Kinds Of Inequalities Research Articles

On inequalities of subgroups and the structure of finite groups

Let G be a group and H be a subgroup of G. We say that H is weakly Φ-supplemented in G if G has a subgroup T such that HT = G and , where denotes the Frattini subgroup of H. In this paper, properties of this new kind of inequalities of subgroups are investigated and new characterizations of nilpotency and supersolubility of finite groups in terms of the new inequalities are obtained. MSC:20D10, 20D15, 20D20.

La igualdad en el lazo social: procesos sociohistóricos y nuevas percepciones de la desigualdad en la sociedad chilena

The theoretical premise defended by this article is that the contents of equality are specified and transformed according to a society's structural and historical conditioning factors. To argue this hypothesis, the article draws on the results of three studies in Chile, showing that two relevant effects are shaped in the interface between the wave of expansion of the principle of equality in recent decades and society's own characteristics: the rise of new demands for equality, with social ties as their main mechanism of expression, and the deepening of the denouncement of a particular kind of inequalities (defined here as interactional).

Identification of three-qubit entanglement

We present a way of identifying all kinds of entanglement for three-qubit pure states in terms of the expectation values of Pauli operators. The necessary and sufficient conditions to classify the fully separable, biseparable, and genuine entangled states are explicitly given. The approach can be generalized to multipartite high-dimensional cases. For three-qubit mixed states, we propose two kinds of inequalities in terms of the expectation values of complementary observables. One inequality has advantages in entanglement detection of the quantum state with positive partial transpositions, and the other is able to detect genuine entanglement. The results give an effective method for experimental entanglement identification.

The Moral Challenges of Economic Equality and Diversity

Attention to economic inequality has increased in the wake of the global financial crisis, and along with this increased attention has come the need for reconsideration of the dynamics of moral reflection on inequality. Inequality is often viewed as a negative in terms of economic and social costs. But there are also moral challenges that arise from inequality. The Christian tradition emphasizes the diversity, and therefore the inequality, of the created order, and as such inequality is not simply a result of sin. After the fall into sin, there are new dynamics which consist of sinful kinds of inequality as well as sinful attitudes towards the gifts and endowments of others. This “grief” at the good of others has been classically understood as the vice of envy (invidia). This article argues for the ongoing relevance of envy as a particularly important moral category for evaluation of economic inequality.

<i>Unisa v Reynhardt</i> [2010] 12 BLLR 1272 (LAC): Does Affirmative Action have a Lifecycle?

The Employment Equity Act (EEA) was enacted to achieve equity in the workplace by prohibiting unfair discrimination and by requiring the implementation of affirmative action measures to ensure the adequate representation of designated groups. To ensure compliance with the EEA a designated employer must ensure that it formulates an affirmative action policy within which employment equity targets are stipulated and met. One of the on-going debates around affirmative action is whether it has a life-span. One school of thought argues that affirmative action requires a legislated sunset clause, in which considerations of race, gender and disability will no longer be implemented by employers, instead of which each employer will look to employ a candidate who is suitably qualified for the vacant post. The other school of thought argues that the need for affirmative action is two-fold: to redress past inequalities, but also to deal with existing inequalities within society. Having a sunset clause this would negate the aim of affirmative action to deal effectively with both kinds of inequalities and also the creation of a representative workforce. In the case of UNISA v. Reynhardt it was held that once an employer has reached his employment equity targets it is no longer justifiable for it to apply affirmative action, but that the principle to be applied is that the most suitably qualified candidate is to be appointed. The non-application of affirmative action is subject to an employer’s commitment to meeting employment equity targets and a recognition by the employer that once these targets are reached they must be maintained within the organization. Consequently, once a disparity exists, affirmative action must again be applied, resulting in the imputation of a distinct lifecycle to affirmative action. Failure on the part of the employer to do this would have the potential of creating reverse discrimination against employees who are not the beneficiaries of affirmative action.

Korn's inequalities: The linear vs. the nonlinear case

It is well known that the linear Korn inequality pervades the theory of three-dimensional linearized elasticity. It is thus conceivable that nonlinear Korn's inequalities could likewise play a role in the theory of three-dimensional nonlinear elasticity. In this paper, we describe the (available to this date) linear and nonlinear Korn's inequalities and we discuss the resemblances, but also the sometimes intriguing differences, that exist between these two kinds of inequalities.

Between the colonial heritage and the first globalization boom: on income inequality in the Southern Cone

AbstractThis paper presents a first estimate of income inequality in the Southern Cone of South America (Brazil 1872 and 1920, Chile 1870 and 1920, Uruguay 1920) and some assumptions with regard to Argentina (1870 and 1920) and Uruguay (1870). We find that income distribution was relatively high on the eve of the first globalization boom. Thus, inequality is not only the result of globalization, but also a structural feature. Inequality increased between 1870 and 1920, both within individual countries and between countries. Globalization forces do not result in obvious outcomes. Rather, the effect of globalization on inequality depends on the expansion of the frontier and institutional persistence and change in old and new areas. Inequality was clearly high in the wake of the globalization process. This was a particular kind of inequality, which was part of a set of institutions closely linked to the exports of primary goods, sluggish technological change and limited human capital formation.

Universal Bounds and Semiclassical Estimates for Eigenvalues of Abstract Schrödinger Operators

We prove trace inequalities for a self-adjoint operator on an abstract Hilbert space, which extend those known previously for Laplacians and Schrodinger operators, freeing them from restrictive assumptions on the nature of the spectrum and allowing operators of much more general form. In particular, we allow for the presence of continuous spectrum, which is a necessary underpinning for new proofs of Lieb-Thirring inequalities. We both sharpen and extend universal bounds on spectral gaps and moments of eigenvalues {lambda(k)} of familiar types, and in addition we produce novel kinds of inequalities that are new even in the model cases. These include a family of differential inequalities for generalized Riesz means and a theorem stating that arithmetic means of {lambda(p)(k)}(k=1)(n) with p 8.

Distinguishing disability: parents, privilege, and special education

Students in special education programs can have widely divergent experiences. For some, special education amounts to a dumping ground where schools unload problem students, while for others, it provides access to services and accommodations that drastically improve chances of succeeding in school and beyond. Distinguishing Disability argues that this inequity in treatment is directly linked to the disparity in resources possessed by the students' parents. Since the mid-1970s, federal law has empowered parents of public school children to intervene in virtually every aspect of the decision making involved in special education. However, Colin Ong-Dean reveals that this power is generally available only to those parents with the money, educational background, and confidence needed to make effective claims about their children's disabilities and related needs. Ong-Dean documents this class divide by examining a wealth of evidence, including historic rates of learning disability diagnosis, court decisions, and advice literature for parents of disabled children. In an era of expanding special education enrollment, Distinguishing Disability is a timely analysis of the way this expansion has created new kinds of inequality.

»Nothwendige Gleichheit der Strafen bey aller Verschiedenheit der Stände im Staat«?

Abstract: (In)equality played a major role in judicial discussions about criminal law as well as in legislation between the late 18th and the middle of the 19th century. Particularly disputed was whether the same penalties should be applied to all, regardless of their social status. Opponents of this view argued that equal punishment could have dissimilar effects on the convicts depending on their individual circumstances. Between 1780 and 1820 criminal law in Germany was dictated by estate lines and therefore clashed with middle class claims for equal rights. Since equality before the law in the early 1800s was established as a basic principle e. g. in constitutions, different penalties for the same offence could not be justified with the inequality of estates anymore. Although this was generally accepted by jurists, they dismissed demands for a so-called formal equality and favoured substantial equality instead. As a consequence, German penal codes implemented a privileged penalty which could only be imposed on educated and respectable citizens. Provided that education and respectability were to be found in members of the middle classes only, a new kind of inequality was thereby established.

Mapping digital divide in neighborhoods: Wi-Fi access in Baton Rouge, Louisiana

As the Internet becomes widely available, one possible effect is to level the playing field for all members of the society. The opposite effect is to produce a new kind of inequality, commonly referred to as the ‘digital divide’. This study uses the access point mapping technique to obtain the Wi-Fi access point density and analyzes its association with various demographic and socioeconomic attributes in neighborhoods. Fieldwork in Baton Rouge, Louisiana, indicates that low-income households headed by a black, single, female parent with multiple children and no college degree have the lowest rates of Wi-Fi ownership. Results from research following the technique can help inform planners in implementing municipal Wi-Fi networks and can also be used as a proxy measure for socioeconomic attributes that are not updated in a timely manner and are often expensive to collect.

Editorial Introduction

Editorial Introduction

Inequalities for single crystal rod growth by edge-defined film-fed growth (E.F.G.) technique

A boundary value problem in the case of the second order axi-symmetric Young–Laplace differential equation (some of whose solutions describe the static meniscus free surface, i.e. the static liquid bridge free surface between the shaper and the crystal, occurring in single crystal rod growth) is analyzed. The analysis concerns the dependence of the solution of an initial value problem of the equation on a parameter p (the controllable part of the pressure difference Δ p across the free surface). Inequalities are established for p which are necessary or sufficient conditions for the existence of a solution which represents a stable and convex free surface of a static meniscus. The analysis is numerically illustrated for the static menisci occurring in the NdYAG laser single crystal rod growth from the melt by edge-defined film-fed growth (E.F.G.) technique. This kind of inequalities can be useful in the experiment planning and technology design.

The Need for Death

‘Social precognition’ is the forerunner of new developments in science and technology such as extended life or immortality. While life-extension may have been neglected by philosophers or social scientists, it has been explored in depth by creative writers. They underline the threat of new kinds of inequality and of the conservatism of a society that protects the interests of the long-lived. They also question the quality of a longer life as likely to be lonely and empty rather than wise, peaceful and fulfilled.

Empirical Stratification Theory: Ibn Khaldun (1377) to Today

The current dispersion of stratification research into several seemingly unrelated topics such as social mobility and various kinds of inequality (racial, ethnic, gender, income, etc.) is unfortunate and unnecessary. It is unfortunate because a good theory can improve understanding of each of these and goes on to open new avenues for the development of theory itself. It is unnecessary because a general theory of stratification in fact exists, though this is not immediately obvious because its expressions have evolved with the passage of time, and because its basic unity is obscured by terminological differences among its contributors. The theory's original form was written in 1377 by Ibn Khaldun as the basis of his theory of human organization (sociology), and was buttressed by his profound knowledge of pre-14 th Century societies. His form of it is a conceptually simple framework consisting of a two-class hierarchy of absolute power, together with an analysis of the rise, dissolution, and replacement of power holding groups. Beginning around a century ago this framework was augmented and elaborated both in terms of a more refined set of dimensions of types of power and of modern statistical concepts by which to describe the structural variations of power in societal stratification systems in any society. The paper reviews the evolution of the theory and brings it up to date. Measurement methods as well the theory's implications are discussed.

Two Types of Inequality

This article analyzes the mathematical connections between two kinds of inequality: inequality between persons (e.g., income inequality) and inequality between subgroups (e.g., racial inequality). The authors define a general inequality parameter in two-parameter continuous distributions. This parameter governs all measures of personal inequality (e.g., the Gini coefficient) and governs as well the gap (difference or ratio) between the means of subdistributions. It is thus established that in the distributions analyzed here, as personal inequality increases, so does inequality between subgroups. This general inequality parameter also governs Lorenz dominance and all quantities in the decomposition of Theil's mean logarithmic deviation into between-subgroup and within-subgroup components in the Pareto case. Thus, the general inequality parameter captures the ``deep structure'' of inequality. Finally, a whole-distribution graphical tool is introduced for assessing personal and subgroup inequality. Substantively, this work suggests that in societies characterized by special income distributions, whenever inequality disrupts social cohesion, it attacks on two fronts, via subgroup inequality as well as personal inequality.

Gender Inequalities in Education

The terrain of gender inequalities in education has seen much change in recent decades. This article reviews the empirical research and theoretical perspectives on gender inequalities in educational performance and attainment from early childhood to young adulthood. Much of the literature on children and adolescents attends to performance differences between girls and boys. Of course, achievement in elementary and secondary school is linked to the level of education one ultimately attains including high school completion, enrollment in postsecondary education, college completion, and graduate and professional school experiences. We recommend three directions for future research: (a) interdisciplinary efforts to understand gender differences in cognitive development and noncognitive abilities in early childhood, (b) research on the structure and practices of schooling, and (c) analyses of how gender differences might amplify other kinds of inequalities, such as racial, ethnic, class, or nativity inequalities.

Coding Theorems on the Threshold Scheme for a General Source

In this paper, coding theorems on the (t, m) -threshold scheme for a general source are discussed, where m means the number of the shares and t means a threshold. The (t,m) -threshold scheme treated in this paper encrypts n source outputs Xn to m shares at once and is required to satisfy the two conditions that 1) Xn is reproduced from arbitrary t shares, and 2) almost no information of Xn is revealed from any t - 1 shares. It is shown that the (t,m) -threshold scheme must satisfy certain inequalities including the limit inferiors in probability. One of the inequalities is closely related to the minimum length of the fair random bits needed to a dealer for realizing the (t, m) -threshold scheme. In addition, it is shown that a certain variation of Shamir's threshold scheme meets the two conditions. The same approach can be taken to the problems of Shannon's cipher system with the perfect secrecy and fixed-length source coding with vanishing decoding error probability. It is shown that the same kind of inequalities, which indicate the converse coding theorems, hold in both two cases.

African-American Roots Tourism in Brazil

The novelty of African-American roots tourism to Brazil is that to some extent it defies the secondary position occupied by Brazil in the African diaspora, a context marked by the hegemony of U.S.-centric conceptions of blackness. At the same time, roots tourism entails three kinds of inequalities: the disparity between those who have access to travel and those who do not, the belief of many African-American tourists that they can exchange what they view as their “modernity” for the “traditions” of the local black communities with whom they interact during their travels, and the much greater access of African-Americans to the means by which Africa and the diaspora can be represented. Blacks located in the North and the South of the American continent have unequal access to global currents of power. Thus, at the same time that it offers the possibility of challenging traditional North-South flows of cultural exchange, African-American roots tourism confirms the existing hierarchy within the black Atlantic.

Inequalities for Single Crystal Ribbon Growth by Edge-Defined Film-Fed Growth Technique

The axi-symmetric Young-Laplace differential equation is analyzed. Solutions of this equation can describe the outer or inner free surface of a static meniscus (the static liquid bridge free surface between the shaper and the crystal surface) occurring in single crystal tube growth. The analysis concerns the dependence of solutions of the equation on a parameter which represents the controllable part of the pressure difference across the free surface. Inequalities are established for which are necessary or sufficient conditions for the existence of solutions which represent a stable and convex outer or inner free surfaces of a static meniscus. The analysis is numerically illustrated for the static menisci occurring in silicon tube growth by edge-defined film-fed growth (EFGs) technique. This kind of inequalities permits the adequate choice of the process parameter . With this aim this study was undertaken.