A Family of Fifth-Order Runge-Kutta Pairs

The construction of a Runge-Kutta pair of order with the minimal number of stages requires the solution of a nonlinear system of order conditions in unknowns. We define a new family of pairs which includes pairs using function evaluations per integration step as well as pairs which additionally use the first function evaluation from the next step. This is achieved by making use of Kutta's simplifying assumption on the original system of the order conditions, i.e., that all the internal nodes of a method contributing to the estimation of the endpoint solution provide, at these nodes, cost-free second-order approximations to the true solution of any differential equation. In both cases the solution of the resulting system of nonlinear equations is completely classified and described in terms of five free parameters. Optimal Runge-Kutta pairs with respect to minimized truncation error coefficients, maximal phase-lag order and various stability characteristics are presented. These pairs were selected under the assumption that they are used in Local Extrapolation Mode (the propagated solution of a problem is the one provided by the fifth-order formula of the pair). Numerical results obtained by testing the new pairs over a standard set of test problems suggest a significant improvement in efficiency when using a specific pair of the new family with minimized truncation error coefficients, instead of some other existing pairs.

     

由单片机AT89C51构成的定时控制系统

介绍了单片机ＡＴ８９Ｃ５１,给出了由ＡＴ８９Ｃ５１构成的定时控制系统,并将此系统与ＣＰＵ８０３１构成的单片机系统比较,具有结构简单、可靠性高的特点．     

五邑大学财务信息系统的设计与实现

基于五邑大学财务管理工作的实际情况,提出了我校财务信息系统的设计思想,包括系统功能模块结构、各模块的主要功能与特点等。并就目前实施现状提出今后的发展计划。     

煤炭院校会计信息系统设计

本论文论述了“煤炭院校会计信息系统”的代码设计、数据库设计和功能设计三项内容,并给出了完整的“煤炭院校会计信息系统”功能模块图。     

Solutions of alkali soaps and water in fatty acids IX. The location of theL 2-phase in three-component systems of sodium soap — fatty acid — water,in view of the occurrence of acid soaps

Previous studies of the occurrence of acid soaps in systems containing a longchain sodium soap and the corresponding fatty acid, and the study of phase equilibria in the system sodium octanoate — octanoic acid — water, performed by our group at the beginning of the 1960s, show that the isotropic liquidL ₂-phase of the last mentioned system in its whole region of existence is situated in that part in which acid soaps occur. This provides an explanation for the fact that theL ₂-phase itself contains acid sodium octanoates in all regions. TheL ₂-phase has its origin in the water-free melt of fatty acid and neutral soap in which these components react with each other under the formation of an acid soap. When water is added to the system, this water-free acid soap is transformed into different hydrated acid soaps. In a large region of concentration, there is an extremely close relation between theL ₂-phase and the liquid-crystalline lamellarD-phase, which itself consists of hydrated acid soaps. At its outermost water-rich tip, theL ₂-phase is in equilibrium with theL ₁-phase of the system, just above the+LAC, that is, with the most dilute aqueous soap solution in which acid soap still may be formed in aqueous environment. Formation of acid soap is a fundamental requirement for the existence of this isotropic liquidL ₂-phase.     

On the stabilizer subgroup of a fair of matrices

Let (F,G) be a pair of matrices defined over an arbitrary field, Fn × n, Gn × m. Consider the natural action of GL_n x GL_m on this pair given by (F,G) ? (gFg^-1,gGh^-1), where (g,h) ∈ GL_n × GL_m. This action is of interest in system theory as well as the representation theory of quivers. In this paper we study the stabilizer subgroup of this action stab(F,G), i.e.

$\text{{(g,h) ∈ GL}{}_{\mathrm{n}}\text{x GL}{}_{\mathrm{m}}\text{|gFg}{}^{-1}\text{= F,gGh}{}^{-1}\text{= G}}$

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Uniform Rice-like CdS Particles Prepared from Water-in-oil Microemulsions

IntroductionNano-sized semiconductors are of great interestdue to their special optical and electronic proper-ties[1,2].As one of the mostimportantⅡ—Ⅵsemicon-ductors,CdS has importantapplications in many fields,such as the solar cell field,non linear o…     

Li2Br(NH2): Das erste ternäre Alkalimetallamidhalogenid

Li₂Br(NH₂): The First Ternary Alkali Metal Amide Halide The pseudobinary system LiNH₂/LiBr was investigated by X-ray methods. The crystal structure of the compound Li₂Br(NH₂) was solved by single crystal data: Li₂Br(NH₂): Pnma, Z = 8, a = 12.484(2) Å, b = 7.959(1) Å, c = 6.385(1) Å, Z(F_o) with (F_o)² ≧ 3σ(F_o)² = 348, Z (parameter) = 51, R/R_w = 0.019/0.021 Li₂Br(NH₂) crystallizes in a new type of structure. To one another isolated chains of [Li₂Li_4/2(NH₂)₂²⁺] show the motif of closest rod packing. They are connected via bromide ions in a distorted cubic primitive arrangement.     

IR-spectral investigation of the structure of glasses in the Fe2O3-V2O5 system

The structure of glasses in the Fe₂O₃-V₂O₅ system in the 0–50 mol% Fe₂O₃ range is studied by IR-spectroscopy. It is found that the introduction of Fe₂O₃ favours the transformation of the VO₅-groups into VO₄ ones. This effect may be shown with the aid of IR-spectra, owing to the fact that these glasses are characterized by two high-frequency bands at 1020 and 930 cm^–1. The first is determined by the vibrations of the short V=O nonbridging bonds in the VO₅-groups, while the second is assigned to the vibrations of the V—O-bonds in deformed VO₄-tetrahedra.

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IR-spektroskopische Strukturuntersuchung von Gläsern des Systems Fe₂O₃-V₂O₅

Zusammenfassung Die Struktur von Gläsern des Systems Fe₂O₃-V₂O₅ in dem Bereich von 0–50 Molprozent Fe₂O₃ wurde mit Hilfe der IR-Spektroskopie untersucht. Zusatz von Fe₂O₃ begünstigt die Umwandlung der VO₅- in VO₄-Gruppen. Das kann in den IR-Spektren durch zwei Banden bei 1020 und 930 cm^–1 festgestellt werden. Die erste wird durch Schwingungen der kurzen V=O-Nichtbrücken-bindungen in den VO₅-Gruppen verursacht, die zweite wird auf Schwingungen der V—O-Bindungen in dem deformierten VO₄-Tetraeder zurückgeführt.

     

浅议会计电算化内部控制制度

本文主要讨论了在会计电算化下，如何从岗位设置、权限配置、操作管理及硬软件等方面加强内部控制制度。