Results 1 to 10 of about 7,620,730 (87)
Towards quantized complex numbers: $q$-deformed Gaussian integers and the Picard group [PDF]
Open Communications in Nonlinear Mathematical Physics, 2021 This work is a first step towards a theory of "$q$-deformed complex numbers". Assuming the invariance of the $q$-deformation under the action of the modular group I prove the existence and uniqueness of the operator of translations by~$i$ compatible with
V. Ovsienko
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Applied Sciences, 2022 For dimensions two, three and four, we derive hyperbolic complex algebraic structures on the basis of suitably defined vector products and powers which allow in a standard way a series definitions of the hyperbolic vector exponential function.
W. Richter
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On Complex Numbers in Higher Dimensions
Axioms, 2022 The geometric approach to generalized complex and three-dimensional hyper-complex numbers and more general algebraic structures being based upon a general vector space structure and a geometric multiplication rule which was only recently developed is ...
W. Richter
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Concepts of Neutrosophic Complex Numbers
International journal of neutrosophic science, 2021 In this paper, concept of neutrosophic complex numbers and its properties were presented inculding the conjugate of neutrosophic complex number, division of neutrosophic complex numbers, the inverted neutrosophic complex number and the absolute value of ...
Y. A. Alhasan
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Three-Complex Numbers and Related Algebraic Structures
Symmetry, 2021 Three-complex numbers are introduced for using a geometric vector product in the three-dimensional Euclidean vector space R3 and proving its equivalence with a spherical coordinate product.
W. Richter
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Symmetry, 2020 Dispensing with the common property of distributivity and replacing classical trigonometric functions with their l p -counterparts in Euler’s trigonometric representation of complex numbers, classes of l p -complex numbers are introduced and some of ...
W. Richter
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Frieze patterns over integers and other subsets of the complex numbers [PDF]
Journal of combinatorial algebra, 2017 We study (tame) frieze patterns over subsets of the complex numbers, with particular emphasis on the corresponding quiddity cycles. We provide new general transformations for quiddity cycles of frieze patterns.
M. Cuntz, T. Holm
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A Study on Dual-Generalized Complex and Hyperbolic-Generalized Complex Numbers
, 2020 This work is intended to introduce the theories of dual-generalized complex and hyperbolicgeneralized complex numbers. The algebraic properties of these numbers are taken into consideration.
N. Gürses, G. Y. Şentürk, S. Yüce
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On the Fourier transform of Bessel functions over complex numbers—II: The general case [PDF]
Transactions of the American Mathematical Society, 2016 In this paper, we prove an exponential integral formula for the Fourier transform of Bessel functions over complex numbers, along with a radial exponential integral formula. The former will enable us to develop the complex spectral theory of the relative
Zhi Qi
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De-Moivre and Euler Formulae for Dual-Complex Numbers
Universal Journal of Mathematics and Applications, 2019 In this study, we generalize the well-known formulae of De-Moivre and Euler of complex numbers to dual-complex numbers. Furthermore, we investigate the roots and powers of a dual-complex number by using these formulae. Consequently, we give some examples
M. Güngör, Ömer Tetik
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