The Ring of Invariants of Three (3 × 3)-Matrices over a Field of Prime Characteristic

We find a minimal system of generators and a homogeneous system of parameters for the algebra of invariants of three matrices of third order over a field of an arbitrary characteristic.     

On the dynamic electromechanical loading of dielectric elastomer membranes

Dielectric elastomer actuators (DEAs) have received considerable attention recently due to large voltage-induced strains, which can be over 100%. Previously, a large deformation quasi-static model that describes the out-of-plane deformations of clamped diaphragms was derived. The numerical model results compare well with quasi-static experimental results for the same configuration. With relevance to dynamic applications, the time-varying response of initially planar dielectric elastomer membranes configured for out-of-plane deformations has not been reported until now. In this paper, an experimental investigation and analysis of the dynamic response of a dielectric elastomer membrane is reported. The experiments were conducted with prestretched DEAs fabricated from 0.5 mm thick polyacrylate films and carbon grease electrodes. The experiments covered the electromechanical spectrum by investigating membrane response due to (i) a time-varying voltage input and (ii) a time-varying pressure input, resulting in a combined electromechanical loading state in both cases. For the time-varying voltage experiments, the membrane had a prestretch of three and was passively inflated to various predetermined states, and then actuated. The pole strains incurred during the inflation were as high as 25.6%, corresponding to slightly less than a hemispherical state. On actuation, the membrane would inflate further, causing a maximum additional strain of 9.5%. For the time-varying pressure experiments, the prestretched membrane was inflated and deflated mechanically while a constant voltage was applied. The membrane was cycled between various predetermined inflation states, the largest of which was nearly hemispherical, which with an applied constant voltage of 3 kV corresponded to a maximum polar strain of 28%. The results from these experiments reveal that the response of the membrane is a departure from the classical dynamic response of continuum membrane structures. The dynamic response of the membrane is that of a damped system with specific deformation shapes reminiscent of the classical membrane mode shapes but without same-phase oscillation, that is to say all parts of the system do not pass through the equilibrium configuration at the same time. Of particular interest is the ability to excite these deformations through a varying electrical load at constant mechanical pressure.     

Activation energies for metastable to stable phase transition of 4,4'-di-n-heptyl- oxyazoxybenzene

Complexes of adenine, AdH, with cobalt, nickel and copper chlorides were prepared and their thermodynamic functions were determined. The complexing processes are endothermic in nature. The thermal behaviour of complexes was followed up by using TG and DTA analyses. The stoichiometry of thermal decomposition of the investigated complexes was suggested. This revised version was published online in August 2006 with corrections to the Cover Date.     

Synthesis and optical properties of tetraphenylmethane-based tetrahedral fluorescent compounds and their water-soluble PEG-linked polymers

The synthesis and optical properties of tetrahedral fluorescent compounds comprising of tetraphenylmethane as the core and oligothiophenes as the chromophoric arms, and their water-soluble poly(ethylene glycol)-linked polymers are reported.     

Sterically stabilized emulsion polymerization of styrene: Pseudo‐semicontinuous approach

The sterically stabilized emulsion polymerization of styrene initiated by a water‐soluble initiator at different temperatures has been investigated. The rate of polymerization (R_p) versus conversion curve shows the two non‐stationary‐rate intervals typical for the polymerization proceeding under non‐stationary‐state conditions. The shape of the R_p versus conversion curve results from two opposite effects—the increased number of particles and the decreased monomer concentration at reaction loci as the polymerization advances. At elevated temperatures the monomer emulsion equilibrates to a two‐phase or three‐phase system. The upper phase is transparent (monomer), and the lower one is blue colored, typical for microemulsion. After stirring such a multiphase system and initiation of polymerization, the initial coarse polymer emulsion was formed. The average size of monomer/polymer particles strongly decreased up to about 40% conversion and then leveled off. The initial large particles are assumed to be highly monomer‐swollen particles formed by the heteroagglomeration of unstable polymer particles and monomer droplets. The size of the “highly monomer” swollen particles continuously decreases with conversion, and they merge with the growing particles at about 40–50% conversion. The monomer droplets and/or large highly monomer‐swollen polymer particles also serve as a reservoir of monomer and emulsifier. The continuous release of nonionic (hydrophobic) emulsifier from the monomer phase increases the colloidal stability of primary particles and the number of polymer particles, that is, the particle nucleation is shifted to the higher conversion region. Variations of the square and cube of the mean droplet radius with aging time indicate that neither the coalescence nor the Ostwald ripening is the main driving force for the droplet instability. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 804–820, 2003     

Sensitivity of trust-region algorithms to their parameters

In this paper, we examine the sensitivity of trust-region algorithms on the parameters related to the step acceptance and update of the trust region. We show, in the context of unconstrained programming, that the numerical efficiency of these algorithms can easily be improved by choosing appropriate parameters. Recommended ranges of values for these parameters are exhibited on the basis of extensive numerical tests. MSC classification: 65K05, 90C26, 90C30     

Structural and electrical properties of crystalline (1−x)Ta2O5−xTiO2 thin films fabricated by metalorganic decomposition

Polycrystalline (1−x)Ta₂O₅−xTiO₂ thin films were formed on Si by metalorganic decomposition (MOD) and annealed at various temperatures. As-deposited films were in the amorphous state and were completely transformed to crystalline after annealing above 600 °C. During crystallization, a thin interfacial SiO₂ layer was formed at the (1−x)Ta₂O₅−xTiO₂/Si interface. Thin films with 0.92Ta₂O₅–0.08TiO₂ composition exhibited superior insulating properties. The measured dielectric constant and dissipation factor at 1 MHz were 9 and 0.015, respectively, for films annealed at 900 °C. The interface trap density was 2.5×10¹¹ cm⁻² eV⁻¹, and flatband voltage was −0.38 V. A charge storage density of 22.8 fC/μm² was obtained at an applied electric field of 3 MV/cm. The leakage current density was lower than 4×10⁻⁹ A/cm² up to an applied electric field of 6 MV/cm.     

Mössbauer study on LiFePO4 cathode material for lithium ion batteries

Crystalline LiFePO₄ has been synthesized using solid-state, spray pyrolysis, and wet chemical methods. The crystal parameters were obtained from Rietveld’s refinement methods of the X-ray diffraction patterns. A detailed investigation of the Fe valency carried out using Mössbauer spectroscopy at room temperature indicates that Fe is predominantly present in its bivalent state.     

Numerical analysis of a model of cure process for composites

We consider a composite material composed of fibres included in a resin which becomes solid when it is heated up (reaction of reticulation). The mathematical modelling of the cure process is given by a kinetic equation describing the evolution of the reaction of reticulation coupled with the heat equation. In this paper, we are interested in the computation of approximate solutions. We propose a family of discretized problems depending on two parameters (β₁, β₂) ε [0, 1]² which split the linear and non‐ linear terms in implicit and explicit parts. We prove the stability and convergence of the discretization for any (β₁, β₂) ε [½, 1 ] × [0, 1]. We present also some numerical results. Copyright © 2006 John Wiley & Sons, Ltd.     

Reducing system of parameters and the Cohen-Macaulay property

Let R be a local ring and let (x ₁, …, x _r) be part of a system of parameters of a finitely generated R-module M, where r < dim_R M. We will show that if (y ₁, …, y _r) is part of a reducing system of parameters of M with (y ₁, …, y _r) M = (x ₁, …, x _r) M then (x ₁, …, x _r) is already reducing. Moreover, there is such a part of a reducing system of parameters of M iff for all primes P ε Supp M ∩ V _R(x ₁, …, x _r) with dim_R R/P = dim_R M − r the localization M _P of M at P is an r-dimensional Cohen-Macaulay module over R _P. Furthermore, we will show that M is a Cohen-Macaulay module iff y _d is a non zero divisor on M/(y ₁, …, y _d−1) M, where (y ₁, …, y _d) is a reducing system of parameters of M (d:= dim_R M).