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| Author | : Willi Freeden |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 609 |
| Release | : 2008-12-14 |
| Genre | : Science |
| ISBN | : 3540851127 |
In recent years, the Geomathematics Group, TU Kaiserslautern, has worked to set up a theory of spherical functions of mathematical physics. This book is a collection of all the material that group generated during the process.
| Author | : Stephen D. Casey |
| Publisher | : Springer Nature |
| Total Pages | : 580 |
| Release | : 2024-01-04 |
| Genre | : Mathematics |
| ISBN | : 3031411307 |
During his long and distinguished career, J. Rowland Higgins (1935-2020) made a substantial impact on many mathematical fields through his work on sampling theory, his deep knowledge of its history, and his service to the community. This volume is a tribute to his work and legacy, featuring chapters written by distinguished mathematicians that explore cutting-edge research in sampling, approximation, signal analysis, and other related areas. An introductory chapter provides a biography of Higgins that explores his rich and unique life, along with a bibliography of his papers; a brief history of the SampTA meetings – of which he was a Founding Member – is also included. The remaining articles are grouped into four sections – classical sampling, theoretical extensions, frame theory, and applications of sampling theory – and explore Higgins’ contributions to these areas, as well as some of the latest developments.
| Author | : David H. Laidlaw |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 379 |
| Release | : 2009-03-30 |
| Genre | : Mathematics |
| ISBN | : 3540883789 |
This book provides researchers an inspirational look at how to process and visualize complicated 2D and 3D images known as tensor fields. With numerous color figures, it details both the underlying mathematics and the applications of tensor fields.
| Author | : Willi Freeden |
| Publisher | : Birkhäuser |
| Total Pages | : 591 |
| Release | : 2018-05-03 |
| Genre | : Mathematics |
| ISBN | : 3319714589 |
This book presents, in a consistent and unified overview, results and developments in the field of today ́s spherical sampling, particularly arising in mathematical geosciences. Although the book often refers to original contributions, the authors made them accessible to (graduate) students and scientists not only from mathematics but also from geosciences and geoengineering. Building a library of topics in spherical sampling theory it shows how advances in this theory lead to new discoveries in mathematical, geodetic, geophysical as well as other scientific branches like neuro-medicine. A must-to-read for everybody working in the area of spherical sampling.
| Author | : Willi Freeden |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 1371 |
| Release | : 2010-08-13 |
| Genre | : Mathematics |
| ISBN | : 364201545X |
During the last three decades geosciences and geo-engineering were influenced by two essential scenarios: First, the technological progress has changed completely the observational and measurement techniques. Modern high speed computers and satellite based techniques are entering more and more all geodisciplines. Second, there is a growing public concern about the future of our planet, its climate, its environment, and about an expected shortage of natural resources. Obviously, both aspects, viz. efficient strategies of protection against threats of a changing Earth and the exceptional situation of getting terrestrial, airborne as well as spaceborne data of better and better quality explain the strong need of new mathematical structures, tools, and methods. Mathematics concerned with geoscientific problems, i.e., Geomathematics, is becoming increasingly important. The ‘Handbook Geomathematics’ as a central reference work in this area comprises the following scientific fields: (I) observational and measurement key technologies (II) modelling of the system Earth (geosphere, cryosphere, hydrosphere, atmosphere, biosphere) (III) analytic, algebraic, and operator-theoretic methods (IV) statistical and stochastic methods (V) computational and numerical analysis methods (VI) historical background and future perspectives.
| Author | : W. Freeden |
| Publisher | : |
| Total Pages | : 458 |
| Release | : 1998 |
| Genre | : Mathematics |
| ISBN | : |
Geomathematics offers an useful means of assimilating and assessing the ever increasing flow of data from geoscientific and satellite sources, as well as an objective basis for the interpretation, classification, and solution of problems. This volume provides the necessary foundation in sphere oriented mathematics for graduate students and researchers interested in any of the diverse topics of constructive approximation in this area. Aspects of approximation by spherical harmonics, such as spherical splines and wavelets, are discussed in detail, and methods for handling different types of data, such as scalar, vectorial, and tensorial, are each considered in turn. This book presents the most up-to-date structures and methods for the efficient handling of sophisticated measurements and observations, thus reducing time and costs.
| Author | : Charles K Chui |
| Publisher | : World Scientific |
| Total Pages | : 454 |
| Release | : 1995-11-07 |
| Genre | : Mathematics |
| ISBN | : 981454907X |
This is the collection of the refereed and edited papers presented at the 8th Texas International Conference on Approximation Theory. It is interdisciplinary in nature and consists of two volumes. The central theme of Vol. I is the core of approximation theory. It includes such important areas as qualitative approximations, interpolation theory, rational approximations, radial-basis functions, and splines. The second volume focuses on topics related to wavelet analysis, including multiresolution and multi-level approximation, subdivision schemes in CAGD, and applications.
| Author | : Fernando Sansò |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 356 |
| Release | : 2013-03-09 |
| Genre | : Science |
| ISBN | : 366210735X |
Just as in the era of great achievements by scientists such as Newton and Gauss, the mathematical theory of geodesy is continuing the tradition of producing exciting theoretical results, but today the advances are due to the great technological push in the era of satellites for earth observations and large computers for calculations. Every four years a symposium on methodological matters documents this ongoing development in many related underlying areas such as estimation theory, stochastic modelling, inverse problems, and satellite-positioning global-reference systems. This book presents developments in geodesy and related sciences, including applied mathematics, among which are many new results of high intellectual value to help readers stay on top of the latest happenings in the field.
| Author | : Willi Freeden |
| Publisher | : Birkhäuser |
| Total Pages | : 938 |
| Release | : 2018-06-11 |
| Genre | : Mathematics |
| ISBN | : 3319571818 |
Written by leading experts, this book provides a clear and comprehensive survey of the “status quo” of the interrelating process and cross-fertilization of structures and methods in mathematical geodesy. Starting with a foundation of functional analysis, potential theory, constructive approximation, special function theory, and inverse problems, readers are subsequently introduced to today’s least squares approximation, spherical harmonics reflected spline and wavelet concepts, boundary value problems, Runge-Walsh framework, geodetic observables, geoidal modeling, ill-posed problems and regularizations, inverse gravimetry, and satellite gravity gradiometry. All chapters are self-contained and can be studied individually, making the book an ideal resource for both graduate students and active researchers who want to acquaint themselves with the mathematical aspects of modern geodesy.
| Author | : Willi Freeden |
| Publisher | : Springer |
| Total Pages | : 140 |
| Release | : 2019-05-17 |
| Genre | : Mathematics |
| ISBN | : 3030130541 |
The authors introduce geomathematics as an active research area to a wider audience. Chapter 1 presents an introduction to the Earth as a system to apply scientific methods. Emphasis is laid on transfers from virtual models to reality and vice versa. In the second chapter geomathematics is introduced as a new scientific area which nevertheless has its roots in antiquity. The modern conception of geomathematics is outlined from different points of view and its challenging nature is described as well as its interdisciplinarity. Geomathematics is shown as the bridge between the real world and the virtual world. The complex mathematical tools are shown from a variety of fields necessary to tackle geoscientific problems in the mathematical language. Chapter 3 contains some exemplary applications as novel exploration methods. Particular importance is laid on the change of language when it comes to translate measurements to mathematical models. New solution methods like the multiscale mollifier technique are presented. Further applications discussed are aspects of reflection seismics. Chapter 4 is devoted to the short description of recent activities in geomathematics. The Appendix (Chapter 5) is devoted to the GEM – International Journal on Geomathematics founded ten years ago. Besides a detailed structural analysis of the editorial goals an index of all papers published in former issues is given.
