On the Robustness of Gaussian Elimination with Partial Pivoting

It has been recently shown that large growth factors might occur in Gaussian Elimination with Partial Pivoting (GEPP) also when solving some plausibly natural systems. In this note we argue that this potential problem could be easily solved, with much smaller risk of failure, by very small (and low cost) modifications of the basic algorithm, thus confirming its inherent robustness. To this end, we first propose an informal model with the goal of providing further support to the comprehension of the stability properties of GEPP. We then report the results of numerical experiments that confirm the viewpoint embedded in the model. Basing on the previous observations, we finally propose a simple scheme that could be turned into (even more) accurate software for the solution of linear systems.     

Polyurethane vascular prostheses in pigs

Microporous, compliant vascular prostheses made from segmented polyurethanes of various molecular stability, have been implanted in the infrarenal aorta of young pigs. Prostheses prepared from a hydrolytically suble polyetherurethane showed a limited patency up to 1 month. Composite prostheses with the wall made from a hydrolytically stable polyurethane and the lumen side prepared from a degradable polyurethane, were patent up to one year. A degradable layer of this composite prosthesis induced the growth of a neo-artery. Prostheses prepared from a degradable polyurethane alone, were substituted within 4 months with a functional neo-artery.Presented in part at the 17th International Biomaterials Symposium, San Diego, California, April 1985.     

Solubility of copper (I) bromide in aqueous solutions of potassium bromide

The solubilities of cuprous bromide were measured at 24.8°C in aqueous KBr and in aqueous KBr-KNO₃ mixtures. The results have been analyzed to give equilibrium constanns from formation of neutral and negatively charged complexes of CuBr, and sets of virial parameters suitable for calculation of activity coefficients for the complexes.     

Analysis of effective service time with age dependent interruptions and its application to optimal rollback policy for database management

A stochastic model is developed describing a service system subject to inhomogeneous Poisson interruptions with age dependent interruption periods. By studying the probabilistic flow of the underlying multivariate Markov process, the Laplace transform of the effective service time is explicitly obtained. For general renewal interruptions, only the expected effective service time is derived. As an application, an optimal checkpoint policy is examined for database management. It is shown that an optimal policy maximizing the ergodic availability of the database is to implement a checkpoint as soon as the cumulative uptime of the database reaches a prespecified constantk ^*. A computational procedure is then developed for findingk ^* and numerical results are exhibited.This work was supported in part by the National Science Foundation under Grant No. ECS-8600992 and by the IBM Program of Support for Education in the Management of Information Systems.     

Global stability of a three-dimensional bio-reactor with inhibition responses

A three-dimensional bio-reactor model of exploitative competition of two predator organisms with inhibition responses for the same renewable organism with reproductive properties is considered. By constructing a modified Lyapunov function and using LaSalle’s invariant principle, it is shown that the lower “break-even” concentration predator organism survives in the competition.      

具有变时滞的离散双向联想记忆神经网络的全局指数稳定性

利用Lyapunov函数和线性矩阵不等式(LMI),给出了判定一类双向联想记忆(BAM)神经网络模型的指数稳定的充分性条件.该条件去掉了以往论文中所要求的激活函数单调,可微分的条件,而且所得结果利用里的工具易于检测.并举例说明本文结果的有效性.     

Water-dispersible hydroxyapatite nanorods synthesized by a facile method

A simple and effective method, using calcium nitrate and triammonium phosphate as starting materials, for the preparation of water-dispersible hydroxyapatite nanorods (HAp) was reported. The process primarily involves the preparation of HAp with the addition of sodium citrate (NaC) and the exchange of absorbed ions (NaC) with sodium hexame taphosphate (NaP). The end products were investigated using various means in order to confirm the particles’ crystal phase and morphology and to understand how to improve their stability. The results demonstrate that the resulting HAp at 90 °C is rod-like with length of 300-400 nm and width of 40-60 nm. The zeta potential values of pure HAp, HAp-NaC, HAp-NaC/NaP are from −15.20, −30.89 to −44.84 mV. The settling time test shows the HAp-NaC/NaP could keep stable above 7 months without any creaming or visible sedimentation. The amount of NaC and the reaction temperature play significant roles in the whole process due to the formation of Ca containing precipitates.     

Periodic orbits around the collinear libration points in the restricted three body problem when the smaller primary is a triaxial rigid body and bigger primary is a source of radiation pressure

Periodic orbits belonging to the stromgren families A, B and C around the collinear libration points in the restricted three body problem have been studied when the smaller primary is a triaxial rigid body and more massive body is a source of radiation pressure. These families are determined in three different cases: (i) classical case, (ii) when bigger primary is a source of radiation pressure, (iii) when smaller primary is a triaxial rigid body and bigger primary is a source of radiation pressure. The Liapunov stability of each periodic solution has also been examined.      

Synthesis of PrBa2Cu4O8 by Solution Method under Ambient Oxygen Pressure

A highly homogeneous and nearly monophasic PrBa₂Cu₄O₈ compound has been synthesized at 1 atm of oxygen via a route employing polymeric ethylenediamine/citric acid precursors. The PrBa₂Cu₄O₈ compound with a trace amount of BaCuO₂ was synthesized for the first time by sintering the pellets at the temperature of 875 °C under ambient oxygen pressure. The temperature coefficient of the resistivity is positive below 190 K while above 190 K is negative. The superconducting transition was not detected down to 4.2 K. Samples were characterized by X-ray diffraction, scanning electron microscopy, thermal analysis, and transport and magnetic measurements.     

THE STABILITY OF LINEAR MULTISTEP METHODS FOR LINEAR SYSTEMS OF NEUTRAL DIFFERENTIAL EQUATIONS

1. IntroductionFor a large class of electrical ~ks containing IOssless transmission lines the describingequations can be reduced to a system of neutral differential equations.This paper deals with the numerical solution of initial value problems for syste…