Define f on the integers n > 1 by the recurrence f(n) mAn{n, minm[ 2f(m) + 3f(n/m)}. The function f has f(n) n as its upper envelope, attained for all prime n. The goal of this paper is to determine the corresponding lower envelope. It is shown that this has the form f(n) C(logn)1+1/ for certain constants and C, in the sense that for any > 0, the inequality f(n) <_ (C+)(logn) 1+1/’ holds for in...

In this article we consider linear operators satisfying a generalized commutation relation of a type of the Heisenberg-Lie algebra. It is proven that a generalized inequality of the Hardy's uncertainty principle lemma follows. Its applications to time operators and abstract Dirac operators are also investigated.

Discrete inequalities, in particular the discrete analogues of the Gronwall–Bellman inequality, have been extensively used in the analysis of finite difference equations. The aim of the present paper is to establish some fractional difference inequalities of Gronwall–Bellman type which provide explicit bounds for the solutions of fractional difference equations.

In this note we prove a discrete analogue of the continuous Halanay inequality and apply it to derive sufficient conditions for the global asymptotic stability of the equilibrium of certain generalized difference equations. The relation with some numerical schemes for functional delay differential equations is discussed.

So far there have been few results presented on the attracting and quasi-invariant sets for impulsive stochastic difference equations with continuous time. The main aim of this work is to close this gap. By establishing a difference inequality with continuous time, we obtain the attracting and quasi-invariant sets of systems under consideration. An example is given to illustrate the theory. Mat...

according to the ahlowalia hypothesis (1995), the growth of total factor productivity (tfp) beside infrastructure investments of government lead to income inequality decrease in rural areas of countries. the main objective of this study is to investigate the effects of public investments such as agricultural r&amp;e, road, education and irrigation on income inequality in rural areas of iran. in...

introduction: inequalities in urban environment are a significant concern. socioeconomic level plays an important role in these inequalities. inequality in environmental hazards is recognized as potential determinants of health disparities. materials & methods: in this study, we used individual and cumulative environmental hazard inequality indices to compare the inequality among 379 neighborho...

in this paper, an optimization problem with a linear objective function subject to a consistent finite system of fuzzy relation inequalities using the max-product composition is studied. since its feasible domain is non-convex, traditional linear programming methods cannot be applied to solve it. we study this problem and capture some special characteristics of its feasible domain and optimal s...

We give a trace inequality related to the uncertainty relation of Wigner-Yanase-Dyson skew information. This inequality corresponds to a generalization of the uncertainty relation derived by S.Luo [6] for the quantum uncertainty quantity excluding the classical mixture.

this paper investigates asymmetric behaviors of income inequality and consumption expenditures inequalities, the relationships between them and sketches their trends in the iranian households’ survey for the period of 1979 to 2006. for this purpose, and to analyze the relationships between variables panel data methodology was employed. results indicate that all the fluctuations of income inequa...