商品描述
This self-contained book offers an extensive state-of-the-art exposition of rotational integral geometry, a field that has reached significant maturity over the past four decades. Through a unified description of key results previously scattered across various scientific journals, this book provides a cohesive and thorough account of the subject. Initially, rotational integral geometry was driven by applications in fields such as optical microscopy. Rotational integral geometry has now evolved into an independent mathematical discipline. It contains a wealth of theorems paralleling those in classical kinematic integral geometry for Euclidean spaces, such as the rotational Crofton formulae, rotational slice formulae, and principal rotational formulae. The present book presents these for very general tensor valuations in a convex geometric setting. It also discusses various applications in the biosciences, explained with a mathematical audience in mind. This book is intended for a diverse readership, including specialists in integral geometry, and researchers and graduate students working in integral, convex, and stochastic geometry, as well as geometric measure theory.
商品描述(中文翻譯)
這本獨立的書籍提供了旋轉積分幾何的廣泛前沿論述，這是一個在過去四十年中已達到顯著成熟的領域。通過對先前散見於各種科學期刊的關鍵結果進行統一描述，本書提供了該主題的連貫且全面的說明。最初，旋轉積分幾何是由於在光學顯微鏡等領域的應用而推動的。如今，旋轉積分幾何已演變為一個獨立的數學學科。它包含了大量與歐幾里得空間的經典運動學積分幾何相平行的定理，例如旋轉克羅夫頓公式、旋轉切片公式和主要旋轉公式。本書針對非常一般的張量評價在凸幾何環境中呈現這些公式。它還討論了在生物科學中的各種應用，並以數學讀者為目標進行解釋。本書旨在吸引多樣化的讀者群，包括積分幾何的專家，以及從事積分、凸和隨機幾何以及幾何測度理論的研究人員和研究生。
作者簡介
Eva B. Vedel Jensen obtained a Doctor of Science degree in 1987 from Aarhus University (AU). She has been a staff member at the Department of Mathematics, AU, since 1976, as full professor since 1998. Since 2020, she has been affiliated to AU as professor emerita. Member of the Danish Natural Science Research Council, 2001-2007, and Royal Danish Academy of Sciences and Letters, 2010-. In 2010, she received The Order of Dannebrog and in 2013 she became honorary doctor at University of Bern. In 2010-2020, she was the scientific director of Centre for Stochastic Geometry and Advanced Bioimaging with rotational integral geometry as one of the focus points. She is the author of two research monographs and approximately 90 scientific papers (stereology, integral geometry, stochastic geometry, geometric measure theory, probability theory, statistics). Markus Kiderlen obtained an Erasmus Diploma in mathematics from the Université Grenoble Alpes in 1990 and a Doctor of Science degree in 1999 from the Karlsruhe Institute of Technology (KIT). After a postdoc period at KIT, he has been a staff member at the Department of Mathematics, AU, since 2004, as associate professor since 2007. In 2011-2020 he was co-leader of the project Image analysis and spatial statistics within the DFG research unit Geometry and Physics of Random Spatial Systems. He was leader of the Stochastic Geometry Group within the Centre for Stochastic Geometry and Advanced Bioimaging in 2016-2020. He has published an edited volume on Tensor Valuations and Their Applications in Stochastic Geometry and Imaging together with Eva B. Vedel Jensen and approximately 45 peer-reviewed papers on stereology, convex and integral geometry, stochastic geometry, geometric tomography and inverse problems.
作者簡介(中文翻譯)
Eva B. Vedel Jensen 於1987年獲得奧胡斯大學（Aarhus University, AU）科學博士學位。自1976年以來，她一直是AU數學系的教職員，自1998年起擔任正教授。自2020年起，她以名譽教授身份隸屬於AU。她曾是丹麥自然科學研究委員會的成員（2001-2007），以及丹麥皇家科學與文學院的成員（2010-至今）。在2010年，她獲得丹麥國王勳章（The Order of Dannebrog），並於2013年成為伯恩大學的名譽博士。在2010年至2020年間，她擔任隨機幾何與先進生物成像中心的科學主任，並將旋轉積分幾何作為重點之一。她是兩本研究專著的作者，並發表了約90篇科學論文（立體學、積分幾何、隨機幾何、幾何測度論、概率論、統計學）。
Markus Kiderlen 於1990年在格勒諾布爾阿爾卑斯大學（Université Grenoble Alpes）獲得數學的Erasmus文憑，並於1999年在卡爾斯魯厄理工學院（Karlsruhe Institute of Technology, KIT）獲得科學博士學位。在KIT完成博士後研究後，自2004年以來，他一直是AU數學系的教職員，自2007年起擔任副教授。在2011年至2020年間，他是DFG研究單位「隨機空間系統的幾何與物理」中「影像分析與空間統計」項目的共同負責人。他在2016年至2020年間擔任隨機幾何與先進生物成像中心的隨機幾何小組負責人。他與Eva B. Vedel Jensen共同出版了一本編輯卷《Tensor Valuations and Their Applications in Stochastic Geometry and Imaging》，並發表了約45篇經過同行評審的論文，涵蓋立體學、凸與積分幾何、隨機幾何、幾何斷層成像及反問題。
