ABSTRACT: In this paper we derive guaranteed hybrid gain, sector, and disk margins for nonlinear optimal and inverse optimal hybrid regulators that minimize a nonlinear-nonquadratic hybrid performance functional. Furthermore, we develop a hybrid return difference inequality to provide connections between dissipativity and optimality of nonlinear hybrid controllers. Specifically, we show that op...

The aim of this paper is to show that Jensen’s Inequality and an extension of Chebyshev’s Inequality complement one another, so that they both can be formulated in a pairing form, including a second inequality, that provides an estimate for the classical one. 1. Introduction The well known fact that the derivative and the integral are inverse each other has a lot of interesting consequences, on...

This paper aims to take a holistic approach to studying fear of crime by testing predictors at multiple levels of analyses. Data from the European Social Survey (N = 56,752 from 29 countries) were used to test and extend the Income Inequality and Sense of Vulnerability Hypotheses. The findings confirm that (1) individuals in societies with greater income inequalities are more fearful of crime, ...

The main purpose of this paper is to investigate the impact of gender inequality in education on rural poverty in Pakistan using Logit regression analysis on primary data sets. It is concluded that gender inequality in education has adverse impact on rural poverty. The empirical findings suggest that female-male enrolment ratio, female-male literacy ratio, Female-male ratio of total years of sc...

The paper presents a sharp Jackson inequality and a corresponding inverse one for best trigonometric approximation in terms of moduli of smoothness that are equivalent to zero on the trigonometric polynomials up to a certain degree. Sharp relations between such moduli of different order are also considered.

In the framework of inverse problems, we consider the question of aggregating estimators taken from a given collection. Extending usual results for the direct case, we propose a new penalty to achieve the best aggregation. An oracle inequality provides the asymptotic behavior of this estimator. We investigate here the price for considering indirect observations.

This paper is devoted to the adaptive Morley element algorithms for a biharmonic eigenvalue problem in [Formula: see text] ([Formula: see text]). We combine the Morley element method with the shifted-inverse iteration including Rayleigh quotient iteration and the inverse iteration with fixed shift to propose multigrid discretization schemes in an adaptive fashion. We establish an inequality on ...

Uncertainty theory is a branch of mathematics that deals with human uncertainty, and uncertain variable is used to model an uncertain quantity. Uncertainty exists not only in real quantities but also in complex quantities. Complex uncertain variable is mainly used to model a complex uncertain quantity. In uncertainty theory, inverse uncertainty distribution provides an easy way to calculate exp...

The efficiency of the MLE is demonstrated indirectly by using the following theorem. Theorem [7, p. ZSS]: If an estimator exists such that equality is satisfied in the Cramer-Rao inequality, it can be determined as a solution of the maximum likelihood equation. We will show that such an estimator exists. This implies that the covariance matrix of the MLE is given by the inverse of the Fisher in...

Considerable attention has been given to Hilbert inequalities and Hilbert-type inequalities and their various generalizations by several authors including Handley et al. 1 , Minzhe and Bicheng 2 , Minzhe 3 , Hu 4 , Jichang 5 , Bicheng 6 , and Zhao 7, 8 . In 1998, Pachpatte 9 gave some new integral inequalities similar to Hilbert inequality see 10, page 226 . In 2000, Zhao and Debnath 11 establi...