Oscillation of third-order neutral differential equations with damping and distributed delay

The present paper focuses on the oscillation of the third-order nonlinear neutral differential equations with damping and distributed delay. The oscillation of the third-order damped equations is often discussed by reducing the equations to the second-order ones. However, by applying the Riccati transformation and the integral averaging technique, we give an analytical method for the estimation of Riccati dynamic inequality to establish several oscillation criteria for the discussed equation, which show that any solution either oscillates or converges to zero. The results make significant improvement and extend the earlier works such as (Zhang et al. in Appl. Math. Lett. 25:1514–1519 2012). Finally, some examples are given to demonstrate the effectiveness of the obtained oscillation results.

Study of nonlinear Pachpatte’s inequalities on time scales

In this paper, we develop a fundamental dynamic inequality, a generalization of comparison theorem and reproduce the proofs of some nonlinear integral Pachpatte’s inequalities by using their continuous analogue. We also unify and extend these improved integral Pachpatte’s inequalities and their corresponding discrete analogues on arbitrary time scales. The results are used to make qualitative analysis of higher order dynamic equations.

Higher integrability theorems on time scales from reverse Hölder's inequalities

In this paper, we establish some new reverse dynamic inequalities and use them to prove some higher integrability theorems for decreasing functions on time scales. In order to derive our main results, we first prove a new dynamic inequality for convex functions related to the inequality of Hardy, Littlewood and P?lya, known from the literature. Then, we prove a refinement of the famous Hardy inequality on time scales for a class of decreasing functions. As an application, our results are utilized to formulate the corresponding reverse integral and discrete inequalities, which are essentially new.

Law and the Political Economy of the World

The interpenetration of global political and economic life has placed questions of ‘political economy’ on the scholarly agenda across the social sciences. The author argues that international law could contribute to understanding and transforming centre–periphery patterns of dynamic inequality in global political economic life. The core elements of both economic and political activity – capital, labour, credit, and money, as well as public or private power and right – are legal institutions. Law is the link binding centres and peripheries to one another and structuring their interaction. It is also the vernacular through which power and wealth justify their exercise and shroud their authority. The author proposes rethinking international law as a terrain for political and economic struggle rather than as a normative or technical substitute for political choice, itself indifferent to natural flows of economic activity.

Oscillation criteria for nonlinear neutral functional dynamic equations on time scales

In this paper, we establish some new sufficient conditions for oscillation of the second-order neutral functional dynamic equation $$\left[ {r\left( t \right)\left[ {m\left( t \right)y\left( t \right) + p\left( t \right)y\left( {\tau \left( t \right)} \right)} \right]^\Delta } \right]^\Delta + q\left( t \right)f\left( {y\left( {\delta \left( t \right)} \right)} \right) = 0$$ on a time scale $$\mathbb{T}$$ which is unbounded above, where m, p, q, r, T and δ are real valued rd-continuous positive functions defined on $$\mathbb{T}$$. The main investigation of the results depends on the Riccati substitutions and the analysis of the associated Riccati dynamic inequality. The results complement the oscillation results for neutral delay dynamic equations and improve some oscillation results for neutral delay differential and difference equations. Some examples illustrating our main results are given.

Book Reviews

Helen F. Ladd of Duke University reviews “The Money Myth: School Resources, Outcomes, and Equity” by W. Norton Grubb,. The EconLit Abstract of the reviewed work begins “Examines how inequalities in resources other than money, such as leadership, instruction, and tracking policies, contribute to the deepening divide in the quality and success of American education. Discusses moving beyond money--the variety of educational resources; multiple resources, multiple outcomes--testing the improved school finance with the National Educational Longitudinal Survey of the Class of 1988; when money does matter--explaining the weak effects of school funding; families as resources--the effects of family background and demographic effects; students as resources--the effects of connectedness to schooling; equity and inequality--from static to dynamic conceptions; dynamic inequality--schooling outcomes over time; correcting dynamic inequality in practice--exploring what schools do for low-performing students; making resources matter--implications for school-level practice; supporting the improved school finance--district, state, and federal roles; the implications for litigation of the improved school finance; and the implications for reform--conceptions of schooling and the role of the welfare state. Grubb is Professor and David Gardner Chair in Higher Education at the School of Education, University of California, Berkeley, and Faculty Coordinator of the Principal Leadership Institute. Index.”