Analysis of numerical integration in p-version finite element eigenvalue approximation

We study the effect of numerical integration when the p-version of the finite element method is used to approximate the eigenpairs of elliptic partial differential operators. We obtain optimal orders of convergence for approximate eigenvalues and eigenvectors under a certain set of requirements on the quadrature rules employed. This is the same set of conditions that has been shown (in an earlier work) to be sufficient for the optimal approximation of the solutions of the corresponding source problems.     

Polymerization of vinylcarbazole on copper(II)-13X molecular sieves: Role of copper(II) salts

Copper(II)-exchanged-13X molecular sieves, prepared from four copper(II) salts, namely, sulfate, nitrate, chloride, and acetate, and their activities in the polymerization of N-vinylcarbazole at a fixed copper ion exchange level were studied. From the kinetic characteristics of polymerization it was established that the variation in activities of the Cu-exchanged sieves is due primarily to the difference in the pH of the original salt solution, which is responsible for the varying degree of proton exchange with the zeolite during copper ion exchange. A first-order dependence of the rate of polymerization was observed with respect to H⁺ ion concentration of the original copper-salt solution. It was further established that the rate of polymerization of exchanged copper ion, at a hypothetical zero proton concentration, is low. A mechanism of polymerization of NVC on copper-exchanged-13X zeolite was suggested on the basis of the results obtained.     

Kinetics and mechanism of Pb2+ ion promoted aquation of tris-oxalatochromate(III) in acid perchlorate media

Summary In low acid (0.02 M HClO₄) media, Pb²⁺ ion strongly catalyses the aquation of Cr(ox) ₃ ^3– to givecis-Cr(ox)₂(OH₂) ₂ ^– ion. The catalytic efficiency of Pb²⁺ as represented by the second order rate constant, k_pb (3.76 × 10^–4 M^–1 s^–1 at 25 °C; I, 1.0 M perchlorate), for the Pb²⁺ catalysed path is remarkably higher than might be expected on the basis of K_pb-ox, the first formation constant for the lead-oxalate complex. This catalytic superiority of Pb²⁺ has been found to result mainly from a comparatively much lower H (65.2 ±0.8 kJ mol^–1) value which more than compensates for the relatively unfavourable S value (–93.2 ±2.4 JK^–1mol^–1) for this catalysed path. This low S value is, however, in line with the entropy of hydration of Pb²⁺ ion. These facts, together with the different LFER plots, have been utilised to propose a plausible mechanism for such catalysed reactions.     

Crotocaudin; a rearranged labdane type norditerpene from Croton caudatus geisel

The structure and stereochemistry of crotocaudin, a new norditerpene occurring as a minor constituent in Crotoncaudatus Geisel (Euphorbiaceae) have been established as ent-8S,10S-15,16-epoxy-19-norcleroda-4,11,13(16), 14-tetraene 18,6S: 20,12-diolactone 7 from the detailed studies of ¹H NMR spectra using lanthanide shift reagents, decoupling experiments and chemical reactions. The congener, teucvidin, ent-10S-15,16-epoxy-19-norcleroda-4,13(16), 14-triene-18,6S: 20,12R-diolactone 1 was obtained as a major component besides several triterpenoids viz taraxerone 2, taraxerol 3 and taraxeryl acetate 4. ¹³C NMR and ¹H NMR spectra and a few novel reactions of teucvidin and its conversion to teucvin, ent-(6R,12R)-15,16-epoxy-19-nor-9,4-friedolabda-4,13(16),14-triene-18,6:20, 12-diolactone 6 are also reported.     

Crystal and molecular structure of a new biguanide metal complex, [Cu(AMNH)2]Cl2

The crystal structure of C₆H₁₆N₈O₂·CuCl₂, a biguanide metal complex, has been determined by X-ray diffraction data using MoK radiation. The compound crystallizes in the monoclinic space groupP2₁/a, witha=11.074(4),b=12.061(4),c=5.312(3)Å and=102.8(1)°.The structure was solved by direct methods and refined by full-matrix least-squares to a finalR value 0.037 with 1245 unique reflections. The complex molecule is centrosymmetric, with the Cu atom (0.5,0.5,0.5) on a crystallographic center of symmetry. The complex molecule is rhombic planar with a trans configuration.     

Mechanism and kinetics of thermal decomposition of precipitates of the zinc oxide-aluminium oxide system from non-isothermal tg curves

Kinetics of decomposition of the precipitates of the ZnO&2sbndAl₂O₃ system, prepared by coprecipitation and mechanical mixing of the individual precipitates, have been studied. The decomposition of zinc basic carbonate is a first order rate process with an activation energy of 34.5 kcal/mole (Coats and Redfern equation). The decomposition of aluminium hydroxide is also best described as a first order rate process with one break in the Coats and Redfern plot corresponding to activation energies of 29.4 and 8.3 kcal/mole respectively. The entire course of decomposition of coprecipitated as well as mechanically mixed samples cannot be described by any one of the many rate equations available. Consequently, the Coats and Redfern equation has been employed. The plots indicate one or two breaks and thus two to three values of activation energy are reported. From the results it is to be concluded that decomposition of these precipitates is a heterogeneous process. The first step is definitely the decomposition of zinc basic carbonate followed by decomposition of aluminium hydroxide and/or interaction of the two precipitates resulting in the formation of “precursor” to spinel. The results of our earlier investigation on the same system (especially the formation of precursors) are well supported by the results reported in this investigation. p]A new equation (a modified form of the Elovich equation) has been proposed for such heterogeneous decomposition processes. The proposed equation also appears to be the general form of the equations where diffusion is the rate controlling process.     

Studies on catalytic decomposition of CO over transition metal ion (TMI) doped alumina-boria catalyst systems

ESCA and ESR studies on TMI incorporating alumina-boria catalyst systems for CO conversion show the presence of carbidic phase and no valence change of the incorporated copper in the spent catalyst.     

A comparative study on thermoresponsive magnetic nanohydrogels: role of surface-engineered magnetic nanoparticles

A comparative study of thermoresponsive poly(N-isopropylacrylamide)(PNIPAAm)-chitosan (CS)-based magnetic nanohydrogels (MNHGs) encapsulating functionalized Fe₃O₄ nanoparticles (NPs) in terms of the parameters governing their suitability for real hyperthermia is reported. Iron oxide NPs functionalized with (a) citric acid (CA-Fe₃O₄), (b) ethylenediamine (Amine-Fe₃O₄) and (c) dimercaptosuccininc (DMSA-Fe₃O₄) have been synthesized and their encapsulation into MNHGs was obtained through physical encapsulation method. The structural characterizations of synthesized materials include X-ray diffraction, FT-IR, TGA, ICP-AES and X-ray photoelectron spectroscopy (XPS). Encapsulation of the functionalized NPs into MNHGs were observed in TEM micrographs, while SEM and AFM micrographs confirmed their spherical morphology (~250–300 nm). Lower critical solution temperature (LCST) variation was measured by UV–visible spectrophotometer and differential scanning calorimetry (DSC). MNHGs exhibited sufficient magnetization and heating ability for hyperthermia. Typically, hydrogels containing CA-Fe₃O₄ (50 mg/ml) raised the temperature of the medium to 43 °C, a suitable dose for in vivo application in tumor-bearing mice.     

Single amplifier biquad based inductor-free Chua’s circuit

The present paper reports an inductor-free realization of Chua??s circuit, which is designed by suitably cascading a single amplifier biquad based active band pass filter with a Chua??s diode. The system has been mathematically modeled with three-coupled first-order autonomous nonlinear differential equations. It has been shown through numerical simulations of the mathematical model and hardware experiments that the circuit emulates the behaviors of a classical Chua??s circuit, e.g., fixed point behavior, limit cycle oscillation, period doubling cascade, chaotic spiral attractors, chaotic double scrolls and boundary crisis. The occurrence of chaotic oscillation has been established through experimental power spectrum, and quantified with the dynamical measure like Lyapunov exponents.