Anharmonic Oscillator Driven by Additive Ornstein–Uhlenbeck Noise

We present an analytical study of a nonlinear oscillator subject to an additive Ornstein–Uhlenbeck noise. Known results are mainly perturbative and are restricted to the large dissipation limit (obtained by neglecting the inertial term) or to a quasi-white noise (i.e., a noise with vanishingly small correlation time). Here, in contrast, we study the small dissipation case (we retain the inertial term) and consider a noise with finite correlation time. Our analysis is non perturbative and based on a recursive adiabatic elimination scheme a reduced effective Langevin dynamics for the slow action variable is obtained after averaging out the fast angular variable. In the conservative case, we show that the physical observables grow algebraically with time and calculate the associated anomalous scaling exponents and generalized diffusion constants. In the case of small dissipation, we derive an analytic expression of the stationary probability distribution function (PDF) which differs from the canonical Boltzmann–Gibbs distribution. Our results are in excellent agreement with numerical simulations.     

A Lagrangean Relaxation Approach to Course Timetabling

A study of mathematical programming approaches to time-tabling has resulted in the development of an algorithm based on Lagrangean relaxation embedded in a branch and bound procedure. The algorithm is still under development for larger scale problems, but this paper reports on its application to a more modest-sized problem based on published real data.     

Molecular orbital studies on diazine mono and di N-oxides

Pariser-Parr-Pople, iterative extended Huckel, CNDO/2 and MINDO/2 methods have been applied to diazine mono and di N-oxides. Electronic transitions and chemical reactivity of these molecules are explained. Dipole moments, heats of formation and binding energy are calculated.     

Synthesis and characterization of a new resin functionalized with 2-naphthol-3,6-disulfonic acid and its application for the speciation of chromium in natural water

A polystyrene divinyl benzene (8%) copolymer has been functionalized by coupling it through NN group with 2-naphthol-3,6-disulfonic acid (NDSA). The resulting resin has been characterized by elemental analysis, thermogravimetric analysis and infrared spectra. The hydrogen ion, water regain and metal ion capacities of the resin have been determined. Two forms of chromium show different exchange capacities at different pH values, viz. Cr(III) selectively retained at pH 6.5 whereas Cr(VI) retained at pH 1.5. Hence complete separation of the two forms of chromium is possible. The kinetic studies show that the exchange of Cr(III) and Cr(VI) follows second-order kinetics. The metal ion concentration was measured by flame atomic absorption spectrometry. The method has been successfully applied for the speciation of chromium in natural water samples.     

Application of a new resin functionalised with 6-mercaptopurine for mercury and silver determination in environmental samples by atomic absorption spectrometry

Polystyrene–divinylbenzene (8%) has been functionalised by coupling it through an ---N=N--- group with 6-mercaptopurine. The resulting chelating resin has been characterised by using elemental analysis, thermogravimetric analysis and infrared spectra. The resin is highly selective for Hg(II) and Ag(I) and has been used for preconcentrating Hg(II) and Ag(I) prior to their determination by atomic absorption spectrometry. The maximum sorption capacity for Hg(II) and Ag(I) was found to be 1.74 and 0.52 mmol g⁻¹, respectively, over the pH range 5.5–6.0. The calibration range for Hg(II) was linear up to 10 ng ml⁻¹ with a 3σ detection limit of 0.02 ng ml⁻¹; the calibration range for Ag(I) was linear up to 5 μg ml⁻¹ with a detection limit of 29 ng ml⁻¹. The recoveries of the metals were found to be 99.7±3.8 and 101.3±4.1% at the 95% confidence level for both Hg(II) and Ag(I). In column operation, it has been observed that Hg(II) and Ag(I) in trace quantities can be selectively separated from geological, medicinal and environmental samples.     

Induced Correspondence of a Local π‐Aromatic Sextet in Heteroannulenes: Synthesis and Characterization

Acid‐catalyzed [3+3] condensation reactions of two hitherto unknown tripyrrane moieties with pentafluorobenzaldehyde has led to the formation of new generation heteroannulene (4.1.4.1) and mutant heteroannulene (1.1.1.1.1.1). Inclusion of local π‐aromatic sextets, namely the N‐methyl pyrrole rings through β,β‐linkages and α,β‐linkages, has led to the isolation of first ever heteroannulenes cross‐conjugated at four points and two points respectively within the macrocycles.     

Polymer‐supported palladium: A hybrid system for multifunctional catalytic application

Polymer‐supported palladium was synthesized by applying a single‐step wet chemical synthesis route and the resultant composite material was characterized by means of various techniques. Infrared and UV–visible spectra provided information on the chemical structure of the polymer. Microscopy techniques showed the general morphology of the polymer. The oxidation state of palladium was determined using the X‐ray photoelectron spectroscopy method. The synthesized material was applied as a heterogeneous catalyst for the Heck coupling reaction and also as an electrocatalyst for the oxidation of cysteine.     

Kinetics and Mechanism of the Ligand Substitution Reaction of the Di-<Emphasis Type="Italic">μ</Emphasis>-hydroxobis(bipyridyl)dipalladium(II) Ion with some Bio-relevant Ligands

The interaction of di-μ-hydroxobis(bipyridyl)dipalladium(II) with the selected bio-relevant ligands: thioglycolic acid (HL¹), glutathione(HL²) and DL-penicillamine(HL³) has been studied spectrophotometrically in aqueous medium as a function of complex and ligand concentrations, pH, and temperature at constant ionic strength. Two consecutive reaction steps are observed: the first step is dependent on the incoming ligand concentration and the second step which is independent, is assigned to ring closure. The activation parameters, conductivity data and IR data obtained also support the proposed mechanism.     

Invariant Solutions of Inhomogeneous Universe with Electromagnetic Field in Lyra Geometry

The present study deals with the cylindrically symmetric inhomogeneous cosmological models for perfect fluid distribution with electro-magnetic field in Lyra geometry. Lie group analysis has been used to identify the generators (symmetries) that leave the given system of partial differential equations (field equations) invariant. With the help of canonical variables associated with these generators, the assigned system of partial differential equations is reduced to an ordinary differential equations whose simple solutions provide nontrivial solutions of the original system. They obtained a new class of invariant (similarity) solutions by considering the potentials of metric and displacement field are functions of coordinates t and x. The physical behavior of the derived models are also discussed.