Approximate Solutions by Truncated Taylor Series Expansions of Nonlinear Differential Equations and Related Shadowing Property with Applications

This paper investigates the errors of the solutions as well as the shadowing property of a class of nonlinear differential equations which possess unique solutions on a certain interval for any admissible initial condition. The class of differential equations is assumed to be approximated by well-posed truncated Taylor series expansions up to a certain order obtained about certain, in general nonperiodic, sampling points t(i) is an element of [t(0), t(J)] for i = 0, 1, . . . , J of the solution. Two examples are provided.

On Nonnegative Solutions of Fractional q-Linear Time-Varying Dynamic Systems with Delayed Dynamics

This paper is devoted to the investigation of nonnegative solutions and the stability and asymptotic properties of the solutions of fractional differential dynamic linear time-varying systems involving delayed dynamics with delays. The dynamic systems are described based on q-calculus and Caputo fractional derivatives on any order.

In the footstep of Hermes: the meaning of the hermeneutics and symbolism

Translated by Michael Marder

Socioeconomic impacts of National Parks: a case study from the North-east of England

[EN] Enforcement of rural policy measures within National Parks may have a particular importance as they may contribute to reach socioeconomic objectives devised for such areas. So this paper approaches as case study the application of a relevant rural development measure in the Northumberland National Park (NNP) –England, North East— over the period 2000-2008 in order to explore whether NNP makes any difference in terms of enforcing rural policy measures. The main research findings indicate that NNP may have some sort of positive impact on rural development, but support relying on tourism monoculture may be a background reason for undesired negative consequences.