The drill pipe model described by the wave equation with boundary conditions is reduced through the d’Alembert transformation to a difference equation model. Assuming that the boundary condition at the bottom is perturbed by bounded additive noise, an ultimate bound for the velocity at the bottom of the pipe is obtained. The proposal of a Lyapunov functional for the distributed model allows to ...

Reprints available directly from the publisher Photocopying permitted by license only (C) 1999 OPA (Overseas Publishers Association) N.V. In our preceding note, we discussed a generalized Schwarz inequality, an improvement of the Heinz-Kato-Furuta inequality and an inequality related to the Furuta inequality. In succession, we give further discussions on them from the viewpoint of the covarianc...

xnþ1 1⁄4 f ðn; xn; . . . ; xn2kÞ; n $ 0; where f is continuous, and the zero solution is assumed to be the unique equilibrium. We focus our discussion on two techniques motivated by stability results for functional differential equations (FDEs) that proved recently to be useful in the frame of difference equations too. The first one involves the use of discrete inequalities and monotonicity arg...

* Correspondence: [email protected]; [email protected] Yangtze Center of Mathematics, Sichuan University, Chengdu 610064, P. R. China Full list of author information is available at the end of the article Abstract In this paper, we consider a class of impulsive difference equations with distributed delays. By establishing an impulsive delay difference inequality and using the propertie...

Based on Riccati transformation and the inequality technique, we establish some new sufficient conditions for oscillation of the second-order neutral delay dynamic equations on time scales. Our results not only extend and improve some known theorems, but also unify the oscillation of the second-order nonlinear delay differential equation and the second-order nonlinear delay difference equation ...

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...

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.

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...