Simulation of the nonlinear vibration of a string using the Cellular Automata based on the reflection rule

In this study, the nonlinear dynamic responses of a string are simulated using the Cellular Automata method based on the reflection rule. In the case of nonlinear systems, the velocity of wave propagation is not constant and depends on the amplitude. A new treatment of the dynamic time step is proposed for the Cellular Automata method considering the effect of the propagation velocity. As numerical examples, first, the dynamic responses of a string with linear characteristic are simulated using the Cellular Automata method. A typical resonance curve can be obtained. Second, the dynamic responses of a string with nonlinear characteristic are simulated using the proposed method. Some characteristic types of vibration can be obtained. It is concluded that the linear and nonlinear dynamic responses of a string may be obtained by simulation using the Cellular Automata method.     

Multiple harmonic series related to multiple Euler numbers

In this paper, we define the multiple Euler numbers and consider some multiple harmonic series of Mordell-Tornheim's type, which is a partial sum of the Mordell-Tornheim zeta series defined by Matsumoto. Indeed, we prove a certain reducibility of these series as well as the multiple zeta values.     

Evaluation formulas for Tornheim's type of alternating double series

In this paper, we give some evaluation formulas for Tornheim's type of alternating series by an elementary and combinatorial calculation of the uniformly convergent series. Indeed, we list several formulas for them by means of Riemann's zeta values at positive integers.

     

Existence of solution for Eguchi-Oki-Matsumura equation describing phase separation and order-disorder transition in binary alloys

In this paper we consider the Eguchi-Oki-Matsumura equation which consists of the fourth- and second-order coupled equations of parabolic type. It is shown that this system admits the unique global solution.     

Electron-transfer reactions and functionalization of cytochrome P450cam monooxygenase system in reverse micelles

Enzyme-based electron-transfer reactions involved in the cytochrome P450 monooxygenase system were investigated in nanostructural reverse micelles. A bacterial flavoprotein, putidaredoxin reductase (PdR), was activated and shown to be capable of catalyzing the electron transport from NADH to electron-carrier proteins such as cytochrome b5 (tCyt-b5) and putidaredoxin (Pdx) in reverse micelles. Ferric tCyt-b5 in reverse micelles was effectively converted to its ferrous form by the exogenous addition of separately prepared reverse micellar solution harboring PdR and NADH. The fact that direct interactions of macromolecular proteins should be possible in the reverse micellar system encouraged us to functionalize a multicomponent monooxygenase system composed of the bacterial cytochrome P450cam (P450cam), putidaredoxin (Pdx), and PdR in reverse micelles. The successful camphor hydroxylation reaction catalyzed by P450cam was significantly dependent on the coexistence of Pdx, PdR, and NADH but not H2O2, suggesting that the oxygen-transfer reactions proceeded via a "monooxygenation" mechanism. This is the first report of a multicomponent cytochrome P450 system exhibiting enzymatic activity in organic media.     

Al(Cap)3 as initiator in the anionic polymerization of ε-caprolactam at high temperature

Mechanism for polymerization of ε-caprolactam in the presence of both sodium and aluminum caprolactamate was investigated at 171°C. The role of Al(Cap)₃ as an initiator was revealed. The apparent rate constant of propagation reaction decreased with the increase in the concentration of Al(Cap)₃, as the two different metal salts interact even at 171°C. The activation energy of the overall polymerization reaction with this catalyst system was estimated to be 41.18 kcal/mole.     

Determination of the specific interaction of disubstituted aromatic compounds on hydrous zirconium oxide-loaded porous polymer resin

Summary A porous polymer resin loaded with hydrous zirconium oxide (Zr-gel) was evaluated as a stationary phase for the liquid chromatographic separation of disubstituted aromatic compounds. The prepared Zr-gel was used to separate disubstituted phenols andortho-substituted benzoic acid derivatives in reversed-phase mode. The retention time of catechol was greater than those of other disubstituted phenols; this implies that the Zr-gel has specificity for the phenolic hydroxyl group. The retention behavior ofortho-substituted benzoic acid derivatives on the Zr-gel was also evaluated in reversedphase mode using buffer. Phthalic acid was specifically retained in the vicinity of pH 6.0, which has been regarded as the equal adsorbic point. Similar behavior was also observed for salicylic acid, although the retention time of salicylic acid was less than that of phthalic acid. It seems that the specific retention behavior of hydrous zirconium oxide is a result of complexation with ligands such as hydroxyl and carboxyl groups. The results of this study have revealed that the retention mechanism of hydrous zirconium oxide is a combination of ion exchange and interaction based on complexation with ligands.     

A racemization test in peptide synthesis using 4-(4,6-dimethoxy-1,3,5-triazin-2-yl)-4-methylmorpholinium chloride (DMT-MM)

Racemization of the C-terminal amino acid (Ala) has been studied in various solvents during coupling between 4-methoxybenzyloxycarbonyl (Z(OMe))-Gly-L-Ala-OH and phenylalanine benzyl ester (H-Phe-OBzl) with 4-(4,6-dimethoxy-1,3,5-thiazin-2-yl)-4-methylmorpholinium chloride (DMT-MM). The reaction occurred without substantial racemization in AcOEt, tetrahydrofuran (THF), N,N-dimethylformamide (DMF), CH3CN, and 2-PrOH, while a slight racemization was observed in dimethyl sulfoxide (DMSO), EtOH, and MeOH. The extent of racemization may correlate with the polarity of the solvents.