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.     

Analysis of anomalous vibrational and rotational distributions in the CN(B2Σ+) state produced in the reaction of Ar(3P0,2) metastables with BrCN

The CN(B²Σ⁺ - X²Σ⁺) tail band emission system for μ′ = 11–20 resulting from the energy transfer reaction Ar(³P_0,2) + BrCN in a flowing afterglow apparatus was measured. The vibrational and rotational distributions were determined as a function of argon pressure. Numerous perturbed rotational lines were observed; analysis of the dependences of these lines on argon pressure, with the aid of experimental information already published, led to the following assignments as to the origins of the perturbations: For μ′ = 11, N′ = 20 and μ′ = 13, N′ = 9, the perturbing state is a ⁴Σ⁺; for μ′ = 12, N′ = 10 and 14, μ′ = 14, N′ = 7 and 10, and μ′ = 17, N′ ≈ 17–19 the perturbing state is A ²Π_i. The perturbed rotational line, μ′ = 11, N′ = 20, is found to be the primary source of intensity in the μ′ =11 vibrational band, but in all other cases the perturbed rotational lines do not significantly aid in the populating of the vibrational state. The anomalously high vibrational populations found in the tail band emission system (μ′ = 12, 14, 17 and 18), as well as the significantly high rotational excitations observed in the μ′ = 12–20 vibrational bands, apparently arise directly from the reaction intermediate.     

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.     

High-order harmonic generation from boron plasma in the extreme-ultraviolet range

We demonstrate the generation of up to the 63rd harmonic (lambda = 12.6 nm) of a Ti:sapphire laser pulse (150 fs, 10 mJ), using a prepulse- (210-ps,24-mJ) produced boron plasma as the nonlinear medium. The influence of various parameters on the harmonic conversion efficiency was analyzed. The steep decrease in intensity for low-order harmonics (up to 19th order) was followed by a plateau. Typical conversion efficiencies were evaluated to be 10(-4) (for a 3rd harmonic) to 10(-7) (within the plateau region). Harmonic generation appeared to be efficient for the plasma that comprised neutral atoms and singly ionized boron.     

Non-destructive analysis of the two subspecies of African elephants, mammoth, hippopotamus, and sperm whale ivories by visible and short-wave near infrared spectroscopy and chemometrics

Visible (VIS) and short-wave near infrared (SW-NIR) spectroscopy was used for non-destructive analysis of ivories. VIS-SW-NIR (500-1000 nm) spectra were measured in situ for five kinds of ivories, that is two subspecies of African elephants, mammoth, hippopotamus, and sperm whale. Chemometrics analyses were carried out for the spectral data from 500 to 1000 nm region. The five kinds of ivories were clearly discriminated from each other on the scores plot of two principal components (PCs) obtained by principal component analysis (PCA). It was noteworthy that the ivories of the two subspecies of African elephants were discriminated by the scores of PC 1. The loadings plot for PC 1 showed that the discrimination relies on the intensity changes in bands due to collagenous proteins and water interacting with proteins. It was found that the scores plot of PC 2 is useful to distinguish between the ivories of the two subspecies of African elephants and the other ivories. We also developed a calibration model that predicted the specific gravity of five kinds of ivories from their VIS-SW-NIR spectral data using partial least squares (PLS)-1 regression. The correlation coefficient and root mean square error of cross validation (RMSECV) of this model were 0.960 and 0.037, respectively.     

Generation of harmonics of femtosecond radiation from the surface of aluminum targets

The results of a study of the generation of harmonics from a laser plasma resulting from the interaction of radiation of femtosecond duration (λ=1.06 μm, t=475 fs, and I～2×10¹⁷ W cm^?2) with aluminum targets are presented. The observed frequency shift of harmonics to the short-wavelength region (1.6 and 5.1 nm for the second and fifth harmonics, respectively) is determined by a collisionless absorption resulting from an anomalous skin effect. The efficiencies of conversion into the second and fifth harmonics in an s-polarized pumping field were lower than the conversion efficiencies in a p-polarized pumping field by a factor of eight and a factor of two, respectively (for intensities I<10¹⁷ W cm^?2). With a further increase in the pumping intensity, these values decreased to 0.8 and 0.5, respectively. The mechanisms of such behavior of the conversion process are considered.     

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).