Preface......Page 6
Contents......Page 8
1.1 The Navier-Stokes Equations......Page 10
1.2 A Little Bit of History......Page 11
1.3 Fundamentals of Control Theory......Page 16
1.4 Some Applications of Control Theory......Page 17
2.1 Three Motivations......Page 18
2.2 A Bi-objective Control Problem......Page 20
2.3 A Null Controllability Problem......Page 24
References......Page 26
1 Introduction......Page 30
2.1 Filippov's Convention......Page 31
2.2 Contact Between a Smooth Vector Field X and a Codimension One Submanifold M of R3......Page 32
2.3 Classification of Singularities of ZΞ©r......Page 34
2.5 Subclasses of Ξ©0 and Ξ©1......Page 35
3 Main Results......Page 36
4 Asymptotic Stability in Ξ©0Ξ©r......Page 38
5 Asymptotic Stability in Ξ©1Ξ©r......Page 39
References......Page 42
1 Introduction......Page 43
2.1 The RTBP......Page 45
2.2 Two Regularisations......Page 46
2.2.1 McGehee Regularisation......Page 47
2.2.2 Levi-Civita Regularisation......Page 48
2.3 The Collision Manifold......Page 49
2.4.1 Existence of Four 1-EC Orbits......Page 52
2.4.2 Results for n-EC Orbits......Page 53
References......Page 54
1 Introduction......Page 56
2 Preliminaries......Page 57
2.2 Special Jordan Algebras......Page 58
2.4 The Socle of Nondegenerate Jordan Algebras......Page 60
3 Algebras of Quotients of Local Algebras at Non-PI-elements......Page 61
4 Algebras of Quotients of Local Algebras at PI-Elements......Page 63
5 Maximal Algebras of Quotients of Jordan Algebras with Nonzero PI-Elements......Page 64
References......Page 65
1 The Model......Page 67
1.1 Chemorepulsion Production Systems......Page 68
1.2 Some Properties......Page 69
2.1 The Numerical Difficulties......Page 70
2.2 Numerical Approach Using (P)......Page 72
2.3 Numerical Approach Using the Scheme US......Page 73
2.4 Numerical Approach Using the Scheme UZSW......Page 74
2.5 Numerical Simulations......Page 75
2.5.2 Energy Stability......Page 76
3 Conclusions......Page 77
References......Page 78
1 Introduction......Page 80
2 The Initial Value Formulation of GR......Page 82
3.1 The Compact Case......Page 84
3.1.1 Existence of Reference Solutions......Page 87
3.1.2 Solutions Around Symmetric Data......Page 88
3.1.3 Neighbourhoods of Umbilical Reference Solutions with Conformal Killing Fields......Page 89
3.2 The Asymptotically Euclidean Case......Page 90
4 Ricci-Flat Embedding of Lorentzian Manifolds......Page 93
References......Page 95
1 Introduction......Page 97
2 Exact General Solution to Eq.(2)......Page 99
3 A Three-Parametric Family of Solutions Corresponding to K0=0......Page 101
4 Three-Parameter Families of Solutions Corresponding to K0 = 1627......Page 102
5 Graphical Representations of Some Solutions......Page 103
References......Page 106
1 Introduction......Page 108
2 Regular Orbits......Page 111
3 Prefrattini Subgroups and Normalisers......Page 112
References......Page 115
1 Introduction......Page 117
2 Poisson Algebras Admitting a Multiplicative Basis, and Graphs......Page 119
3 Relating the Graphs Given by Different Choices of Bases......Page 121
4 Minimality and Weak Symmetry......Page 124
References......Page 128
1 Introduction......Page 129
2 Stable Gauss Maps and its Graphs......Page 130
3 Fold Gauss Maps and its Graph......Page 131
4 Lips and Beaks Transition and Surgeries......Page 133
5 Graphs with Weight of Fold Gauss Maps......Page 134
References......Page 136
1 Introduction......Page 137
2 The Geometric Setting......Page 139
2.1 Doubly Warped Product Spacetimes......Page 141
3 Rigidity of H-Hypersurfaces with Hβ₯H......Page 143
References......Page 149
1 Introduction......Page 150
2 Preliminaries......Page 151
3.1 Associative Algebra with Characteristic Sequence (n-2,2)......Page 152
3.2 Associative Algebra with Characteristic Sequence (n-2,1.1)......Page 159
References......Page 161
1 Introduction......Page 162
2 Preliminaries......Page 163
3 The Case of Compact Spacelike Hypersurfaces......Page 164
4 The Case of Complete Noncompact Spacelike Hypersurfaces......Page 168
5 The Case of Higher Order Mean Curvatures......Page 171
References......Page 174
1 Affine Geometry......Page 176
2 Strongly Projectively Flat Geometries......Page 178
3 The Quasi-Einstein Equation......Page 179
References......Page 186