國立高雄大學圖資館 |

登入

回首頁

Rotational integral geometry and its applications

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Rotational integral geometry and its applicationsby Eva B. Vedel Jensen, Markus Kiderlen.
作者:	Jensen, Eva B. Vedel.
其他作者:	Kiderlen, Markus.
出版者:	Cham :Springer Nature Switzerland :2025.
面頁冊數:	ix, 263 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Integral geometry.
電子資源:	https://doi.org/10.1007/978-3-031-87047-7
ISBN:	9783031870477$q(electronic bk.)

Rotational integral geometry and its applications
Jensen, Eva B. Vedel.

Rotational integral geometry and its applications[electronic resource] /by Eva B. Vedel Jensen, Markus Kiderlen. - Cham :Springer Nature Switzerland :2025. - ix, 263 p. :ill. (some col.), digital ;24 cm. - Springer monographs in mathematics,2196-9922. - Springer monographs in mathematics..

- 1. Introduction -- 2. Convex Bodies and their Classical Integral Geometry -- 3. Integral Geometric Transformations -- 4. Rotational Crofton Formulae for Intrinsic Volumes -- 5. Rotational Crofton Formulae for Minkowski Tensors -- 6. Rotational Slice Formulae -- 7. Further Rotational Integral Geometric Formulae -- 8. Applications to Particle Populations -- 9. Implementation in Optical Microscopy.

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.

ISBN: 9783031870477$q(electronic bk.)

Standard No.: 10.1007/978-3-031-87047-7doiSubjects--Topical Terms:

306357
Integral geometry.

LC Class. No.: QA672

Dewey Class. No.: 516.362

Rotational integral geometry and its applications
LDR:02749nmm a2200373 a 4500 001 683338
003 DE-He213
005 20250613131650.0
006 m d
007 cr nn 008maaau
008 251212s2025 sz s 0 eng d
020 $a 9783031870477$q(electronic bk.)
020 $a 9783031870460$q(paper)
024 7 $a 10.1007/978-3-031-87047-7 $2 doi
035 $a 978-3-031-87047-7
040 $a GP $c GP
041 0 $a eng
050 4 $a QA672
072 7 $a PBM $2 bicssc
072 7 $a PBD $2 bicssc
072 7 $a MAT012020 $2 bisacsh
072 7 $a PBM $2 thema
072 7 $a PBD $2 thema
082 0 4 $a 516.362 $2 23
090 $a QA672 $b .J54 2025
100 1 $a Jensen, Eva B. Vedel. $3 242040
245 1 0 $a Rotational integral geometry and its applications $h [electronic resource] / $c by Eva B. Vedel Jensen, Markus Kiderlen.
260 $a Cham : $b Springer Nature Switzerland : $b Imprint: Springer, $c 2025.
300 $a ix, 263 p. : $b ill. (some col.), digital ; $c 24 cm.
338 $a online resource $b cr $2 rdacarrier
490 1 $a Springer monographs in mathematics, $x 2196-9922
505 0 $a - 1. Introduction -- 2. Convex Bodies and their Classical Integral Geometry -- 3. Integral Geometric Transformations -- 4. Rotational Crofton Formulae for Intrinsic Volumes -- 5. Rotational Crofton Formulae for Minkowski Tensors -- 6. Rotational Slice Formulae -- 7. Further Rotational Integral Geometric Formulae -- 8. Applications to Particle Populations -- 9. Implementation in Optical Microscopy.
520 $a 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.
650 0 $a Integral geometry. $3 306357
650 1 4 $a Convex and Discrete Geometry. $3 277230
650 2 4 $a Probability Theory. $3 913371
650 2 4 $a Measure and Integration. $3 273777
700 1 $a Kiderlen, Markus. $3 787706
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a Springer monographs in mathematics. $3 557774
856 4 0 $u https://doi.org/10.1007/978-3-031-87047-7
950 $a Mathematics and Statistics (SpringerNature-11649)