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Totally Nonnegative Matrices
Totally nonnegative matrices arise in a remarkable variety of mathematical applications. This book is a comprehensive and self-contained study of the essential theory of totally nonnegative matrices, defined by the nonnegativity of all subdeterminants. It explores methodological background, historical highlights of key ideas, and specialized topics. The book uses classical and ad hoc tools, but a unifying theme is the elementary bidiagonal factorization, which has emerged as the single most important tool for this particular class of matrices. Recent work has shown that bidiagonal factorizations may be viewed in a succinct combinatorial way, leading to many deep insights. Despite slow develo...
Mechanics for a New Millennium
This volume contains the proceedings of the 2000 International Congress of Theoretical and Applied Mechanics. The book captures a snapshot view of the state of the art in the field of mechanics and will be invaluable to engineers and scientists from a variety of disciplines.
Mechanics of Poroelastic Media
In Mechanics of Poroelastic Media the classical theory of poroelasticity developed by Biot is developed and extended to the study of problems in geomechanics, biomechanics, environmental mechanics and materials science. The contributions are grouped into sections covering constitutive modelling, analytical aspects, numerical modelling, and applications to problems. The applications of the classical theory of poroelasticity to a wider class of problems will be of particular interest. The text is a standard reference for researchers interested in developing mathematical models of poroelasticity in geoenvironmental mechanics, and in the application of advanced theories of poroelastic biomaterials to the mechanics of biomaterials.
Analysis on Graphs and Its Applications
This book addresses a new interdisciplinary area emerging on the border between various areas of mathematics, physics, chemistry, nanotechnology, and computer science. The focus here is on problems and techniques related to graphs, quantum graphs, and fractals that parallel those from differential equations, differential geometry, or geometric analysis. Also included are such diverse topics as number theory, geometric group theory, waveguide theory, quantum chaos, quantum wiresystems, carbon nano-structures, metal-insulator transition, computer vision, and communication networks.This volume contains a unique collection of expert reviews on the main directions in analysis on graphs (e.g., on discrete geometric analysis, zeta-functions on graphs, recently emerging connections between the geometric group theory and fractals, quantum graphs, quantum chaos on graphs, modeling waveguide systems and modeling quantum graph systems with waveguides, control theory on graphs), as well as research articles.
Mechanics of Curved Composites
This book is the frrst to focus on mechanical aspects of fibrous and layered composite material with curved structure. By mechanical aspects we mean statics, vibration, stability loss, elastic and fracture problems. By curved structures we mean that the reinforcing layers or fibres are not straight: they have some initial curvature, bending or distortion. This curvature may occur as a result of design, or as a consequence of some technological process. During the last two decades, we and our students have investigated problems relating to curved composites intensively. These investigations have allowed us to study stresses and strains in regions of a composite which are small compared to the...
Structural Synthesis of Parallel Robots
This book represents the fifth part of a larger work dedicated to the structural synthesis of parallel robots. The originality of this work resides in the fact that it combines new formulae for mobility, connectivity, redundancy and overconstraints with evolutionary morphology in a unified structural synthesis approach that yields interesting and innovative solutions for parallel robotic manipulators. This is the first book on robotics that presents solutions for coupled, decoupled, uncoupled, fully-isotropic and maximally regular robotic manipulators with Schönflies motions systematically generated by using the structural synthesis approach proposed in Part 1. Overconstrained non-redundant...
Engineering Mechanics
Here is a systematic and clearly laid out text on structural and continuum mechanics. Containing hundreds of diagrams, drawings and examples, this work dovetails theoretical developments and figures in a beautifully conceived treatment of the subject. The book also covers stresses and strains in simple elements subjected to extension, bending, shear and torsion. For elementary structures, simple load displacements are obtained using both classical mathematics descriptions and engineering methods like Williot diagrams.
Mechanics of Components with Treated or Coated Surfaces
Surface treatment is an efficient means for protection of various products against corrosion and also for increasing strength or resistance to wear or fatigue. Also certain electrical, chemical or optical properties may be achieved only by creating special surface layers. Many examples can be given: leaf springs with shot-peened surfaces; carburised and hardened tooth gears; coated cutting tips for machining; chemical appliances made of glass strengthened by ion exchange; enamelled vessels and containers; components for engines or turbines with heat insulating ceramic surface layers; chemical equipment made from low-carbon steel clad with a layer of stainless steel or other more expensive ma...
