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.     

Photosensitized oxygenation of phenylpyruvic acid derivatives as a model for p-hydroxyphenylpyruvate dioxygenase

Dye-sensitized photooxygenation of enol ethers of methyl phenylpyruvates ($\text{3}$) produced diendoperoxides $\text{4}$ in aprotic solvents, whereas in methanol hydroxylated product $\text{6}$ was obtained. The reaction scheme is discussed in comparison uith that for the enzymic transformation.     

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.     

Anisotropic excitonic molecules in CdS and CdSe

Luminescence lines due to excitonic molecules are observed in CdS and CdSe. The line shape is analyzed by taking account of the broadening due to elastic collision. It is pointed out that the anisotropy of the effective hole masses makes the molecular binding energies much larger than evaluated by using the geometrical means of the hole masses.     

Response of an elastically supported plate strip to a moving load

A theoretical analysis is presented of the steady state response of a plate strip constrained elastically along its edges against rotation and translation under the action of a moving transverse line load. Within the classical plate theory the solutions are obtained by using Fourier and Laplace transformation methods with respect to space variables. Numerical results are given for a plate strip with both edges identically constrained and a normal line load of constant intensity travelling along the plate strip with a constant speed. The first five speeds of the applied load for which a resonance effect occurs in the system are plotted as functions of the edge constraint parameters. The profiles of the displacement and the moment of the plate are also shown graphically for several values of the load speed and the edge constraint parameters.     

Combinatorial problems on series-parallel graphs

This paper outlines the results and motivation of the paper [1], in which we showed, in a unified manner, that there exist linear time algorithms for many combinatorial problems defined on the class of series-parallel graphs.     

Spontaneous luminescence due to high density electron-hole plasma in GaAs under nano- and pico-second pulse excitation

Spontaneous luminescence due to high density electron-hole plasma in GaAs is observed at 4.2 K under nano- and pico-second pulse excitation. From the pico-second time-resolved spectra, it is found that the hot carriers are cooled down rapidly within 150 psec, and the changes of spectra are not appreciable in the later stage. One may consider, together with results of the spectral shape analysis, that the electron-hole liquid formation is improbable at least within the time range observed.     

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.