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| Author | : Leonid Libkin |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 320 |
| Release | : 2013-03-09 |
| Genre | : Mathematics |
| ISBN | : 3662070030 |
Emphasizes the computer science aspects of the subject. Details applications in databases, complexity theory, and formal languages, as well as other branches of computer science.
| Author | : Heinz-Dieter Ebbinghaus |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 363 |
| Release | : 2005-12-29 |
| Genre | : Mathematics |
| ISBN | : 3540287884 |
This is a thoroughly revised and enlarged second edition that presents the main results of descriptive complexity theory, that is, the connections between axiomatizability of classes of finite structures and their complexity with respect to time and space bounds. The logics that are important in this context include fixed-point logics, transitive closure logics, and also certain infinitary languages; their model theory is studied in full detail. The book is written in such a way that the respective parts on model theory and descriptive complexity theory may be read independently.
| Author | : Heinz-Dieter Ebbinghaus |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 336 |
| Release | : 2013-06-29 |
| Genre | : Mathematics |
| ISBN | : 3662031825 |
Finite model theory has its origin in classical model theory, but owes its systematic development to research from complexity theory. The book presents the main results of descriptive complexity theory, that is, the connections between axiomatizability of classes of finite structures and their complexity with respect to time and space bounds. The logics that are important in this context include fixed- point logics, transitive closure logics, and also certain infinitary languages; their model theory is studied in full detail. Other topics include DATALOG languages, quantifiers and oracles, 0-1 laws, and optimization and approximation problems. The book is written in such a way that the resp. parts on model theory and descriptive complexity theory may be read independently.
| Author | : Erich Grädel |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 447 |
| Release | : 2007-06-04 |
| Genre | : Computers |
| ISBN | : 3540688048 |
Finite model theory,as understoodhere, is an areaof mathematicallogic that has developed in close connection with applications to computer science, in particular the theory of computational complexity and database theory. One of the fundamental insights of mathematical logic is that our understanding of mathematical phenomena is enriched by elevating the languages we use to describe mathematical structures to objects of explicit study. If mathematics is the science of patterns, then the media through which we discern patterns, as well as the structures in which we discern them, command our attention. It isthis aspect oflogicwhichis mostprominentin model theory,“thebranchof mathematical logic which deals with the relation between a formal language and its interpretations”. No wonder, then, that mathematical logic, and ?nite model theory in particular, should ?nd manifold applications in computer science: from specifying programs to querying databases, computer science is rife with phenomena whose understanding requires close attention to the interaction between language and structure. This volume gives a broadoverviewof some central themes of ?nite model theory: expressive power, descriptive complexity, and zero–one laws, together with selected applications to database theory and arti?cial intelligence, es- cially constraint databases and constraint satisfaction problems. The ?nal chapter provides a concise modern introduction to modal logic,which emp- sizes the continuity in spirit and technique with ?nite model theory.
| Author | : Alexandre Ern |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 531 |
| Release | : 2013-03-09 |
| Genre | : Mathematics |
| ISBN | : 1475743556 |
This text presenting the mathematical theory of finite elements is organized into three main sections. The first part develops the theoretical basis for the finite element methods, emphasizing inf-sup conditions over the more conventional Lax-Milgrim paradigm. The second and third parts address various applications and practical implementations of the method, respectively. It contains numerous examples and exercises.
| Author | : Heinz-Dieter Ebbinghaus |
| Publisher | : Springer |
| Total Pages | : 327 |
| Release | : 2014-03-12 |
| Genre | : Mathematics |
| ISBN | : 9783662031834 |
Finite model theory has its origin in classical model theory, but owes its systematic development to research from complexity theory. The book presents the main results of descriptive complexity theory, that is, the connections between axiomatizability of classes of finite structures and their complexity with respect to time and space bounds. The logics that are important in this context include fixed- point logics, transitive closure logics, and also certain infinitary languages; their model theory is studied in full detail. Other topics include DATALOG languages, quantifiers and oracles, 0-1 laws, and optimization and approximation problems. The book is written in such a way that the resp. parts on model theory and descriptive complexity theory may be read independently.
| Author | : Nitin S. Gokhale |
| Publisher | : FINITE TO INFINITE |
| Total Pages | : 27 |
| Release | : 2008 |
| Genre | : Engineering |
| ISBN | : 8190619500 |
Highlights of the book: Discussion about all the fields of Computer Aided Engineering, Finite Element Analysis Sharing of worldwide experience by more than 10 working professionals Emphasis on Practical usuage and minimum mathematics Simple language, more than 1000 colour images International quality printing on specially imported paper Why this book has been written ... FEA is gaining popularity day by day & is a sought after dream career for mechanical engineers. Enthusiastic engineers and managers who want to refresh or update the knowledge on FEA are encountered with volume of published books. Often professionals realize that they are not in touch with theoretical concepts as being pre-requisite and find it too mathematical and Hi-Fi. Many a times these books just end up being decoration in their book shelves ... All the authors of this book are from IIT€™s & IISc and after joining the industry realized gap between university education and the practical FEA. Over the years they learned it via interaction with experts from international community, sharing experience with each other and hard route of trial & error method. The basic aim of this book is to share the knowledge & practices used in the industry with experienced and in particular beginners so as to reduce the learning curve & avoid reinvention of the cycle. Emphasis is on simple language, practical usage, minimum mathematics & no pre-requisites. All basic concepts of engineering are included as & where it is required. It is hoped that this book would be helpful to beginners, experienced users, managers, group leaders and as additional reading material for university courses.
| Author | : Amir R. Khoei |
| Publisher | : John Wiley & Sons |
| Total Pages | : 600 |
| Release | : 2015-02-23 |
| Genre | : Science |
| ISBN | : 1118457684 |
Introduces the theory and applications of the extended finite element method (XFEM) in the linear and nonlinear problems of continua, structures and geomechanics Explores the concept of partition of unity, various enrichment functions, and fundamentals of XFEM formulation. Covers numerous applications of XFEM including fracture mechanics, large deformation, plasticity, multiphase flow, hydraulic fracturing and contact problems Accompanied by a website hosting source code and examples
| Author | : O. C. Zienkiewicz |
| Publisher | : Elsevier |
| Total Pages | : 653 |
| Release | : 2005-08-09 |
| Genre | : Technology & Engineering |
| ISBN | : 0080455581 |
This is the key text and reference for engineers, researchers and senior students dealing with the analysis and modelling of structures – from large civil engineering projects such as dams, to aircraft structures, through to small engineered components. Covering small and large deformation behaviour of solids and structures, it is an essential book for engineers and mathematicians. The new edition is a complete solids and structures text and reference in its own right and forms part of the world-renowned Finite Element Method series by Zienkiewicz and Taylor. New material in this edition includes separate coverage of solid continua and structural theories of rods, plates and shells; extended coverage of plasticity (isotropic and anisotropic); node-to-surface and 'mortar' method treatments; problems involving solids and rigid and pseudo-rigid bodies; and multi-scale modelling. Dedicated coverage of solid and structural mechanics by world-renowned authors, Zienkiewicz and Taylor New material including separate coverage of solid continua and structural theories of rods, plates and shells; extended coverage for small and finite deformation; elastic and inelastic material constitution; contact modelling; problems involving solids, rigid and discrete elements; and multi-scale modelling
| Author | : P.G. Ciarlet |
| Publisher | : Elsevier |
| Total Pages | : 551 |
| Release | : 1978-01-01 |
| Genre | : Mathematics |
| ISBN | : 0080875254 |
The objective of this book is to analyze within reasonable limits (it is not a treatise) the basic mathematical aspects of the finite element method. The book should also serve as an introduction to current research on this subject. On the one hand, it is also intended to be a working textbook for advanced courses in Numerical Analysis, as typically taught in graduate courses in American and French universities. For example, it is the author’s experience that a one-semester course (on a three-hour per week basis) can be taught from Chapters 1, 2 and 3 (with the exception of Section 3.3), while another one-semester course can be taught from Chapters 4 and 6. On the other hand, it is hoped that this book will prove to be useful for researchers interested in advanced aspects of the numerical analysis of the finite element method. In this respect, Section 3.3, Chapters 5, 7 and 8, and the sections on “Additional Bibliography and Comments should provide many suggestions for conducting seminars.
