Function bounds for solutions of Volterra integro dynamic equations on time scales

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 $\mathbb{T}=\mathbb{R}$ and $\mathbb{T}=\mathbb{Z}$. Extending the scope of time scale variant of Gronwall's inequality we determine function bounds for the solutions of the integro dynamic equation

Oscillatory Behavior of Solutions of Third-Order Delay and Advanced Dynamic Equations

In this paper, we consider oscillation criteria for certain third-order delay and advanced dynamic equations on unbounded time scales. A time scale T is a nonempty closed subset of the real numbers. Examples will be given to illustrate some of the results

Existence of periodic solutions in totally nonlinear delay dynamic equations

By means of a fixed point theorem we offer sufficient conditions for the existence of periodic solutions of totally nonlinear delay dynamic equations, where the solution maps a periodic time scale into another time scale

Resource management for flood response in Mexico

Emergency logistics is acquiring a crucial role aiming to provide adequate care and support for people affected by catastrophic situations; dealing with a large number of stakeholders, scarcity of resources and high stakes. Considering the importance of balancing resources from different participants to improve operations, this research introduces a bi-criteria response optimisation model aiming to maximise the service provided to disaster victims while making efficient use of resources. The model provides support for relief distribution, inventory management and resource allocation. But beyond the optimisation of logistical decisions, the model is able to determine which organisations to use at the appropriate timeframe, so as to prevent shortages and convergence. The model is applied to a case study on a flood in Mexico in order to compare its results with real activities performed by authorities and draw conclusions

Quadratic pencil of difference equations: jost solutions, spectrum, and principal vectors

Click on the link to view the abstract. Quaestiones Mathematicae 33(2010), 305–32