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Dirac and Maxwell Systems in Split Octonions: 《Journal of Applied Mathematics and Physics》2023年第7期1977-1995,共19页Merab Gogberashvili Alexandre Gurchumelia; The known equivalence of 8-dimensional chiral spinors and vectors, also referred to as triality, is discussed for (4 + 4)-space. Split octonionic representation of SO(4, 4) and Spin(4, 4) groups and the trilinear inva...; 关键词：Split Octonions TRIALITY SO(4 4) Dirac and Maxwell Equations

Powers of Octonions: 《Applied Mathematics》2021年第2期75-84,共10页W. E. Ahmed; As it is known, Binomial expansion, De Moivre’s formula, and Euler’s formula are suitable methods for computing the powers of a complex number, but to compute the powers of an octonion number in easy way, we need to...; 关键词：OCTONION Matrix Algebra

Quantum Computing with Octonions: 《Peking Mathematical Journal》2019年第3期239-273,共35页Michael Freedman Modjtaba Shokrian-Zini Zhenghan Wang; There are two schools of“measurement-only quantum computation”.The first(Phys.Rev.Lett.86(22),5188-5191(2001))using prepared entanglement(cluster states)and the second(Phys.Rev.Lett.101(1),010501(2008))using collect...; 关键词：Quantum computing MEASUREMENT Equiangular projections OCTONIONS

Split Octonion Reformulation for Electromagnetic Chiral Media of Massive Dyons: 《Communications in Theoretical Physics》2017年第12期701-710,共10页B.C.Chanyal; In an explicit, unified, and covariant formulation of an octonion algebra, we study and generalize the electromagnetic chiral fields equations of massive dyons with the split octonionic representation. Starting with 2...; 关键词：OCTONIONS Zorn vector matrix chiral media constitutive relations Poynting theorem

The Analyticity for the Product of Analytic Functions on Octonions and Its Applications: 《Advances in Pure Mathematics》2017年第12期692-705,共14页Jianquan Liao Jinxun Wang; Given two left Oc-analytic functions f, g in some open set Ω of R8, we obtain some sufficient conditions for fg is also left Oc-analytic in Ω. Moreover, we prove?fλ that is a left Oc-analytic function for any const...; 关键词：OCTONIONS Oc-Analytic Functions Stein-Weiss Conjugate Harmonic System Cauchy-Kowalewski PRODUCT

Multidimensional Laplace Transforms over Quaternions, Octonions and Cayley-Dickson Algebras, Their Applications to PDE: 《Advances in Pure Mathematics》2012年第2期63-103,共41页Sergey Victor Ludkovsky; Multidimensional noncommutative Laplace transforms over octonions are studied. Theorems about direct and inverse transforms and other properties of the Laplace transforms over the Cayley-Dickson algebras are proved. A...; 关键词：Laplace Transform Quaternion Skew Field OCTONION ALGEBRA Cayley-Dickson ALGEBRA Partial Differential Equation NON-COMMUTATIVE Integration

AN IMPROVEMENT OF THE OCTONIONIC TAYLOR TYPE THEOREM被引量：3: 《Acta Mathematica Scientia》2011年第2期561-566,共6页廖建全李兴民; Supported by the Doctoral Station Grant of Chinese Education Committee (20050574002); We prove that the octonionic polynomials Vl 1k……lk. are independent of the associative orders k. This improves the oetonionic Taylor type theorem.; 关键词：OCTONIONS associative order Taylor type theorem

THE ALL-ASSOCIATIVITY OF OCTONIONS AND ITS APPLICATIONS被引量：2: 《Analysis in Theory and Applications》2010年第4期326-338,共13页Jianquan Liao Jinxun Wang Xingmin Li; Supported in part by the Doctoral Station Grant of Chinese Education Committee (20050574002), P. R. China; Using an elementary method, we give a new proof of the all-associativity of octonions. As some applications, the known Taylor theorem is improved, and a new definition and new properties of octonionic determinant are ...; 关键词：OCTONIONS ASSOCIATIVITY PERMUTATION DETERMINANT

The Paley-Wiener theorem in the non-commutative and non-associative octonions被引量：3: 《Science China Mathematics》2009年第1期129-141,共13页LI XingMin PENG LiZhong QIAN Tao; supported by the National Basic Research Program of China (Grant No. 1999075105);the National Natural Science Foundation of China (Grant No. 10471002);Research Foundation for Doctoral Programm (Grant No. 20050574002); The Paley-Wiener theorem in the non-commutative and non-associative octonion analytic function space is proved.; 关键词：octonionic exponential function octonionic Taylor expansion Fourier transform Paley-Weiner theorem 42B35 30G35 17A35

Associative Cones and Integrable Systems: 《Chinese Annals of Mathematics,Series B》2006年第2期153-168,共16页Chuu-Lian TERNG; Partially supported by NSF grant DMS-0529756.; Abstract We identify R^7 as the pure imaginary part of octonions. Then the multiplication in octonions gives a natural almost complex structure for the unit sphere S^6. It is known that a cone over a surface M in S^6 ...; 关键词：OCTONIONS Associative cone Almost complex curve Primitive map

OCTONIONS