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Relative bipolarisation indices are usually constructed making sure that they achieve their minimum value of bipolarisation if and only if distributions are perfectly egalitarian. However, the literature has neglected discussing the existence of a benchmark of maximum relative bipolarisation. Consequently there is no discussion as to the implications of maximum bipolarisation for the optimal normalisation of relative bipolarisation indices either. In this note we characterize the situation of maximum relative bipolarisation as the only one consistent with the key axioms of relative bipolarisation. We illustrate the usefulness of incorporating the concept of maximum relative bipolarisation in the design of bipolarisation indices by identifying, among the family of rank-dependent Wang–Tsui indices, the only subclass fulfilling a normalisation axiom that takes into account both benchmarks of minimum and maximum relative bipolarisation.

The relative bipolarisation literature features examples of indices which depend on the median of the distribution, including the renowned Foster–Wolfson index. This study shows that the use of the median in the design and computation of relative bipolarisation indices is both unnecessary and problematic. It is unnecessary because we can rely on existing well-behaved, median-independent indices. It is problematic because, as the study shows, median-dependent indices violate the basic transfer axioms of bipolarisation (defining spread and clustering properties), except when the median is unaffected by the transfers. The convenience of discarding the median from index computations is further illustrated with a numerical example in which median-independent indices rank distributions according to the basic transfer axioms while median-dependent indices do not.

A multidimensional calculation method is used to investigate the flow in a motored two‐stroke engine. The governing equations are written in a moving‐coordinate system such that the grid can move with the piston. Grid lines are added into or deleted from the computational domain, depending on opening or closure of the ports. The EPISO algorithm is modified and adopted as the solution procedure. Calculations are performed on an engine of loop‐scavenged type. Details of the gas exchange process and the flow structure in the cylinder are shown. The effects of the engine speed, inlet discharge coefficient and the angle of boost port are examined.

Large strain model can be formulated in terms of the Lagrangian or the Eulerian frame. In this paper, the Eulerian type large strain models are studied. Numerical examples on the Lagrangian and Eulerian types large strain models are investigated and compared. It is found that the differences in the choice of large strain model under large strain and rotation problems are noticeable but not significant if small load step is used for analysis. Furthermore, we have also found that unsymmetrical formulation instead of symmetrical formulation should be adopted for Eulerian type large strain models.

A growing polarization of society accompanied by an erosion of the middle class is receiving increasing attention in recent German economic and social policy discussion. Our study contributes to this discussion in two ways: First, on a theoretical level we propose extended multidimensional polarization indices based on a constant elasticity of substitution (CES)-type well-being function and present a new measure to multidimensional polarization, the mean minimum polarization gap, 2DGAP. This polarization intensity measure provides transparency with regard to each single attribute, which is important for targeted policies, while at the same time respecting their interdependent relations. Second, in an empirical application, time is incorporated, in addition to the traditional income measure, as a fundamental resource for any activity. In particular, genuine personal leisure time will account for social participation in the sense of social inclusion/exclusion and Amartya Sen’s capability approach.

Instead of arbitrarily choosing the attribute parameters in the CES well-being function, the interdependent relations of time and income are evaluated by the German population. With the German Socio-Economic Panel (GSOEP) and detailed time use diary data from the German Time Use Surveys (GTUSs) 1991/1992 and 2001/2002, we quantify available and extended multidimensional polarization measures as well as our new approach to measuring the polarization of the working poor and affluent in Germany.

There are three prominent empirical results: Genuine personal leisure time in addition to income is an important and significant polarization attribute. Compensation is of economic and statistical significance. The new minimum 2DGAP approach reveals that multidimensional polarization increased in the 1990s in Germany.

The relationship between income inequality and polarization is an empirical fact: a change in equality might occur together with a change in polarization. At the same time, polarization might emerge while inequality remains constant. The outcome of this process entails relevant information on the evolution of the income distribution. We exploit the LIS database to perform a relative distribution analysis for six European countries. Our aim is describing how disposable income distributions evolved over time. The results indicate that polarization increased in all the considered countries, being the largest in the United Kingdom and the smallest in Italy. Nonetheless, in all the countries downgrading prevails over upgrading: the relevance of the middle class getting poorer is larger than the one of the middle class getting richer.

The purpose of this paper is to present an improved model based on center potential instead of surface potential which is physically more relevant and accurate. Also, additional analytic insights have been provided to make the model independent and robust so that it can be extended to a full range compact model.

The design methodology used is center potential based analytical modeling using Psuedo-2D Poisson equation, with ingeniously developed boundary conditions, which help achieve reasonably accurate results. Also, the depletion width calculation has been suitably remodeled, to account for proper physical insights and accuracy.

The proposed model has considerable accuracy and is able to correctly predict most of the physical phenomena occurring inside the broken gate Tunnel FET structure. Also, a good match has been observed between the modeled data and the simulation results. I_on/I_ambipolar ratio of 10^(−8) has been achieved which is quintessential for low power SOCs.

The modeling approach used is different from the previously used techniques and uses indigenous boundary conditions. Also, the current model developed has been significantly altered, using very simple but intuitive technique instead of complex mathematical approach.

Purpose: Most of the characterizations of inequality or poverty indices assume some invariance condition, be that scale, translation, or intermediate, which imposes value judgments on the measurement. In the unidimensional approach, Zheng (2007a, 2007b) suggests replacing all these properties with the unit-consistency axiom, which requires that the inequality or poverty rankings, rather than their cardinal values, are not altered when income is measured in different monetary units. The aim of this paper is to introduce a multidimensional generalization of this axiom and characterize classes of multidimensional inequality and poverty measures that are unit consistent.

Design/methodology/approach: Zheng (2007a, 2007b) characterizes families of inequality and poverty measures that fulfil the unit-consistency axiom. Tsui (1999, 2002), in turn, derives families of the multidimensional relative inequality and poverty measures. Both of these contributions are the background taken to achieve our characterization results.

Findings: This paper merges these two generalizations to identify the canonical forms of all the multidimensional subgroup- and unit-consistent inequality and poverty measures. The inequality families we derive are generalizations of both the Zheng and Tsui inequality families. The poverty indices presented are generalizations of Tsui's relative poverty families as well as the families identified by Zheng.

Originality/value: The inequality and poverty families characterized in this paper are unit and subgroup consistent, both of them being appropriate requirements in empirical applications in which inequality or poverty in a population split into groups is measured. Then, in empirical applications, it makes sense to choose measures from the families we derive.

We propose a framework for the measurement of income mobility over several time periods, based on the notion that multi-period mobility amounts to measuring the degree of association between the individuals and the time periods. More precisely we compare the actual income share of individuals at a given time in the total income of all individuals over the whole period analyzed, with their “expected” share, assumed to be equal to the hypothetical income share in the total income of society over the whole accounting period that an individual would have had at a given time, had there been complete independence between the individuals and the time periods. We then show that an appropriate way of consistently measuring multi-period mobility should focus on the absolute rather than the traditional (relative) Lorenz curve and that the relevant variable to be accumulated should be the difference between the “a priori” and “a posteriori” shares previously defined. Moving from an ordinal to a cardinal approach to measuring multi-period mobility, we then propose classes of mobility indices based on absolute inequality indices. We illustrate our approach with an empirical application using the EU-SILC rotating panel dataset. Our empirical analysis seems to vindicate our approach because it clearly shows that income mobility was higher in the new EU countries (those that joined the EU in 2004 and later). We also observe that income mobility after 2008 was higher in three countries that were particularly affected by the financial crisis: Greece, Portugal, and Spain.