Evaluation Of The Probability Integral To High Precision
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Evaluation of the Probability Integral to High Precision by Francis Dominic Murnaghan Pdf
The 'converging factor' for an asymptotic series representing a function f(x) is that number by which the (n + 1) term of the series must be multiplied so that the result of adding this product to the sum of the first n terms will be f(x). The determination to high precision of this factor for the asymptotic series representing the probability integral is described. Tables of this factor to 63 decimal places are included for n ranging from 2 to 64. (Author).
High Performance Algorithms and Software in Nonlinear Optimization by Renato de Leone,Almerico Murli,Panos M. Pardalos,Gerardo Toraldo Pdf
This book contains a selection of papers presented at the conference on High Performance Software for Nonlinear Optimization (HPSN097) which was held in Ischia, Italy, in June 1997. The rapid progress of computer technologies, including new parallel architec tures, has stimulated a large amount of research devoted to building software environments and defining algorithms able to fully exploit this new computa tional power. In some sense, numerical analysis has to conform itself to the new tools. The impact of parallel computing in nonlinear optimization, which had a slow start at the beginning, seems now to increase at a fast rate, and it is reasonable to expect an even greater acceleration in the future. As with the first HPSNO conference, the goal of the HPSN097 conference was to supply a broad overview of the more recent developments and trends in nonlinear optimization, emphasizing the algorithmic and high performance software aspects. Bringing together new computational methodologies with theoretical ad vances and new computer technologies is an exciting challenge that involves all scientists willing to develop high performance numerical software. This book contains several important contributions from different and com plementary standpoints. Obviously, the articles in the book do not cover all the areas of the conference topic or all the most recent developments, because of the large number of new theoretical and computational ideas of the last few years.
Asymptotics and Special Functions by F. W. J. Olver Pdf
Asymptotics and Special Functions provides a comprehensive introduction to two important topics in classical analysis: asymptotics and special functions. The integrals of a real variable and contour integrals are discussed, along with the Liouville-Green approximation and connection formulas for solutions of differential equations. Differential equations with regular singularities are also considered, with emphasis on hypergeometric and Legendre functions. Comprised of 14 chapters, this volume begins with an introduction to the basic concepts and definitions of asymptotic analysis and special functions, followed by a discussion on asymptotic theories of definite integrals containing a parameter. Contour integrals as well as integrals of a real variable are described. Subsequent chapters deal with the analytic theory of ordinary differential equations; differential equations with regular and irregular singularities; sums and sequences; and connection formulas for solutions of differential equations. The book concludes with an evaluation of methods used in estimating (as opposed to bounding) errors in asymptotic approximations and expansions. This monograph is intended for graduate mathematicians, physicists, and engineers.
Asymptotics and Special Functions by Frank Olver Pdf
A classic reference, intended for graduate students mathematicians, physicists, and engineers, this book can be used both as the basis for instructional courses and as a reference tool.
Stochastic Processes by Pierre Del Moral,Spiridon Penev Pdf
Unlike traditional books presenting stochastic processes in an academic way, this book includes concrete applications that students will find interesting such as gambling, finance, physics, signal processing, statistics, fractals, and biology. Written with an important illustrated guide in the beginning, it contains many illustrations, photos and pictures, along with several website links. Computational tools such as simulation and Monte Carlo methods are included as well as complete toolboxes for both traditional and new computational techniques.
Smart Structures and Materials by Aurelio L. Araujo,Carlos A. Mota Soares Pdf
This work was compiled with expanded and reviewed contributions from the 7th ECCOMAS Thematic Conference on Smart Structures and Materials, that was held from 3 to 6 June 2015 at Ponta Delgada, Azores, Portugal. The Conference provided a comprehensive forum for discussing the current state of the art in the field as well as generating inspiration for future ideas specifically on a multidisciplinary level. The scope of the Conference included topics related to the following areas: Fundamentals of smart materials and structures; Modeling/formulation and characterization of smart actuators, sensors and smart material systems; Trends and developments in diverse areas such as material science including composite materials, intelligent hydrogels, interfacial phenomena, phase boundaries and boundary layers of phase boundaries, control, micro- and nano-systems, electronics, etc. to be considered for smart systems; Comparative evaluation of different smart actuators and sensors; Analysis of structural concepts and designs in terms of their adaptability to smart technologies; Design and development of smart structures and systems; Biomimetic phenomena and their inspiration in engineering; Fabrication and testing of smart structures and systems; Applications of smart materials, structures and related technology; Smart robots; Morphing wings and smart aircrafts; Artificial muscles and biomedical applications; Smart structures in mechatronics; and Energy harvesting.
Statistical Multiple Integration by Nancy Flournoy,Robert K. Tsutakawa,American Mathematical Society,Institute of Mathematical Statistics,Society for Industrial and Applied Mathematics Pdf
High dimensional integration arises naturally in two major sub-fields of statistics: multivariate and Bayesian statistics. Indeed, the most common measures of central tendency, variation, and loss are defined by integrals over the sample space, the parameter space, or both. Recent advances in computational power have stimulated significant new advances in both Bayesian and classical multivariate statistics. In many statistical problems, however, multiple integration can be the major obstacle to solutions. This volume contains the proceedings of an AMS-IMS-SIAM Joint Summer Research Conference on Statistical Multiple Integration, held in June 1989 at Humboldt State University in Arcata, California. The conference represents an attempt to bring together mathematicians, statisticians, and computational scientists to focus on the many important problems in statistical multiple integration. The papers document the state of the art in this area with respect to problems in statistics, potential advances blocked by problems with multiple integration, and current work directed at expanding the capability to integrate over high dimensional surfaces.
Orbital Data Applications for Space Objects by Lei Chen,Xian-Zong Bai,Yan-Gang Liang,Ke-Bo Li Pdf
This book introduces readers to the application of orbital data on space objects in the contexts of conjunction assessment and space situation analysis, including theories and methodologies. It addresses the main topics involved in space object conjunction assessment, such as: orbital error analysis of space objects; close approach analysis; the calculation, analysis and application of collision probability; and the comprehensive assessment of collision risk. In addition, selected topics on space situation analysis are also presented, including orbital anomaly and space event analysis, and so on. The book offers a valuable guide for researchers and engineers in the fields of astrodynamics, space telemetry, tracking and command (TT&C), space surveillance, space situational awareness, and space debris, as well as for graduates majoring in flight vehicle design and related fields.
