Relevant bibliographies by topics / Dual-complex numbers

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Academic literature on the topic 'Dual-complex numbers'

Author: Grafiati
Published: 2 June 2025
Last updated: 31 July 2025

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Journal articles on the topic "Dual-complex numbers"

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Prasad, B. "Dual complex Fibonacci p-numbers." Chaos, Solitons & Fractals 145 (April 2021): 109922. http://dx.doi.org/10.1016/j.chaos.2020.109922.

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Aydın, Fügen Torunbalcı. "Dual-complex k-Fibonacci numbers." Chaos, Solitons & Fractals 115 (October 2018): 1–6. http://dx.doi.org/10.1016/j.chaos.2018.08.015.

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Fjelstad, Paul, and Sorin G. Gal. "n-Dimensional dual complex numbers." Advances in Applied Clifford Algebras 8, no. 2 (1998): 309–22. http://dx.doi.org/10.1007/bf03043102.

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KÖME, Sure, Cahit KÖME, and Yasin YAZLİK. "Dual-complex generalized k-Horadam numbers." Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics 70, no. 1 (2021): 117–29. http://dx.doi.org/10.31801/cfsuasmas.780861.

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Shuster, John A., and Jens Köplinger. "Elliptic complex numbers with dual multiplication." Applied Mathematics and Computation 216, no. 12 (2010): 3497–514. http://dx.doi.org/10.1016/j.amc.2010.04.069.

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Bród, Dorota, Anetta Szynal-Liana, and Iwona Włoch. "On a new one-parameter generalization of dual-complex Jacobsthal numbers." Acta Universitatis Sapientiae, Mathematica 13, no. 1 (2021): 127–44. http://dx.doi.org/10.2478/ausm-2021-0007.

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Abstract In this paper we define dual-complex numbers with generalized Jacobsthal coefficients. We introduce one-parameter generalization of dual-complex Jacobsthal numbers - dual-complex r-Jacobsthal numbers. We investigate some algebraic properties of introduced numbers, among others Binet type formula, Catalan, Cassini, d’Ocagne and Honsberger type identities. Moreover, we present the generating function, summation formula and matrix generator for these numbers. The results are generalization of the properties for the dual-complex Jacobsthal numbers.
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Güngör, Mehmet Ali, and Ayşe Zeynep Azak. "Investigation of Dual-Complex Fibonacci, Dual-Complex Lucas Numbers and Their Properties." Advances in Applied Clifford Algebras 27, no. 4 (2017): 3083–96. http://dx.doi.org/10.1007/s00006-017-0813-z.

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Bród, Dorota, Anetta Szynal-Liana, and Iwona Włoch. "Two generalizations of dual-complex Lucas-balancing numbers." Acta Universitatis Sapientiae, Mathematica 14, no. 2 (2022): 220–30. http://dx.doi.org/10.2478/ausm-2022-0014.

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Abstract In this paper, we study two generalizations of dual-complex Lucas-balancing numbers: dual-complex k-Lucas balancing numbers and dual-complex k-Lucas-balancing numbers. We give some of their properties, among others the Binet formula, Catalan, Cassini, d’Ocagne identities.
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Ait-amrane, Nacima Rosa, and Elif Tan. "On unrestricted dual-generalized complex Horadam numbers." Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics 73, no. 2 (2024): 517–28. http://dx.doi.org/10.31801/cfsuasmas.1406328.

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This research introduces a novel category of dual-generalized complex numbers, with components represented by unrestricted Horadam numbers. We present various recurrence relations, summation formulas, the Binet formula, and the generating function associated with these numbers. Additionally, a comprehensive bilinear index-reduction formula is derived, which encompasses Vajda’s, Catalan’s, Cassini’s, D’Ocagne’s, and Halton’s identities as specific cases.
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Şentürk, Gülsüm Yeliz, and Nurten Gürses. "Dual quaternion theory over HGC numbers." Journal of Discrete Mathematical Sciences & Cryptography 27, no. 1 (2024): 117–42. http://dx.doi.org/10.47974/jdmsc-1611.

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Knowing the applications of quaternions in various fields, such as robotics, navigation, computer visualization and animation, in this study, we give the theory of dual quaternions considering Hyperbolic-Generalized Complex (HGC) numbers as coefficients via generalized complex and hyperbolic numbers. We account for how HGC number theory can extend dual quaternions to HGC dual quaternions. Some related theoretical results with HGC Fibonacci/Lucas numbers are established, including their dual quaternions. Given HGC Fibonacci/Lucas numbers, their special matrix correspondences have been identifie
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Books on the topic "Dual-complex numbers"

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Witten, Edward. Two Lectures on the Jones Polynomial and Khovanov Homology. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198784913.003.0001.

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In the first of these two lectures I describe a gauge theory approach to understanding quantum knot invariants as Laurent polynomials in a complex variable q. The two main steps are to reinterpret three-dimensional Chern-Simons gauge theory in four dimensional terms and then to apply electric-magnetic duality. The variable q is associated to instanton number in the dual description in four dimensions. In the second lecture, I describe how Khovanov homology can emerge upon adding a fifth dimension.
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Book chapters on the topic "Dual-complex numbers"

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Matsuda, Genki, Shizuo Kaji, and Hiroyuki Ochiai. "Anti-commutative Dual Complex Numbers and 2D Rigid Transformation." In Mathematics for Industry. Springer Japan, 2014. http://dx.doi.org/10.1007/978-4-431-55007-5_17.

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Brigaglia, Aldo. "Segre and the Foundations of Geometry: From Complex Projective Geometry to Dual Numbers." In From Classical to Modern Algebraic Geometry. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-32994-9_4.

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Kamdem Teyou, Louis Mozart, Caglar Demir, and Axel-Cyrille Ngonga Ngomo. "Embedding Knowledge Graphs in Degenerate Clifford Algebras." In Frontiers in Artificial Intelligence and Applications. IOS Press, 2024. http://dx.doi.org/10.3233/faia240627.

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Clifford algebras are a natural extension of division algebras, including real numbers, complex numbers, quaternions, and octonions. Previous research in knowledge graph embeddings has focused exclusively on Clifford algebras of a specific type, which do not include nilpotent base vectors—elements that square to zero. In this work, we introduce a novel approach by incorporating nilpotent base vectors with a nilpotency index of two, leading to a more general form of Clifford algebras named degenerate Clifford algebras. This generalization to degenerate Clifford algebras does allow for covering
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Kaye, Phillip, Raymond Laflamme, and Michele Mosca. "Linear Algebra and the Dirac Notation." In An Introduction to Quantum Computing. Oxford University Press, 2006. http://dx.doi.org/10.1093/oso/9780198570004.003.0005.

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We assume the reader has a strong background in elementary linear algebra. In this section we familiarize the reader with the algebraic notation used in quantum mechanics, remind the reader of some basic facts about complex vector spaces, and introduce some notions that might not have been covered in an elementary linear algebra course. The linear algebra notation used in quantum computing will likely be familiar to the student of physics, but may be alien to a student of mathematics or computer science. It is the Dirac notation, which was invented by Paul Dirac and which is used often in quan
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Miestamo, Matti. "Implicational hierarchies and grammatical complexity." In Language Complexity as an Evolving Variable. Oxford University PressOxford, 2009. http://dx.doi.org/10.1093/oso/9780199545216.003.0006.

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Abstract This chapter examines the usability of Greenbergian implicational hierarchies (Greenberg 1966) in cross-linguistic research on language complexity. Recently an increasing number of linguists have started to question the conventional wisdom according to which all languages are equally complex. McWhorter (2001a) proposes a metric for measuring the overall complexity of grammars of languages. One of the criteria employed in the metric pays attention to the number of grammatically expressed semantic or pragmatic distinctions: for example, a language that has a singular, a plural, and a du
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Salzman, Harold, and Stephen R. Rosenthal. "The Structure of Software Design." In Software by Design. Oxford University Press, 1994. http://dx.doi.org/10.1093/oso/9780195083408.003.0008.

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The software industry really came of age in the 1970s and 1980s. This was a time of technological transformation in the workplace. The computer expanded from the backroom to the front office and evolved from simple data processing to integrated information systems. The growth of the independent software vendor led to an important change in software design. User firms began to purchase large, standard or semicustom systems from thirdparty vendors rather than purchasing software with hardware and having most applications software custom designed by an in-house programming staff. This added anoth
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Liu, Chengliang, Liang Gong, and Wei Zhang. "Manipulating Complex Robot Behavior for Autonomous and Continuous Operations." In Service Robotics. IntechOpen, 2020. http://dx.doi.org/10.5772/intechopen.92254.

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Service robot control faces challenges of dynamic environment and complex behavior, which mainly include eye-hand coordination and continuous operations. However, current programming scheme lacks the ability of managing such tasks. In this chapter, we propose a methodology of software development paradigm for the continuous operation of the dual-arm picking robot. First, a dual-arm robot is built for picking with the purpose of selectively harvesting in plant factory. Second, a hierarchical control software is framed by means of “Sense Plan Act” (SPA) paradigm. Third, based on the previous des
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Goldsmith, Mike. "2. Water waves." In Waves: A Very Short Introduction. Oxford University Press, 2018. http://dx.doi.org/10.1093/actrade/9780198803782.003.0002.

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Water waves may in fact be the most complex of all; out at sea, the water surface is a summation of an ever-changing mix of waves of many sizes, speeds, and directions, thanks largely to the fact that some waves can last for weeks, and in that time they can travel thousands of kilometres. Until recently, many wave parameters were hard to measure, but accurate measurements can now be made by a number of techniques including dual frequency radar altimetry. ‘Water waves’ describes many different waves and how they build, including capillary waves, breakers, edge waves, harbour resonance, seiches,
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Green, Mark, Phillip Griffiths, and Matt Kerr. "Classification of Mumford-Tate Subdomains." In Mumford-Tate Groups and Domains. Princeton University Press, 2012. http://dx.doi.org/10.23943/princeton/9780691154244.003.0008.

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This chapter develops an algorithm for determining all Mumford-Tate subdomains of a given period domain. The result is applied to the classification of all complex multiplication Hodge structures (CM Hodge structures) of rank 4 and when the weight n = 1 and n = 3, to an analysis of their Hodge tensors and endomorphism algebras, and the number of components of the Noether-Lefschetz locus. The result is that one has a complex but very rich arithmetic story. Of particular note is the intricate structure of the components of the Noether-Lefschetz loci in D and in its compact dual, and the two inte
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Desai, Ashwin, and Goolam Vahed. "Modi Meets Mohandas." In A History of the Present. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780199498017.003.0009.

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This chapter examines the complex relationship between diaspora and citizenship. Mohandas Karamchand Gandhi famously developed his tactic of satyagraha on South African soil, cementing a deep relationship with India. Against this background, this chapter examines new diasporic connections between Indian South Africans and India, buoyed by the Indian government’s introduction of a number of measures such as a new ministry, an annual official diaspora convention in India, and the offer of special status for members of the Indian diaspora, but fell short of granting dual citizenship, arguably ove
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Conference papers on the topic "Dual-complex numbers"

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Yoon, Seokkwan, Patricia Diaz, William Chan, Colin Theodore, and STC D Douglas. "Computational Aerodynamic Modeling of Small Quadcopter Vehicles." In Vertical Flight Society 73rd Annual Forum & Technology Display. The Vertical Flight Society, 2017. http://dx.doi.org/10.4050/f-0073-2017-11993.

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High-fidelity computational simulations have been performed which focus on rotor-fuselage and rotor-rotor aerodynamic interactions of small quad-rotor vehicle systems. The three-dimensional unsteady Navier-Stokes equations are solved on overset grids using high-order accurate schemes, dual-time stepping, low Mach number preconditioning, and hybrid turbulence modeling. Computational results for isolated rotors are shown to compare well with available experimental data. Computational results in hover reveal the differences between a conventional configuration where the rotors are mounted above t
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Gaska, Thomas, Doug Summerville, Marilyn Gaska, and Yu Chen. "Model Based Engineering for Advanced Integrated Modular Avionics - Focus and Challenges." In Vertical Flight Society 73rd Annual Forum & Technology Display. The Vertical Flight Society, 2017. http://dx.doi.org/10.4050/f-0073-2017-12031.

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Advanced Integrated Modular Avionics (A-IMA) will drive new focus and challenges for Model Based Engineering (MBE). First, there is the need to bridge MBE to legacy system elements that were developed without MBE along with the need to handle hybrid Open System Architecture / Integrated Modular Avionics (OSA/IMA) based architectures. Second, there is the need for MBE to be reusable and interoperable across product development cycles as technology insertions occur. Third, there is the need for integration of MBE into synthesizable descriptions that can also be effectively validated for mixed ge
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Cheng, Harry H., and Sean Thompson. "Dual Polynomials and Complex Dual Numbers for Analysis of Spatial Mechanisms." In ASME 1996 Design Engineering Technical Conferences and Computers in Engineering Conference. American Society of Mechanical Engineers, 1996. http://dx.doi.org/10.1115/96-detc/mech-1221.

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Abstract Complex dual numbers w̌1=x1+iy1+εu1+iεv1 which form a commutative ring are for the first time introduced in this paper. Arithmetic operations and functions of complex dual numbers are defined. Complex dual numbers are used to solve dual polynomial equations. It is shown that the singularities of a dual input-output displacement polynomial equation of a mechanism correspond to its singularity positions. This new method of identifying singularities provides clear physical insight into the geometry of the singular configurations of a mechanism, which is illustrated through analysis of sp
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Cheng, Harry H. "Computations of Dual Numbers in the Extended Finite Dual Plane." In ASME 1993 Design Technical Conferences. American Society of Mechanical Engineers, 1993. http://dx.doi.org/10.1115/detc1993-0378.

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Abstract The numerical computational aspects of dual numbers in the CH programming language are presented in this paper. Dual is a built-in data type in CH. Dual numbers and dual metanumbers are described in the extended dual plane and extended finite dual plane. The arithmetic and relational operations, and built-in mathematical functions are defined for both dual numbers and dual metanumbers of DualZero, DualInf, and DualNaN. Due to polymorphism, the syntax of dual arithmetic and relational operations, and built-in dual functions are the same as those for real and complex numbers in the CH p
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Thompson, Sean, and Harry H. Cheng. "Computer-Aided Displacement Analysis of Spatial Mechanisms." In ASME 1994 Design Technical Conferences collocated with the ASME 1994 International Computers in Engineering Conference and Exhibition and the ASME 1994 8th Annual Database Symposium. American Society of Mechanical Engineers, 1994. http://dx.doi.org/10.1115/detc1994-0052.

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Abstract Recently, Cheng (1993) introduced the CH programming language. CH is designed to be a superset of ANSI C with all programming features of FORTRAN. Many programming features in CH are specifically designed and implemented for design automation. Handling dual number as a basic built-in data type in the language is one example. Formulas with dual numbers can be translated into CH programming statements as easily as formulas with real and complex numbers. In this paper we will show that both formulation and programming with dual numbers are remarkably simple for analysis of complicated sp
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Sun, Zixiang, Feng Gao, John Chew, and Dario Amirante. "LES Investigation of Low Rossby Number Buoyant Flow in Rotating Cavities." In ASME Turbo Expo 2022: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2022. http://dx.doi.org/10.1115/gt2022-81338.

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Abstract Flow and heat transfer in axial compressor disc cavities involve strong interaction of axial throughflow at the disc bores with centrifugal buoyant flow in the cavities. This paper presents large eddy simulation (LES) of flow and heat transfer in rotating cavities with a heated shroud and a relatively weak axial cooling throughflow. The conditions considered for a single cavity configuration correspond to Rossby numbers Ro = 0.2 and 0.3, rotational Reynolds numbers ReΩ = 3.2 × 105 and 7.7 × 105, and buoyancy parameters βΔT = 0.24 and 0.26. Reasonable agreement of the results with shro
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Ni, Michael, Ron-Ho Ni, and John P. Clark. "LES Modeling of High-Lift High-Work LP Turbine Profiles: Part I: Approach." In ASME Turbo Expo 2023: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2023. http://dx.doi.org/10.1115/gt2023-102625.

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Abstract The Low Pressure Turbine (LPT), commonly used in both commercial and military engines, generally experiences low Reynolds numbers at high altitude cruise conditions. Understanding the complex flow physics in an LPT stage is critical in providing adequate work output while maintaining target efficiency at low Reynolds number situations. With the complex laminar to turbulent transition flow physics in mind, the high lift LPT design requires an understanding of the turbulent transition response to design and operating conditions which is not currently met with existing design methodologi
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Lin, Shing-Hong, Thomas F. Krile, and John F. Walkup. "Optical polynomial processing based on the bilinear transform." In OSA Annual Meeting. Optica Publishing Group, 1986. http://dx.doi.org/10.1364/oam.1986.thl1.

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With the motivation to extend linear/bilinear operators to a more general class of nonlinear operators via a Volterra series (polynomial) approximation, we look into optical polynomial implementations using a factored representation so that presently known bilinear techniques can be employed. Since there are two inputs and one kernel in the generalized bilinear transform, the two inputs act as polynomial input variables and the elements in the kernel represent coefficients of the quadratic polynomial. Thus higher polynomial processing can be realized by iterating the bilinear transform. A dual
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Arnold, Mark G., and Sylvain Collange. "A Dual-Purpose Real/Complex Logarithmic Number System ALU." In 2009 IEEE 19th IEEE Symposium on Computer Arithmetic (ARITH). IEEE, 2009. http://dx.doi.org/10.1109/arith.2009.26.

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Germain, G., B. Gaurier, M. Le Boulluec, E. Fontaine, and J. Capul. "Vortex and Wake Effects on Closely Spaced Marine Risers." In ASME 2006 Pressure Vessels and Piping/ICPVT-11 Conference. ASMEDC, 2006. http://dx.doi.org/10.1115/pvp2006-icpvt-11-93839.

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The present paper describes some ongoing research performed for a better understanding of the hydrodynamic loads acting on a riser placed in the wake of an upstream one. Experiments on model tests scaled with real configurations for dual riser interaction in uniform and steady current are presented. A particular attention is paid on how fluid interaction between two cylinders of equal diameter in tandem configuration can significantly modify their structural response in term of amplitude and frequency, compared to that of a single cylinder. The circulation water channel allows to reach Reynold
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