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The purpose of this paper is to discuss the necessary condition of the relative error between continuous function transformation after inverse transformation and original sequence is not larger than the relative error between transformed sequence and its corresponding simulation sequence.

First, explore the function transformation feature of after inverse transformation the relative error not enlarged, then combine this feature with the function transformation feature of not enlarge the class ratio dispersion, not reduce the smoothness which author have got, and obtain a kind of special transformation that not enlarge class ratio dispersion, not reduce the smoothness and after inverse transformation keep the relative not enlarged. Meanwhile, offer the concrete form of this special function type to monotone increasing continuous function transformation and monotone decreasing continuous function transformation, respectively, and study its properties.

This paper finds the concise and important feature of monotonically increasing function transformation after inverse transformation whether the relative error enlarge or not is at first, the concise and important feature of monotonically decreasing function transformation after inverse transformation relative error not enlarged is. And find that the ideal function transformation which both reduces class ratio dispersion strictly and keeps error of inverse transformation not enlarged is non-exist for monotone increasing function transformation and monotone decreasing function transformation.

Use the necessary condition given by this paper, it may use to judge whether function transformation can keep relative error of inverse transformation not enlarged by easy data calculation before build modeling, therefore, choose the best function transformation. These results tell the authors: the paper cannot treat any functions as the same that whether the relative error of inverse transformation will not enlarge (or not reduced), but the authors should divide them into two parts to discuss that it will be expanded in some range or be reduced in some range. It will affect the future direction of the research, not to find the function transform both satisfies the class ratio dispersion reduced and keep the relative error of inverse transformation not enlarged, but to study which kind of function transform will narrow class ratio dispersion in some range, after the modeling accuracy improvement, but after the inverse transformation the relative error enlarged, and at this time the simulation accuracy is still higher than the simulation accuracy of original data modeling directly. Which kind of function transform will expand class ratio dispersion in some range, after the modeling accuracy diminution, but after the inverse transformation the relative error not enlarged, and now the simulation accuracy is still higher than the simulation accuracy of original data modeling directly, too.

Let peers no longer spend energy in seeking the function transformation which both reduce class ratio dispersion and keep relative error of inverse transformation not enlarged. At the same time, also remind peers that even if a function transformation reduces class ratio dispersion greatly, the data modeling accuracy improves a lot after transformation, but the error of inverse transformation is may quite large, still. Besides, even if function transformation increases class ratio dispersion, the data modeling accuracy is not good after transformation, the ideal situation after inverse transformation would occur, and the possibility cannot be excluded.

According to the fact that the single function transformation which can both reduce the class ratio dispersion and keep the relative error no enlargement after the inverse transformation does not exist, this paper provides the separable binary function transformation F(x(k),k)=f(x(k))⋅g(k). The authors select the appropriate f(x(k)) and g(k) to get F(x(k),k)=f(x(k))⋅g(k). The sequence {F(x(k),k)}k=1n can not only improve the modeling accuracy but also ensure that the inverse transformation relative error has no enlargement.

First of all, to meet that the sequence reduces the class ratio dispersion after binary function transformation, the sufficient and necessary condition of binary function transformation with reduced class ratio dispersion is obtained. Secondly, to meet the condition that the inverse transformation relative error is not enlarged, the necessary condition of separable binary function transformation is obtained respectively for monotonically increasing and monotonically decreasing function f(x). Finally, the feasibility and correctness of this method are illustrated by example analysis and application.

The sufficient and necessary condition of binary function transformation with reduced class ratio dispersion and the necessary condition of separable binary function transformation with the inverse transformation relative error no enlargement.

According to the properties of separable binary function transformation provided in this paper, the grey prediction function model is established, which can improve the modeling accuracy.

This paper provides a binary function transformation, and researches the sufficient and necessary condition of binary function transformation with reduced class ratio dispersion and the necessary condition of separable binary function transformation with the inverse transformation relative error no enlargement. It is easy for scholars to carry out the pretest before selecting the separable binary function transformation. The binary function transformation is the further extension of single function transformation, which broadens and enriches the choice of function transformation.

The purpose of this paper is to introduce the new class ratio dispersion, the new smooth degree sequence and the comparison criterion of the new smooth degree and to propose the new prior check of grey modeling in order to meet the modeling demand of the optimized grey models which have the white exponential law of coincidence.

This paper introduces the corresponding new concepts and new comparison criterion which can reflect the approach degree of the raw data and the normal geometric progression by analogy with the traditional class ratio dispersion, smooth degree sequence and comparison criterion.

To the optimized grey models, the new concepts and the new comparison criterion can be regarded as the prior check of grey modeling.

First, the new concepts and the new comparison criterion can reflect the approach degree of the raw data and the normal geometric progression, and this paper proposes the prior check of grey modeling to the optimized grey models. Second, this paper proposes the quantificational valuation criterion – the concept of the smooth degree which can reflect the approach degree of a single sequence and the normal geometric progression, and ends the status quo that there is only the comparison criterion of the smooth degree between two sequences but not the quantificational valuation criterion of a single sequence.

Traditional indices of bi-dimensional inequality and polarization were developed for cardinal variables and cannot be used to quantify dispersion in ordinal measures of socioeconomic status and health. This chapter develops two approaches to the measurement of inequality and bi-polarization using only ordinal information. An empirical illustration is given for 24 European Union countries in 2004–2006 and 2011. Results suggest that inequalities and bi-polarization in income and health are especially large in Estonia and Portugal, and that inequalities have significantly increased in recent years in Austria, Belgium, Finland, Germany, and the Netherlands, whereas bi-polarization significantly decreased in France, Portugal, and the United Kingdom.

The purpose of this study is to explain the poor informativeness of earnings in dual-class firms by examining the quality of earnings and the information environment.

The earnings informativeness, earnings quality and information environment of dual-class firms are compared with a matched sample of single-class firms. The authors have performed the returns-earnings association tests, examine the quality of earnings by using proxies for discretionary accruals, and examine the information environment by employing four empirical constructs: the analyst forecast dispersion, absolute forecast errors, Amihud’s (2002) illiquidity measure, and the bid-ask spread.

The results show that the quality of earnings is better while the quality of the information environment is worse in dual-class firms compared to single-class firms. Overall, the results suggest that an inferior information environment is a plausible explanation for the low informativeness of dual-class firms’ earnings.

The results provide empirical support for Dechow et al. (2010) that the use of the earnings-returns association measure to draw conclusions about the quality of earnings is not appropriate in the presence of a poor information environment.

This is the first study to empirically show that low earnings informativeness in dual-class firms can be explained by the inferior quality of the information environment.

“It should also be noted that the objective of convergence and equal distribution, including across under-performing areas, can hinder efforts to generate growth. Contrariwise, the objective of competitiveness can exacerbate regional and social inequalities, by targeting efforts on zones of excellence where projects achieve greater returns (dynamic major cities, higher levels of general education, the most advanced projects, infrastructures with the heaviest traffic, and so on). If cohesion policy and the Lisbon Strategy come into conflict, it must be borne in mind that the former, for the moment, is founded on a rather more solid legal foundation than the latter” European Commission (2005, p. 9)Adaptation of Cohesion Policy to the Enlarged Europe and the Lisbon and Gothenburg Objectives.

A previous paper had shown that milling organic pigments at elevated temperatures often improves colour development through better wetting. The present investigation shows that heat can, nevertheless, have an overall adverse effect on colour strength and hue of pigments which partially dissolve (and subsequently recrystallise) in a vehicle system under the combined action of heat and impact. Likewise, metastable polymorphic pigments should be dispersed at the lowest possible temperature to minimise hue shifts and/or loss of colour strength.

Addresses the standardization of the measurements and the labels for concepts commonly used in the study of work organizations. As a reference handbook and research tool, seeks to improve measurement in the study of work organizations and to facilitate the teaching of introductory courses in this subject. Focuses solely on work organizations, that is, social systems in which members work for money. Defines measurement and distinguishes four levels: nominal, ordinal, interval and ratio. Selects specific measures on the basis of quality, diversity, simplicity and availability and evaluates each measure for its validity and reliability. Employs a set of 38 concepts ‐ ranging from “absenteeism” to “turnover” as the handbook’s frame of reference. Concludes by reviewing organizational measurement over the past 30 years and recommending future measurement reseach.

In this paper, we review the literature on pay variation (e.g., pay dispersion, pay compression, pay range) in organizations. Pay variation research has increased markedly in the past two decades and much progress has been made in terms of understanding its consequences for individual, team, and organizational outcomes. Our review of this research exposes several levels-related assumptions that have limited theoretical and empirical progress. We isolate the issues that deserve attention, develop an illustrative multilevel model, and offer a number of testable propositions to guide future research on pay structures.

Recent theory and research suggests that local relational networks among business organizations play an important role in establishing and preserving a locale's identity. Such networks facilitate the development, dissemination, and enforcement of norms and cognitive frames that guide local business behavior. They also provide a vehicle for the consolidation of local business interests and for the coordination of local business strategic action. We examine the factors that influenced the likelihood that the CEOs of large corporations sat on the board of directors of large locally headquartered commercial banks in the 1960s. We focused on the 1960s because doing so allows us to make use of an exceptional comprehensive data set on the attributes and relationships of large firms and their leaders. We examine connections to commercial banks because these banks played a crucial role in community development in the 1960s. We find that both the class attributes of corporate CEOs (as reflected in their ownership of the firm and their affiliation with elite educational, social, and policy-making institutions) and the organizational attributes of their firms (as reflected in their financial structure, geographic reach, and age) influenced a CEO's propensity to sit on the board of a locally headquartered bank. These results suggest that future research on participation in local relational networks should take into account both class and organizational theories. They also suggest that future research on the class and organizational underpinnings of relational networks should pay closer attention to spatial relations.