Noether's Theorem for Control Problems on Time Scales

We prove a generalization of Noether's theorem for optimal control problems defined on time scales. Particularly, our results can be used for discrete-time, quantum, and continuous-time optimal control problems. The generalization involves a one-parameter family of maps which depend also on the control and a Lagrangian which is invariant up to an addition of an exact delta differential. We apply our results to some concrete optimal control problems on an arbitrary time scale.Comment: This is a preprint of a paper whose final and definite form is published in International Journal of Difference Equations ISSN 0973-6069, Vol. 9 (2014), no. 1, 87--10

Optimal Control for a Steady State Dead Oil Isotherm Problem

We study the optimal control of a steady-state dead oil isotherm problem. The problem is described by a system of nonlinear partial differential equations resulting from the traditional modelling of oil engineering within the framework of mechanics of a continuous medium. Existence and regularity results of the optimal control are proved, as well as necessary optimality conditions.Comment: This is a preprint of a paper whose final and definitive form will appear in Control and Cybernetics. Paper submitted 24-Sept-2012; revised 21-March-2013; accepted for publication 17-April-2013. arXiv admin note: text overlap with arXiv:math/061237

Perturbation Theory for Metastable States of the Dirac Equation with Quadratic Vector Interaction

The spectral problem of the Dirac equation in an external quadratic vector potential is considered using the methods of the perturbation theory. The problem is singular and the perturbation series is asymptotic, so that the methods for dealing with divergent series must be used. Among these, the Distributional Borel Sum appears to be the most well suited tool to give answers and to describe the spectral properties of the system. A detailed investigation is made in one and in three space dimensions with a central potential. We present numerical results for the Dirac equation in one space dimension: these are obtained by determining the perturbation expansion and using the Pad\'e approximants for calculating the distributional Borel transform. A complete agreement is found with previous non-perturbative results obtained by the numerical solution of the singular boundary value problem and the determination of the density of the states from the continuous spectrum.Comment: 10 pages, 1 figur

Assessment of the Effects of Growth Enhancement Support Scheme (GESS) on the Output of Dry Season Rice Farmers before and after Scheme Participation in Sokoto State, Nigeria

The study assessed the effects of Growth Enhancement Support Scheme (GESS) on the output of dry season rice farmers before and after participation. A multistage sampling technique was used to select farmers for the study. Data for the study were collected from 250 farmers using structured questionnaire. The data obtained was analyzed using descriptive and inferential statistics. The results of the showed that the age of the majority of the farmers fall between the ages of 30-39 years, married and had one form of education or the other. Based on the findings, the main source of information (46.8%) regarding the awareness of GESS programme was the district heads and majority (94.4%) of the farmers were registered with the scheme. About 40% of the farmers registered with the scheme because inputs provided by the scheme are supplied to only register farmers at a subsidized rate. The result of t-test analysis showed a significant difference (

Introduction: new trends on dynamical systems and differential equations

The main contributions of [Int. J. Dyn. Syst. Differ. Equ., Vol. 8, Nos. 1/2 (2018)], consisting of 11 papers selected and revised from the international conference IMAME’2016, are highlighted.publishe