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THE ALL-ASSOCIATIVITY OF octonions AND ITS APPLICATIONS

Analysis in Theory and Applications 2010年第4期26卷 326-338页

作者： Jianquan Liao Jinxun Wang Xingmin Li Capital Normal University China University of Macao China South China Normal University 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 ... 详细信息

关键词： octonions associativity permutation determinant

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Quantum Computing with octonions

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Peking Mathematical Journal 2019年第3期2卷 239-273页

作者： Michael Freedman Modjtaba Shokrian-Zini Zhenghan Wang Station Q Microsoft ResearchSanta BarbaraCA 93106USA Department of Mathematics University of CaliforniaSanta BarbaraCA 93106USA Microsoft Station Q Department of MathematicsUniversity of CaliforniaSanta BarbaraCA 93106-6105USA

There are two schools of“measurement-only quantum computation”.The first(***.86(22),5188-5191(2001))using prepared entanglement(cluster states)and the second(***.101(1),010501(2008))using collections of anyons which,according to how they were produced,also have an entanglement *** abstract the common principle behind both approaches and find the notion of a graph or even continuous family of equiangular *** notion is the leading character in the *** largest continuous family,in a sense made pre-cise in Corollary 4.2,is associated with the octonions and this example leads to a universal computational *** quantum computation also fits into this rubric as a limiting case:nearby projections are nearly equiangular,so as a gapped ground state space is slowly varied,the corrections to unitarity are small.

关键词： Quantum computing Measurement Equiangular projections octonions

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The Analyticity for the Product of Analytic Functions on octonions and Its Applications

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Advances in Pure Mathematics 2017年第12期7卷 692-705页

作者： Jianquan Liao Jinxun Wang Department of Mathematics Guangdong University of Education Guangzhou China School of Finance Guangdong University of Foreign Studies Guangzhou China

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 constants λ∈Oc if and only if is a complex Stein-Weiss conjugate harmonic system. Some applications and connections with Cauchy-Kowalewski product are also considered.

关键词： octonions Oc-Analytic Functions Stein-Weiss Conjugate Harmonic System Cauchy-Kowalewski Product

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AN IMPROVEMENT OF THE OCTONIONIC TAYLOR TYPE THEOREM

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Acta Mathematica Scientia 2011年第2期31卷 561-566页

作者：廖建全李兴民 School of Mathematical Science Capital Normal University School of Computer South China Normal University

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

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Split Octonion Reformulation for Electromagnetic Chiral Media of Massive Dyons

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Communications in Theoretical Physics 2017年第12期67卷 701-710页

作者： B.C.Chanyal Department of Physics G.B.Pant University of Agriculture & Technology

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 × 2 Zorn's vector matrix realization of split-octonion and its dual Euclidean spaces, we represent the unified structure of split octonionic electric and magnetic induction vectors for chiral media. As such, in present paper, we describe the chiral parameter and pairing constants in terms of split octonionic matrix representation of Drude-Born-Fedorov constitutive relations. We have expressed a split octonionic electromagnetic field vector for chiral media, which exhibits the unified field structure of electric and magnetic chiral fields of dyons. The beauty of split octonionic representation of Zorn vector matrix realization is that, the every scalar and vector components have its own meaning in the generalized chiral electromagnetism of dyons. Correspondingly, we obtained the alternative form of generalized Proca–Maxwell's equations of massive dyons in chiral media. Furthermore, the continuity equations, Poynting theorem and wave propagation for generalized electromagnetic fields of chiral media of massive dyons are established by split octonionic form of Zorn vector matrix algebra.

关键词： octonions Zorn vector matrix chiral media constitutive relations Poynting theorem

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