An Effective Version of Belyi's Theorem

We compute bounds on covering maps that arise in Belyi's Theorem. In particular, we construct a library of height properties and then apply it to algorithms that produce Belyi maps. Such maps are used to give coverings from algebraic curves to the projective line ramified over at most three points. The computations here give upper bounds on the degree and coefficients of polynomials and rational functions over the rationals that send a given set of algebraic numbers to the set {0,1,∞} with the additional property that the only critical values are also contained in {0,1,∞}.     

Tournament Competition and its Merits for Coevolutionary Algorithms

In a competitive coevolutionary algorithm, the competition strategy, selecting opposing individuals, has a great influence on the performance of the algorithm. Therefore, a good competition strategy is crucial for an effective and efficient competitive coevolutionary algorithm. In this paper, we propose a new competition strategy called tournament competition. We investigate its characteristics and merits when applied to adversarial problems. To verify the performance of the new strategy, we first classify adversarial problems into two types: solution-test problems and game problems. We apply the strategy to both types. A set of experiments compares our strategy to several existing competition strategies and analyzes several aspects such as solution quality, evolution speed, and coevolutionary balance. The experimental results indicate that some of the existing competition strategies give different patterns according to problem types. The results also support that the proposed tournament strategy has the potential for finding good solutions, regardless of problem types.     

A Generating Tree Approach to <Emphasis Type="Italic">k</Emphasis>-Nonnesting Partitions and Permutations

We describe a generating tree approach to the enumeration and exhaustive generation of k-nonnesting set partitions and permutations. Unlike previous work in the literature which uses the connections of these objects to Young tableaux and restricted lattice walks, our approach deals directly with partition and permutation diagrams. We provide explicit functional equations for the generating functions, with k as a parameter. Key to the solution is a superset of diagrams that permit semi-arcs. Many of the resulting counting sequences also count other well-known objects, such as Baxter permutations, and Young tableaux of bounded height.     

Note on Perfect Forests in Digraphs

A spanning subgraph F of a graph G is called perfect if F is a forest, the degree of each vertex x in F is odd, and each tree of F is an induced subgraph of G. Alex Scott (Graphs Combin 17 (2001), 539–553) proved that every connected graph G contains a perfect forest if and only if G has an even number of vertices. We consider four generalizations to directed graphs of the concept of a perfect forest. While the problem of existence of the most straightforward one is NP‐hard, for the three others this problem is polynomial‐time solvable. Moreover, every digraph with only one strong component contains a directed forest of each of these three generalization types. One of our results extends Scott's theorem to digraphs in a nontrivial way.     

Strong interaction between a buoyancy bubble and a free surface

The growth and collapse of buoyant vapor bubbles close to a free surface in an inviscid incompressible fluid is investigated in this paper. The strong interaction between the deforming bubble and the free surface is simulated numerically by a boundary-integral method (Taib 1985; Blake et al., 1987). Improvements are made in the calculation of the singular integrals, the use of nonuniform boundary elements, and the choice of time-step size. The present numerical results agree better with the experimental observations of Blake and Gibson (1981) than previous numerical predictions for bubbles initiated at one maximum radius from the free surface. There is also concurrence of flow features with the experiments for a bubble initiated as close as half maximum radius from the free surface, where other numerical efforts have failed. The effects of buoyancy on bubbles initiated close to a free surface are also investigated. Vastly different features, depending on the distance of the bubble to the free surface and the buoyancy-force parameter, have been observed.     

A general and mild two-step procedure for the synthesis of aryl and heteroaryl sulfonamides from the corresponding iodides

A mild two-step preparation of aryl and heteroaryl sulfonyl chlorides and sulfonamides from their corresponding iodides is developed. Acid labile functionalities are shown to be stable under both the copper-catalysed coupling and the subsequent oxidative chlorination.     

The numerical simulations of explosion and implosion in air: use of a modified Harten's TVD scheme

Numerical simulations of explosion and implosion in air are carried out with a modified Harten's TVD scheme. The new scheme has a high resolution for contact discontinuities in addition to maintaining the good features of Harten's TVD scheme. In the numerical experiment of spherical explosion in air, the second shock wave (which does not exist in the one‐dimensional shock tube problem) and its subsequent implosion on the origin have been successfully captured. The positions of the main shock wave, the contact discontinuity and the second shock wave have shown satisfactory agreement with those predicted from previous analysis. The numerical results are also compared with those obtained experimentally. Finally, simulations of a cylindrical explosion and implosion in air are carried out. Results of the cylindrical implosion in air are compared with those of previous work, including the interaction of the reflected main shock wave with the contact discontinuity and the formation of a second shock wave. All these attest to the successful use of the modified Harten's TVD scheme for the simulations of shock waves arising from explosion and implosion. Copyright © 1999 John Wiley & Sons, Ltd.     

甲基乙烯基克里奇中间体的激发态动力学：不同的圆锥交叉点决定顺反构型的不同无辐射弛豫通道

本文为了揭示甲基乙烯基克里奇中间体(MVCI)的不同异构体的光化学过程的异同,进而深入理解甲基和乙烯基的不同贡献,在多参考态完全活化空间CASSCF和多参考态二阶微扰理论CASPT2水平开展了电子结构计算,并基于CASSCF方法进行了轨线面跃迁非绝热动力学模拟.结果表明,从第一激发态S₁出发的优势反应通道为关环为双环氧乙烷的过程,其中,围绕C-O键为顺式的两种构型关环进度明显慢于反式,说明了乙烯基上的氢与端位氧原子间形成的分子内氢键约束了C-O键的旋转. 更为重要的是,首次在克里奇中间体的光化学中发现,甲基和乙烯基两个重基团的协同作用造成C3原子处呈明显的三角锥化,进而在垂直区域导致两个结构不同、分别趋近顺式和反式构型的势能面交叉点. 从不同初始构型出发的轨线,其无辐射跃迁对两类不同交叉点的偏好造成了各构型间显著不同的动力学行为.