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Paper Abstract and Keywords
Presentation 2023-10-11 15:35
A Complex Vector-Scalar Ring theory
Osamu Ichiyoshi (HNfB21C) SAT2023-57
Abstract (in Japanese) (See Japanese page) 
(in English) The quaternion is an expansion of complex number to three dimensions of imaginary numbers. It is a useful tool in calculating rotation of vectors around a given axis in the three dimensional space. The imaginary numbers in quaternion can be replaced with real vectors in the three-dimensional space to give a Vector-Scalar (VS). The set of whole vector-scalars is algebraically equivalent to that of quaternions; they form rings. The transition is made by a definition of vector-scalar product (x) as follows. For vectors u and v, u (x) v = u x v – (u.v), where u x v and (u.v) are respectively normal vector product and scalar product. For any vector l with unit length, l (x) l = -1, which is similar to the imaginary number i. In fact the following formula e^(lθ) = cos(θ) + l.sin(θ) can be defined just as Euler’s formula in complex number theory. The coefficients in VS can take complex values to achieve a fundamental unification of vector-scalars and complex numbers. Functions in VS domain can be defined in much the same manners as in complex plane enabling to solve wide ranges of vectors and scalars problems.
Keyword (in Japanese) (See Japanese page) 
(in English) vector / scalar / vector-scalar / vector-scalar product / rotation / axis / coordinate conversion / quaternion  
Reference Info. IEICE Tech. Rep., vol. 123, no. 204, SAT2023-57, pp. 50-55, Oct. 2023.
Paper # SAT2023-57 
Date of Issue 2023-10-03 (SAT) 
ISSN Online edition: ISSN 2432-6380
All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034)
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Conference Information
Committee SAT KOSST  
Conference Date 2023-10-10 - 2023-10-11 
Place (in Japanese) (See Japanese page) 
Place (in English) Central Hotel Marianne(Korea, Busan) 
Topics (in Japanese) (See Japanese page) 
Topics (in English)  
Paper Information
Registration To SAT 
Conference Code 2023-10-SAT-KOSST 
Language English (Japanese title is available) 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) A Complex Vector-Scalar Ring theory 
Sub Title (in English)  
Keyword(1) vector  
Keyword(2) scalar  
Keyword(3) vector-scalar  
Keyword(4) vector-scalar product  
Keyword(5) rotation  
Keyword(6) axis  
Keyword(7) coordinate conversion  
Keyword(8) quaternion  
1st Author's Name Osamu Ichiyoshi  
1st Author's Affiliation Human Network for Better 21 Century (HNfB21C)
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Speaker Author-1 
Date Time 2023-10-11 15:35:00 
Presentation Time 25 minutes 
Registration for SAT 
Paper # SAT2023-57 
Volume (vol) vol.123 
Number (no) no.204 
Page pp.50-55 
Date of Issue 2023-10-03 (SAT) 

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