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.

This book covers different omics aspects related to the extracellular matrix (ECM), namely specific omics resources focused on the extracellular matrix (e.g., databases, repositories and atlases), quantitative proteomics applied to specific extracellular matrices (e.g. basement membranes), biological processes such as ECM degradation (degradomics), cell-matrix interactions (adhesomes), signaling pathways, biomarker discovery and diseases, and interactomics (extracellular matrix interaction networks including not only protein-protein but also protein-glycosaminoglycan interactions).

This volume examines matrix theory and its application in solving a series of problems related to natural phenomena and applied science.

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.