“神光-Ⅱ”装置倍频激光直接驱动冲击波平面性的实验研究

 设计了3套针对“神光-Ⅱ”倍频激光直接驱动的透镜阵列均匀辐照系统，并对冲击波的平面性进行了实验研究。结果表明，冲击波的平面性与透镜阵列参数、平面靶厚度、靶面位置等有关，采用列阵元数为121的透镜阵列进行激光束匀滑驱动的冲击波平面性最好，间接说明它在靶面的激光辐照是最均匀的；另外，随着靶厚的增加，冲击波平面性变差，平面区变小；而且冲击波平面性随靶面离焦位置的变化成一定的周期性变化，第2套透镜阵列焦点处的冲击波平面性最好。     

G---的平面性

设G是一个简单图,其全图G 是以V(G)∪E(G)为顶点集的图,其中顶点x和y相邻当且仅当下面的一个条件成立: (i) x,y∈ V(G) ,且x和y在G中相邻, (ii) x,y∈ E(G) ,且x和y在G中相邻, (iii) x和y分别属于V(G)和E(G) ,且它们在G中关联. G---是全图的补图.在这篇文章中,证明了G---是平面的充要条件是 V(G) ≤ 3或者G同构于2K2,C4, K4- e,K4, 2K1 K3, K1,4, K1 K1,3,2K1 P3.     

Planarization and fragmentability of some classes of graphs

The coefficient of fragmentability of a class of graphs measures the proportion of vertices that need to be removed from the graphs in the class in order to leave behind bounded sized components. We have previously given bounds on this parameter for the class of graphs satisfying a given constant bound on maximum degree. In this paper, we give fragmentability bounds for some classes of graphs of bounded average degree, as well as classes of given thickness, the class of k-colourable graphs, and the class of n-dimensional cubes. In order to establish the fragmentability results for bounded average degree, we prove that the proportion of vertices that must be removed from a graph of average degree at most in order to leave behind a planar subgraph (in fact, a series-parallel subgraph) is at most , provided or the graph is connected and . The proof yields an algorithm for finding large induced planar subgraphs and (under certain conditions) a lower bound on the size of the induced planar subgraph it finds. This bound is similar in form to the one we found for a previous algorithm we developed for that problem, but applies to a larger class of graphs.     

Planarity recognition of large polycyclic aromatic hydrocarbons by various octadecylsilica stationary phases in non-aqueous reversed-phase liquid chromatography

Summary Planarity recognition of polycyclic aromatic hydrocarbons has been investigated using bonded octadecyl stationary phases synthesized in different ways. Retention results indicate apparent differences among the functionalities of the stationary phases, a fact found useful for identifying the functionality of commercially available octadecylsilica (ODS) phases. Retention behevior can be explained by the slit-like structures of polymeric oDS phases, as evidenced by suspension¹³C NMR measurements.     

Out-of-plane deformation of the azulene ring in crystal structures of simply substituted azulene derivatives

The crystal structures of 1,3-bis(4-bromophenyl)- and 1,3-di(2-thienyl)azulenes (5 and 6) were elucidated by X-ray analysis. Two aryl groups connect to the azulenyl core with dihedral angles of 34.9-41.6° and the two aryl planes of the groups slant against the azulene ring toward different ways in their crystal structures. It was also found that the azulene rings of 5 and 6 showed a slight out-of-plane deformation in the way that the hydrogen atoms at the 4- and 8-positions are apart from the neighboring aryl ortho-hydrogen atoms to fill in the vacant space made by the slanting aryl planes.     

Theoretical approach to the out-of-plane deformation of 1,3-disubstituted azulenes

Computational calculations at B3LYP/6-311++G(d,p) and MP2/6-311++G(d,p) levels were employed to analyze the structure and conformation of 1,3-bis(4-bromophenyl)azulene (1), 1,3-bis(2-thienyl)azulene (2), and 1,3-bis(2-pyrrollyl)azulene (3) in order to rationalize the out-of-plane deformation found in the azulene cores of 1 and 2 in the crystalline state, whereas compound 3 shows a totally planar azulene moiety. Our results indicate that 1,3-disubstituted azulenes possess two almost equally stable and easily convertible minimum energy conformers, which differ in the relative orientation of the substituent groups and in the planarity degree of the azulene core. An absolute planarity index (P) is introduced to quantify the out-of-plane distortion found in the azulenes under study. The aromaticity of minimum energy conformers was evaluated by means of geometric (HOMA), magnetic (NICS), and energetic (the frequency of the lowest out-of-plane vibration, ν_min) aromaticity indicators, which suggest that compound 3 possesses the most aromatic azulene core within the group. Calculated molecular dipole moments suggest that the conformation of 1,3-disubstituted azulenes in the crystalline state can be explained in terms of electrostatic intermolecular interactions rather than relative stability of planar and non-planar conformers.     

On the sphericity testing of single source digraphs

A digraph D=(V,A) is called spherical, if it has an upward embedding on the round sphere which is an embedding of D on the round sphere so that all edges are monotonic arcs and all point to a fixed direction, say to the north pole. It is easy to see that [S.M. Hashemi, Digraph embedding, Discrete Math. 233 (2001) 321-328] for upward embedding, plane and sphere are not equivalent, which is in contrast with the fact that they are equivalent for undirected graphs. On the other hand, it has been proved that sphericity testing for digraphs is an NP-complete problem [S.M. Hashemi, A. Kisielewicz, I. Rival, The complexity of upward drawings on spheres, Order 14 (1998) 327-363]. In this work we study sphericity testing of the single source digraphs. In particular, we shall present a polynomial time algorithm for sphericity testing of three connected single source digraphs.