Uniform stability estimates for solutions and their gradients to the Boltzmann equation: A unified approach

As to the Cauchy problem for the spatially inhomogeneous Boltzmann equation with cut-off, we prove uniform stability estimates for solutions and their gradients in a unified and elementary way.     

On the absolute instability of semi-implicit schemes for hydrostatic models

The dependence of the linear stability of two-time-level finite-difference semi-implicit schemes on the choice of reference temperature profile is studied. Particular vertical profiles of the temperature are considered to derive analytical conditions of stability. Analysis is made for general form of different model parameters such as the number of vertical levels and their distribution, the time step size, and the values of the viscosity coefficients. The derived conditions of stability are more restrictive than those for three-time-level schemes, but obtained necessary and sufficient condition for constant vertical lapse rates of the temperature has the form frequently applied to three-time-level schemes: the basic temperature profile should be warmer than the actual one. Performed numerical experiments show that the last restriction is neither necessary nor sufficient condition of stability for general temperature profiles.     

Haar-like expansions and boundedness of a Riesz operator on a solvable Lie group

Consider the group of affine transformations of the line. Denote by X and Y the right-invariant vector fields corresponding to the s and t directions, respectively, and let We prove that the first-order Riesz operator is of weak type (1, 1) with respect to left Haar measure. This operator is therefore also bounded on . Our results provide answers, in a particular instance, to the open question of the boundedness of Riesz operators on Lie groups of exponential growth. The main parts of the proof concern the behaviour of the kernel of the operator at infinity, and exploit cancellation. A key technique is to use expansion with respect to scales of Haar-like functions. Received March 16, 1998; in final form June 22, 1998     

Strong convergence theorem for nonexpansive semigroups in Hilbert space

The purpose of this paper is to prove the strong convergence of a method combining the descent method and the hybrid method in mathematical programming for finding a point in the common fixed point set of a semigroup of nonexpansive mappings in Hilbert space.     

Dsc Evaluations in F.c.c. Solid Solutions of Short-range-order Kinetics As Influenced by Bound Vacancies

A modified first order kinetic law, which describes the roles of bound and unbound vacancies, is proposed in order to predict defect decay and short-range-order kinetics of quenched binary alloys during linear heating experiments. The model has been applied to differential scanning calorimetry (DSC) curves of Cu–5 at%Zn quenched from different temperatures. Activation energy for migration of solute-vacancy complexes was also assessed from the kinetics of short-range-order using DSC traces. A value of 89.5±0.32 kJ mol^–1 was obtained. The relative contribution of bound and unbound vacancies to the ordering process as influenced by quenching temperature was determined. In conjunction, a parametric study of the initial total defect concentration and effective energy for defect migration was performed in order to envisage their influence on the calculated DSC profiles. This revised version was published online in August 2006 with corrections to the Cover Date.     

A new macrolide and glycosides from the stem of Sargentodoxa cuneata

A new macrolide glycoside,cuneataside F was isolated from the n-butanol extract of the stem of Sargentodoxa cuneata. The structure was elucidated on the basis of extensive 1D and 2D NMR as well as HRESI-MS spectroscopic analysis.     

On the computational complexity of cut-reduction

Using appropriate notation systems for proofs, cut-reduction can often be rendered feasible on these notations. Explicit bounds can be given. Developing a suitable notation system for Bounded Arithmetic, and applying these bounds, all the known results on definable functions of certain such theories can be reobtained in a uniform way.     

Graded cellular bases for the cyclotomic Khovanov-Lauda-Rouquier algebras of type A

This paper constructs an explicit homogeneous cellular basis for the cyclotomic Khovanov-Lauda-Rouquier algebras of type A.     

On the category of quotient Banach spaces after Wegner

We study Waelbroeck's category of Banach quotients after Wegner, focusing on its basic homological and functional analytic properties.