Smarandache Sequences: Explorations and Discoveries with a Computer Algebra System

We study Smarandache sequences of numbers, and related problems, via a Computer Algebra System. Solutions are discovered, and some conjectures presented.Comment: To appear in the 2003 December issue of the Smarandache Notions Journa

Noether's Symmetry Theorem for Variational and Optimal Control Problems with Time Delay

We extend the DuBois-Reymond necessary optimality condition and Noether's symmetry theorem to the time delay variational setting. Both Lagrangian and Hamiltonian versions of Noether's theorem are proved, covering problems of the calculus of variations and optimal control with delays.Comment: This is a preprint of a paper whose final and definite form will appear in the international journal Numerical Algebra, Control and Optimization (NACO). Paper accepted for publication 15-March-201

A general delta-nabla calculus of variations on time scales with application to economics

We consider a general problem of the calculus of variations on time scales with a cost functional that is the composition of a certain scalar function with delta and nabla integrals of a vector valued field. Euler-Lagrange delta-nabla differential equations are proved, which lead to important insights in the process of discretisation. Application of the obtained results to a firm that wants to program its production and investment policies to reach a given production rate and to maximise its future market competitiveness is discussed

Optimal control with time delays via the penalty method

We prove necessary optimality conditions of Euler-Lagrange type for a problem of the calculus of variations with time delays, where the delay in the unknown function is different from the delay in its derivative. Then, a more general optimal control problem with time delays is considered. Main result gives a convergence theorem, allowing us to obtain a solution to the delayed optimal control problem by considering a sequence of delayed problems of the calculus of variations

Necessary condition for an Euler-Lagrange equation on time scales

We prove a necessary condition for a dynamic integrodifferential equation to be an Euler-Lagrange equation. New and interesting results for the discrete and quantum calculus are obtained as particular cases. An example of a second order dynamic equation, which is not an Euler-Lagrange equation on an arbitrary time scale, is given. © 2014 Monika Dryl and Delfim F. M. Torres

Discovery of a new radio galaxy within the error box of the unidentified gamma-ray source 3EG J1735-1500

We report the discovery of a new radio galaxy within the location error box of the gamma-ray source 3EG J1735-1500. The galaxy is a double-sided jet source forming a large angle with the line of sight. Optical observations reveal a V ~ 18 magnitude galaxy at the position of the radio core. Although the association with the EGRET source is not confirmed at the present stage, because there is a competing, alternative gamma-ray candidate within the location error contours which is also studied here, the case deserves further attention. The new radio galaxy can be used to test the recently proposed possibility of gamma-ray emitting radio galaxies beyond the already known case of Centaurus A.Comment: 12 pages, 3 figures. Accepted for publication in Ap

Gravitational microlensing of gamma-ray blazars

We present a detailed study of the effects of gravitational microlensing on compact and distant $\gamma$-ray blazars. These objects have $\gamma$-ray emitting regions which are small enough as to be affected by microlensing effects produced by stars lying in intermediate galaxies. We analyze the temporal evolution of the gamma-ray magnification for sources moving in a caustic pattern field, where the combined effects of thousands of stars are taken into account using a numerical technique. We propose that some of the unidentified $\gamma$-ray sources (particularly some of those lying at high galactic latitude whose gamma-ray statistical properties are very similar to detected $\gamma$-ray blazars) are indeed the result of gravitational lensing magnification of background undetected Active Galactic Nuclei (AGNs).Comment: 30 pages, 27 figures. Four figures are being submitted only as .gif files, and should be printed separately. The abstract below has been shortened from the actual version appearing in the pape

Mathematical modelling, simulation, and optimal control of the 2014 Ebola outbreak in West Africa

The Ebola virus is currently one of the most virulent pathogens for humans. The latest major outbreak occurred in Guinea, Sierra Leone, and Liberia in 2014. With the aim of understanding the spread of infection in the affected countries, it is crucial to modelize the virus and simulate it. In this paper, we begin by studying a simple mathematical model that describes the 2014 Ebola outbreak in Liberia. Then, we use numerical simulations and available data provided by the World Health Organization to validate the obtained mathematical model. Moreover, we develop a new mathematical model including vaccination of individuals. We discuss different cases of vaccination in order to predict the effect of vaccination on the infected individuals over time. Finally, we apply optimal control to study the impact of vaccination on the spread of the Ebola virus. The optimal control problem is solved numerically by using a direct multiple shooting method

Cerenkov radiation and scalar stars

We explore the possibility that a charged particle moving in the gravitational field generated by a scalar star could radiate energy via a recently proposed gravitational \v{C}erenkov mechanism. We numerically prove that this is not possible for stable boson stars. We also show that soliton stars could have \v{C}erenkov radiation for particular values of the boson mass, although diluteness of the star grows and actual observational possibility decreases for the more usually discussed boson masses. These conclusions diminish, although do not completely rule out, the observational possibility of actually detecting scalar stars using this mechanism, and lead us to consider other forms, like gravitational lensing.Comment: Accepted for publication in Class. Quantum Gra