A new nonlinear sum-difference inequality in two variables which generalize some existing results and can be used as handy tools in the analysis of certain partial difference equation is discussed. An example to show boundedness of solutions of a difference value problem is also given. Keywords—Sum-Difference inequality, Nonlinear, Boundedness.

Some new criteria for the oscillation of certain difference equations with mixed nonlinearities are established. The main tool in the proofs is an inequality due to Hardy, Littlewood, and Pólya. c © 2006 Elsevier Ltd. All rights reserved.

We establish a general form of sum-difference inequality in two variables, which includes both two distinct nonlinear sums without an assumption of monotonicity and a nonconstant term outside the sums. We employ a technique of monotonization and use a property of stronger monotonicity to give an estimate for the unknown function. Our result enables us to solve those discrete inequalities consid...

People learn language from their social environment. As individuals differ in their social networks, they might be exposed to input with different lexical distributions, and these might influence their linguistic representations and lexical choices. In this article we test the relation between linguistic performance and 3 social network properties that should influence input variability, namely...

background: more than a billion people have some form of disabilities worldwide. persons living with a disability have many needs (including physically, mentally, and socially needs). estimating the size of disabled population is a challenge in health systems. an innovative indirect method to estimate the size of populations is network scale up (nsu) having widely used for hidden populations. t...

The relation between divorce, co-parenting conflicts, and children's adjustment problems has been well established. An unresolved question for research and clinical interventions, however, is how conflicts between parents are maintained and/or escalate. This cross-sectional research tested the hypothesis that co-parenting conflicts in divorced couples are associated with perceived social networ...

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.

The rise of social media platforms has fundamentally altered the public discourse by providing easy to use and ubiquitous forums for the exchange of ideas and opinions. Elected officials often use such platforms for communication with the broader public to disseminate information and engage with their constituencies and other public officials. In this work, we investigate whether Twitter conver...