1) was unexpectedly obtained as an analytically pure, homogeneous tan-colored solid, in which two DMSO ligands are coordinated to the ruthenium(II) atom. The cytotoxic potential of the complex was tested on C33A, DLD-1, and HepG-2 cancer cells and human normal embryonic lung fibroblasts cell MRC-5; the viability of the treated cells was evaluated by MTT assay. The mode of cell death was assessed by morphological study of DNA damage and apoptosis assays. Compound M1 induced cell death in a dose-dependent manner, and the mode of cell death was essentially apoptosis though necrosis was also noticed. Cell cycle analysis by flow cytometry indicated that M1 caused cell cycle arrest and accumulated cells in S phase.     

A note on 3‐partite graphs without 4‐cycles

Let $C_4$ be a cycle of order 4. Write $ex\left(n,n,n,C_4\right)$ for the maximum number of edges in a balanced 3‐partite graph whose vertex set consists of three parts, each has $n$ vertices that have no subgraph isomorphic to $C_4$. In this paper, we show that $ex\left(n,n,n,C_4\right)\ge \frac{3}{2}n\left(p+1\right)$, where $n=\frac{p\left(p?1\right)}{2}$ and $p$ is a prime number. Note that $ex\left(n,n,n,C_4\right)\le \left(\frac{3\sqrt{2}}{2}+o\left(1\right)\right)n^{\frac{3}{2}}$ from Tait and Timmons's works. Since for every integer $m$, one can find a prime $p$ such that $m\le p\le \left(1+o\left(1\right)\right)m$, we obtain that $\underset{n\to \infty }{\lim }\frac{ex\left(n,n,n,C_4\right)}{\frac{3\sqrt{2}}{2}{n}^{\frac{3}{2}}}=1$.     

微波瑞利散射法测定空气电火花激波等离子体射流的时变电子密度

大气压空气电火花激波等离子体射流的电子密度在亚微秒时间尺度上瞬变,其电子密度的测定很难.基于微波瑞利散射原理,本文测量了空气电火花冲击波流注放电等离子体射流的时变电子密度.实验结果表明:测量系统的标定参数A为1.04 × 105 V·Ω·m–2;空气流注放电等离子体射流的电子密度与等离子体射流的半径和长度有关,结合高速放电影像展示的等离子体射流的等效半径和等效长度,测定的电子密度在1020 m–3的量级,且随时间先快速增长至峰值再成指数衰减.此外,本文还探讨了等离子体射流的不同等效尺度对测定结果的影响;分析结果表明,采用时变等效半径和时变等效长度的计算结果最有效,且第1个快速波峰是由光电离的电离波导致的.     

Spontaneous translation of nanodroplet over a heterogeneous surface due to thermal cycles: role of solid–liquid interfacial fluctuations

ABSTRACT

We study the molecular-scale features of the solid surface that result in the spontaneous motion of a nanodroplet due to the periodic variation of temperature. We first employ a thermodynamic model to predict the variation of solid–fluid interfacial properties that can result in the above motion. The model identifies a composite (surface couple) made of two surfaces that are characterised by a large difference between the entropic parts of the solid–liquid interfacial free energies. In order to understand the molecular-scale features of the two surfaces that may form a surface couple, we performed grand canonical Monte Carlo simulations of Lennard Jones fluid and crystalline surfaces made of Lennard Jones-like atoms. We then used the cumulant expansions of the perturbation formulas to divide the interfacial entropy into two parts: The one that is directly affected by the solid–fluid attraction (direct part), and the other (indirect part) that is indirectly affected by the solid–fluid attraction via the alteration of interfacial fluctuations. Our results indicate that two surfaces form a surface couple if the differences between their chemical natures lead to large differences in the indirect part of the interfacial entropy, while the direct part remains relatively unaffected.     

Exceptional Cycles in the Bounded Derived Categories of Quivers

An exceptional n-cycle in a Hom-finite triangulated category with Serre functor has been recently introduced by Broomhead,Pauksztello and Ploog.When n=1,it is a spherical object.We explicitly determine all the exceptional cycles in the bounded derived category D^b(kQ)of a finite quiver Q without oriented cycles.In particular,if Q is an Euclidean quiver,then the length type of exceptional cycles in D^b(kQ)is exactly the tubular type of Q;if Q is a Dynkin quiver of type E_m(m=6,7,8),or Q is a wild quiver,then there are no exceptional cycles in D^b(kQ);and if Q is a Dynkin quiver of type An or D_n,then the length of an exceptional cycle in D^b(kQ)is either h or h/2,where h is the Coxeter number of Q.