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.     

Vanadium(III) chloride catalyzed Biginelli condensation: solution phase library generation of dihydropyrimidin-(2H)-ones

The three component condensation of an aldehyde, a β-keto ester and urea (thiourea) in the presence of a catalytic amount of VCl₃ is disclosed for the solution phase synthesis of dihydropyrimidinones. The ease of synthesis and work-up allowed the parallel synthesis of a 48-membered library of dihydropyrimidinones quickly and efficiently in good yields.     

Variation of interband interaction strength in odd-A nuclei

Bandcrossing in 31 rotational bands of 25 different odd-A nuclei in the rare-earth region has been analysed by using a two-band mixing formalism with a constant band interaction within the framework of the effective decoupling picture. The interband interaction strengthV between the one-quasiparticle band and the three-quasiparticle band exhibits a variation with the neutron number which is not different from the oscillatory behaviour observed in even-even nuclei and does not show signs of any appreciable phase shifting as predicted by theory. However, the overall range of variation ofV is greater than that observed in even-even systems.     

The Ulam number of infinite graphs

The following is a conjecture of Ulam: In any partition of the integer lattice on the plane into uniformly bounded sets, there exists a set that is adjacent to at least six other sets. Two sets are adjacent if each contain a vertex of the same unit square. This problem is generalized as follows. Given any uniformly bounded partitionP of the vertex set of an infinite graphG with finite maximum degree, letP (G) denote the graph obtained by letting each set of the partition be a vertex ofP (G) where two vertices ofP (G) are adjacent if and only if the corresponding sets have an edge between them. The Ulam number ofG is defined as the minimum of the maximum degree ofP (G) where the minimum is taken over all uniformly bounded partitionsP. We have characterized the graphs with Ulam number 0, 1, and 2. Restricting the partitions of the vertex set to connected subsets, we obtain the connected Ulam number ofG. We have evaluated the connected Ulam numbers for several infinite graphs. For instance we have shown that the connected Ulam number is 4 ifG is an infinite grid graph. We have settled the Ulam conjecture for the connected case by proving that the connected Ulam number is 6 for an infinite triangular grid graph. The general Ulam conjecture is equivalent to proving that the Ulam number of the infinite triangular grid graph equals 6. We also describe some interesting geometric consequences of the Ulam number, mainly concerning good drawings of infinite graphs.     

A novel capacitive pressure sensor structure with high sensitivity and quasi-linear responseUne nouvelle structure de capteur de pression capacitif avec haute sensibilitée et réponse quasi-linéaire

This paper describes a new capacitive structure of pressure sensor to increase simultaneously the sensitivity and the linearity of the transducer. This structure contains two capacitors which change in response to pressure, but in opposite senses. To increase even more the sensitivity of each capacitor, the pressure sensitive diaphragm carries a central boss. The optimal position and the length of the boss are also calculated. To cite this article: A. Ettouhami et al., C. R. Mecanique 332 (2004).     

Synthesis of a novel cis-proline-derived cyclic type VI beta-turn mimic via ring-closing metathesis

A cis-proline derived cyclic mimic of a type VI beta-turn is synthesized via a ring-closing metathesis reaction. The solution NMR conformational study indicates that the major conformer of the cyclic peptide adopts a type VIa beta-turn in CDCl(3) and a type VIb beta-turn in DMSO-d(6).     

Reverse turn induced pi-facial selectivity during polyaniline-supported cobalt(II) salen catalyzed aerobic epoxidation of N-cinnamoyl L-proline derived peptides

A novel chemo- and diastereoselective aerobic epoxidation of the N-cinnamoyl peptides catalyzed by polyaniline-supported cobalt(II) salen (PASCOS) is described. The N-cinnamoyl proline derived peptides 1 show a high pi-facial selectivity during these epoxidations. The origin of this diastereoselectivity in 1 has been attributed to (i) the propensity of the N-cinnamoyl proline amide to exist predominantly as trans rotamer in CDCl3, DMSO-d6, and CH3CN medium and (ii) existence of these peptides as organized structures (gamma- and beta-turns) due to the presence of intramolecular hydrogen bonds. An extensive solution NMR and MD simulation study on 1d and 1f indicates that the origin of the high pi-facial selectivity is due to the well-defined gamma- and beta-turns which result in the hindrance of one face of the cinnamoyl double bond in the transition state of the epoxidation reaction.     

A theoretical study of electronic spectra of radical cations of some dihydroxynaphthalenes

Electronic transition energies of radical cations of 1.2-, 1.3-, 1.6-, and 1.7?dihydroxynaphthalenes are calculated using an open-shell SCF method with configuration interaction. The results are critically analyzed and a correlation diagram is given that shows the energy-shift and intensity variation in the electronic transitions when moving from one system to another, thus revealing the characteristic behavior of the transitions depending on the positions of the hydroxyl substituents. An interesting relation connecting the electronic spectroscopy with the UV photoelectron spectroscopy is suggested on the basis of which the first ionization potentials (IPS ) of the substituted aromatic systems can be inferred from the calculated energy of the A-type (HOMO → LUMO ) transitions for their radical cations. Furthermore, the predictability of the IP s is found to be considerably increased with the incorporation of “molecular size” in the regression.     

Oxidative transformation of ciprofloxacin by alkaline permanganate – A kinetic and mechanistic study

This spectroscopic study presents the kinetics and degradation pathways of oxidation of ciprofloxacin by permanganate in alkaline medium at constant ionic strength of 0.04 mol⁻³. Orders with respect to substrate, oxidant and alkali concentrations were determined. Effect of ionic strength and solvent polarity of the medium on the rate of the reaction was studied. The oxidation products were identified by LC-ESI-MS technique. Product characterization of ciprofloxacin reaction mixtures indicates the formation of three major products corresponding to m/z 263, 306, and 348 (corresponding to full or partial dealkylation of the piperazine ring). The piperazine moiety of ciprofloxacin is the predominant oxidative site to KMnO₄. Product analyses showed that oxidation by permanganate results in dealkylation at the piperazine moiety of ciprofloxacin, with the quinolone ring essentially intact. The reaction kinetics and product characterization point to a reaction mechanism that likely begins with formation of a complex between ciprofloxacin and the KMnO₄, followed by oxidation at the aromatic N1 atom of piperazine moiety to generate an anilinyl radical intermediate. The radical intermediates subsequently undergo N-dealkylation. Investigations of the reaction at different temperatures allowed the determination of the activation parameters with respect to the slow step of proposed mechanism. The proposed mechanism and the derived rate laws are consistent with the observed kinetics.