Results 1 to 10 of about 1,018 (285)
Some modern developments in the theory of real division algebras; pp. 53–59 [PDF]
Proceedings of the Estonian Academy of Sciences, 2010 The study of real division algebras was initiated by the construction of the quaternion and the octonion algebras in the mid-19th century. In spite of its long history, the problem of classifying all finite-dimensional real division algebras is still ...
Erik Darpö
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Exponential and logarithm of multivector in low-dimensional (n = p + q < 3) Clifford algebras
Nonlinear Analysis, 2022 The aim of the paper is to give a uniform picture of complex, hyperbolic, and quaternion algebras from a perspective of the applied Clifford geometric algebra.
Adolfas Dargys, Artūras Acus
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NTRU in quaternion algebras of bounded discriminant [PDF]
, 2023 The NTRU assumption provides one of the most prominent problems on which to base post-quantum cryptography. Because of the efficiency and security of NTRU-style schemes, structured variants have been proposed, using modules.
Ling, Cong, Mendelsohn, Andrew
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Proper ARMA Modeling and Forecasting in the Generalized Segre’s Quaternions Domain
Mathematics, 2022 The analysis of time series in 4D commutative hypercomplex algebras is introduced. Firstly, generalized Segre’s quaternion (GSQ) random variables and signals are studied.
Jesús Navarro-Moreno +2 more
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Shorter quantum circuits via single-qubit gate approximation [PDF]
Quantum, 2023 We give a novel procedure for approximating general single-qubit unitaries from a finite universal gate set by reducing the problem to a novel magnitude approximation problem, achieving an immediate improvement in sequence length by a factor of 7/9 ...
Vadym Kliuchnikov +4 more
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SciPost Physics Proceedings, 2023 The paper develops, within a new representation of Clifford algebras in terms of tensor products of quaternions called hyperquaternions, several applications.
Patrick R. Girard, Romaric Pujol, Patrick Clarysse, Philippe Delachartre
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Fascinating Number Sequences from Fourth Order Difference Equation Via Quaternion Algebras
Discussiones Mathematicae - General Algebra and Applications, 2021 The balancing and Lucas-balancing numbers are solutions of second order recurrence relations. A linear combination of these numbers can also be obtained as solutions of a fourth order recurrence relation.
Patra Asim
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On split quaternion equivalents for Quaternaccis, shortly Split Quaternaccis
Open Mathematics, 2021 In this paper, we introduce generalizations of Quaternacci sequences (Quaternaccis), called Split Quaternacci sequences, which arose on a base of split quaternion algebras.
Bajorska-Harapińska Beata +3 more
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Splitting of differential quaternion algebras
, 2023 We study differential splitting fields of quaternion algebras with derivations. A quaternion algebra over a field $k$ is always split by a quadratic extension of $k$.
Singh, Anupam +2 more
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About Some Split Central Simple Algebras
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2014 In this paper we study certain quaternion algebras and symbol algebras which split.
Savin Diana
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