2008, XIV, 305 p. 43 illus., Hardcover
ISBN: 978-0-387-78900-2
Due: October 2008
Contains a plethora of exercises, examples, and illustrations
This book is intended to be a thorough introduction to the subject of ordered sets and lattices, with an emphasis on the latter. It can be used for a course at the graduate or advanced undergraduate level or for independent study. Prerequisites are kept to a minimum, but an introductory course in abstract algebra is highly recommended, since many of the examples are drawn from this area.
The book has an excellent choice of topics, including a chapter on well ordering and ordinal numbers, which is not usually found in other texts. The approach is user-friendly and the presentation is lucid. There are more than 240 carefully chosen exercises.
Topic coverage includes: modular, semimodular and distributive lattices, boolean algebras, representation of distributive lattices, algebraic lattices, congruence relations on lattices, free lattices, fixed-point theorems, duality theory and more.
Steven Roman is the author of many successful textbooks, including Advanced Linear Algebra, 3rd Edition (Springer 2007), Field Theory, 2nd Edition (Springer 2005), and Introduction to the Mathematics of Finance (2004).
Preface.- Partially Ordered Sets.- Well-Ordered Sets.- Lattices.- Modular and Distributive Lattices.- Boolean Algebras.- The Representation of Distributive Lattices.- Algebraic Lattices.- Prime and Maximal Ideals: Separation Theorems.- Congruence Relations on Lattices.- Duality for Distributive Lattices: The Priestley Topology.- Free Lattices.- Fixed-Point Theorems.- Appendix A: A Bit of Topology.- Appendix B: A Bit of Category Theory.- References.- Index of Symbols.- Index
Series: Sources and Studies in the History of Mathematics and Physical Sciences
2009, Approx. 1085 p. In 2 volumes, not available separately., Hardcover
ISBN: 978-1-84882-072-2
Due: November 2008
Ganita-yukti-bhasa (Rationales in Mathematical Astronomy) of Jyesthadeva (c.1530) is a seminal text of the Kerala school of astronomy. It is composed in the Malayalam language and presents detailed yuktis or explanations and demonstrations for the results and processes of mathematical astronomy. The text, comprising fifteen chapters, is naturally divided into two parts, mathematics and astronomy, and purports to give an exposition of the techniques and theories employed in the computation of planetary motions as set forth in the great treatise Tantrasangraha (c.1500) of Nilakantha Somayaji. Even though the importance of Ganita-yukti-bhasa was brought to the attention of modern scholarship by C.M Whish in the 1830s, a critical edition of the entire Malayalam text is published here for the first time along with an English translation and detailed explanatory notes.
The mathematics part is divided into seven chapters. The topics covered are Parikarma (logistics), Dasaprasna (ten problems), Bhinnaganita (fractions), Trairasika (rule of three), Kuttakara (linear indeterminate equations), Paridhi and Vyasa (infinite series and approximations for the ratio of the circumference and diameter of a circle) and Jyanayana (infinite series and approximations for sines). A distinguishing feature of the work is that it presents detailed demonstrations of the famous results attributed to Madhava (c.1340-1420), such as infinite series for p, the arc-tangent and the sine functions, and the estimation of correction terms and their use in the generation of faster convergent series. Demonstrations are also presented for some of the classical results of Aryabhata (c.499) on Kuttakara or the process of solution of linear indeterminate equations, of Brahmagupta (c.628) on the diagonals and the area of a cyclic quadrilateral, and of Bhaskara (c.1150) on the surface area and volume of a sphere.
The astronomy part is divided into eight chapters. The topics covered are Grahagati (computation of mean and true longitudes of planets), Bhugola and Bhagola (Earth and celestial spheres), Pancadasa-prasna (fifteen problems relating to ascension, declination, longitude, etc.), Chaya-ganita (determination of time, place, direction, etc., from gnomonic shadow), Grahana (eclipses), Vyatipata (when the sun and moon have the same declination), Darsana-samskara (visibility correction for planets) and Candra-srngonnati (phases of the moon). A distinguishing feature of this work is that it gives a detailed exposition of the revised planetary model proposed by Nilakantha which, for the first time in the history of astronomy, gives the correct formulation of the equation of centre and the latitudinal motion of the interior planets, Mercury and Venus. Another unique feature of Ganita-yukti-bhasa is that it presents systematic derivations of most of the results of spherical astronomy (pertaining to diurnal and shadow problems, parallax, eclipses, and so on) that are discussed in Indian astronomy.
Volume I: The Eight Mathematical Operations; The Ten Questions and Answers; Arithmetics of Fractions; Rule of Three; Kuttakara; Circle and Circumference; Derivation of Sines.
Volume II: Computation of True Planets; Earth and Celestial Spheres; The Fifteen Problems; Gnomonic Shadow; Eclipse; Vyatipata; Maudhya and Visibility Corrections of Planets.
Series: Nonconvex Optimization and Its Applications , Vol. 89
2009, XXVI, 477 p. 95 illus., Hardcover
ISBN: 978-3-540-85633-7
Due: December 4, 2008
This up-to-date book is on algorithms for large-scale unconstrained and bound constrained optimization. Optimization techniques are shown from a conjugate gradient algorithm perspective.
Large part of the book is devoted to preconditioned conjugate gradient algorithms. In particular memoryless and limited memory quasi-Newton algorithms are presented and numerically compared to standard conjugate gradient algorithms.
The special attention is paid to the methods of shortest residuals developed by the author. Several effective optimization techniques based on these methods are presented.
Because of the emphasis on practical methods, as well as rigorous mathematical treatment of their convergence analysis, the book is aimed at a wide audience. It can be used by researches in optimization, graduate students in operations research, engineering, mathematics and computer science. Practitioners can benefit from numerous numerical comparisons of professional optimization codes discussed in the
Conjugate directions methods for quadratic problems.- Conjugate gradient methods for nonconvex problems.- Memoryless quasi-Newton methods.- Preconditioned conjugate gradient algorithms.- Limited memory quasi-Newton algorithms.- A method of shortest residuals and nondifferentiable optimization.- The method of shortest residuals for smooth problems.- The preconditioned shortest residuals algorithm.- Optimization on a polyhedron.- Problems with box constraints.- The preconditioned shortest residuals algorithm with box.- Conjugate gradient reduced-Hessian method.- Elements of topology and analysis.- Elements of linear algebra
Series: Operator Theory: Advances and Applications , Vol. 189
2009, Approx. 340 p., Hardcover
ISBN: 978-3-7643-8968-0
Due: November 2008
This volume consists of seventeen peer-reviewed papers related to lectures on pseudo-differential operators presented at the meeting of the ISAAC Group in Pseudo-Differential Operators (IGPDO) held at the Middle East Technical University in Ankara,Turkey on August 13-18, 2007, and invited papers by experts in the field. Included in this volume are such topics as analysis and partial differential equations related to the Heisenberg group; global analysis and pseudo-differential analysis on non-compact manifolds and manifolds with singularities; Fourier integral operators and Colombeau algebras with applications to partial differential equations; exotic pseudo-differential operators and regularity results on quasi-elliptic operators and hypoelliptic operators; Stockwell transforms in time-frequency analysis; and pseudo-differential operators on Lie groups with related results to sampling. This volume is a useful complement to the volumes “Advances in Pseudo-Differential Operators”, “Pseudo-Differential Operators and Related Topics” and “Modern Trends in Pseudo-Differential Operators” published in the same series in, respectively, 2004, 2006 and 2007.
2009, Approx. 350 p. 110 illus., Hardcover
ISBN: 978-0-387-85594-3
Due: January 2009
Delay Differential Equations: Recent Advances and New Directions cohesively presents contributions from leading experts on the theory and applications of functional and delay differential equations (DDEs).
Researchers will benefit from a unique focus on theory, symbolic, and numerical methods, which illustrate how the concepts described can be applied to practical systems ranging from automotive engines to remote control over the Internet. Comprehensive coverage of recent advances paired with analytical contributions are included, in addition to computational techniques and illustrative examples of the application of current results drawn from biology, physics, mechanics, and control theory
Lyapunov-Krasovskii Functional Approach for Coupled Differential-Difference Equations with Multiple Delays.- Networked Control and Observation for Master-Slave Systems.- Developments in Control of Time-Delay Systems for Automotive Powertrain Applications.- Stability Analysis and Control of Linear Periodic Delayed Systems Using Chebyshev and Temporal Finite Element Methods.- Bifurcations, Center Manifolds, and Periodic Solutions.- Center Manifold Analysis of the Delayed Lienard Equation.- Calculating Center Manifolds for Delay Differential Equations Using Maple.- Numerical Solution of Delay Differential Equations.- Effects of Time Delay on Synchronization and Firing Patterns in Coupled Neuronal Systems.- Delayed Random Walks: Investigating the Interplay Between Delay and Noise.