A method to trace sharp interface of two fluids in calculations involving shocks

A numerical method that can treat a contact discontinuity as a sharp discontinuity is proposed by introducing a density function. The surface of the density function representing the discontinuity can be described with alomost one grid on an Eulerian formulation throughout the calculation even if the surface distortion is large. The algorithm is based on the CIP (cubic-interpolated propagation) method combined with variable transformation. Smearings of the discontinuity are overcome without using any special treatment to the surface. Dependent variables on both sides of the surface are computed in a normal procedure. The present scheme is applied both to a compressible flow and quasi-incompressible flow accompanying shock discontinuities. The result exhibits advantages of this method in robustness and efficiency.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Global Convergence Properties of Nonlinear Conjugate Gradient Methods with Modified Secant Condition

Conjugate gradient methods are appealing for large scale nonlinear optimization problems. Recently, expecting the fast convergence of the methods, Dai and Liao (2001) used secant condition of quasi-Newton methods. In this paper, we make use of modified secant condition given by Zhang et al. (1999) and Zhang and Xu (2001) and propose a new conjugate gradient method following to Dai and Liao (2001). It is new features that this method takes both available gradient and function value information and achieves a high-order accuracy in approximating the second-order curvature of the objective function. The method is shown to be globally convergent under some assumptions. Numerical results are reported.     

DIBAL-mediated reductive transformation of trans-dimethyl tartrate acetonide into ε-hydroxy α,β-unsaturated ester and its derivatives

Stepwise, selective DIBAL reduction of the acetonide diester derived from tartaric acid followed by the Horner-Emmons reaction effectively provided desymmetrized hydroxy mono-olefination products in a one-pot operation.     

Semi-orthogonal decomposability of the derived category of a curve

We show that the bounded derived category of coherent sheaves on a smooth projective curve except the projective line admits no non-trivial semi-orthogonal decompositions.     

Organic molecular beam deposition combined with a laser-induced chemical reaction

Received: 12 March 1998/Accepted: 15 March 1998     

The relation of various metabolic bone markers in renal hemodialysis patients classified by serum estradiol levels

The bone metabolic markers showed the significant differences in age and sex of the hemodialysis patients with renal insufficiency. It is likely that the evaluations of bone change and biochemical metabolic markers should be based on serum estradiol level, sex and age of the renal hemodialysis patients.