The electronic viewpoint on the morphology of the microclusters

Although the five-fold symmetry conflicts with the crystalline long range order, it can appear in some finite systems. In order to search for such possibility in the microclusters in the small size limit and to clarify the roles of the electrons in the morphology, the electronic states are studied in the tight binding scheme. The single electron spectra coming from thes- andp-atomic orbitals are derived for three types of the 13-atom clusters; with the fcc-like configuration, the hcp-like and the icosahedral. If the transfer integral between two surface atoms is put equal to that between the central and a surface atom in the icosahedral case, this configuration has the lowest total electronic energy in many cases studied, but not always. The fact that a surface atom has larger number of neighbours in the icosahedral configuration is surely of great advantage. It, however, is not almighty in the quantum case.On leave from Department of Physics, Faculty of Science, Kyoto University, Kyoto 606, Japan. A part of this work was done there     

Convergence of the arithmetic-geometric mean procedure for the complex variables and the calculation of the complete elliptic integrals with complex modulus

The convergence of the arithmetic-geometric mean procedure is checked for complex variables. The procedure is shown to be useful for the evaluation of the complete elliptic integrals of the first and second kinds with complex modulus. It is suggested that the procedure will be useful also for the numerical calculation of the elliptic integrals and the Jacobian elliptic functions with complex modulus in general.     

Stroboscopic phase portrait and strange attractors

External periodic modulation of a nonlinear oscillator may lead to a chaotic output behaviour. This phenomenon is attributed to the existence of a strange attractor, which embodies essentially a folding motion as is met in Bernoulli shift or the Baker's transformation.     

A linear algorithm for the domination number of a series-parallel graph

A vertex u in an undirected graph G = (V, E) is said to dominate all its adjacent vertices and itself. A subset D of V is a dominating set in G if every vertex in G is dominated by a vertex in D, and is a minimum dominating set in G if no other dominating set in G has fewer vertices than D. The domination number of G is the cardinality of a minimum dominating set in G.The problem of determining, for a given positive integer k and an undirected graph G, whether G has a dominating set D in G satisfying ¦D¦ ≤ k, is a well-known NP-complete problem. Cockayne have presented a linear time algorithm for finding a minimum dominating set in a tree. In this paper, we will present a linear time algorithm for finding a minimum dominating set in a series-parallel graph.     

Persistent pi radical cations: self-association and its steric control in the condensed phase

Pi Radical cations, which are highly reactive in general, can be made persistently stable by appropriate structural modification with heteroatoms, pi-conjugated systems, and alkyl substituents. Many of these pi radical cations undergo self-association in the condensed phase. The steric control of such self-association of stabilized pi radical cations is the subject of the present article. Such an association can result in the formation of pi- and/or sigma-dimers. The pi-dimerization in particular is now considered as an important intermolecular interaction for model studies of a charge-transport phenomenon in positively doped conducting polymers. On the other hand, the intermolecular interactions can be suppressed when the pi-system is modified with sterically demanding structural units, for example, by annelation with bicycloalkene frameworks. This structural modification not only brings about unusual stabilization of the radical cations but provides valuable information on the electronic structure/properties of the positively charged pi-systems in a segregated state.     

Micro-patterning of multiple organic molecules by laser implantation

Micrometer pixelated arrays comprised of different functional organic molecules were formed on a polymer film using a laser implantation and transfer dry processing technique. The spatial distribution of the implanted organic molecules and the extended pattern that they formed could be controlled with high resolution as determined using fluorescence microscopy. The individual molecular implant pixels had a diameter of less than 4 m. This method of molecular manipulation is both precise and reproducible and could therefore be used in many applications such as molecular devices, molecular sensors, non-linear optical devices, drug delivery and opto-electronic displays. PACS 81.05.Lg; 81.16.Mk; 81.65.Cf     

Total synthesis of leustroducsin B

A convergent total synthesis of leustroducsin B (1), which is known to exhibit a variety of biological activities, was successfully carried out. Notable features of our synthesis include construction of the C8 stereocenter by lipase-mediated desymmetrization of meso-diol 4 (90.2% ee) and preparation of the C9-C11 anti-diol moiety by the addition of alkynylzinc reagent 20 to the aldehyde 19. Furthermore, a new diol protecting group, p-silyloxybenzylidene, was developed for the deprotection from densely functionalized substrates under weakly acidic conditions. The protecting group was easily removed in a two-step procedure ((HF)3.Et3N; AcOH-THF-H2O).