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.     

On the Embedding of Ordered Semigroups into Ordered Group

It was shown in [7] that any right reversible, cancellative ordered semigroup can be embedded into an ordered group and as a consequence, it was shown that a commutative ordered semigroup can be embedded into an ordered group if and only if it is cancellative. In this paper we introduce the concept of L-maher and R-maher semigroups and use a technique similar to that used in [7] to show that any left reversible cancellative ordered L or R-maher semigroup can be embedded into an ordered group.     

Silver(I)-selective coated-wire electrode based on an octahydroxycalix[4]arene derivative.

The performance of octahydroxycalix[4]arene derivative used as a neutral carrier for silver polymeric membrane electrode was studied. The sensor gave a good Nernstian response of 58 +/- 1 mV per decade for silver ion in the activity range 3.3 x 10(-6) to 3.3 x 10(-2) M Ag+. The limit of detection reached 2.1 x 10(-6) M Ag+ and exhibited high selectivity for silver ion against the alkali, alkaline earth and transition metal ions. The sensor can be used in wide pH range from 1.5 to 6.5. The response time of the sensor is less than 20 s. The potentiometric sensor was used as the indicator electrode in the titration of Ag+ ions by sodium chloride solution.     

Approximation diophantienne sur les courbes elliptiques à multiplication complexe

Let $\text{E}$ be an elliptic curve with complex multiplication, defined over $\text{Q}$. We consider linear forms on $\text{Lie}\text{(}\text{E}{}^{\mathrm{n}}\text{)}$ with coefficients in the CM field of $\text{E}$. Within this framework, we present a new measure of linear independence for elliptic logarithms in (logb)(loga)ⁿ. Like recent advances in this domain (works by Ably, David, Hirata-Kohno), our result is best possible in terms of the height of the linear forms (logb) while providing a better estimate in the height of algebraic points considered (loga), removing a term in logloga. To cite this article: M. Ably, É. Gaudron, C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

Rheological properties of polyacrylates used as synthetic road binders

Most adhesives and binders, including bitumen for asphalt mixture production, are presently produced from petrochemicals after the refining of crude oil. The fact that crude oil reserves are a finite resource means that in the future, it may become necessary to produce these materials from alternative and probably renewable sources. Suitable resources of this kind may include polysaccharides, plant oils and proteins. This paper deals with the synthesis of polymer binders from monomers that could, in future, be derived from renewable resources. These binders consist of polyethyl acrylate (PEA) of different molecular weight, polymethyl acrylate (PMA) and polybutyl acrylate (PBA), which were synthesised from ethyl acrylate, methyl acrylate and butyl acrylate, respectively, by atom transfer radical polymerisation. The rheological properties of these binders were determined by means of oscillatory testing using a dynamic shear rheometer and combinations of stress/strain, temperature and frequency sweeps. The results indicate that PEA can be produced to have rheological properties similar to that of ‘soft’ 100/150 penetration grade bitumen, PMA with similar rheological properties to that of ‘hard’ 10/20 penetration grade bitumen, while PBA, due to its highly viscous nature and low dynamic moduli, cannot be used on its own as a binder. The synthetic polymers were found to be thermo-rheologically simple, and the shift factors, used to produce the dynamic moduli master curves, were found to fit an Arrhenius function.     

Oxidation of Aromatic Amines to Quinones by Iodic Acid under Microwave Irradiation in the Presence of Montmorillonite K10 and Silica Gel

A variety of aromatic amines are oxidized to their corresponding quinones in excellent yields by supported iodic acid under microwave irradiation and solvent free conditions.     

Osmium(VIII)-catalyzed oxidation of pentamethylene sulfide

Although pentamethylene sulfide (tetrahydrothiopyran) lacks acidic hydrogen, Os^VIII has been found to catalyze its oxidation by alkaline K₃Fe(CN)₆ to produce 3-hydroxypentamethylene sulfide as the only product. The kinetics reveal first-order dependence on ferricyanide and Os^VIII, and zero order on pentamethylene sulfide and OH^–. The effects of introduced electrolytes, K₄Fe(CN)₆, relative permittivity and temperature have also been studied. On the basis of kinetic evidence, a mechanism that involves anation of the osmium catalyst (sulfide/water interchange) followed by intramolecular proton abstraction, followed by an electron transfer step has been proposed and discussed.     

Studies on the chemical constituents of the South China Sea sponge Phacellia fusca

Three pyrrololactam alkaloids have been isolated from the marine sponge Phacellia fusca Schmidt collected from the South China Sea, and their structures were determined as 1–3 , on the grounds of spectral data. This is the first report of these compounds from this sponge. The structure of 1 was confirmed by X-ray analysis.