E-Book Overview
This book contains a collection of papers presented at the 2nd Tbilisi Salerno Workshop on Mathematical Modeling in March 2015. The focus is on applications of mathematics in physics, electromagnetics, biochemistry and botany, and covers such topics as multimodal logic, fractional calculus, special functions, Fourier-like solutions for PDE’s, Rvachev-functions and linear dynamical systems. Special chapters focus on recent uniform analytic descriptions of natural and abstract shapes using the Gielis Formula. The book is intended for a wide audience with interest in application of mathematics to modeling in the natural sciences.
E-Book Content
Atlantis Transactions in Geometry Johan Gielis Paolo Emilio Ricci Ilia Tavkhelidze Editors Modeling in Mathematics Proceedings of the Second Tbilisi-Salerno Workshop on Modeling in Mathematics Atlantis Transactions in Geometry Volume 2 Series editor Johan Gielis, Antwerpen, Belgium The series aims at publishing contemporary results in geometry including large parts of analysis and topology. The series will publish books of both theoretical and applied nature. Theoretical volumes will focus among other topics on submanifold theory, Riemannian and pseudo-Riemannian geometry, minimal surfaces and submanifolds in Euclidean geometry. Applications are found in biology, physics, engineering and other areas. More information about this series at http://www.atlantis-press.com/series/15429 Johan Gielis Paolo Emilio Ricci Ilia Tavkhelidze • Editors Modeling in Mathematics Proceedings of the Second Tbilisi-Salerno Workshop on Modeling in Mathematics Editors Johan Gielis Bio-Engineering Sciences University of Antwerp Antwerp Belgium Ilia Tavkhelidze Faculty of Exact and Natural Sciences Ivane Javakhishvili Tbilisi State University Tbilisi Georgia Paolo Emilio Ricci International Telematic University UniNettuno Roma Italy Atlantis Transactions in Geometry ISBN 978-94-6239-260-1 ISBN 978-94-6239-261-8 DOI 10.2991/978-94-6239-261-8 (eBook) Library of Congress Control Number: 2017932628 © Atlantis Press and the author(s) 2017 This book, or any parts thereof, may not be reproduced for commercial purposes in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system known or to be invented, without prior permission from the Publisher. Printed on acid-free paper Contents Fractional–Calculus–Based FDTD Algorithm for Ultra–Wideband Electromagnetic Pulse Propagation in Complex Layered Havriliak–Negami Media . . . . . . . . . . . . . . . . . . . . . Diego Caratelli, Luciano Mescia and Pietro Bia 1 Spherical Harmonic Solution of the Robin Problem for the Laplace Equation in Supershaped Shells . . . . . . . . . . . . . . . . . . . Diego Caratelli, Pierpaolo Natalini and Paolo Emilio Ricci 17 Evolution Equations Involving Matrices Raised to Non-Integer Exponents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Giuseppe Dattoli, Silvia Licciardi, Federico Nguyen and Elio Sabia 31 Hermite Calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Giuseppe Dattoli, Bruna Germano, Silvia Licciardi and Maria Renata Martinelli 43 Modal Epistemic Łukasiewicz Logic with Constant and Its Application in Immune System . . . . . . . . . . . . . . . . . . . . . . . . . . . Antonio Di Nola, Revaz Grigolia and Nunu Mitskevich 53 Potential Fields of Self Intersecting Gielis Curves for Modeling and Generalized Blending Techniques . . . . . . . . . . . . . . . . Yohan Fougerolle, Frédéric Truchetet and Johan Gielis 67 A Bioge