A Modification of an Algorithm by Golub and Plemmons for Large Linear Least Squares in the Context of Doppler Positioning

This paper considers the solution of the geodetic Doppler multi-stationadjustment, i.e. the problem of computing the positions of severalstations observing the Doppler shift on radio frequencies emittedby several artificial satellites passing over the horizon. Amodification of an algorithm due to Golub and Plemmons, forsolving large linear least-squares problems where the observationmatrix has a block dual angular form, is proposed in this framework.This modification is shown to reduce substantially both datatransfer between the tracking stations and the main computingcentre, and the total computational effort required to obtainthe solution of the problem. Preliminary numerical results arediscussed and some further comments presented.     

Effect of excess Pb on crystallinity and ferroelectric properties of PZT(40/60) films on LaNiO3 coated Si substrates by MOD technique

Pb(Zr_0.4Ti_0.6)O₃ [PZT(40/60)] films were deposited onto LaNiO₃ (LNO) coated Si substrates by metal-organic decomposition (MOD) technique. Excess Pb was incorporated in the film by using excess Pb (2%–15%) in the solution. The crystallinity and ferroelectric properties of PZT films were investigated by using X-ray diffraction (XRD), RT66A test system and HP4194 impedance analyzer, respectively. Rayleigh law was employed to analyze the defect concentration in the films. The results show that all the PZT films show the (1 0 0) preferential orientation with complete perovskite structure except for the 2% film displaying some pyrochlore phase. The (1 0 0) preferential orientation is mainly attributed to LNO bottom electrode, which has the highly (1 0 0) preferential orientation. The 10% film shows the best polarization and dielectric properties. The remnant polarization and coercive field are about 10.1 μC/cm² and 73 kV/cm under an electric field around 330 kV/cm, respectively. And the dielectric constant and dissipation factor are about 656 and 0.022 at a frequency of 1 kHz, respectively. The good ferroelectric properties of the 10% film are mainly attributed to the low defect concentration in the film.     

Generating,scheduling and rostering of shift crew-duties: Applications at the Hong Kong International Airport

In the context of manpower planning, goal programming (GP) is extremely useful for generating shift duties of fixed length. A fixed-length duty consists of a fixed number of contiguous hours of work in a day, with a meal/rest break somewhere preferably around the middle of these working hours. It is such properties that enable the straightforward, yet flexible GP modeling. We propose GP models for an integrated problem of crew duties assignment, for baggage services section staff at the Hong Kong International Airport. The problem is solved via decomposition into its duties generating phase—a GP planner, followed by its GP scheduling and rostering phase. The results can be adopted as a good crew schedule in the sense that it is both feasible, satisfying various work conditions, and “optimal” in minimizing idle shifts.     

A note on the inventory models for deteriorating items with ramp type demand rate

In this research we study the inventory models for deteriorating items with ramp type demand rate. We first clearly point out some questionable results that appeared in (Mandal, B., Pal, A.K., 1998. Order level inventory system with ramp type demand rate for deteriorating items. Journal of Interdisciplinary Mathematics 1, 49–66 and Wu, K.S., Ouyang, L.Y., 2000. A replenishment policy for deteriorating items with ramp type demand rate (Short Communication). Proceedings of National Science Council ROC (A) 24, 279–286). And then resolve the similar problem by offering a rigorous and efficient method to derive the optimal solution. In addition, we also propose an extended inventory model with ramp type demand rate and its optimal feasible solution to amend the incompleteness in the previous work. Moreover, we also proposed a very good inventory replenishment policy for this kind of inventory model. We believe that our work will provide a solid foundation for the further study of this sort of important inventory models with ramp type demand rate.     

交比和Poincaré度量在平面拟共形映射下的偏差

研究了交比和Poincaré度量在平面拟共形映射下的偏差估计,得到了如下两个结果(1)若f是■~2到■~2上的k-拟共形映射,则对任意x_1,x_2,x_3,x_4∈■~2有16~((1/k)-1)(|(x_1,x_2,x_3,x_4)| 1)~(1/k)■|(f(x_1),f(x_2),f(x_3),f(x_4))| 1 ■16~(k-1)(|(x_1,x_2,x_3,x_4)| 1)~k;(2)若f是R~2到R~2上的k-拟共形映射,D是R~2中的任一真子域,则对任意x_1,x_2∈D有(1/k)λ_D(x_1,x_2) 4((1/k)-1)log 2■λ_(f(D))(f(x_1),f(x_2)) ■kλ_D(x_1,x_2) 4(k-1)log 2.