Relevant bibliographies by topics / Hypercomplex number systems

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Hypercomplex number systems'

Author: Grafiati
Published: 29 July 2024
Last updated: 31 July 2024

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Journal articles on the topic "Hypercomplex number systems"

1

Gu, Ying-Qiu. "Clifford Algebras, Hypercomplex Numbers and Nonlinear Equations in Physics." Geometry, Integrability and Quantization 25 (2023): 47–72. http://dx.doi.org/10.7546/giq-25-2023-47-72.

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Hypercomplex number systems are vector algebras with the definition of multiplication and division of vectors, satisfying the associativity and distributive law. In this paper, some new types of hypercomplex numbers and their fundamental properties are introduced, the Clifford algebra formalisms of hydrodynamics and gauge field equations are established, and some novel consistent conditions helpful to understand the properties of solutions to nonlinear physical equations are derived. The coordinate transformation and covariant derivatives of hypercomplex numbers are also discussed. The basis e
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Kalinovsky, Ya A., Yu E. Boyarinova, Ya V. Khitsko, and A. S. Sukalo. "Use of Methods for Generating Isomorphic Hypercomplex Number Systems to Increase the Efficiency of Multiplying Hypercomplex Numbers." Èlektronnoe modelirovanie 40, no. 5 (2018): 27–40. http://dx.doi.org/10.15407/emodel.40.05.027.

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Кalinovskiy, Ya А., and Yu E. Boiarinova. "Method for Representing an Exponent in a Fifth-dimensional Hypercomplex Number Systems Using a Hypercomplex Computing Software." Èlektronnoe modelirovanie 43, no. 6 (2021): 3–18. http://dx.doi.org/10.15407/emodel.43.06.003.

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The structure of method for constructing a representation of an exponential function in hypercomplex number systems (HNS) by the method of solving an associated system of linear differential equations is considered. Brief information about the hypercomplex computing software (HCS) is given. With the use of HCS, the necessary cumbersome operations on symbolic expressions were performed when constructing the representation of the exponent in the fifthdimensional HNS. Fragments of programs in the environment of HCS and results of symbolic calculations are resulted.
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Hauser, Jochem, and Walter Dröscher. "Gravity Beyond Einstein? Part II: Fundamental Physical Principles, Number Systems, Novel Groups, Dark Energy, and Dark Matter, MOND." Zeitschrift für Naturforschung A 74, no. 5 (2019): 387–446. http://dx.doi.org/10.1515/zna-2018-0559.

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AbstractThis article attempts to explain the underlying physics of several recent experiments and astrophysical observations that have been mystifying the physics community for quite some time. So far, none of the advanced theories beyond the standard models of particle physics and cosmology have shown sufficient potential to resolve these mysteries. The reason for this failure may lie in the fact that these theories are based on the concept of extra space dimensions that appears to be in conflict with numerous experiments, in particular with recent Large Hadron Collider data. Therefore, the n
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KALINOVSKY, Ya A., and Yu E. BOYARINOVA. "The Metod for Research of Isomorphism of Indecomposable Hypercomplex Number Systems." Èlektronnoe modelirovanie 39, no. 3 (2017): 61–76. http://dx.doi.org/10.15407/emodel.39.03.061.

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Wang, Xingyuan, and Tao Jin. "Hyperdimensional generalized M–J sets in hypercomplex number space." Nonlinear Dynamics 73, no. 1-2 (2013): 843–52. http://dx.doi.org/10.1007/s11071-013-0836-5.

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Cariow, Aleksandr, and Oleg Finko. "Special Issue: Real, Complex and Hypercomplex Number Systems in Data Processing and Representation." Applied Sciences 13, no. 11 (2023): 6563. http://dx.doi.org/10.3390/app13116563.

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The evolution of human society is inevitably associated with the widespread development of computer technologies and methods, and the constant evolution of the theory and practice of data processing, as well as the need to solve increasingly complex problems in computational intelligence, have inspired the use of complex and advanced mathematical methods and formalisms for representing and processing big data sets [...]
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DEMİR, SÜLEYMAN, MURAT TANIŞLI, and TÜLAY TOLAN. "OCTONIC GRAVITATIONAL FIELD EQUATIONS." International Journal of Modern Physics A 28, no. 21 (2013): 1350112. http://dx.doi.org/10.1142/s0217751x13501121.

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Generalized field equations of linear gravity are formulated on the basis of octons. When compared to the other eight-component noncommutative hypercomplex number systems, it is demonstrated that associative octons with scalar, pseudoscalar, pseudovector and vector values present a convenient and capable tool to describe the Maxwell–Proca-like field equations of gravitoelectromagnetism in a compact and simple way. Introducing massive graviton and gravitomagnetic monopole terms, the generalized gravitational wave equation and Klein–Gordon equation for linear gravity are also developed.
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Klipkov, S. I. "On a new approach to the construction of hypercomplex number systems of rank two over the field of complex numbers." Ukrainian Mathematical Journal 63, no. 1 (2011): 158–68. http://dx.doi.org/10.1007/s11253-011-0494-z.

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Kalinovsky, J. A., Y. E. Boyarinova, and J. V. Khitsko. "Method of Selecting Hypercomplex Number Systems for Modeling Digital Reversing Filters of the 3rd and 4th Orders." Èlektronnoe modelirovanie 41, no. 4 (2019): 03–18. http://dx.doi.org/10.15407/emodel.41.04.003.

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Dissertations / Theses on the topic "Hypercomplex number systems"

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Bushman, Nathan. "Hypercomplex Numbers and Early Vector Systems: A History." The Ohio State University, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=osu1585666516546138.

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Хіцко, Яна Володимирівна. "Математичне моделювання задач криптографії та обробки сигналів з використанням неканонічних гіперкомплексних числових систем". Thesis, НТУУ "КПІ", 2016. https://ela.kpi.ua/handle/123456789/15092.

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Дисертація присвячена математичному моделюванню задач криптографії та обробки сигналів з використанням неканонічних гіперкомплексних числових систем, застосування яких зменшує кількість обчислень при функціонуванні таких моделей та дозволяє оптимізувати їх за окремими характеристиками. Результати моделювання задачі розділення секрету показали, що застосування неканонічних гіперкомплексних числових систем, починаючи з вимірності 4, зменшує кількість потрібних обчислень у порівнянні із застосуванням канонічних гіперкомплексних числових систем. Розроблено методи побудови структур неканонічних г
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Books on the topic "Hypercomplex number systems"

1

M, Berezanskiĭ I͡U. Harmonic analysis in hypercomplex systems. Kluwer Academic, 1998.

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Quaternionic Analysis: Functions of one quaternionic variable. Independent, 2023.

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Kalyuzhnyi, A. A., and Yu M. Berezansky. Harmonic Analysis in Hypercomplex Systems. Springer, 2014.

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Berezansky, Yu M., and A. A. Kalyuzhnyi. Harmonic Analysis in Hypercomplex Systems. Springer, 2013.

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Berezansky, Yu M., and A. A. Kalyuzhnyi. Harmonic Analysis in Hypercomplex Systems. Yu M Berezansky, 2010.

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Berezansky, Y. M., and A. A. Kalyuzhnyi. Harmonic Analysis in Hypercomplex Systems (Mathematics and Its Applications). Springer, 1998.

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Book chapters on the topic "Hypercomplex number systems"

1

Schlote, Karl-Heinz. "Hermann Günther Grassmann and the Theory of Hypercomplex Number Systems." In Boston Studies in the Philosophy of Science. Springer Netherlands, 1996. http://dx.doi.org/10.1007/978-94-015-8753-2_14.

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Kalinovsky, Yakiv, Yuliya Boyarinova, Iana Khitsko, and Liubov Oleshchenko. "Digital Filters Optimization Modelling with Non-canonical Hypercomplex Number Systems." In Advances in Computer Science for Engineering and Education II. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-16621-2_42.

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Kantor, I. L., and A. S. Solodovnikov. "Lemma on Homogeneous Systems of Equations." In Hypercomplex Numbers. Springer New York, 1989. http://dx.doi.org/10.1007/978-1-4612-3650-4_11.

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Petoukhov, Sergey, Elena Petukhova, Ludmila Hazina, Ivan Stepanyan, Vitaliy Svirin, and Tamara Silova. "The Genetic Coding, United-Hypercomplex Numbers and Artificial Intelligence." In Advances in Intelligent Systems and Computing. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-67349-3_1.

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Isokawa, Teijiro, Nobuyuki Matsui, and Haruhiko Nishimura. "Quaternionic Neural Networks." In Complex-Valued Neural Networks. IGI Global, 2009. http://dx.doi.org/10.4018/978-1-60566-214-5.ch016.

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Quaternions are a class of hypercomplex number systems, a four-dimensional extension of imaginary numbers, which are extensively used in various fields such as modern physics and computer graphics. Although the number of applications of neural networks employing quaternions is comparatively less than that of complex-valued neural networks, it has been increasing recently. In this chapter, the authors describe two types of quaternionic neural network models. One type is a multilayer perceptron based on 3D geometrical affine transformations by quaternions. The operations that can be performed in this network are translation, dilatation, and spatial rotation in three-dimensional space. Several examples are provided in order to demonstrate the utility of this network. The other type is a Hopfield-type recurrent network whose parameters are directly encoded into quaternions. The stability of this network is demonstrated by proving that the energy decreases monotonically with respect to the change in neuron states. The fundamental properties of this network are presented through the network with three neurons.
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Conference papers on the topic "Hypercomplex number systems"

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Dimiev, Stancho, Peter Stoev, and Vladimir Todorov. "Cyclic hypercomplex number systems." In APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS (AMEE '12): Proceedings of the 38th International Conference Applications of Mathematics in Engineering and Economics. AIP, 2012. http://dx.doi.org/10.1063/1.4766806.

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Watanabe, Ricardo Augusto, Estevao Esmi Laureano, and Cibele Cristina Trinca Watanabe. "Fuzzy Octonion Numbers and Fuzzy Hypercomplex Numbers." In 2019 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE). IEEE, 2019. http://dx.doi.org/10.1109/fuzz-ieee.2019.8858970.

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Zhang, Shuai, Lina Yao, Lucas Vinh Tran, Aston Zhang, and Yi Tay. "Quaternion Collaborative Filtering for Recommendation." In Twenty-Eighth International Joint Conference on Artificial Intelligence {IJCAI-19}. International Joint Conferences on Artificial Intelligence Organization, 2019. http://dx.doi.org/10.24963/ijcai.2019/599.

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This paper proposes Quaternion Collaborative Filtering (QCF), a novel representation learning method for recommendation. Our proposed QCF relies on and exploits computation with Quaternion algebra, benefiting from the expressiveness and rich representation learning capability of Hamilton products. Quaternion representations, based on hypercomplex numbers, enable rich inter-latent dependencies between imaginary components. This encourages intricate relations to be captured when learning user-item interactions, serving as a strong inductive bias as compared with the real-space inner product. All
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