The paper presents ab abstract definition of linear inequality concepts leading to linearly invariant measures and characterizes the class of linear concepts completely. Two general methods of deriving ethical measures are proposed. They imply an Atkinson-Kolm-Sen index and a new dual index reflecting the inequality of living standard. Then all separable social welfare orderings which generate ...

From the start individualization theory is the investigation of the paradigm shift in social inequality. Furthermore it shows, how the transnationalization of social inequalities bursts the framework of institutional responses - nation state (parties), trade unions, welfare state systems and the national sociologies of social classes. In this essay I shall try to conceptually elucidate the 'cos...

A novel optimal Finite Word Length (FWL) controller design is proposed in the framework ofμ theory. A computationally tractable close-loop stability measure with FWL implementation considerations of the controller is derived based on the μ theory, and the optimal FWL controller realizations are obtained by solving the resulting optimal FWL realization problem using linear matrix inequality tech...

Recently Frank & Seiringer have shown an isoperimetric inequality for nonlocal perimeter functionals arising from Sobolev seminorms of fractional order. This isoperimetric inequality is improved here in a quantitative form.

We prove a more general version of the Grüss inequality by using the recent theory of combined dynamic derivatives on time scales and the more general notions of diamond-α derivative and integral. For the particular case when α = 1, one gets a delta-integral Grüss inequality on time scales; for α = 0 a nabla-integral Grüss inequality. If we further restrict ourselves by fixing the time scale to...

Abstract. We prove integral formulas for closed hypersurfaces in C, which furnish a relation between elementary symmetric functions in the eigenvalues of the complex Hessian matrix of the defining function and the Levi curvatures of the hypersurface. Then we follow the Reilly approach to prove an isoperimetric inequality. As an application, we obtain the “Soap Bubble Theorem” for starshaped dom...

A well known question in differential geometry is to control the constant in isoperimetric inequality by intrinsic curvature conditions. In dimension 2, the constant can be controlled by the integral of the positive part of the Gaussian curvature. In this paper, we showed that on simply connected conformally flat manifolds of higher dimensions, the role of the Gaussian curvature can be replaced...

We approach the question of which soluble groups are automatic. We describe a class of nilpotent-by-abelian groups which need to be studied in order to answer this question. We show that the nilpotent-by-cyclic groups in this class have exponential isoperimetric inequality and so cannot be automatic.

We give a very general isoperimetric comparison theorem which, as an important special case, gives hypotheses under which the spherically symmetric (n− 1)-spheres of a spherically symmetric n-manifold are isoperimetric hypersurfaces, meaning that they minimize (n − 1)-dimensional area among hypersurfaces enclosing the same n-volume. This result greatly generalizes the result of Bray (Ph.D. thes...

The paper considers social welfare functions and ethical inequality measures for linear inequality concepts when households may differ in needs. The welfare functions are nested, i.e. separable in the level of welfare attained by the homogeneous subpopulations, and possess a homogeneity property depending on the inequality concept imposed. Several principles of transfers between different house...