On the uniform decay for the Korteweg–de Vries equation with weak damping

The aim of this work is to consider the Korteweg–de Vries equation in a finite interval with a very weak localized dissipation namely the H^?1‐norm. Our main result says that the total energy decays locally uniform at an exponential rate. Our analysis improves earlier works on the subject (Q. Appl. Math. 2002; LX (1):111–129; ESAIM Control Optim. Calculus Variations 2005; 11 (3):473–486) and gives a satisfactory answer to a problem suggested in (Q. Appl. Math. 2002; LX (1):111–129). Copyright © 2007 John Wiley & Sons, Ltd.     

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.     

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     

Shape transition from InAs quantum dash to quantum dot on InP(3 1 1)A

We report on the shape transition from InAs quantum dashes to quantum dots (QDs) on lattice-matched GaInAsP on InP(3 1 1)A substrates. InAs quantum dashes develop during chemical-beam epitaxy of 3.2 monolayers InAs, which transform into round InAs QDs by introducing a growth interruption without arsenic flux after InAs deposition. The shape transition is solely attributed to surface properties, i.e., increase of the surface energy and symmetry under arsenic deficient conditions. The round QD shape is maintained during subsequent GaInAsP overgrowth because the reversed shape transition from dot to dash is kinetically hindered by the decreased ad-atom diffusion under arsenic flux.     

Synthesis of alkenes from tertiary esters utilizing the triphenylphosphine-iodine system

The treatment of tertiary esters with triphenylphosphine and iodine under mild conditions gives the most stable alkene in good yield. Formates, acetates and trifluoroacetates were studied.     

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.     

Comment on “The Free Will Theorem”

In a recent paper Conway and Kochen, Found. Phys. 36, 2006, claim to have established that theories of the Ghirardi-Rimini-Weber (RW) type, i.e., of spontaneous wave function collapse, cannot be made relativistic. On the other hand, relativistic GRW-type theories have already been presented, in my recent paper, J. Stat. Phys. 125, 2006, and by Dowker and Henson, J. Stat. Phys. 115, 2004. Here, I elucidate why these are not excluded by the arguments of Conway and Kochen.