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Table of Contents
Intro
Preface
Contents
Part I Plenary Lecture
A Review of Univariate and Multivariate Multifractal Analysis Illustrated by the Analysis of Marathon Runners Physiological Data
1 Introduction
2 Univariate Multifractal Analysis
2.1 The Multifractal Spectrum
2.2 Alternative Formulations of the Multifractal Formalism
2.3 Pointwise Exponents
2.4 Orthonormal Wavelet Decompositions
2.5 Wavelet Pointwise Regularity Characterizations
2.6 Towards a Classification of Pointwise Singularities
2.7 Mathematical Results Concerning the Multifractal Formalism
2.8 Generic Results
2.9 Implications on the Analysis of Marathon Runners Data
3 Multivariate Multifractal Analysis
3.1 Multivariate Spectrum
3.2 Probabilistic Interpretation of Scaling Functions
3.3 Multivariate Multifractal Formalism
3.4 Fractional Brownian Motions in Multifractal Time
3.5 Multivariate Analysis of Marathon Physiological Data
4 Conclusion
References
Part II Applications of Dynamical Systems Theory in Biology
Wavefronts in Forward-Backward Parabolic Equations and Applications to Biased Movements
1 Introduction
2 A Biological Model with Biased Movements
3 Wavefronts in a Forward-Backward-Forward Parabolic Model
4 Wavefronts in a Biological Model with Biased Movements
References
Bohr-Levitan Almost Periodic and Almost Automorphic Solutions of Equation x'(t)= f(t-1, x(t-1))
f(t,x(t))
1 Introduction
2 Non-autonomous (Cocycle) Dynamical Systems
2.1 Cocycles
2.2 Bebutov's Dynamical Systems
2.3 Bohr-Levitan Almost Periodic, Almost Automorphic and Recurrent Motions
2.4 B. A. Shcherbakov's Principle of Comparability of Motions by Their Character of Recurrence
2.5 Monotone Non-autonomous Dynamical Systems
3 Functional-Differential Equations with Finite Delay
4 A Class of Delay Differential Equations with a First Integral
References
Periodic Solutions in a Differential Delay Equation Modeling Megakaryopoiesis
1 Introduction
2 Cone and Return Map
3 Periodic Solutions
4 Further Extensions
References
Discrete and Continuous Models of the COVID-19 Pandemic Propagation with a Limited Time Spent in Compartments
1 Introduction
2 Discrete Model
3 Continuous Model
4 Model Identification
References
Part III Challenges in STEM Education
Some Aspects of Usage of Digital Technologies in MathematicsEducation
1 Introduction
2 PISA Testing and Mathematical Literacy
3 The Aspect of Visualization in Geometry Teaching
4 Constructivist Theory of Learning
5 Conclusions
References
Teaching of STEM Lectures During the COVID-19 Time
1 Introduction: The CEEPUS Network
2 Math Teaching by Using GeoGebra
2.1 Selected Examples in GeoGebra for Online Teaching for Future Math Teachers
2.2 Concept of Geometric Place with GeoGebra
2.3 Extending Problem
3 Conclusions
Preface
Contents
Part I Plenary Lecture
A Review of Univariate and Multivariate Multifractal Analysis Illustrated by the Analysis of Marathon Runners Physiological Data
1 Introduction
2 Univariate Multifractal Analysis
2.1 The Multifractal Spectrum
2.2 Alternative Formulations of the Multifractal Formalism
2.3 Pointwise Exponents
2.4 Orthonormal Wavelet Decompositions
2.5 Wavelet Pointwise Regularity Characterizations
2.6 Towards a Classification of Pointwise Singularities
2.7 Mathematical Results Concerning the Multifractal Formalism
2.8 Generic Results
2.9 Implications on the Analysis of Marathon Runners Data
3 Multivariate Multifractal Analysis
3.1 Multivariate Spectrum
3.2 Probabilistic Interpretation of Scaling Functions
3.3 Multivariate Multifractal Formalism
3.4 Fractional Brownian Motions in Multifractal Time
3.5 Multivariate Analysis of Marathon Physiological Data
4 Conclusion
References
Part II Applications of Dynamical Systems Theory in Biology
Wavefronts in Forward-Backward Parabolic Equations and Applications to Biased Movements
1 Introduction
2 A Biological Model with Biased Movements
3 Wavefronts in a Forward-Backward-Forward Parabolic Model
4 Wavefronts in a Biological Model with Biased Movements
References
Bohr-Levitan Almost Periodic and Almost Automorphic Solutions of Equation x'(t)= f(t-1, x(t-1))
f(t,x(t))
1 Introduction
2 Non-autonomous (Cocycle) Dynamical Systems
2.1 Cocycles
2.2 Bebutov's Dynamical Systems
2.3 Bohr-Levitan Almost Periodic, Almost Automorphic and Recurrent Motions
2.4 B. A. Shcherbakov's Principle of Comparability of Motions by Their Character of Recurrence
2.5 Monotone Non-autonomous Dynamical Systems
3 Functional-Differential Equations with Finite Delay
4 A Class of Delay Differential Equations with a First Integral
References
Periodic Solutions in a Differential Delay Equation Modeling Megakaryopoiesis
1 Introduction
2 Cone and Return Map
3 Periodic Solutions
4 Further Extensions
References
Discrete and Continuous Models of the COVID-19 Pandemic Propagation with a Limited Time Spent in Compartments
1 Introduction
2 Discrete Model
3 Continuous Model
4 Model Identification
References
Part III Challenges in STEM Education
Some Aspects of Usage of Digital Technologies in MathematicsEducation
1 Introduction
2 PISA Testing and Mathematical Literacy
3 The Aspect of Visualization in Geometry Teaching
4 Constructivist Theory of Learning
5 Conclusions
References
Teaching of STEM Lectures During the COVID-19 Time
1 Introduction: The CEEPUS Network
2 Math Teaching by Using GeoGebra
2.1 Selected Examples in GeoGebra for Online Teaching for Future Math Teachers
2.2 Concept of Geometric Place with GeoGebra
2.3 Extending Problem
3 Conclusions