Multidimensional Spaces Rosenfeld

The monograph is devoted to integral representations for holomorphic functions in several complex variables, such as Bochner-Martinelli, Cauchy-Fantappiè, Koppelman, multidimensional logarithmic residue etc., and their boundary properties. The applications considered are problems of analytic continuation of functions from the boundary of a bounded domain in C^n. In contrast to the well-known Hartogs-Bochner theorem, this book investigates functions with the one-dimensional property of holomorphic extension along complex lines, and includes the problems of receiving multidimensional boundary analogs of the Morera theorem.

A color time-varying image can be described as a three-dimensional vector (representing the colors in an appropriate color space) defined on a three-dimensional spatiotemporal space. In conventional analog television a one-dimensional signal suitable for transmission over a communication channel is obtained by sampling the scene in the vertical and tem­ poral directions and by frequency-multiplexing the luminance and chrominance informa­ tion. In digital processing and transmission systems, sampling is applied in the horizontal direction, too, on a signal which has been already scanned in the vertical and temporal directions or directly in three dimensions when using some solid-state sensor. As a conse­ quence, in recent years it has been considered quite natural to assess the potential advan­ tages arising from an entire multidimensional approach to the processing of video signals. As a simple but significant example, a composite color video signal, such as the conven­ tional PAL or NTSC signal, possesses a three-dimensional spectrum which, by using suitable three-dimensional filters, permits horizontal sampling at a rate which is less than that re­ quired for correctly sampling the equivalent one-dimensional signal. More recently it has been widely recognized that the improvement of the picture quality in current and advanced television systems requires well-chosen signal processing algorithms which are multidimen­ sional in nature within the demanding constraints of a real-time implementation.

Applications that require a high degree of distribution and loosely-coupled connectivity are ubiquitous in various domains, including scientific databases, bioinformatics, and multimedia retrieval. In all these applications, data is typically voluminous and multidimensional, and support for advanced query operators is required for effective querying and efficient processing. To address this challenge, we adopt a hybrid P2P architecture and propose novel indexing and query processing algorithms. We present a scalable framework that relies on data summaries that are distributed and maintained as multidimensional routing indices. Different types of data summaries enable efficient processing of a variety of advanced query operators.

This book gathers selected papers presented at the conference “Advances in 3D Image and Graphics Representation, Analysis, Computing and Information Technology,” one of the first initiatives devoted to the problems of 3D imaging in all contemporary scientific and application areas. The two volumes of the book cover wide area of the aspects of the contemporary multidimensional imaging and outline the related future trends from data acquisition to real-world applications based on new techniques and theoretical approaches.

This book gathers selected papers presented at the conference “Advances in 3D Image and Graphics Representation, Analysis, Computing and Information Technology,” one of the first initiatives devoted to the problems of 3D imaging in all contemporary scientific and application areas. The two volumes of the book cover wide area of the aspects of the contemporary multidimensional imaging and outline the related future trends from data acquisition to real-world applications based on new techniques and theoretical approaches.

Our society has entered a data-driven era, one in which not only are enormous amounts of data being generated daily but there are also growing expectations placed on the analysis of this data. Some data have become simply too large to be displayed and some have too short a lifespan to be handled properly with classical visualization or analysis methods. In order to address these issues, this book explores the potential solutions where we not only visualize data, but also allow users to be able to interact with it. Therefore, this book will focus on two main topics: large dataset visualization and interaction. Graphic cards and their image processing power can leverage large data visualization but they can also be of great interest to support interaction.

Edited by Nobel Prize winner Ilya Prigogine and renowned authority Stuart A. Rice, the Advances in Chemical Physics series provides a forum for critical, authoritative evaluations in every area of the discipline. In a format that encourages the expression of individual points of view, experts in the field present comprehensive analyses of subjects of interest. Advances in Chemical Physics remains the premier venue for presentations of new findings in its field.

This book is a useful resources for government policy analysts, academics, students of higher education and business practitioners interested in African economies and the key economic issues these economies are facing in 2020.

In this book we study sprays and Finsler metrics. Roughly speaking, a spray on a manifold consists of compatible systems of second-order ordinary differential equations. A Finsler metric on a manifold is a family of norms in tangent spaces, which vary smoothly with the base point. Every Finsler metric determines a spray by its systems of geodesic equations. Thus, Finsler spaces can be viewed as special spray spaces. On the other hand, every Finsler metric defines a distance function by the length of minimial curves. Thus Finsler spaces can be viewed as regular metric spaces. Riemannian spaces are special regular metric spaces. In 1854, B. Riemann introduced the Riemann curvature for Riemannian spaces in his ground-breaking Habilitationsvortrag.

by Gennadiy Vladimirovich Zhizhin (Author)
In the study of the structure of substances in recent decades, phenomena in the higher dimension was discovered that was previously unknown