关于Ramsey数下界的部分结果

本文得到 Ramsey数下界的一个计算公式 :R( l,s+ t-2 )≥ R( l,s) + R( l,t) -1 ,(式中 l、s、t≥ 3) .用此公式算得的 Ramsey数的下界比用其它公式算得的下界好 .     

Electrode “edge effects” analyzed by the Green function method

An exact method based on Green's equation is used to find the diffusion-controlled faradaic current for certain electrode geometries that incorporate edges and vertices. Thereby the magnitudes of the time-independent current density associated with angled electrode/electrode and electrode/insulator junctions are calculated. As well, the square-root-of-time-dependent currents associated with vertices, receive attention. These terms extend to longer times, the Cottrell formulation appropriate for short times. Though most of the problems solved here have been tackled previously, the novel Green function approach is shown to be straightforward and intuitive.     

Finite element investigation of the ground states of the helium trimers 4He3 and 4He2–3He

A three‐dimensional finite element method is applied to the ground states of the symmetric and asymmetric atomic helium trimers ⁴He₃ and ⁴He₂–³He. Three different He–He interaction potentials of hard‐core nature were studied. Two extrapolation procedures based on the convergence properties of the finite element method are investigated. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

阿秒光脉冲技术的发展和应用

阿秒光脉冲的产生方法获得2023年诺贝尔物理学奖,引起了人们的广泛兴趣。阿秒脉冲是通过周期量级的飞秒脉冲产生高次谐波得到的,其中需要许多关键技术,包括飞秒脉冲压缩技术、脉冲载波相位的稳定控制以及脉冲强度的提高。文章简要介绍阿秒脉冲的产生方法,及其发展趋势和应用。     

磁场对含稀土铝锂合金断裂特征的影响

以含铈铝锂合金为研究对象，研究了磁场对含稀土铝锂合金时效过程的影响，从断裂特征及微观组织两方面分析了磁场作用规律。实验结果表明：未加磁场时，合金的断裂特征以理断裂为主；扁平晶粒厚度不匀，在磁场作用下，此合金的断裂特征与微观组织发生明显改观，随磁感应强度增强，合金主断裂面上准解理断裂特征减弱，同时二次裂纹增多，分层比较升高；扁平晶粒厚度变薄，尺寸趋于均匀。用少体物理理论，探讨了磁场对含稀土合金原子扩散过程的影响，为进一步研究稀土元素在磁场中的行为及其局域效应提供了一定的实验依据。     

基于少模光纤的全光纤熔融模式选择耦合器的设计及实验研究

提出了三种基于少模光纤的全光纤熔融模式选择耦合器. 根据模式匹配原理采用单模光纤与少模光纤熔融连接方式, 运用耦合模理论及光束传播法模拟分析了模式选择耦合器的结构参数对模式选择及耦合特性的影响, 实现了单模光纤中基模到少模光纤中不同阶模式的转换, 以满足不同的应用需求. 实验上以2× 2熔融光纤耦合器为例, 采用对称和非对称熔融拉锥方式, 分别实现了从基模到LP₁₁, LP₂₁模式的转换. 实验结果表明所得到的LP₁₁, LP₂₁模式在1530–1560 nm的波长带宽范围内均有较高的模式纯净度, 且模式耦合效率高于80%, 与理论模拟结果基本一致.     

disjoint cycles containing specified independent vertices

Let k1 be an integer and G be a graph of order n3k satisfying the condition that σ₂(G)n+k-1. Let v₁,…,v_k be k independent vertices of G, and suppose that G has k vertex-disjoint triangles C₁,…,C_k with v_iV(C_i) for all 1ik.Then G has k vertex-disjoint cycles such that

(i) for all 1ik.

(ii) , and

(iii) At least k-1 of the k cycles are triangles.

The condition of degree sum σ₂(G)n+k-1 is sharp.

On 3-Steiner simplicial orderings

Let G be a connected graph and S a nonempty set of vertices of G. A Steiner tree for S is a connected subgraph of G containing S that has a minimum number of edges. The Steiner interval for S is the collection of all vertices in G that belong to some Steiner tree for S. Let k≥2 be an integer. A set X of vertices of G is k-Steiner convex if it contains the Steiner interval of every set of k vertices in X. A vertex x∈X is an extreme vertex of X if X?{x} is also k-Steiner convex. We call such vertices k-Steiner simplicial vertices. We characterize vertices that are 3-Steiner simplicial and give characterizations of two classes of graphs, namely the class of graphs for which every ordering produced by Lexicographic Breadth First Search is a 3-Steiner simplicial ordering and the class for which every ordering of every induced subgraph produced by Maximum Cardinality Search is a 3-Steiner simplicial ordering.     

On dynamics of vertices of locally connected polynomial Julia sets

Let be a polynomial whose Julia set is locally connected. Then a non-preperiodic non-precritical vertex of must have the limit set which coincides with the limit set of an appropriately chosen recurrent critical point of . In particular, if all critical points of are non-recurrent then all vertices of are preperiodic or precritical.

     

The structure of matrices with a maximum multiplicity eigenvalue

There is remarkable and distinctive structure among Hermitian matrices, whose graph is a given tree T and that have an eigenvalue of multiplicity that is a maximum for T. Among such structure, we give several new results: (1) no vertex of T may be “neutral”; (2) neutral vertices may occur if the largest multiplicity is less than the maximum; (3) every Parter vertex has at least two downer branches; (4) removal of a Parter vertex changes the status of no other vertex; and (5) every set of Parter vertices forms a Parter set. Statements (3), (4) and (5) are also not generally true when the multiplicity is less than the maximum. Some of our results are used to give further insights into prior results, and both the review of necessary background and the development of new structural lemmas may be of independent interest.