Modeling in Mathematics
Proceedings of the Second Tbilisi-Salerno Workshop on Modeling in Mathematics
1st Edition
Published on 20. April 2017
X, 185 pages
978-94-6239-261-8 (ISBN)
Description
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.
More details
Other editions
Additional editions
Johan Gielis | Paolo Emilio Ricci | Ilia Tavkhelidze
Modeling in Mathematics
Proceedings of the Second Tbilisi-Salerno Workshop on Modeling in Mathematics
Book
04/2017
Atlantis Press (Zeger Karssen)
€128.39
Shipment within 10-15 days
Content
- Intro
- Contents
- Introduction
- Fractional--Calculus--Based FDTD Algorithm for Ultra--Wideband Electromagnetic Pulse Propagation in Complex Layered Havriliak--Negami Media
- 1 Introduction
- 2 Mathematical Formulation
- 3 Numerical Results
- 4 Conclusion
- References
- Spherical Harmonic Solution of the Robin Problem for the Laplace Equation in Supershaped Shells
- 1 Introduction
- 2 The Laplacian in Stretched Spherical Coordinates
- 3 The Robin Problem for the Laplace Equation
- 4 Numerical Procedure
- 4.1 Example 1
- 4.2 Example 2
- 5 Conclusion
- References
- Evolution Equations Involving Matrices Raised to Non-Integer Exponents
- 1 Introduction
- 2 Fractional Matrix Exponentiation
- 3 A Physical Application
- 4 Final Comments
- References
- Hermite Calculus
- 1 Introduction
- 2 The Umbral Method and Generalized Hermite Polynomials
- 3 Final Comments
- References
- Modal Epistemic Lukasiewicz Logic with Constant and Its Application in Immune System
- 1 Introduction
- 2 Multimodal Epistemic 3-Valued Lukasiewicz Logics EL3c(n)
- 2.1 3-Valued Descriptive Kripke Models
- 2.2 Axiomatization
- 3 On the Cells of Immune System
- 4 Description of Immune System by Descriptive Kripke Frames
- 4.1 The Epistemic Aspects of Immune System
- 5 Conclusion and Perspectives
- References
- Potential Fields of Self Intersecting Gielis Curves for Modeling and Generalized Blending Techniques
- 1 Introduction
- 2 From Gielis Curves to Radial Distance Fields
- 3 R-Functions
- 3.1 Systems of R-Functions and Some Properties
- 3.2 From the Geometric Interpretations of Binary R-Functions to Generalized Blending
- 4 Potential Field Equation for Rational Gielis Curves
- 5 Conclusions and Future Work
- References
- A Biogeometrical Model for Corolla Fusion in Asclepiad Flowers
- 1 Introduction
- 2 Gielis Flower Domains and Associated Laplacian
- 3 Leaf Shapes and Phyllotaxy
- 4 Corolla Shapes in Asclepiad Flowers
- 5 A Three-Element System for Fusion in Corolla
- 6 Fourier--Bessel Solution for the Helmholtz Equation
- 7 Leaves and Corollas
- 8 Fourier Projection Method as a General Method for BVP
- 9 Fast Forward Evolution: Combining Stochastic and Deterministic Techniques
- 10 Conclusion
- References
- A Note About Generalized Forms of the Gielis Formula
- 1 Introduction
- 2 Notable Properties of the Gielis Formula
- 3 Plane Non Symmetric Curves
- 3.1 Basic Increasing Function f(?)
- 3.2 Closed Curves
- 3.3 Curves Passing Through the Origin
- 4 The Three Dimensional Case
- 5 Conclusion
- References
- Avoiding Higher Matrix Powers in the Solution of Linear Dynamical Systems
- 1 Introduction
- 1.1 Recalling Fk,n Functions and Lucas Polynomials of the Second Kind
- 2 Matrix Powers Representation
- 3 Matrix Functions Representation
- 3.1 The Riesz--Fantappiè Formula
- 4 The Discrete Time Case
- 5 The Continuous Time Case
- 5.1 Avoiding Series Expansion by Using the Riesz--Fantappiè Formula
- 6 Conclusion
- References
- On a Geometric Model of Bodies with ``Complex'' Configuration and Some Movements
- 1 Introduction
- 1.1 Notations
- 1.2 Analytic Representation of Generalised Twisted and Rotated Figures and Generalised Möbius-Listing's Bodies
- 1.3 Elementary Displacements
- 1.4 Volume of Generalized Twisted and Rotated Bodies
- 1.5 Center of Gravity of Generalized Twisted and Rotated Bodies
- 1.6 Laplace Operator on the Generalized Twisted and Rotated bodies
- 1.7 About Some Geometrical Properties of Some Subclasses of Surfaces GTR2n
- References
- Some Properties of ``Bulky'' Links, Generated by Generalised Möbius--Listing's Bodies GMLmn{0}
- 1 Introduction
- 2 General Notations, Definitions and Remarks
- 2.1 Relations Between the Set of Generalized Möbius--Listing's Surfaces GMLmn{?} and the Sets of Ribbon Knots and Ribbon Links
- 2.2 Relations Between the Set of Generalized Möbius--Listing's Bodies GML4n{?} and the Sets of Bulky Knots and Bulky Links
- 2.3 Relations Between the Set of Generalized Möbius--Listing's Bodies GML5n{?} and the Sets of Bulky Knots and Bulky Links
- 2.4 Similarity and Difference. Relations Between the Sets of Generalized Möbius--Listing's Bodies and Surfaces With Different Numbers of Symmetry
- References
