Matrix

This book investigates the time-dependent behavior of fiber-reinforced ceramic-matrix composites (CMCs) at elevated temperatures. The author combines the time-dependent damage mechanisms of interface and fiber oxidation and fracture with the micromechanical approach to establish the relationships between the first matrix cracking stress, matrix multiple cracking evolution, tensile strength, tensile stress-strain curves and tensile fatigue of fiber-reinforced CMCs and time.

Fundamentals of Matrix-Analytic Methods targets advanced-level students in mathematics, engineering and computer science. It focuses on the fundamental parts of Matrix-Analytic Methods, Phase-Type Distributions, Markovian arrival processes and Structured Markov chains and matrix geometric solutions.

In teaching linear statistical models to first-year graduate students or to final-year undergraduate students there is no way to proceed smoothly without matrices and related concepts of linear algebra; their use is really essential. Our experience is that making some particular matrix tricks very familiar to students can substantially increase their insight into linear statistical models (and also multivariate statistical analysis). In matrix algebra, there are handy, sometimes even very simple “tricks” which simplify and clarify the treatment of a problem—both for the student and for the professor. Of course, the concept of a trick is not uniquely defined—by a trick we simply mean here a useful important handy result.

This book is primarily intended as a research monograph that could also be used in graduate courses for the design of parallel algorithms in matrix computations.

This book reports research and new developments in the field of collagen structure, function, and biomechanics and discusses the relevance of hyaluronic acid and its therapeutic uses. It gives readers a glimpse of what is current in this area and we hope it piques their interest in learning more about ECM biology.

In this set of lecture notes, we present a culmination of results on infinite matrices which were evolved by the members of the Katowice Br-anch of the Mathematics Institute of the Polish Academy of Sciences. In the early history of functional analysis Hsliding humpH methods were used extensively to establish some of the early abstract results in functional analysis. For example, the first proofs of versions of the Uniform Boundedness Principle by Hahn and Banach and Hildebrand utilized sliding hump methods ([18], [39], [42], [35]).