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Table of 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 Exponents1 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 Łukasiewicz Logic with Constant and Its Application in Immune System; 1 Introduction; 2 Multimodal Epistemic 3-Valued Łukasiewicz Logics EŁ3c(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 Frames4.1 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 Flowers1 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
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 Exponents1 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 Łukasiewicz Logic with Constant and Its Application in Immune System; 1 Introduction; 2 Multimodal Epistemic 3-Valued Łukasiewicz Logics EŁ3c(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 Frames4.1 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 Flowers1 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