Успехи математических наук, т.50, вып. 1(301), 1995. — 68 с. Геометрия кривых на S 2 Кватернионы и теорема тройственности Кватернионы и кривизны Характеристическая цепь и сферические индексы гиперповерхности Точные лагранжевы кривые на сфере и их индексы Маслова Инвариант Беннекена и сферический инвариант J + Псевдофункции
Geometry, Integrability and Quantization September 1-10, 1999, Varna, Bulgaria. — Ivailo M. Mladenov and Gregory L. Naber, Editors. — Sofia: Coral Press, 2000. — pp. 127-143. In this paper we introduce and define the quaternion; we give a brief introduction to its properties and algebra, and we show, what appears to be, its primary application — the quaternion rotation...
German Physical Society, Spring Conference Kassel 2006, - 22 c. In the last one and a half centuries, the analysis of quaternions has not only led to further de-velopments in mathematics but has also been and remains an important catalyst for the further development of theories in physics. At the same time, Hestenes’ geometric algebra provides a didactically promising...
Hypercomplex Systems, Toronto, Canada, 2003 - 6 c.
This paper shows how to write Maxwell's Equations in Hamilton's Quaternions. The fact that the quaternion product is non-commuting leads to distinct left and right derivatives which must both be included in the theory. A new field component is then revealed, which reduces part of the degree of freedom found in the gauge, but...
Sarnoff Corporation, Princeton, NJ 08543-5300, 2005. - 10 c.
Quaternions are an important tool to describe the orientation of a molecule. This paper considers the use of quaternions in matching two conformations of a molecule, in interpolating rotations, in performing statistics on orientational data, in the random sampling of rotations, and in establishing grids in orientation...
Dipartimento di Fisica, Universit`a di Lecce - Lecce, 73100, Italy, 1996. - 8 c.
Quaternion analysis is considered in full details where a new analyticity condition in complete
analogy to complex analysis is found. The extension to octonions is also worked out.
2008, - 11 c.
A method of reducing general quaternion functions of first degree, i.e., linear quaternion functions, to quaternary canonical form is given. Linear quaternion functions, once reduced to canonical form, can be maintained in this form under functional composition. furthermore, the composition operation is symbolically identical to quaternion multiplication, making...
Computers and Mathematics with Applications, 53, (1), 2007, - 8 c.
An involution is usually defined as a mapping that is its own inverse. In this paper, we study quaternion involutions that have the additional properties of distribution over addition and multiplication. We review formal axioms for such involutions, and we show that the quaternions have an infinite number of...
Успехи математических наук, том 36, вып. 2(218), март-апрель 1981. - 81 с.
Статья посвящена важнейшим результатам теории тэта-функций, их связи с римановыми поверхностями и абелевыми многообразиями. Материал статьи в основном восходит к классическим работам Абеля, Якоби, Римана. Изложен метод Кричевера И. М. построения точных решений нелинейных уравнений. Этот метод позволяет...
Presented at the Conference: The Mathematical Heritage of Sir William Rowan Hamilton, 1993,- 37 c.
150 years after the discovery of quaternions, Hamilton's conjecture that quaternions are a fundamental language for physics is reevaluated and shown to be essentially correct, provided one admits complex numbers in both classical and quantum physics, and accepts carrying along the...
Rice University Studies. — 1963. — V. 49, No. 4. — P. 1 — 12. The three different topics here discussed are alike in that they demonstrate how partial differential equations may be solved by methods from the theory of functions of a complex variable. Remarks about Hadamard's variational formula Symmetric hyperbolic systems in the complex domain General solutions and the method of...
Geometry, Integrability and Quantization September 1-10, 1999, Varna, Bulgaria. — Ivailo M. Mladenov and Gregory L. Naber, Editors. — Sofia: Coral Press, 2000. — pp. 127-143. In this paper we introduce and define the quaternion; we give a brief introduction to its properties and algebra, and we show, what appears to be, its primary application — the quaternion rotation...
In Honor of Kang-Tae Kim’s 60th Birthday, Gyeongju, Korea, 2017. Springer Nature Singapore Pte Ltd., 2018, — xiii+361 p. — (Springer Proceedings in Mathematics & Statistics, 246). — ISBN: 978-981-13-1672-2. The 12th Korean Conference on Several Complex Variables (the KSCV12 Symposium) was held at Gyeongju in Korea during the week of July 3 – 7, 2017. This event was organized on...
The Annals of Mathematics, Second Series. — Vol. 76. — No. 3. — (Nov., 1962). — pp. 547-559. In mathematics, the corona theorem is a result about the spectrum of the bounded holomorphic functions on the open unit disc, conjectured by Kakutani (1941) and proved by Lennart Carleson (1962).
Israel Journal of Mathematics. — 1980. — 37 (1-2). — 113-119. An expository account is given of T. Wolff’s recent elementary proof of Carleson’s Corona Theorem (1962). The Corona Theorem answers affirmatively a question raised by S. Kakatani (1957) as to whether the open unit disc in the complex plane is dense in the maximal ideal space of the Banach algebra of bounded analytic...
Article. - viXra.org. Functions and Analysis. https://vixra.org/abs/2010.0210 - 2020 - 16 с. Abstract: To automate cumbersome, error-prone and tedious manual procedures of calculations with quaternionic holomorphic (ℍ -holomorphic) functions we have developed and present here a special programmes pack in the Wolfram Mathematica programming language. By using this pack a lot of...
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