Improved lattice action for Wilson fermions

An improved lattice action for gauge theories with Wilson fermions is presented.     

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.     

Determination of radioactive and stable cobalt in marine biological materials (author's transl)]

Studies were made to develop the method for rapid determination of radioactive and stable cobalt in a single specimen of marine biological materials. The sample was dried, ashed, and dissolved in acid. The cobalt was extracted with 1-nitroso-2-naphthol benzene and determined by absorptiometry on the benzene phase. Then, the organic solution was evaporated to dryness, and the residue was treated with nitric-perchloric acid mixture to decompose any organic matter, and taken up with hydrochloric acid. The cobolt was extracted from the solution with TIO A-toluene, and the radioactive cobalt was determined by liquid scintillation counting on the toluene phase. Examinations were made on the chemical yield and on the decontamination factor of the fission product nuclides. Analysis were made on the marine biological samples of Urazoko Bay, Fukui prefecture. Agreement of the radioactive cobalt data between that by the present method and that by Ge(Li) gamma ray spectometry was good. Also, the stable cobalt value by the present method agreed well with that by neutron activation analysis method.     

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.     

Formation of cyclic organosilicon compounds via organopolysilyl anions starting from methoxymethyldisilanes. A mechanistic study

In the presence of a catalytic amount of sodium methoxide, sym-dimethoxytetramethyldisilane was converted into α,ω-dimethoxypermethylpolysilanes, MeO(SiMe₂)_nOMe where n ? 3, at room temperature. On the other hand, similar treatment of the disilane in THF solution gave cyclic polysilanes, (Me₂Si)_n where n = 5–7. Decomposition of the disilane in the presence of diphenylacetylene afforded a trisilacyclopentene derivative under similar conditions. This compound was obtained also by the reaction between α,ω-dimethoxypermethylpolysilanes and diphenylacetylene in the presence of sodium methoxide. These cyclic products most likely were formed via permethyl polysilyl anion intermediates derived from α,ω-dimethoxypermethylpolysilanes. Also, the formation of α,ω-dimethoxypermethylpolysilanes could be elucidated in terms of the mechanism involving the base-assisted, concerted nucleophilic substitution or stepwise substitution by silyl anions, rather than the successive dimethylsilylene (Me₂Si:) insertion reaction.