Estimation of the laser beam enabling rectangular processing by the inverse diffraction theory

A small rectangular laser spot has been widely studied for laser processing and laser repair technology. It is usually made by converging the input beam with the lens. Faithful reproduction of the laser spot is dependent on NA of the imaging lens. The small rectangular spot can be obtained by high NA lens, which is limited by many factors, such as high energy loss due to the reflection on the surface, large mass and volume, and strong sensitivity to aberrations and misalignment. On the other hand, the beam cannot be faithfully reproduced because of the diffraction with the low NA lens which has no such the limitations. One of the alternative ways to produce small rectangular profiles by using the low NA lens system is to estimate the input beam profile leading to the output profile of the sharp rectangular shape.     

Polymerization initiated by the charge-transfer complex of styrene and maleic anhydride in the presence of cumene and of cumene and liquid sulfur dioxide

A polymerization was induced with a charge-transfer type of complex consisting of styrene and maleic anhydride in the presence a solvent such as ethyl benzene, cumene, or p-cymene. No polymer was obtained either when the solvent was missing from the polymerization system or when benzene, toluene, or xylene, which are relatively stable to hydrogen abstraction, was added to the polymerization system. An effective initiation, however, took place when cumene or p-cymene, each of which has a labile hydrogen on an α carbon, was added. On the basis of elementary analysis and infrared spectroscopy the formation of copolymer containing substantially equimolar amounts of styrene and maleic anhydride was ascertained. This polymerization was inhibited by the addition of DPPH, suggesting that the system styrene–maleic anhydride–cumene functions much as a conventional free-radical initiator. On the other hand, when a solution of cumene and liquid sulfur dioxide was added to the polymerization system, polystyrene was obtained. This polymerization was inhibited by the addition of a base such as dimethyl-formamide or dimethyl sulfoxide, indicating that the polymerization proceeds through carbonium ion intermediates. The addition of ethyl benzene or of p-cymene brought about the same result as cumene. It is conceivable that the polymerization is induced by the abstraction of hydrogen attached at the α position of cumene by means of the charge-transfer complex of styrene and maleic anhydride.     

Maxwell speed distribution and analogue Hawking–Unruh temperature in an ontological model of a Harmonic oscillator ground state

Within an ontological (hidden variable) model of quantum fluctuation, one can discuss the actual   properties of a system regardless (independent) of measurement. Here we apply an ontological model proposed earlier to investigate a Harmonic oscillator in the quantum mechanical ground state. We first show that the actual speed of the oscillator fluctuates randomly following the Maxwell–Boltzmann distribution. On the other hand, the actual energy obeys a broad Gamma distribution with an average 3?ω/2$3?\omega /2$, where ω$\omega$ is the classical angular frequency, so that one may conclude that the outcome of a single energy measurement reveals the average of the actual energy. The distribution of actual speed (energy) thus formally resembles the distribution of speed (energy) of an ideal gas in thermal equilibrium of temperature T_g=?ω/2$T_g=?\omega /2$. We shall then argue that T_g$T_g$ can be written in a form analogous to the Hawking temperature for a Schwarzschild black hole in which the average distance of the oscillator from the origin plays the analogous role of the radius of the black hole event horizon. It can also be written in a form analogous to the Unruh temperature experienced by a body moving with a uniform acceleration. In the analogy, the oscillator suffers an effective acceleration which balances the attractive force of the trapping Harmonic potential, thus keeps its average position away from the origin.     

Vertex‐disjoint cycles containing specified vertices in a bipartite graph

A minimum degree condition is given for a bipartite graph to contain a 2‐factor each component of which contains a previously specified vertex. © 2004 Wiley Periodicals, Inc. J Graph Theory 46: 145–166, 2004     

SH-wave in a cylindrically anisotropic solid

Propagation of a transient SH-wave in a cylindrically anisotropic elastic solid is considered and an exact closed form solution for a special class of anisotropy is obtained. This is a case where a square root of the shear rigidity ratio is an integer. In this case we find an interesting wave pattern. However, the singularity at the wave front is of the same order as the one in the isotropic solid.     

Biodegradations of block copolymers composed of L- or D,L-lactide and six-membered cyclic carbonates prepared with organolanthanide initiators

Diblock copolymerizations of L - or D,L -lactide (LA) with trimethylene carbonate (TMC) or 2,2-dimethyltrimethylene carbonate (2,2-DTMC) with SmMe(C₅Me₅)₂-(tetrahydrofuran) as an initiator and triblock copolymerizations of L - or D,L -LA/cyclic carbonates/L - or D,L -LA with [Sm(C₅Me₅)₂]₂(PhCCCCPh) as an initiator generated the desired block copolymers. This article describes the comparison of biodegradabilities by proteinase K and a compost and mechanical properties between the resulting di- or triblock copolymers and random copolymers composed of L - or D,L -LA and cyclic carbonates. The scanning electron microscopic profiles of resulting polymers were measured to understand the morphological change during biodegradation. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 3572–3588, 2003     

Bioaccumulation of arsenic and its fate in a freshwater food chain

Accumulation, biomethylation and excretion of arsenic by an autotrophic freshwater alga, and the transport and transformation of the arsenic in the freshwater food chain [alga (autotroph)-moina (planktonic grazer) or shrimp (herbivore)-guppy (carnivore)] were investigated. These experimental results lead to the conclusion that total arsenic concentrations in organisms after accumulation from foods decreased one order of magnitude per elevation of the trophic level and biomethylation of the arsenic increased successively with an elevation in the trophic level. Predominant methylated arsenic species in moina and guppy were dimethyl- and trimethyl-arsenic compounds, respectively. Shrimp accumulated dimethyl- and trimethyl-arsenic compounds in nearly equivalent quantities. No or little monomethylarsenic compound was detected either in herbivores or carnivores.     

Aggregates formation and pH response of mixed dodecyl-terminated copolypeptides containing tryptophan

In this study, two kinds of amphiphilic copolypeptide, C₁₂-poly(N-hydroxyethyl L-glutamine-co-L-tryptophan) (C₁₂-EGT-T) and C₁₂-poly(L-glutamic acid-co-L-tryptophan) (C₁₂-GAT-T) were prepared. By using the mixture of these amphiphilic copolypeptides, pH response of aggregate formation, critical aggregate concentration, the sizes of the aggregates and sustained-release behavior of model substances were investigated. The mixture of the amphiphilic copolypeptides formed aggregates in aqueous medium and showed the ability to uptake model substances such as pyrene and 5-fluorouracil into their hydrophobic moiety. Moreover, pH response was observed in the sustained-release behavior of model substances and the pH region where these properties changed was from pH 7.4 to pH 4.5 in the mixture of C₁₂-EGT-T/C₁₂-GAT-T at 50/50 (mol/mol). These results could be explained by dissociation of trifluoroacetic-acid-treated tryptophan residues in the hydrophilic moieties and destabilization of the aggregates by electrostatic repulsion.