Maximal Lyapunov exponent and rotation numbers for two coupled oscillators driven by real noise

Asymptotic expansions for the exponential growth rate, known as the Lyapunov exponent, and rotation numbers for two coupled oscillators driven by real noise are constructed. Such systems arise naturally in the investigation of the stability of steady-state motions of nonlinear dynamical systems and in parametrically excited linear mechanical systems. Almost-sure stability or instability of dynamical systems depends on the sign of the maximal Lyapunov exponent. Stability conditions are obtained under various assumptions on the infinitesimal generator associated with real noise provided that the natural frequencies are noncommensurable. The results presented here for the case of the infinitesimal generator having a simple zero eigenvalue agree with recent results obtained by stochastic averaging, where approximate ItÔ equations in amplitudes and phases are obtained in the sense of weak convergence.Dedicated to Thomas K. Caughey on the occasion of his 65th birthday.     

Variation of wave impedance of shielded suspended dielectric guide

A shielded suspended dielectric guide is a dielectric rectangular slab enclosed by regular metallic side walls from all the sides. This type of structure is used in dual mode phase shifter where the size of the normal rectangular wave guide is reduced at the ends, where a dielectric material is embeded in ferrite core. Hence impedance variation of a phase shifter at its transition may be easily calculated using shielded suspended dielectric guide which is a prime parameter for optimum efficiency of wave launching.     

Environment-induced decoherence II. Effect of decoherence on Bell''s inequality for an EPR pair

According to Bell's theorem, the degree of correlation between spatially separated measurements on a quantum system is limited by certain inequalities if one assumes the condition of locality. Quantum mechanics predicts that this limit can be exceeded, making it nonlocal. We analyse the effect of an environment modelled by a fluctuating magnetic field on the quantum correlations in an EPR singlet as seen in the Bell inequality. We show that in an EPR setup, the system goes from the usual ‘violation’ of Bell's inequality to a ‘non-violation’ for times larger than a characteristic time scale which is related to the parameters of the fluctuating field. We also look at these inequalities as a function of the spatial separation between the EPR pair.     

Synthesis and spectral studies on nickel(II) complexes of amide group-containing ligands

Summary Complexes of nickel(II) with N-(2-carboxyphenyl)benzamide (CPBH), 2-amino-N-(2-carboxyphenyl)benzamide (ACPBH), N-isoxazolyl benzamide (IB), N-anilinobenzamide (AB), N-(2-pyridyl)-3-carboxypropanamide (PCPA) and N-(2-pyridyl)-2-carboxybenzamide (PCBA) have been isolated and characterized by elemental analyses, magnetic susceptibility measurements, thermal studies, i.r. and electronic spectral studies. The electrochemical behaviour of some complexes has also been investigated.     

Kinetics and mechanism of the oxidation of acetaldehyde by chromic acid in perchloric acid

Summary The oxidation of MeCHO by chromium(VI) has been studied in HClO₄ medium over a wide range of experimental conditions and has been found to obey the rate law;v=k[MeCHO][HCrO ₄ ^– ][H⁺]. The calculated H and-S values for the reaction are 30±2kJ mol^–1 and 171±7J mol^–1deg^–1, respectively. The mechanism is discussed in terms of carbon-hydrogen bond cleavage.     

Platinum carbonyl derived catalysts on inorganic and organic supports: a comparative study

Fumed silica, silica gel, silica-alumina and cross-linked (5.5%) polystyrene have been functionalized with quaternary ammonium groups and the Chini cluster [Pt₁₂(CO)₂₄]²⁻ has been anchored onto these functionalized materials by ion pairing. A catalyst has also been prepared by the adsorption of Na₂[Pt₁₂(CO)₂₄] on unfunctionalized fumed silica. The catalytic activities of the resultant materials, and that of commercially purchased 5% platinum on alumina have been studied for the hydrogenation of a variety of unsaturated compounds. The substrates studied are: α-acetamidocinnamic acid, cyclohexanone, acetophenone, methyl pyruvate, ethyl acetoacetate, nitrobenzene and benzonitrile. Compared to the polystyrene supported catalyst, the inorganic oxide supported catalysts have higher surface areas and for most of the substrates have notably higher activities. The functionalized fumed silica-based catalyst gives higher conversions than functionalized silica gel and silica-alumina-based catalysts. In the hydrogenation of acetophenone and ethyl acetoacetate, the functionalized fumed silica-based catalyst show superior activity compared to the commercial platinum catalyst, and the catalyst made by conventional adsorption method. In benzonitrile hydrogenation with all the cluster-derived catalysts a hydrazine derivative is selectively formed, but when the commercial platinum catalyst is used benzyl amine is the main product.