Sensitivity of trust-region algorithms to their parameters

In this paper, we examine the sensitivity of trust-region algorithms on the parameters related to the step acceptance and update of the trust region. We show, in the context of unconstrained programming, that the numerical efficiency of these algorithms can easily be improved by choosing appropriate parameters. Recommended ranges of values for these parameters are exhibited on the basis of extensive numerical tests. MSC classification: 65K05, 90C26, 90C30     

Reducing system of parameters and the Cohen-Macaulay property

Let R be a local ring and let (x ₁, …, x _r) be part of a system of parameters of a finitely generated R-module M, where r < dim_R M. We will show that if (y ₁, …, y _r) is part of a reducing system of parameters of M with (y ₁, …, y _r) M = (x ₁, …, x _r) M then (x ₁, …, x _r) is already reducing. Moreover, there is such a part of a reducing system of parameters of M iff for all primes P ε Supp M ∩ V _R(x ₁, …, x _r) with dim_R R/P = dim_R M − r the localization M _P of M at P is an r-dimensional Cohen-Macaulay module over R _P. Furthermore, we will show that M is a Cohen-Macaulay module iff y _d is a non zero divisor on M/(y ₁, …, y _d−1) M, where (y ₁, …, y _d) is a reducing system of parameters of M (d:= dim_R M).     

Boundary-Value Problem of Drainage in a Fresh Groundwater Fringe above Saline Groundwater

A multiparameter boundary-value problem of fresh infiltration water seepage in a drained fringe above quiescent saline water is solved in the direct statement and studied in detail.     

Guaranteed-accuracy approximation of reachable sets for a linear dynamic system subject to impulse actions

A method is proposed for approximating the reachable set of a dynamic system with a state space dimension no higher than six-eight considered on a finite time interval. The system is governed by linear differential equations with piecewise constant coefficients and impulse actions specified at prescribed times. The method is based on guaranteed-accuracy polyhedral approximations of reachable sets at researcher-specified times. Every approximation is constructed using the preceding one. A procedure is described for choosing parameters of the method that ensure the required accuracy with close-to-minimal time costs.     

Characterization of semiconductor laser frequency chirp based on signal distortion in dispersive optical fiber

In the paper, the simple method of laser chirp parameters estimation is presented. It is based on measuring time-domain distortions of chirped signal transmitted through dispersive fiber and finding laser chirp parameters by matching measured distortions to calculated ones. Experiments undertaken with 1.55 μm telecommunication grade distributed feedback (DFB) lasers and standard single-mode fiber are described, together with some practical remarks on measurement setup and main conclusions.     

Studies on the Structure and Properties of Cordierite Synthesized by Talc-Magnesite

Homogeneous cordierite has been synthesized at low cost by talc-magnesite and coal gangue as the main raw materials. The mechanism of synthesizing cordierite under such a com- posing system of raw materials, and the effect of temperature on the crystal cell parameters and microstructure and thermal expansion coefficient of cordierite crystal have been studied via testing methods of XRD, SEM, etc. The result shows that the homogeneous cordierite can be synthesized by the systematic composing materials of “talc-magnesite—coal gangue—talc” with heat pre- servation at 1350 ℃ for 1 h; as the keeping time is prolonged, Al3+ and Mg2+ in cordierite crystal are replaced by a few impurity ions such as Fe3+, Fe2+, etc., and the crystal cell parameters of cordierite present an increase trend; as the high-temperature heat preservation is prolonged, the content of glassy phase in the sample is increased, its density is improved, and its thermal expansion coeffi- cient presents an increase trend.     

Industrial multi-stage continuous filtration process: influence of operating parameters

This paper presents a theoretical study of the effects of operating parameters on the behaviour of an industrial crossflow filtration unit. A continuous three stage unit and its application to yeast cell harvesting are considered. A model of standard industrial processing is developed, and the influence of dead volumes, start-up procedure, crossflow and permeation velocities and maximum transmembrane pressure are investigated. Concentration factors are discussed with respect to the effects due to dead volumes.     

Reliable evaluation of temperature-independent parameters in correlation of vapour–liquid equilibrium data

A new algorithm/program has been elaborated for simultaneous processing of different sets of vapour–liquid equilibrium data. The program was tested with six binary hexane + isomeric pentanol systems, each of them measured at three different isobaric conditions and one isothermal system of tert-butyl-methyl-ether + 2-methyl-2-propanol measured at three different temperatures. The correlation uses the maximum likelihood method, taking into account real behaviour of vapour phase. The parameters obtained are valid within the whole temperature range of the data, and are consistent in comparison with those obtained from individual correlations of isobars or isotherms. Results are presented for the Wilson and NRTL equations.     

ZBLAN玻璃中三价铒离子 2H11/2,4S3/2辐射跃迁的量子效率

为了探讨铒离子掺杂材料的激光制冷可能性, 依据测量样品的吸收光谱, 计算了Er3 掺杂的ZBLAN玻璃材料的Judd-Ofelt参数, 得到Ω2=3.01×10-20 cm2, Ω4=1.59×10-20 cm2, Ω6=1.03×10-20 cm2, 进而获得了2H11/2, 4S3/2及其以下各能级间跃迁的跃迁几率、分支比、寿命等数据. 测量了77 K到315 K温度范围内Er3 较强的两个绿色发射2H11/2, 4S3/2→4I15/2的发射谱及荧光寿命. 讨论了2H11/2, 4S3/2这样处于热平衡中的两个能级的量子效率的计算方法, 进而计算了它们的量子效率, 并与其它材料进行了比较.     

气液色谱法研究双—(O,O''''—二正辛基二硫代磷酸酯)合镍(Ⅱ)与五员杂环化合物加合反应的热力学性质

气液色谱法是研究酸碱相互作用热力学性质的有效方法之一,适合于气液表面化学反应的研究,可以得到一些用其他方法难以获得的热力学参数,丰富了表面化学领域的研究,具有重要的理论意义和应用价值。文献[1—4]利用气液色谱法测量了Ni[THDD]_2、Ni[(C_8H_(17)O)_2PS_2]_2与含氮、含氧有机碱加合反应的平衡常数、标准焓变和标准熵变值。作为酸碱加合反应研究的一部份,本文测定了Ni[C_8H_(17)O)_2PS_2]_2与五员杂环化合物呋喃、噻吩和吡咯反应的热力学参数。