ESTIMATES ON THE SOLUTIONS OF CERTAIN HIGHER ORDER FINITE DIFFERENCE EQUATIONS

1IlltroductionLetri(t),i=1,2,-')nbepositivereal-valuedfunctionsdefinedonNo,whereNo={o,1,2,'.}.Forareal-valuedfunctiQnu(t),tENowedefinetheoperatorbbybu(t)=u(t 1)-u(t)andfori22,b'u(t)=b(A'-'u(t))andtheoperatorsLjaredefinedrecursivelybyLou(t)=u(t),Lju(t)=r…     

One‐way analysis of variance with long memory errors and its application to stock return data

Recent empirical results indicate that many financial time series, including stock volatilities, often have long‐range dependencies. Comparing volatilities in stock returns is a crucial part of the risk management of stock investing. This paper proposes two test statistics for testing the equality of mean volatilities of stock returns using the analysis of variance (ANOVA) model with long memory errors. They are modified versions of the ordinary F statistic used in the ANOVA models with independently and identically distributed errors. One has a form of the ordinary F statistic multiplied by a correction factor, which reflects slowly decaying autocorrelations, that is, long‐range dependence. The other is a test statistic such that the degrees of freedom of the denominator in the ordinary F test statistic is calibrated by the so‐called effective sample size. Empirical sizes and powers of the proposed test statistics are examined via Monte Carlo simulation. An application to German stock returns is presented. Copyright © 2007 John Wiley & Sons, Ltd.     

A few practical problems on the application of OD-estimation in motorway networks

In the recent years OD-estimation has become an accepted tool for traffic analysis and control. There are many different OD-estimation models available each of them requiring a strict traffic and network database. In real road network one has to solve many practical problems such as location of detectors, missing of incorrect traffic data, variable route choice, the variability of the OD-matrix and the computing time in large networks. In this paper some results of analysing three different OD-estimators and testing them in a motorway network are presented. Furthermore some problems which arise when carrying out estimations are discussed.     

Multidimensional dependency measures

The problem of dependency between two random variables has been studied throughly in the literature. Many dependency measures have been proposed according to concepts such as concordance, quadrant dependency, etc. More recently, the development of the Theory of Copulas has had a great impact in the study of dependence of random variables specially in the case of continuous random variables. In the case of the multivariate setting, the study of the strong mixing conditions has lead to interesting results that extend some results like the central limit theorem to the case of dependent random variables.In this paper, we study the behavior of a multidimensional extension of two well-known dependency measures, finding their basic properties as well as several examples. The main difference between these measures and others previously proposed is that these ones are based on the definition of independence among n random elements or variables, therefore they provide a nice way to measure dependency.The main purpose of this paper is to present a sample version of one of these measures, find its properties, and based on this sample version to propose a test of independence of multivariate observations. We include several references of applications in Statistics.     

交联高分子网络平衡溶胀化的溶剂依赖性和温度依赖性

对用以表征网络结构非均一性的理论关系作了进一步的分析。理论关系中比例常数k与高分子——溶剂间的相互作用参数χ有关。溶胀的溶剂依赖性和温度依赖性可用统一的α_(溶胀)~3(χ)关系表示。这一关系获得了自由基无规共聚的苯乙烯—二乙烯基苯网络在不同溶剂不同温度下平衡溶胀比实验数据的证实。     

零维多项式组零点的1种直接表示法

给出了零维多项式组所有零点的1种直接表示算法．零点的这种表示方法可避免一般三角化方法引起的误差．此外,该方法较少地依赖符号计算,且核心算法是基于可靠的、数值的区间运算．     

On the calculation of minimum variance estimators for unobservable dependent variables

The determination of minimum variance estimators in an unusual context is considered. The problem arises from an attempt to perform a regression with an unobservable dependent variable. The required minimum variance estimator is shown to satisfy a linear system of equations where the coefficient matrix has a simple structure. Uniqueness of the estimator is established by determining necessary and sufficient conditions on the data which guarantee positive definiteness of this coefficient matrix. Numerical aspects of the method of computation are also briefly explored.     

Synthesis and Characterization of a Trisheteroleptic RuII‐Based Molecular Switch

The synthesis of a trisheteroleptic ruthenium complex [Ru(tb)(dppz)(tmbiH₂)][PF₆]₂ (tb=4,4′‐di‐tert‐butyl‐2,2′‐bipyridine, dppz=dipyrido[3,2‐a:2′,3′‐c]phenazin, tmbiH₂=5,6,5′,6′‐tetramethyl‐2,2′‐bibenzimidazole) is described. In addition, the structural characterisation by means of 1D, 2D ¹H NMR spectroscopy, and mass spectrometry, along with determination of the solid‐state structure of the important precursor Ru(tb)(dppz)Cl₂, supports the proposed octahedral coordination geometry. The capability of tmbiH₂ to form hydrogen bonds is corroborated by the solid‐state structure. The photochemical characteristics of this complex can be described as a combination of the “light switch” effects, which are either attributed to the dppz or to the tmbiH₂ ligand. To illustrate the molecule’s double switchable features, steady‐state absorption and emission measurements were performed, which include the determination of the quantum yield and the pK_a values of the acidic protons of the tmbiH₂ ligand. Notably, the emission lifetimes are sensitive to the solvents used. This phenomenon is due to a proton‐coupled deactivation of the excited metal‐to‐ligand charge transfer (MLCT) state of the complex.     

An evaluation of solid-phase microextraction for analysis of volatile organic compounds in drinking water

Solid-phase microextraction (SPME) has been applied to the quantitative analysis of 60 volatile organic compounds (VOCs) in drinking water. Equilibration curves for the partitioning of the VOCs between the fiber coating and fortified water obtained at 20, 50, and 80 °C are found between the theoretical curves for completely agitated and non-agitated samples. Two important factors for the amount adsorbed by the SPME fiber coating are the extraction time and the fiber coating/water distribution coefficient, K_FW . Both depend on the sample temperature, but in a counteracting manner: Increasing the temperature shortened the equilibration times, especially for the heavier VOCs, but also lead to lower K_FW values, and consequently a lower sensitivity of the method. K_FW values are determined for 33 of the VOCs at 40, 60, and 80°C and the heats of adsorption,–ΔH, are calculated. The nature of the adsorption is found to be exothermic which explains the decreasing sensitivity of the method with increasing temperature. Detection limits were typically from 20 ng/l to 200 ng/l, except for the very light VOCs with which detection difficulties were encountered. For all of the VOCs the linear range extended from the lowest concentration at which they were actually detected to at least 5 mg/l. The precision, 3% average standard deviation when an internal standard was used, was satisfactory for most quantitative routine analysis. SPME was also applied to head-space (HS) analysis of drinking water through the coupled equilibrium between water/head-space/fiber coating. HS-SPME is demonstrated to have shorter equilibration times than SPME directly from the water and equal sensitivities, except for the very light VOCs. Water samples from a drinking water plant contaminated in the low μg/l range with 1,1,1-trichloroethane, trichloroethene and tetrachloroethene were analyzed. There seems to be a reasonable agreement between results obtained by SPME and purge & trap. It is concluded that SPME has a great potential for drinking water analysis.