Algebraic independence results for the values of certain Mahler functions and their application to infinite products

In this paper we establish algebraic independence criteria for the values at an algebraic point of Mahler functions each of which satisfies either a multiplicative type of functional equation or an additive one. As application we construct, using a linear recurrence sequence, an entire function defined by an infinite product such that its values as well as its all successive derivatives at algebraic points other than its zeroes are algebraically independent. Zeroes of such an entire function form a subsequence of the linear recurrence sequence. We prove the algebraic independency by reducing those values at algebraic points to those of Mahler functions.     

Coherent quasi-cw 153 nm light source at 33 MHz repetition rate

We present a quasi-cw laser in a vacuum ultraviolet region at megahertz repetition rate. The narrowband pulses generated from an ytterbium-fiber laser system at 33 MHz repetition rate at the central wavelength of 1074 nm are frequency-converted by successive stages of LiB(3)O(5) crystals and KBe(2)BO(3)F(2) crystals. The generated radiation at 153 nm has the shortest wavelength achieved through phase-matched frequency conversion processes in nonlinear optical crystals to our knowledge.     

Quantum-Like Model for Decision Making Process in?Two Players Game A Non-Kolmogorovian Model

In experiments of games, players frequently make choices which are regarded as irrational in game theory. In papers of Khrennikov (Information Dynamics in Cognitive, Psychological and Anomalous Phenomena. Fundamental Theories of Physics, Kluwer Academic, Norwell, 2004; Fuzzy Sets Syst. 155:4–17, 2005; Biosystems 84:225–241, 2006; Found. Phys. 35(10):1655–1693, 2005; in QP-PQ Quantum Probability and White Noise Analysis, vol. XXIV, pp. 105–117, 2009), it was pointed out that statistics collected in such the experiments have “quantum-like” properties, which can not be explained in classical probability theory. In this paper, we design a simple quantum-like model describing a decision-making process in a two-players game and try to explain a mechanism of the irrational behavior of players. Finally we discuss a mathematical frame of non-Kolmogorovian system in terms of liftings (Accardi and Ohya, in Appl. Math. Optim. 39:33–59, 1999).     

Investigation of adsorption behavior and energy transfer of cationic porphyrins on clay surface at low loading levels by picosecond time-resolved fluorescence measurement

Time-resolved fluorescence and steady-state spectroscopic measurements were performed with +4-charged cationic porphyrins adsorbed on an anionic-type clay (Sumecton SA; SSA) surface at a low molecular loading level (10 % vs. cation-exchange capacity of clay) corresponding to an occupied area of ca 50 nm² per molecule. Absorption spectra indicated no interaction between transition moments of the porphyrins on the clay surface. An efficient energy-transfer process from donor to acceptor porphyrin was observed on the clay surface even under low porphyrin loading conditions. The efficiency of energy transfer obtained from the steady-state measurement was 65 %. Real-time behavior of the porphyrins was successfully captured during energy transfer. The rate constant of the energy transfer obtained from time-resolved fluorescence measurements was found to be 5.3 × 10⁸ s^?1. According to the efficiency and the rate constant, it is proposed that the adsorbed porphyrins did not have a uniform and fixed distribution.     

Novel methodology to control the adsorption structure of cationic porphyrins on the clay surface using the "size-matching rule"

Saponite-type clays that have different cation exchange capacities were successfully synthesized by hydrothermal synthesis. The structure and properties were analyzed by X-ray diffraction, X-ray fluorescence, (27)Al NMR, FT-IR, thermogravimetric and differential thermal analysis, atomic force microscopy, and cation exchange capacity measurement. The intercharge distances on the synthetic saponite (SS) surfaces were calculated to be 0.8-1.9 nm on the basis of a hexagonal array. The complex formation behavior between SS and cationic porphyrins was examined. It turns out that the average intermolecular distance between porphyrin molecules on the SS surface can be controlled, depending on the charge density of the SS. In the case of tetrakis(1-methylpyridinium-4-yl)porphyrin (H(2)TMPyP(4+)), the average intermolecular distances on the SS surface can be controlled from 2.3 to 3.0 nm on the basis of a hexagonal array. It was also found that absorption maxima of porphyrins depend on the charge density of the SS. The adsorption behavior of porphyrin on the SS surface can be rationally understood by the previously reported "size-matching rule". This methodology using host-guest interaction can realize a unique adsorption structure control of the porphyrin molecule on the SS surface, where the gap distance between guest porphyrin molecules is rather large. These findings will be highly valuable to construct photochemical reaction systems such as energy transfer in the complexes.     

Synthetic studies of GKK1032s: the asymmetric synthesis of the decahydrofluorene skeleton via a novel cyclization of silyl enol ether and sequential retro Diels-Alder and intramolecular Diels-Alder reactions

GKK1032s, which were isolated from the culture broth of Penicillium sp. GKK1032, exhibit antitumor activity. We constructed the fully elaborated decahydrofluorene skeleton of GKK1032s. The C-ring was constructed by intramolecular cyclization reaction between a chiral epoxide and silyl enol ether, and the dienophile moiety was introduced concurrently. In addition, the AB-rings were stereoselectively constructed using novel sequential retro Diels-Alder (DA) and intramolecular Diels-Alder (IMDA) reactions. Several further modifications of the IMDA adduct were carried out, leading to the asymmetric synthesis of the desired hydroxyester including nine stereo centers.     

A diffusive sampling device for simultaneous determination of ozone and carbonyls

A new diffusive sampling method for the simultaneous determination of ozone and carbonyls in air has been developed. In this method, silica gel impregnated with a mixture of trans-1,2-bis(2-pyridyl)ethylene (2BPE) and 2,4-dinitrophenylhydrazine (DNPH) is used as the absorbent; further, a porous sintered polyethylene tube (PSP-diffusion filter), which acts as a diffusive membrane, and a small polypropylene syringe (PP-reservoir) for elution of the analytes from the absorbent are used. The carbonyls present in air react with DNPH in the absorbent to form hydrazone derivatives. Concurrently, ozone in the air reacts with 2BPE to form pyridine-2-aldehyde, which immediately reacts with DNPH to form a pyridine-2-aldehyde hydrazone derivative. All the hydrazones derived from airborne carbonyls, including pyridine-2-aldehyde (formed from ozone), are completely separated and analyzed by high-performance liquid chromatography. The sampling rates of ozone (44.6 mL min(-1)) and formaldehyde (72.0 mL min(-1)) are determined by comparison with the rates obtained in an active sampling method. The sampling rates of other carbonyl compounds are calculated from the respective molecular weights according to a rule based on Graham's law. The calculated sampling rates agree with the experimental values. The DSD-BPE/DNPH method is advantageous because it is simple and allows for the simultaneous analysis of ozone and carbonyls.     

Recruitment of enzyme activity in albumin by molecular imprinting

The catalytic activity of bovine serum albumin (BSA) modified physically by molecular imprinting using transition-state analogue (TSA) as a template molecule was studied. The resultant imprinted serum albumin (Imp-BSA) showed the rate acceleration of dehydrofluorination reaction from (4R,4S)-4-fluoro-4-(4-nitrophenyl)butan-2-one ( 1 ) and followed the type of Michaelis-Menten reaction in ethyl acetate solution. The enzymatic activity of Imp-BSA was competitively inhibited by (4R,4S)-4-hydroxy-4-(4-nitrophenyl)butan-2-one ( 4 ).     

One‐Pot Synthesis of Novel Branched Polylactide Through the Copolymerization of Lactide with Mevalonolactone

Polylactide, which is a biodegradable and bio‐absorbable polymer having low immunogenicity and good biocompatibility, has been mainly studied for biomedical applications. Branched polymers have different rheological and mechanical properties compared with their linear counterparts owing to their molecular architectures. We synthesized novel biodegradable polylactide having a branched structure composed of metabolically degradable and/or absorbable materials only. The branched polylactide was obtained from a one‐pot copolymerization of L ‐lactide using metabolic intermediate dl ‐mevalonolactone as a bifunctional comonomer having both lactone ring and pendant hydroxy group. The glass transition point, melting point and crystallinity of the branched polylactide are lower than those of linear polylactide.