A well-posed shooting method for transferable DAE's

Summary Consider a TPBVP for transferable nonlinear DAE's. In general the shooting equation has a singular Jacobian. A multiple shooting method which has a nonsingular Jacobian and also produces consistent initial values for the integration is presented. The estimation of the condition of the Jacobian shows the well-posedness of the method. Some illustrative examples are given     

Structure and Catalytic Behaviour of Saponite and Its Cross-Linking Product

Synthetic saponites have been intercalated with hydroxyl aluminium oligomers and characterized with several techniques. The basal 001 peak of the pillared saponite (PS) is 1. 8 nm. The amount of the aluminium in the tctrahedral sheet is correlative with cross-linking density. The sheet-to-pillar linkage mode may be Si-O-AlpⅥ. The acid sites in pillared saponite may locate either at surface of clay or at that of pillar. The cumene conversion is relative to accessible acid sites on the surface of PS. The pillar density in the PS has an effect on the pore structure which is correlative with shape selectivity during the reaction between ethanol and ammonia.     

ON THE EMPTY CONVEX PARTITION OF A FINITE SET IN THE PLANE

The authors discuss the partition of a finite set of points in the plane into empty convex polygons, and improve some upper bound and lower bound in the related enumeration problems.     

基态和激发态氧振动光谱的量子力学计算

利用分子势能函数的Murrell-Sorbie和PG函数形式,将时域有限差分法应用基态和激发态氧分子的振动能级的量子力学计算,计算结果令人满意.     

液体扩散时的折射率分布和扩散系数的测定

本实验提供一种测量透明度或半透明度液体的折射率和扩散系数的方法。此方法可用于食品工业、日用化学工业、石油工业及制药工业部门。     

Multiple scattering of acoustic waves by a half-space of distributed discrete scatterers with modified T-matrix approach

In studying the multiple scattering of acoustic waves by a half-space of distributed discrete scatterers, the quasicrystalline approximation(QCA) approach together with the hole correction (HC) or the pair distribution functions (PDF) have been used extensively, in which a system of simultaneous equations must be solved to determine the effective propagation constant and the expansion coefficients of the coherent exciting field. In this paper, we analyse the same problem under Foldy's approximation (EFA) by using the so-called modified T-matrix approach (MTMA) which was first proposed by Twersky. Two equations in a considerably simple and clear form are obtained for determining the effective propagation constant and the amplitude of the coherent transmitted field, as the scatterers are identical spheres. The numerical results in the low-frequency limit are also discussed in brief.     

Etched facet and semiconductor/air DBR facet of a AlGaInP laser diode prepared by focused ion beam milling

The study of focused ion beam (FIB) milling for making etched facet and semiconductor/air distributed Bragg reflector (DBR) facets of AlGaInP-based red laser diodes (LD) is presented in this letter. For the Ga ion beam current of 100 pA at fixed accelerated voltage 30 kV, FIB milling rate of GaAs was found to be 0.46 μm³/nC. As a trade-off between high reflectivity and enough technical tolerance, the combination of third Bragg orders of semiconductor wall and air gap was chosen. The deeply etched mirror and distributed Bragg reflector facet consisting of pairs of semiconductor wall/air gap on laser diodes (LD) cavity facets with vertical sidewall on AlGaInP LDs were fabricated by focused Ga ion beam milling. Comparison of the AlGaInP LD with the mirrors between cleaved and FIB made facet was given and discussed.     

Abelian varieties over cyclotomic fields with good reduction everywhere

 For every conductor f{1,3,4,5,7,8,9,11,12,15} there exist non-zero abelian varieties over the cyclotomic field Q(ζ _f ) with good reduction everywhere. Suitable isogeny factors of the Jacobian variety of the modular curve X ₁ (f) are examples of such abelian varieties. In the other direction we show that for all f in the above set there do not exist any non-zero abelian varieties over Q(ζ _f ) with good reduction everywhere except possibly when f=11 or 15. Assuming the Generalized Riemann Hypothesis (GRH) we prove the same result when f=11 and 15. Received: 19 April 2001 / Revised version: 21 October 2001 / Published online: 10 February 2003     

CONTINUOUS DEPENDENCE ON THE TERMINAL CONDITION OF SOLUTIONS TO NONLINEAR REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS

In this paper,we derive the continuous dependence on the terminal condition of solutions to nonlinear reflected backward stochastic differential equations involving the subdifferential operator of a lower semi-continuous,proper and convex function under non-Lipschitz condition by means of the corollary of Bihari inequality.