Preface
Athors’ biography
Chapter 1 Background of ternion and ternion-valued Differential Equations
1.1 Background for quaternions
1.2 Background for DEs
1.2.1 ternion Frenet frames in differential geometry
1.2.2 DEs appears in kinematic modelling and attitude dynamics
1.. DE appears in fluid mechanics
1.2.4 DE appears in quantum mechanics
1.3 History and motivation of our research
Chapter 2 Preliminary ConcepsndNtations
2.1 ternion algebra
2.2 Biquaternion algebra
. Definitions of determinants
2.4 Groups， rings， modules
2.5 Existence and uniqueness of solution to DEs
Chapter 3 Basic Theory of Linear Homogeneous ternion-valued Differential Equations
3.1 Structure of general solutions for 2D DEs
3.2 Structure of general solutions for any finite dimensional DEs based on permutation
3.3 Fundamental matrix and solution to DEs
3.4 Algorithm for computing fundamental matrix
3.4.1 Methd : using expansion of expAt
3.4.2 Method 2: eigenvalue and eigenvector theory
Chapter 4 Algorithm for Linear Homogeneous DEs when Linear Homogeneous System Has Multiple Eigenvalues
4.1 Motivations
4.2 Solving linear homogenous DEs when linear homogeneous system has multiple eigenvalues
4.2.1 Multiple eigenvalues with enough eigenvectors
4.2.2 Multiple eigenvalues with fewer eigenvectors
Chapter 5 Floquet Theory of ternion-valued Differential Equations
5.1 Preliminary results
5.2 Stability of linear homogeneous DEs with constant coefficients
5.3 Floquet theory for DEs
5.4 ternion-valued Hill’s equations
Chapter 6 Solve Linear Nonhomogeneous ternion-valued Differential Equations
6.1 Notations
6.2 Main results
6.3 Some examples
Chapter 7 Linear ternion Dynamic Equations on Time Scale
7.1 Notations and preliminary results
7.1.1 Notations and lemmas
7.1.2 Calculus on time scales
7.2 First order linear DETS
7.3 Linear systems of DETS
7.4 Linear DETS with constant coefficients
Chapter 8 Laplace Transform: a New Approach in Solving Linear ternion Differential Equations
8.1 Introduction
8.2 Biquaternion algebra
8.2.1 Biquaternion exponential function
8.2.2 Fundamental theorem of quaternion algebra and factorization theorem revisited
8.3 Definition and properties of the Laplace transform in biquaternion domain
8.4 Using LT to solve DEs
Chapter 9 Solving ternion Differential Equations with Two-sided Coefficients
9.1 Introduction
9.2 Notations and preliminary results
9.3 Solving DEs with unilateral coefficients
9.4 Solving DEs with two-sided coefficients
9.4.1 Homogeneous linear DEs with two-sided coefficients
9.4.2 Nonhomogeneous linear DEs with two-sided coefficients
Chapter 10 Controllability and Observability of Linear ternionvalued Systems
10.1 Motivations
10.2 Notations and preliminary results
10.3 Main results on the controllabiliyndbservability of linear VS
10.3.1 Controllability
10.3.2 Observability
10.3.3 Duality
Chapter 11 Stability Analysis of ternion-valued Neural Networks
11.1 Notations and preliminary results
11.2 Main results
11.3 Examples
Chapter 12 Convex Function Optimization Problems with ternion Variables
12.1 Notations and preliminary results
12.1.1 ternion algebra analysis
12.1.2 Generalized gradient
12.2 Main results on the convex function optimization problems with quaternion variables
1. Examples and simulations
12.4 Proof of the Proposition 12.1.4
Chapter 13 Penalty Method for Constrained Distributed ternionvariable Optimization
13.1 Introduction
13.2 Preliminaries
13.3 Main results
13.4 An example
Bibliography
非常抱歉，您前期未参加预订活动，
无法支付尾款哦！
