Multiple Coverings of the Plane with Triangles

We prove that any 43-fold covering of the plane with translates of a triangle can be decomposed into two coverings.     

The uv-Decomposition on a Class of D.C. Functions and Optimality Conditions

In this paper,the UV-theory and P-differential calculus are employed to study second-order ex-pansion of a class of D.C.functions and minimization problems.Under certain conditions,some properties ofthe U-Lagrangian,the second-order expansion of this class of functions along some trajectories are formulated.Some first and second order optimality conditions for the class of D.C.optimization problems are given.     

Continuous dependence on the geometry and on the initial time for a class of parabolic problems I

In this paper, we investigate the continuous dependence on the geometry and the initial time for solutions u( x , t) of a class of nonlinear parabolic initial‐boundary value problems. Copyright © 2007 John Wiley & Sons, Ltd.     

Mathematical modelling and analytical solution for workpiece temperature in grinding

This paper deals with modelling the workpiece temperature field produced during the grinding process. The proposed model is given in terms of a two-dimensional boundary-value problem where the interdependence among the grinding wheel, the workpiece and the coolant is described by two variable functions in the boundary condition. An explicit integral form solution is constructed using the Laplace and Fourier transforms and the Green’s function method.     

Observation of spontaneous pattern with six-fold symmetry in disk-shaped ZnO complex microstructures

Using a simple vapor phase transport technique, we have fabricated unique complex disk-shaped ZnO microstructures comprising a small disk coaxially grown on a large one and observed spatially perfect six-fold symmetric patterns. The observed results can be explained based on the spontaneous nanoindentation (NI) effect under the geometric constraints and the explanation can be extended to fathom the growth mechanism of other highly symmetrical ZnO nanostructures. Our results indicate that NI not only can elucidate the mechanical properties of surfaces and thin films but also is an effective approach to fabricate ordered nanostructures with high precision on the location of the building blocks. PACS 81.16.Rf; 81.07.-b; 81.05.Dz     

Preparation of MgB<Subscript>2</Subscript>/Fe superconductor wire by electrical self-heating

MgB₂/Fe wires were prepared by electrical self-heating of in situ powder-in-tube wires for the first time at ambient conditions. Characterization of the wires processed at 750 °C, 800 °C and 850 °C for 15 min by XRD, SEM, ϱ–T, susceptibility and J_C measurements shows that the MgB₂ formed is of high quality particularly with respect to phase purity and transport J_C. The method considerably reduces the overall energy consumption vis-à-vis the production cost, simplifies the complexity of the fabrication procedure and is promising for manufacture of high-quality MgB₂ superconducting wires. PACS 74.70.Ad; 74.62.Bf; 74.25.Fy; 74.25.Ha; 81.20.Hy     

An improved synthesis of isonitrosoacetanilides

A novel two-step synthesis of isonitrosoacetanilides [2-(hydroxyimino)-N-phenylacetamides] has been developed, involving the initial acylation of aniline derivatives with 2,2-diacetoxyacetyl chloride, followed by reaction with hydroxylamine hydrochloride. The method works equally well with a variety of different aniline derivatives, including those with poor aqueous solubility and those containing electron rich ortho-substituents, neither of which react well under traditional conditions.     

Control of the block copolymer morphology in templated epoxy thermosets

It has been found that by the addition of low concentrations of an amphiphilic block copolymer to an epoxy resin, novel disordered morphologies can be formed and preserved through curing. This article will focus on characterizing the influence of the block copolymer and casting solvent on the templated morphology achieved in the thermoset sample. The ultimate goal of this work is to determine the parameters that would control the microphase morphology produced. Epoxy resins blended with a series of amphiphilic block copolymers based on hydrogenated polyisoprene (polyethylene-alt-propylene or PEP) and polyethylene oxide (PEO), specifically, were investigated. In this article, the cure-induced order–order phase transition from the spherical to wormlike micelle morphology will also be discussed. It is proposed that the formation of the wormlike micelle structure from the spherical micelle structure is similar to the phase transition behavior that occurs in dilute block copolymer solutions as a function of the influence of the solvent on micelle morphology. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 3338–3348, 2007     

The Transport Properties of the Cell Membrane Ion Channels in Electric Fields: Bethe Lattice Treatment

The interactive two-state model of cell membrane ion channels in an electric field is formulated on the Bethe lattice by means of the exact recursion relations. The probability of channel opening or maximum fractions of open potassium and sodium channels are obtained by solving a non-linear algebraic equation. Using known parameters for the conventional mean-field theory the model gives a good agreement with the experiment both at low and high trans-membrane potential values. For intermediate voltages, the numerical results imply that collective effects are introduced by trans-membrane voltage.