Semicontinuity and Quasiconvex Functions

Criteria are derived for quasiconvex functions under lower semicontinuity and upper semicontinuity conditions. The results thus obtained generalize earlier results for convex functions. We also give new conditions under which a given function is r-convex in the sense given by Avriel.     

Synthesis and characterization of poly(dimethylsiloxane‐urethane) elastomers: Effect of hard segments of polyurethane on morphological and mechanical properties

A series of poly(dimethylsiloxane‐urethane) elastomers based on hexamethylenediisocyanate, toluenediisocyanate, or 4,4′‐methylenediphenyldiisocyanate hard segment and polydimethylsiloxane (PDMS) soft segment were synthesized. In this study, a new type of soft‐segmented PDMS crosslinker was synthesized by hydrosilylation reaction of 2‐allyloxyethanol with polyhydromethylsiloxane, using Karstedt's catalyst. The synthesized soft‐segmented crosslinker was characterized by FT‐IR, ¹H, and ¹³C NMR spectroscopic techniques. The mechanical and thermal properties of elastomers were characterized using tensile testing, thermogravimetric analysis, differential scanning calorimetry (DSC), and dynamical mechanical analysis measurements. The molecular structure of poly(dimethylsiloxane‐urethane) membranes was characterized by ATR‐FTIR spectroscopic techniques. Infrared spectra indicated the formation of urethane/urea aggregates and hydrogen bonding between the hard and soft domains. Better mechanical and thermal properties of the elastomers were observed. The restriction of chain mobility has been shown by the formation of hydrogen bonding in the soft and hard segment domains, resulting in the increase in the glass‐transition temperature of soft segments. DSC analysis indicates the phase separation of the hard and soft domains. The storage modulus (E′) of the elastomers was increasing with increase in the number of urethane connections between the hard and soft segments. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 2980–2989, 2006     

Algorithmic analysis of theMAP/PH/1 retrial queue

In this paper the distribution of the maximum number of customers in a retrial orbit for a single server queue with Markovian arrival process and phase type services is studied. Efficient algorithm for computing the probability distribution and some interesting numerical examples are presented.     

Convergence of mixed finite element approximations for the shallow arch problem

Summary The stability and convergence of mixed finite element methods are investigated, for an equilibrium problem for thin shallow elastic arches. The problem in its standard form contains two terms, corresponding to the contributions from the shear and axial strains, with a small parameter. Lagrange multipliers are introduced, to formulate the problem in an alternative mixed form. Questions of existence and uniqueness of solutions to the standard and mixed problems are addressed. It is shown that finite element approximations of the mixed problem are stable and convergent. Reduced integration formulations are equivalent to a mixed formulation which in general is distinct from the formulation shown to be stable and convergent, except when the order of polynomial interpolationt of the arch shape satisfies 1tmin (2,r) wherer is the order of polynomial approximation of the unknown variables.     

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.     

The first example of the C-3 alkylation of indoles with cyclopropyl ketones promoted by CeCl3·7H2O/LiI

Indoles undergo smooth alkylation with cyclopropyl ketones in the presence of the CeCl₃·7H₂O/LiI reagent system in refluxing acetonitrile under neutral conditions to produce the corresponding C-3 substituted indole derivatives in good to high yields and with high selectivity. The use of CeCl₃·7H₂O/LiI makes this method simple, convenient, and cost-effective.     

Potential energy curves: A simple and rapid method

The true potential energy curves for different electronic states of diatomic molecules have been constructed by a simplified and modified form of the Jarmain method. To check the validity of this new procedure potential energy curves are constructed for NO⁺, VO, Si₂, AsO, AsO⁺, PF⁺, CO and Bi₂. The results are in good agreement with the Jarmain, RKRV and Lakshman and Rao methods.     

Structural and electrochemical studies of annealed LiNiVO4 thin films

We prepared stoichiometric lithium nickel vanadate amorphous thin films by using r.f. magnetron sputtering under controlled oxygen partial pressure. The amorphous films were heated at various temperatures, 300–600 °C, for 8 h. The as‐deposited and annealed thin films were characterized by Rutherford backscattering spectroscopy, nuclear reaction analysis, Auger electron spectroscopy, X‐ray diffraction, scanning electron microscopy and atomic force microscopy. The electrochemical behavior of the various films was studied by the galvanostatic method. The cells were tested in a liquid electrolyte at room temperature, with lithium metal used as the counter and reference electrode. The best electrochemical storage value was obtained with the thin film annealed at 300 °C, which showed superior capacity and small capacity loss during cycling. Copyright © 2007 John Wiley & Sons, Ltd.