Modern structural applications of crystallography make extensive use of statistical methods, in particular the probability density function (pdf) of the magnitude of the structure factor. Similarly, direct methods of phase determination have been responsible for much of the success of crystallography - methods based on properties of joint pdfs. This monograph, from two authorities in the field of structure factor statics, presents a survey of techniques and theories in this field of research in a self-contained and consistent way, with an emphasis on the probabilistic principles...

This collection of independent articles describes some mathematical problems recently developed in statistical physics and theoretical chemistry. The book introduces and reviews current research on such topics as nonlinear systems and colored noise, stochastic resonance, percolation, the trapping problem in the theory of random walks, and diffusive models for chemical kinetics. Some of these topics have never before been presented in expository book form. Applied mathematicians will be introduced to some contemporary problems in statistical physics. In addition, a number of unsolved problems...

The evolution of the state of many systems modeled by linear partial di?erential equations (PDEs) or linear delay di?erential equations can be described by ope- torsemigroups.Thestate ofsucha systemis anelementin anin?nite-dimensional normed space, whence the name in?nite-dimensional linear system . The study of operator semigroups is a mature area of functional analysis, which is still very active. The study of observation and control operators for such semigroups is relatively more recent. These operators are needed to model the - teraction of a system with the surrounding world via outputs...