الصفحة 1
الصفحة 1
Holomorphic Morse Inequalities and Bergman Kernels
The main analytic tool is the analytic localization technique in local index theory developed by Bismut-Lebeau. The book includes the most recent results in the field and therefore opens perspectives on several active areas of research in complex, Kähler and symplectic geometry. A large number of applications are included, e.g., an analytic proof of the Kodaira embedding theorem, a solution of the Grauert-Riemenschneider and Shiffman conjectures, a compactification of complete Kähler manifolds of pinched negative curvature, the Berezin-Toeplitz quantization, weak Lefschetz theorems, and the asymptotics of the Ray-Singer analytic torsion.
Formal Refinement for Operating System Kernels
The purpose of this book is to show that the formal specification of kernels can be followed by a completely formal refinement process that leads to the extraction of executable code. The formal refinement process ensures that the code meets the specification in a precise sense.
Formal Models of Operating System Kernels
The purpose of this book is to show that the formal specification of kernels is not only possible but also necessary if operating systems are to achieve the levels of reliability and security that is demanded of them today. Specifications of a sequence of kernels of increasing complexity are included, acting as models to enable the designer to identify and reason about the properties of the design – thus making explicit that which is too often left implicit or even unknown.
Direct and inverse Sturm-Liouville problems : A method of solution
This book provides an introduction to the most recent developments in the theory and practice of direct and inverse Sturm-Liouville problems on finite and infinite intervals. A universal approach for practical solving of direct and inverse spectral and scattering problems is presented, based on the notion of transmutation (transformation) operators and their efficient construction. Analytical representations for solutions of Sturm-Liouville equations as well as for the integral kernels of the transmutation operators are derived in the form of functional series revealing interesting special features and lending themselves to direct and simple numerical solution of a wide variety of problems.
Computational Science -- ICCS 2005 ; Vol. 3516 ; 5th International Conference, Atlanta, GA, USA, May 22-25, 2005, Proceedings, Part III
This book constitutes the refereed proceedings of the Fifth International Conference on Computational Science (ICCS 2005) held in Atlanta, Georgia, USA, 2005, Computational science is rapidly maturing as a mainstream discipline. It is central to an ever-expanding variety of ?elds in which computational methods and tools enable new discoveries with greater accuracy and speed. The primary objectives of this conference were to discuss problems and solutions in allareas,toidentifynewissues,toshapefuturedirectionsofresearch,andtohelp users apply various advanced computational techniques. The event highlighted recent developments in algorithms, computational kernels, next generation c- puting systems, tools, advanced numerical methods, data-driven systems, and emerging application ?elds, such as complex systems, ?nance, bioinformatics, computational aspects of wireless and mobile networks, graphics, and hybrid computation.
Computational Science -- ICCS 2005 ; Vol. 3515 ; 5th International Conference, Atlanta, GA, USA, May 22-25, 2005, Proceedings, Part I
This book constitutes the refereed proceedings of the Fifth International Conference on Computational Science (ICCS 2005) held in Atlanta, Georgia, USA, 2005, Computational science is rapidly maturing as a mainstream discipline. It is central to an ever-expanding variety of ?elds in which computational methods and tools enable new discoveries with greater accuracy and speed. The primary objectives of this conference were to discuss problems and solutions in allareas,toidentifynewissues,toshapefuturedirectionsofresearch,andtohelp users apply various advanced computational techniques. The event highlighted recent developments in algorithms, computational kernels, next generation c- puting systems, tools, advanced numerical methods, data-driven systems, and emerging application ?elds, such as complex systems, ?nance, bioinformatics, computational aspects of wireless and mobile networks, graphics, and hybrid computation.
Computational science -- ICCS 2005 ; Vol. 3514 ; 5th International Conference, Atlanta, GA, USA, May 22-25, 2005, Proceedings, Part I
This book constitutes the refereed proceedings of the Fifth International Conference on Computational Science (ICCS 2005) held in Atlanta, Georgia, USA, 2005, Computational science is rapidly maturing as a mainstream discipline. It is central to an ever-expanding variety of ?elds in which computational methods and tools enable new discoveries with greater accuracy and speed. The primary objectives of this conference were to discuss problems and solutions in allareas,toidentifynewissues,toshapefuturedirectionsofresearch,andtohelp users apply various advanced computational techniques. The event highlighted recent developments in algorithms, computational kernels, next generation c- puting systems, tools, advanced numerical methods, data-driven systems, and emerging application ?elds, such as complex systems, ?nance, bioinformatics, computational aspects of wireless and mobile networks, graphics, and hybrid computation.
Kernel Methods for Machine Learning with Math and Python: 100 Exercises for Building Logic
Addresses the fundamentals of kernel methods for machine learning by considering relevant math problems and building Python programs. The book’s main features are as follows: Includes 100 exercises, which have been carefully selected and refined. As their solutions are provided in the main text, readers can solve all of the exercises by reading the book. / The mathematical premises of kernels are proven and the correct conclusions are provided, helping readers to understand the nature of kernels. / Source programs and running examples are presented to help readers acquire a deeper understanding of the mathematics used. / Once readers have a basic understanding of the functional analysis topics covered in Chapter 2, the applications are discussed in the subsequent chapters. Here, no prior knowledge of mathematics is assumed. / Considers both the kernel for reproducing kernel Hilbert space (RKHS) and the kernel for the Gaussian process; a clear distinction is made between the two.
