In the structure theory of real Lie groups, there is still information lacking about the exponential function. Most notably, there are no general necessary and sufficient conditions for the exponential function to be surjective. It is surprising that for subsemigroups of Lie groups, the question of the surjectivity of the exponential function can be answered. Under nature reductions setting aside the "group part" of the problem, subsemigroups of Lie groups with surjective exponential function are completely classified and explicitly constructed in this memoir. There are fewer than one would think and the proofs are harder than one would expect, requiring some innovative twists. The main protagonists on the scene are SL(2, R) and its universal covering group, almost abelian solvable Lie groups (ie. vector groups extended by homotheties), and compact Lie groups. This text will also be of interest to those working in algebra and algebraic geometry.
In the structure theory of real Lie groups, there is still information lacking about the exponential function. Most notably, there are no general necessary and sufficient conditions for the exponential function to be surjective. It is surprising that for subsemigroups of Lie groups, the question of the surjectivity of the exponential function can be answered. Under nature reductions setting aside the group part of the problem, subsemigroups of Lie groups with surjective exponential function are completely classified and explicitly constructed in this memoir. There are fewer than one would think and the proofs are harder than one would expect, requiring some innovative twists.
In the structure theory of real Lie groups, there is still information lacking about the exponential function. Most notably, there are no general necessary and sufficient conditions for the exponential function to be surjective. It is surprising that for subsemigroups of Lie groups, the question of the surjectivity of the exponential function can be answered. Under nature reductions setting aside the "group part" of the problem, subsemigroups of Lie groups with surjective exponential function are completely classified and explicitly constructed in this memoir. There are fewer than one would think and the proofs are harder than one would expect, requiring some innovative twists. The main protagonists on the scene are SL(2, R) and its universal covering group, almost abelian solvable Lie groups (ie. vector groups extended by homotheties), and compact Lie groups. This text will also be of interest to those working in algebra and algebraic geometry.
This book describes an interactive statistical computing environment called 1 XploRe. As the name suggests, support for exploratory statistical analysis is given by a variety of computational tools. XploRe is a matrix-oriented statistical language with a comprehensive set of basic statistical operations that provides highly interactive graphics, as well as a programming environ ment for user-written macros; it offers hard-wired smoothing procedures for effective high-dimensional data analysis. Its highly dynamic graphic capa bilities make it possible to construct student-level front ends for teaching basic elements of statistics. Hot keys make it an easy-to-use computing environment for statistical analysis. The primary objective of this book is to show how the XploRe system can be used as an effective computing environment for a large number of statistical tasks. The computing tasks we consider range from basic data matrix manipulations to interactive customizing of graphs and dynamic fit ting of high-dimensional statistical models. The XploRe language is similar to other statistical languages and offers an interactive help system that can be extended to user-written algorithms. The language is intuitive and read ers with access to other systems can, without major difficulty, reproduce the examples presented here and use them as a basis for further investigation.
The statistical and mathematical principles of smoothing with a focus on applicable techniques are presented in this book. It naturally splits into two parts: The first part is intended for undergraduate students majoring in mathematics, statistics, econometrics or biometrics whereas the second part is intended to be used by master and PhD students or researchers. The material is easy to accomplish since the e-book character of the text gives a maximum of flexibility in learning (and teaching) intensity.
In the last ten years, there has been increasing interest and activity in the general area of partially linear regression smoothing in statistics. Many methods and techniques have been proposed and studied. This monograph hopes to bring an up-to-date presentation of the state of the art of partially linear regression techniques. The emphasis is on methodologies rather than on the theory, with a particular focus on applications of partially linear regression techniques to various statistical problems. These problems include least squares regression, asymptotically efficient estimation, bootstrap resampling, censored data analysis, linear measurement error models, nonlinear measurement models, nonlinear and nonparametric time series models.
The aim of this study is to give a more precise interpretation, using the commemorative form of activity of confraternity, of the function and purpose behind such depictions, in the case of a few selected early medieval images of rulers, from the historical and social contexts of their genesis and the liturgical and commemorative aims of their use.
This groundbreaking book introduces the application of statistical methodologies to e-Commerce data With the expanding presence of technology in today's economic market, the use of the Internet for buying, selling, and investing is growing more popular and public in nature. Statistical Methods in e-Commerce Research is the first book of its kind to focus on the statistical models and methods that are essential in order to analyze information from electronic-commerce (e-Commerce) transactions, identify the challenges that arise with new e-Commerce data structures, and discover new knowledge about consumer activity. This collection gathers over thirty researchers and practitioners from the fields of statistics, computer science, information systems, and marketing to discuss the growing use of statistical methods in e-Commerce research. From privacy protection to economic impact, the book first identifies the many obstacles that are encountered while collecting, cleaning, exploring, and analyzing e-Commerce data. Solutions to these problems are then suggested using established and newly developed statistical and data mining methods. Finally, a look into the future of this evolving area of study is provided through an in-depth discussion of the emerging methods for conducting e-Commerce research. Statistical Methods in e-Commerce Research successfully bridges the gap between statistics and e-Commerce, introducing a statistical approach to solving challenges that arise in the context of online transactions, while also introducing a wide range of e-Commerce applications and problems where novel statistical methodology is warranted. It is an ideal text for courses on e-Commerce at the upper-undergraduate and graduate levels and also serves as a valuable reference for researchers and analysts across a wide array of subject areas, including economics, marketing, and information systems who would like to gain a deeper understanding of the use of statistics in their work.
Explore cutting-edge statistical methodologies for collecting, analyzing, and modeling online auction data Online auctions are an increasingly important marketplace, as the new mechanisms and formats underlying these auctions have enabled the capturing and recording of large amounts of bidding data that are used to make important business decisions. As a result, new statistical ideas and innovation are needed to understand bidders, sellers, and prices. Combining methodologies from the fields of statistics, data mining, information systems, and economics, Modeling Online Auctions introduces a new approach to identifying obstacles and asking new questions using online auction data. The authors draw upon their extensive experience to introduce the latest methods for extracting new knowledge from online auction data. Rather than approach the topic from the traditional game-theoretic perspective, the book treats the online auction mechanism as a data generator, outlining methods to collect, explore, model, and forecast data. Topics covered include: Data collection methods for online auctions and related issues that arise in drawing data samples from a Web site Models for bidder and bid arrivals, treating the different approaches for exploring bidder-seller networks Data exploration, such as integration of time series and cross-sectional information; curve clustering; semi-continuous data structures; and data hierarchies The use of functional regression as well as functional differential equation models, spatial models, and stochastic models for capturing relationships in auction data Specialized methods and models for forecasting auction prices and their applications in automated bidding decision rule systems Throughout the book, R and MATLAB software are used for illustrating the discussed techniques. In addition, a related Web site features many of the book's datasets and R and MATLAB code that allow readers to replicate the analyses and learn new methods to apply to their own research. Modeling Online Auctions is a valuable book for graduate-level courses on data mining and applied regression analysis. It is also a one-of-a-kind reference for researchers in the fields of statistics, information systems, business, and marketing who work with electronic data and are looking for new approaches for understanding online auctions and processes. Visit this book's companion website by clicking here
This book highlights proteasome structures and how they are related to different aspects of proteasome function. Moreover, the book reports on the functional roles these highly developed proteolytic machines play within the cell. It was a great surprise to the scientific world that proteolysis provides crucial functions in cellular regulation. The
Thank you for visiting our website. Would you like to provide feedback on how we could improve your experience?
This site does not use any third party cookies with one exception — it uses cookies from Google to deliver its services and to analyze traffic.Learn More.