We establish a general form of sum-difference inequality in two variables, which includes both more than 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 inequalit...

In previous work, we presented an approach for link prediction using a probabilistic description logic, named crALC. Inference in crALC, considering all the social network individuals, was used for suggesting or not a link. Despite the preliminary experiments have shown the potential of the approach, it seems unsuitable for real world scenarios, since in the presence of a social network with ma...

This paper considers the problem of constructing a multidimensional Lorenz dominance relation (MLDR) satisfying normatively acceptable conditions. One of the conditions, Comonotonizing Majorization (CM), is a weaker form of the condition of Correlation Increasing Majorizaton considered in the literature on multidimensional inequality indices. A condition, called Prioritization of Attributes und...

Introducing shift operators on time scales we construct the integro-dynamic equation corresponding to the convolution type Volterra differential and difference equations in particular cases T = R and T = Z. Extending the scope of time scale variant of Gronwall’s inequality we determine function bounds for the solutions of the integro dynamic equation.

To address various types of delays including the neutral-type arising in dynamical networks, this paper deals with coupled delay differential and continuous-time difference equations and develops stability and robustness criteria. Subsystems described by differential equations are not required to be input-to-state stable. No assumptions on network topology are made. To tackle networks in such a...

In the paper, the authors present an explicit form for a family of inhomogeneous linear ordinary differential equations, find a more significant expression for all derivatives of a function related to the solution to the family of inhomogeneous linear ordinary differential equations in terms of the Lerch transcendent, establish an explicit formula for computing all derivatives of the solution t...

* Correspondence: danhuahe@zisu. edu.cn Department of Mathematics, Zhejiang International Studies University, Hangzhou, 310012, P. R. China Full list of author information is available at the end of the article Abstract In this article, a class of impulsive non-autonomous delay difference equations with continuous variables is considered. By establishing a delay difference inequality with impul...

In this work, we use the generalized Riccati transformation and the inequality technique to establish some new oscillation criteria for the second-order nonlinear delay dynamic equation p t xΔ t γ Δ q t f x τ t 0, on a time scale T, where γ is the quotient of odd positive integers and p(t) and q(t) are positive right-dense continuous rd-continuous functions on T. Our results improve and extend ...

Over the past 10 years two concepts of central significance in the social sciences have come up for rediscussion: ‘space’ and ‘gender’. Today the two concepts are seen as relational, as a production process based on relation and demarcation. Gender and space alike are a provisional result of an – invariably temporal – process of attribution and arrangement that both forms and reproduces structu...