Structural entailment

We give a number of characterizations of structural entailment. In particular, we show that an alter ego structurally entails an algebraic relation s on a finite algebra if and only if s can be obtained via a local construct from . We show, via a range of applications, that, whereas entailment is important in the study of dualisability, structural entailment is important in the study of full and strong dualisability. We also give an application to the transfer of strong dualities that connects this paper to our earlier paper [9] on full versus strong duality. Received June 27, 2003; accepted in final form May 12, 2005.     

The morphology of α-Al2O3 and α-Fe2O3: The importance of surface relaxation

Current methods for predicting crystal morphology from structure ignore the fact that real crystal surfaces are not necessarily exact terminations of the bulk structure. Instead, surfaces relax and in so doing minimise the total surface energy. This lowering of the surface energy and its influence on crystal morphology are here calculated and illustrated for α-Al₂O₃ (corundum) and α-Fe₂O₃ (haematite). The results are compared with previous studies based on Hartman-Perdok theory.     

Trace gold determination by on-line preconcentration with flow injection atomic absorption spectrometry

A reverse-phase extraction column method has been employed as an on-line preconcentration technique for trace gold analysis by flame atomic absorption spectrometry. Di(methylheptyl)methyl phosphonate (DMHMP) loaded onto a macroporous resin was used as the immobilized phase. A thiourea-HCl solution was found successful in eluting the gold. The experimental parameters were optimized by Simplex Optimization, with 17 tests needed to obtain optimal conditions. Sensitivities of 5.2 mug/l. and 2.3 mug/l., with sample frequencies of 45/hr and 48/hr, were obtained by using single and dual-columns respectively. The recoveries for mixed composition samples were 93-110%.     

库仑加线性位基态解析解

应用新发展的单一轨迹积分方法求解库仑加线性位的基态量子波函数,得到基态能量和波函数的一般解析表达式,并讨论了解的收敛性.应用此方法讨论了重夸克偶素系统.     

Existence and Uniqueness of Fixed Points for Markov Operators and Markov Processes

This paper concerns a Markov operator T on a space L₁, and aMarkov process P which defines a Markov operator on a spaceM of finite signed measures. For T, the paper presents necessaryand sufficient conditions for:

a the existence of invariant probabilitydensities (IPDs)

b the existence of strictly positive IPDs,and

c the existence and uniqueness of IPDs.

Similar resultson invariant probability measures for P are presented. The basicapproach is to pose a fixed-point problem as the problem ofsolving a certain linear equation in a suitable Banach space,and then obtain necessary and sufficient conditions for thisequation to have a solution. 1991 Mathematics Subject Classification:60J05, 47B65, 47N30.     

Laser performance studies of para-(phenylene-ethynylene) polymers in organic solvents

The lasing performance of the polymers poly(2,5-dioctadecyloxy-paraphenylene-ethynylene-co-2,5-thienyl) (OPT) and poly(2,5-dioctadecyloxy-paraphenylene-ethynylene-co-2,5-pyridinyl) (OPP) in organic solvents was studied. A two-mirror resonator was transversally pumped using single pulses of the second harmonic of a mode-locked ruby laser. OPT in tetrahydrofuran lased in the region from 480 nm to 525nm and OPP in tetrahydrofuran showed laser action in the region from 460 nm to 490nm. The polymer solutions are characterized by absorption and fluorescence spectroscopic analysis. Effective stimulated emission cross-sections are reported. High excited-state absorption cross-sections and residual ground-state absorption reduce the lasing efficiency. This revised version was published online in November 2006 with corrections to the Cover Date.