Format: 416 pages, height x width: 235x155 mm, 101 Illustrations, color; 10 Illustrations,
black and white; XVIII, 416 p. 111 illus., 101 illus. in color., 1 Hardback
Series: Fundamental Theories of Physics 214
Pub. Date: 24-Dec-2023
ISBN-13: 9783031453113
This book provides a captivating journey through the realms of classical and quantum systems as it unravels the profound influence that noise may have on their static and dynamic properties. The first part of the book offers succinct yet enlightening discussions on foundational topics related to noise. The second part focuses on a variety of applications, where a diverse spectrum of noise effects in physical systems comes to life, meticulously presented and thoughtfully analyzed. Whether you are a curious student or a dedicated researcher, this book is your key to gaining invaluable insights into noise effects in physical systems.
The book has the merit of presenting several topics scattered in the literature and could become a very useful reference. Giovanni Jona-Lasinio, Sapienza Universit? di Roma, Italy
Random variables and probability distributions.- Stochastic
processes.- Kinetic theory.- Statistical mechanics.- Nonlinear
dynamics.- Stationary correlations in the noisy Kuramoto model.- Bifurcation
behavior of a nonlinear system by introducing noise.- Relaxation dynamics of
mean-field classical spin systems.- Critical exponents in mean-field
classical spin systems.- Quantum systems subject to random projective
measurements.
Format: 258 pages, height x width: 235x155 mm, 8 Illustrations, color; 9 Illustrations, black and white; XXII, 258 p. 17 illus., 8 illus. in color., 1 Hardback
Series: Springer Proceedings in Mathematics & Statistics 436
Pub. Date: 12-Jan-2024
ISBN-13: 9789819963485
This book contains chapters on a range of topics in mathematics and mathematical physics, including semigroups, algebras, operator theory and quantum mechanics, most of them have been presented at the International Conference on Semigroup, Algebras, and Operator Theory (ICSAOT-22), held at Cochin, Kerala, India, from 2831 March 2022. It highlights the significance of semigroup theory in different areas of mathematics and delves into various themes that demonstrate the subjects diverse nature and practical applications. One of the key features of the book is its focus on the relationship between geometric algebra and quantum mechanics. The book offers both theoretical and numerical approximation results, presenting a comprehensive overview of the subject. It covers a variety of topics, ranging from C-algebraic models to numerical solutions for partial differential equations.
The content of the book is suitable for active researchers and graduate students who are just beginning their studies in the field. It offers insights and practical applications that would be valuable to anyone interested in the mathematical foundations of physics and related fields. Overall, this book provides an excellent resource for anyone seeking to deepen their understanding of the intersections between mathematics and physics.
P.A. Azeef Muhammed and C. S. Preenu, Cross-connections in Clifford
semigroups.- I.M. Evseev and A.E. Guterman, A range of the multidimensional
permanent on (0,1)-matrices.- Nikita V. Kitov and Mikhail V. Volkov,
Identities in twisted Brauer monoids.- Alanka Thomas and P.G. Romeo, Group
lattices over division rings.- M. N. N. Namboodiri, Structure Of The
Semi-group Of Regular Probability Measures On Locally Compact Hausdorff
Topological Semiroups.- P. Panjarikea, K. Syam Prasad, M. Al-ahan, V. Bhatta
and H. Panackal, On lattice vector spaces over a distributive lattice.- Mark
V. Lawson, Non-commutative Stone duality.- A R Rajan, Compatible and Discrete
Normal Categories.- S. N. Arjun and P. G. Romeo, On category of Lie
algebras.- K.V. Didimos, Application of Geometric Algebra to Kogas Work on
Quantum Mechanics.- R. Salvankar, K. Babushri Srinivas, H. Panackal, and K.
S. Prasad, Generalised essential submodule graph of an R-module.- A. Babu and
N. Asharaf, Numerical solution of one-dimensional hyperbolic telegraph
equation using collocation of cubic B-splines.- G. Krishna Kumar and J.
Augustine.- (n, )-Condition Spectrum of Operator Pencils.- W. Bauer and R.
Fulsche, Resolvent algebra in Fock-Bargmann representation.
Format: 460 pages, height x width: 235x155 mm, XX, 460 p., 1 Hardback
Series: University Texts in the Mathematical Sciences
Pub. Date: 12-Feb-2024
ISBN-13: 9789819976942
This book discusses continuous and discrete systems in systematic and sequential approaches for all aspects of nonlinear dynamics. The unique feature of the book is its mathematical theories on flow bifurcations, oscillatory solutions, symmetry analysis of nonlinear systems, and chaos theory. The logically structured content and sequential orientation provide readers with a global overview of the topic. A systematic mathematical approach has been adopted, and several examples are worked out in detail and exercises have been included. The book is useful for courses in dynamical systems and chaos and nonlinear dynamics for advanced undergraduate and graduate students in mathematics, physics, and engineering.
The second edition of the book includes a new chapter on Reynold and Kolmogrov turbulence. The entire book is thoroughly revised and includes several new topics: center manifold reduction, quasi-periodic oscillation, pitchfork bifurcation, transcritical bifurcation, BogdonovTakens bifurcation, canonical invariant and symmetry properties, turbulent planar plume flow, and dynamics on circle, organized structure in chaos and multifractals.
1. Continuous Dynamical Systems.-
2. Linear Systems.-
3. Phase Plane Analysis.-
4. Stability Theory.-
5. Oscillation.-
6. Theory of Bifurcations.-
7. Hamiltonian Systems.-
8. Symmetry Analysis.-
9. Discrete Dynamical Systems.-
10. Some maps.-
11. Conjugacy Maps.-
12. Chaos.-
13. Fractals.-
14. Turbulence: Reynolds to Kolmogrov and Beyond.-
Index.
Format: height x width: 235x155 mm, Approx. 600 p., 1 Hardback
Series: Algorithms and Computation in Mathematics 31
Pub. Date: 25-Mar-2024
ISBN-13: 9783031475030
Beginning with its origins in the pioneering work of W.T. Tutte in 1947, this monograph systematically traces through some of the impressive developments in matching theory.
A graph is matchable if it has a perfect matching. A matching covered graph is a connected graph on at least two vertices in which each edge is covered by some perfect matching. The theory of matching covered graphs, though of relatively recent vintage, has an array of interesting results with elegant proofs, several surprising applications and challenging unsolved problems.
The aim of this book is to present the material in a well-organized manner with plenty of examples and illustrations so as to make it accessible to undergraduates, and also to unify the existing theory and point out new avenues to explore so as to make it attractive to graduate students.
Part I. Basic Theory.- Part II.- Brick and Brace Generation.- Part III.-
Pfaffian Orientations.- Bibliography.- List of Figures.- Graph Parameters.-
Families of Graphs.- Operations and Relations.- Notation.- Index.- A.
Solutions to Selected Exercises.
ISBN: 978-981-12-8481-6 (hardcover)
ISBN: 978-981-12-8501-1 (softcover)
Graph theory is an area in discrete mathematics which studies configurations (called graphs) involving a set of vertices interconnected by edges. This book is intended as a general introduction to graph theory.
The book builds on the verity that graph theory even at high school level is a subject that lends itself well to the development of mathematical reasoning and proof.
This is an updated edition of two books already published with World Scientific, i.e., Introduction to Graph Theory: H3 Mathematics & Introduction to Graph Theory: Solutions Manual. The new edition includes solutions and hints to selected problems. This combination allows the book to be used as a textbook for undergraduate students. Professors can select unanswered problems for tutorials while students have solutions for reference.
Fundamental Concepts and Basic Results
Graph Isomorphism, Subgraphs, the Complement of a Graph
Bipartite Graphs and Trees
Vertex-Colourings of Graphs
Matchings in Bipartite Graphs
Eulerian Multigraphs and Hamiltonian Graphs
Digraphs and Tournaments
Solutions to Selected Problems
Junior college students, teachers, and undergraduates studying mathematics and computer science.
Pages: 196
ISBN: 978-981-12-8154-9 (hardcover)
ISBN: 978-981-12-8268-3 (softcover)
Ordinary differential equations is a standard course in the undergraduate mathematics curriculum that usually comes after the first university calculus and linear algebra courses taken by a mathematics major. Such courses may also typically be attended by undergraduates from other areas of physical and social sciences, and engineering. The content of such a course has remained fairly static over time, despite the expansion of the topic into other disciplines as a result of the dynamical systems point of view.
This core undergraduate course updated from the dynamical systems perspective can easily be covered in one semester, with room for projects or more advanced topics tailored to the interests of the students.
Preface
List of Figures
List of Tables
Getting Started: The Language of ODEs
Special Structure and Solutions of ODEs
Behavior Near Trajectories and Invariant Sets: Stability
Behavior Near Trajectories: Linearization
Behavior Near Equilibria: Linearization
Stable and Unstable Manifolds of Hyperbolic Equilibria
Lyapunov's Method and the LaSalle Invariance Principle
Bifurcation of Equilibria, I
Bifurcation of Equilibria, II
Center Manifold Theory
Jacobians, Inverses of Matrices, and Eigenvalues
Integration of Some Basic Linear ODEs
Solutions of Some Second Order ODEs Arising in Applications: Newton's Equations
Finding Lyapunov Functions
Center Manifolds Depending on Parameters
Dynamics of Hamilton's Equations
A Brief Introduction to the Characteristics of Chaos
Bibliography
Index
Undergraduate students in mathematics, physical science, social science, and engineering that use ordinary differential equations.