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Hybrid dynamical systems, both continuous and discrete dynamics and variables, have attracted considerable interest recently. This emerging area is found at the interface of control theory and computer engineering, focusing on the analogue and digital aspects of systems and devices. They are essential for advances in modern digital- controller technology. "Qualitative Theory of Hybrid Dynamical Systems" provides a thorough development and systematic presentation of the foundations and framework for hybrid dynamical systems. The presentation offers an accessible, but precise, development of the mathematical models, conditions for existence of limit cycles, and criteria of their stability. The book largely concentrates on the case of discretely controlled continuous-time systems and their relevance for modeling aspects of flexible manufacturing systems and dynamically routed queuing networks. Features and topics: *differential automata*development and use of the concept "cyclic linear differential automata" (CLDA)*switched single-server flow networks coverage*application to specific models of manufacturing systems and queuing networks*select collection of open problems for the subject*self-contained presentation of topics, with the necessary background This new book is an excellent resource for the study and analysis of hybrid dynamical systems used in systems and control engineering. Researchers, postgraduates and professionals in control engineering and computer engineering will find the book an up-to-date development of the relevant new concepts and tools.

Ordinary differential equations --- Electronic controllers --- Digital control systems --- Analog electronic systems --- Applied mathematics. --- Engineering mathematics. --- System theory. --- Control engineering. --- Robotics. --- Mechatronics. --- Applications of Mathematics. --- Systems Theory, Control. --- Control, Robotics, Mechatronics. --- Mechanical engineering --- Microelectronics --- Microelectromechanical systems --- Automation --- Machine theory --- Control engineering --- Control equipment --- Control theory --- Engineering instruments --- Programmable controllers --- Systems, Theory of --- Systems science --- Science --- Engineering --- Engineering analysis --- Mathematical analysis --- Philosophy --- Mathematics

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Numerical mathematics is the branch of mathematics that proposes, develops, analyzes and applies methods from scientific computing to several fields including analysis, linear algebra, geometry, approximation theory, functional equations, optimization and differential equations. Other disciplines, such as physics, the natural and biological sciences, engineering, and economics and the financial sciences frequently give rise to problems that need scientific computing for their solutions. As such, numerical mathematics is the crossroad of several disciplines of great relevance in modern applied sciences, and can become a crucial tool for their qualitative and quantitative analysis. One of the purposes of this book is to provide the mathematical foundations of numerical methods, to analyze their basic theoretical properties (stability, accuracy, computational complexity) and demonstrate their performances on examples and counterexamples which outline their pros and cons. This is done using the MATLAB software environment which is user-friendly and widely adopted. Within any specific class of problems, the most appropriate scientific computing algorithms are reviewed, their theoretical analyses are carried out and the expected results are verified on a MATLAB computer implementation. Every chapter is supplied with examples, exercises and applications of the discussed theory to the solution of real-life problems. This book is addressed to senior undergraduate and graduate students with particular focus on degree courses in Engineering, Mathematics, Physics and Computer Sciences. The attention which is paid to the applications and the related development of software makes it valuable also for researchers and users of scientific computing in a large variety of professional fields.

Numerical analysis. --- Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Applied mathematics. --- Engineering mathematics. --- Applications of Mathematics. --- Analysis. --- Numerical Analysis. --- Mathematical analysis --- Global analysis (Mathematics). --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Math --- Science --- 517.1 Mathematical analysis --- Engineering --- Engineering analysis --- Mathematics

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In September 1997, the Working Week on Resolution of Singularities was held at Obergurgl in the Tyrolean Alps. Its objective was to manifest the state of the art in the field and to formulate major questions for future research. The four courses given during this week were written up by the speakers and make up part I of this volume. They are complemented in part II by fifteen selected contributions on specific topics and resolution theories. The volume is intended to provide a broad and accessible introduction to resolution of singularities leading the reader directly to concrete research problems.

Differential geometry. Global analysis --- 512.76 --- Singularities (Mathematics) --- Geometry, Algebraic --- Birational geometry. Mappings etc. --- 512.76 Birational geometry. Mappings etc. --- Birational geometry. Mappings etc --- Géométrie algébrique --- Singularités (mathématiques) --- Algebraic geometry. --- Topology. --- Applied mathematics. --- Engineering mathematics. --- Algebraic Geometry. --- Applications of Mathematics. --- Engineering --- Engineering analysis --- Mathematical analysis --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Algebraic geometry --- Mathematics --- Géométrie algébrique. --- Géométrie algébrique. --- Singularités (mathématiques)

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These two volumes constitute the Proceedings of the `Conférence Moshé Flato, 1999'. Their spectrum is wide but the various areas covered are, in fact, strongly interwoven by a common denominator, the unique personality and creativity of the scientist in whose honor the Conference was held, and the far-reaching vision that underlies his scientific activity. With these two volumes, the reader will be able to take stock of the present state of the art in a number of subjects at the frontier of current research in mathematics, mathematical physics, and physics. Volume I is prefaced by reminiscences of and tributes to Flato's life and work. It also includes a section on the applications of sciences to insurance and finance, an area which was of interest to Flato before it became fashionable. The bulk of both volumes is on physical mathematics, where the reader will find these ingredients in various combinations, fundamental mathematical developments based on them, and challenging interpretations of physical phenomena. Audience: These volumes will be of interest to researchers and graduate students in a variety of domains, ranging from abstract mathematics to theoretical physics and other applications. Some parts will be accessible to proficient undergraduate students, and even to persons with a minimum of scientific knowledge but enough curiosity.

Quantum theory --- Mathematical physics --- Applied mathematics. --- Engineering mathematics. --- Mathematical physics. --- Group theory. --- Algebra. --- Nuclear physics. --- Heavy ions. --- Economic theory. --- Applications of Mathematics. --- Theoretical, Mathematical and Computational Physics. --- Group Theory and Generalizations. --- Nuclear Physics, Heavy Ions, Hadrons. --- Economic Theory/Quantitative Economics/Mathematical Methods. --- Economic theory --- Political economy --- Social sciences --- Economic man --- Ions --- Atomic nuclei --- Atoms, Nuclei of --- Nucleus of the atom --- Physics --- Mathematics --- Mathematical analysis --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra --- Physical mathematics --- Engineering --- Engineering analysis --- Mathématiques --- Mathematical physics - Congresses --- Quantum theory - Congresses

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This book is devoted to the presentation of some flow problems in porous media having relevant industrial applications. The main topics covered are: the manufacturing of composite materials, the espresso coffee brewing process, the filtration of liquids through diapers, various questions about flow problems in oil reservoirs and the theory of homogenization. The aim is to show that filtration problems arising in very practical industrial context exhibit interesting and highly nontrivial mathematical aspects. Thus the style of the book is mathematically rigorous, but specifically oriented towards applications, so that it is intended for both applied mathematicians and researchers in various areas of technological interest. The reader is required to have a good knowledge of the classical theory of PDE and basic functional analysis.

Filters and filtration --- Fluid dynamics --- Porous materials --- Industrial applications --- Mathematical models --- Mathematical Theory --- Applied Mathematics --- Engineering & Applied Sciences --- Mathematics --- Physical Sciences & Mathematics --- Congresses --- Condensed matter. --- Partial differential equations. --- Thermodynamics. --- Mechanics. --- Applied mathematics. --- Engineering mathematics. --- Condensed Matter Physics. --- Partial Differential Equations. --- Classical Mechanics. --- Applications of Mathematics. --- Engineering --- Engineering analysis --- Mathematical analysis --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Chemistry, Physical and theoretical --- Mechanics --- Heat --- Heat-engines --- Partial differential equations --- Condensed materials --- Condensed media --- Condensed phase --- Materials, Condensed --- Media, Condensed --- Phase, Condensed --- Liquids --- Matter --- Solids --- Fluid dynamics - Congresses. --- Filters and filtration - Mathematical models - Congresses. --- Filters and filtration - Industrial applications - Congresses. --- Porous materials - Congresses. --- Differential equations, Partial.