This book studies the modules arising in Fourier expansions of automorphic forms, namely Fourier term modules on SU(2,1), the smallest rank one Lie group with a non-abelian unipotent subgroup. It considers the “abelian” Fourier term modules connected to characters of the maximal unipotent subgroups of SU(2,1), and also the “non-abelian” modules, described via theta functions. A complete description of the submodule structure of all Fourier term modules is given, with a discussion of the consequences for Fourier expansions of automorphic forms, automorphic forms with exponential growth included. These results can be applied to prove a completeness result for Poincaré series in spaces of square integrable automorphic forms. Aimed at researchers and graduate students interested in automorphic forms, harmonic analysis on Lie groups, and number-theoretic topics related to Poincaré series, the book will also serve as a basic reference on spectral expansion with Fourier-Jacobi coefficients. Only a background in Lie groups and their representations is assumed.

Probability and Mathematical Statistics: A Series of Monographs and Textbooks: Statistics of Directional Data aims to provide a systematic account of statistical theory and methodology for observations which are directions. The publication first elaborates on angular data and frequency distributions, descriptive measures, and basic concepts and theoretical models. Discussions focus on moments and measures of location and dispersion, distribution function, corrections for grouping, calculation of the mean direction and the circular variance, interrelations between different units of angular measurement, and diagrammatical representation. The book then examines fundamental theorems and distribution theory, point estimation, and tests for samples from von Mises populations. The text takes a look at non-parametric tests, distributions on spheres, and inference problems on the sphere. Topics include tests for axial data, point estimation, distribution theory, moments and limiting distributions, and tests of goodness of fit and tests of uniformity. The publication is a dependable reference for researchers interested in probability and mathematical statistics.

This, the second special topical conference on the properties of Non-Metallic Materials at Low Temperatures, was sponsored by the International Cryogenic Materials Conference Board. The potential for plastics materials in the field of cryogenics is vast and as yet only partly explored. In addition, many other materials, which qualify for the title non-metallic but are not 'plastics', have numerous possible outlets in low temperature technology. This conference aimed at providing a forum, whereby specialists from Industry, the Universities and from Government sponsored Institutions could assemble to discuss the extent of our current knowledge. As it transpired, the meeting was also to high light the considerable gaps that still exist in our fundamental understanding of the low temperature behaviour of these materials. On this theme, during the course of the conference, a reference was made to an almost forgotten quotation by Lord Kelvin, who said: "When you cannot measure what you are speaking about, when you cannot express in numbers, your knowledge is of a meagre and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely in your thoughts advanced to the stage of a science, whatever the matter be." This simple statement sums up the aims, objectives and hopefully the achievements of this conference. To discuss and disseminate the current knowledge on non-metallic materials in order that realistic predictions of in-service performance may be made.

This book comprises select proceedings of the International Conference on Emerging Trends in Mechanical Engineering (ICETME 2018). The book covers various topics of mechanical engineering like computational fluid dynamics, heat transfer, machine dynamics, tribology, and composite materials. In addition, relevant studies in the allied fields of manufacturing, industrial and production engineering are also covered. The applications of latest tools and techniques in the context of mechanical engineering problems are discussed in this book. The contents of this book will be useful for students, researchers as well as industry professionals.

Crystal oscillators have been in use now for well over SO years-one of the first was built by W. G. Cady in 1921. Today, millions of them are made every year, covering a range of frequencies from a few Kilohertz to several hundred Mega hertz and a range of stabilities from a fraction of one percent to a few parts in ten to the thirteenth, with most of them, by far, still in the range of several tens of parts per million.Their major application has long been the stabilization of fre quencies in transmitters and receivers, and indeed, the utilization of the frequency spectrum would be in utter chaos, and the communication systems as we know them today unthinkable,'without crystal oscillators. With the need to accommodate ever increasing numbers of users in a limited spectrum space, this traditional application will continue to grow for the fore seeable future, and ever tighter tolerances will have to be met by an ever larger percentage of these devices.

Master the usage of s-parameters in signal integrity applications and gain full understanding of your simulation and measurement environment with this rigorous and practical guide. Solve specific signal integrity problems including calculation of the s-parameters of a network, linear simulation of circuits, de-embedding, and virtual probing, all with expert guidance. Learn about the interconnectedness of s-parameters, frequency responses, filters, and waveforms. This invaluable resource for signal integrity engineers is supplemented with the open-source software SignalIntegrity, a Python package for scripting solutions to signal integrity problems.