| Presentation | 2023-10-11 A Complex Vector-Scalar Ring theory Osamu Ichiyoshi, |
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| PDF Download Page |  PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(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) |
| Keyword(in English) | vector / scalar / vector-scalar / vector-scalar product / rotation / axis / coordinate conversion / quaternion |
| Paper # | SAT2023-57 |
| Date of Issue | 2023-10-03 (SAT) |
| Conference Information | |
| Committee | SAT / KOSST |
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| Conference Date | 2023/10/10(2days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Central Hotel Marianne（Korea, Busan） |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | |
| Chair | Takana Kaho(Shonan Inst. of Tech.) / Byoung-sun Lee(ETRI) |
| Vice Chair | Masashi Kamei(NHK) / Yoji Kishi(KDDI Research) |
| Secretary | Masashi Kamei(NTT) / Yoji Kishi(NHK) / (ETRI) |
| Assistant | Riichiro Nagareda(KDDI Research) / Hideaki Kotake(NICT) |
| Paper Information | |
| Registration To | Technical Committee on Satellite Telecommunications / Korea Society of Satellite Technology |
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| Language | ENG-JTITLE |
| 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) |
| Date | 2023-10-11 |
| Paper # | SAT2023-57 |
| Volume (vol) | vol.123 |
| Number (no) | SAT-204 |
| Page | pp.pp.50-55(SAT), |
| #Pages | 6 |
| Date of Issue | 2023-10-03 (SAT) |