Background & objectives: Women's health is an important indicator for development of countries, because women are more vulnerable than men. Health is not just a biological issue and socioeconomic inequality plays an important role in health outcomes. Therefore, the purpose of this research was to determine the relationship between social and economic inequality and the health status of women. ...

In this paper we prove some results which imply two conjectures proposed by Janous on an extension to the p-th power-mean of the Erdös–Debrunner inequality relating the areas of the four sub-triangles formed by connecting three arbitrary points on the sides of a given triangle.

This monograph surveys the interactions between information mea-sures and estimation measures as well as their applications. The em-phasis is on formulas that express the major information measures,such as entropy, mutual information and relative entropy in terms ofthe minimum mean square error achievable when estimating randomvariables contaminated by Gaussian noise. These ...

We consider an optimal recovery problem for the k-th derivative of the function on an interval from the information on the function itself, given in the mean square metric. As a consequence of the solution we prove one Kolmogorov type inequality for derivatives on an interval and demonstrate that the constant in this inequality can be reduced by considering particular subsets of the function cl...

In this note we give a subdifferential mean value inequality for every continuous Gâteaux subdifferentiable function f in a Banach space which only requires a bound for one but not necessarily all of the subgradients of f at every point of its domain. We also give a subdifferential approximate Rolle’s theorem stating that if a subdifferentiable function oscillates between −ε and ε on the bounda...

Economic literature on inequality measurement is mainly concerned with the comparison of univariate indices of well-being, which record the differences in distribution of income (and/or wealth) within and between populations. However, such an approach is considered an inadequate basis for comparing individual disparities because people differ in many aspects besides income. The analysis of diff...

where < , > denotes the scalar product in E, cn the area of the unit rc-sphere, and dV the volume element of M. The equality sign of (1) holds when and only when M" is imbedded as a hypersphere in an («+ l)-dimensional subspace of E (Chen [3], [4]; see also Chen [1] and Willmore [6], [7]). It is very interesting to know whether the inequality (1) can be improved for some special submanifolds in...

This paper is concerned with sliding mode observer design and observer-based sliding mode controller synthesis for stochastic Itô descriptor systems. A novel integral sliding surface, which involves a product of sliding variable and a negative definite matrix, is constructed for the error system. It is shown that the product term not only has a stabilizing effect on the sliding variable, but al...

This paper studies a discrete-time stochastic LQ problem over an infinite time horizon with state-and control-dependent noises, whereas the weighting matrices in the cost function are allowed to be indefinite. We mainly use semidefinite programming SDP and its duality to treat corresponding problems. Several relations among stability, SDP complementary duality, the existence of the solution to ...