Hypergraph list coloring and Euclidean Ramsey theory

A hypergraph is simple if it has no two edges sharing more than a single vertex. It is s‐list colorable (or s‐choosable) if for any assignment of a list of s colors to each of its vertices, there is a vertex coloring assigning to each vertex a color from its list, so that no edge is monochromatic. We prove that for every positive integer r, there is a function d_r(s) such that no r‐uniform simple hypergraph with average degree at least d_r(s) is s‐list‐colorable. This extends a similar result for graphs, due to the first author, but does not give as good estimates of d_r(s) as are known for d₂(s), since our proof only shows that for each fixed r ≥ 2, d_r(s) ≤ 2 We use the result to prove that for any finite set of points X in the plane, and for any finite integer s, one can assign a list of s distinct colors to each point of the plane so that any coloring of the plane that colors each point by a color from its list contains a monochromatic isometric copy of X. © 2011 Wiley Periodicals, Inc. Random Struct. Alg., 2011     

二氧化铬阴离子光电子能谱的理论研究

凭借密度泛函理论,采用不同基组对中性分子CrO2的基态（ 3B1）以及阴离子CrO2‾的基态（ 4B 1）进行几何优化和振动频率分析;应用量化计算得到的力常数及结构和光谱参数,基于推得的两维四模Franck-Condon重叠积分的代数表示,对CrO2 ( 3B1)－CrO2‾ ( 4B1) 的光脱附过程进行Franck-Condon分析和光谱模拟,理论上得到光电子能谱的谱线相对强度及振动结构分布,理论谱与实验测得的二氧化铬阴离子光电子能谱达到一致,并对光电子能谱的振动结构进行归属及热带分析;另外,在光谱模拟过程中通过迭代Franck-Condon分析过程,推得CrO2‾（ 4B1）与CrO2（ 3B1）平衡几何结构之差：ΔR(Cr-O)= 0.05Å,Δ(O-Cr-O)=12o.     

Nin(n=1-9)小团簇的密度泛函理论研究

采用密度泛函理论(DFT)方法对Nin(n=1-9)团簇的结构, 稳定性和磁性进行了详细的研究. 得到了一些以前文献中没有提到的稳定结构, 并与其它方法得到的结构进行了比较, 得到的最稳定结构与实验结果相一致. 团簇能量的二阶差分、分裂能、HOMO-LUMO能隙随团簇尺寸的演化都没有表现出明显的奇偶振荡行为, 但在n=5、7时均有较大的值, 说明相对应的团簇具有较高的稳定性、较低的化学活性. 团簇磁性的研究表明团簇的平均每原子磁矩随团簇尺寸的增加有一定振荡, 但有逐渐减小的趋势, n≥5时团簇的构型对团簇磁性的影响较小.     

Hyperthermal cluster-surface scattering

Using molecular-dynamics simulation, we study the processes occurring after impact of clusters on a rigid wall. Comparing the impact of model clusters consisting of 13 atoms, or of 13 diatomic molecules with varied bond strength, the systematics in the results of the collision process are investigated. Four regimes of impact-induced cluster fragmentation are identified: intact reflection, shattering into large fragments, complete fragmentation, and molecule dissociation. The effect of the number of degrees of freedom activated in the collision on the translational and internal energies of the reflected fragments is discussed in detail. As a rule, with increasing number of degrees of freedom which can be activated in the collision, the translational energy sinks. On the other hand, for weak intramolecular bonding, intramolecular vibrations are easily excited at small impact energies, reducing the resulting translational energy. The presence of even a very weak attractive well epsilon_w at the surface has a major influence on the sticking behavior of the clusters — and hence also on the absolute reflected energies — even at impact energies E₀ ≫ epsilon_w.     

Study of correlation effects on stability of many-body complexes in III–V nitride quantum dots

The aim of this work is to analyze theoretically the correlation energies, for neutral, positive and negative excitons and bi-excitons in the III–V nitride In_xGa_1−xN/GaN quantum dot; where x=17.5% denotes the indium concentration. So, we propose a model consistent with experimental observations that is small In_xGa_1−xN truncated pyramids with circular base lying on wetting layer, both buried into GaN matrix. The correlation energies of many-body complexes X, X⁻, X⁺ and XX are investigated as a function of the quantum dot radius r_c and the intrinsic electric field.     

Dynamics of selfavoiding tethered membranes. I. Model A dynamics (Rouse model)

The dynamical scaling properties of selfavoiding polymerized membranes with internal dimension D are studied using model A dynamics. It is shown that the theory is renormalizable to all orders in perturbation theory and that the dynamical scaling exponent z is given by . This result applies especially to membranes (D=2) but also to polymers (D=1). Received: 5 September 1997 / Accepted: 17 November 1997     

Relativistic and many-body effects in K, L, and M shell ionization energy for elements with and the determination of the 1s Lamb shift for heavy elements

We report on a calculation of K, L and M inner-shell ionization energy in atoms with atomic numbers in the range . Many-body effects are evaluated for all n =1, 2, and 3 hole states. Those include correlation and effects due to the auto-ionizing nature of the hole states (Auger shift). For high Z we add recent corrected nuclear polarization, and several second-order vacuum polarization corrections. K and L ionization energies are compared with experimental X-ray absorption edges measurements. Excellent agreement with rare gazes and metal vapor measurements is found. We also compare our calculations with X-ray transition energies for all K and L lines that involve K, L and M holes. Finally we use K X-ray lines to deduce an hydrogenlike 1 s Lamb shift for several heavy elements, with far better accuracy than has been obtained by direct measurements of hydrogenlike ions. Received: 25 February 1998 / Accepted: 31 March 1998     

水分子辅助的一碳单元转移机理的密度泛函研究

为验证甘氨酰胺转甲酰基酶 (Glycinamideribonucleotidetransformylase ,GARTfase)催化的一碳单元转移反应是嘌呤“从头合成”过程中一个关键步骤的实验推测 ,用B3LYP方法 ,在 6 31G 基组水平上研究了GARTfase催化反应中水分子辅助的一碳单元转移机理 .该反应一共有两条可能的反应通道 :协同的 (patha)和分步的(pathb) ,计算表明 ,后者具有较低势垒 ,更占优势 .计算结果较好地证实了实验假设 ,并进一步表明 :水分子的参与能够缓解体系的张力 ,更有利于一碳单元转移反应的进行 .