
Modeling in Mathematics
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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
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