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The apeirogon and dual numbers
Symmetry: Culture and Science, 2021Abstract: The richness, diversity, connection, depth and pleasure of studying symmetry continue to open doors. Here we report a connection between Coxeter's Apeirogon and the geometry associated with pictorial space, parabolic rotation and dual numbers.
Johan Gielis, Simone Brasili
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2018
This is the first book focusing exclusively on fuzzy dual numbers. In addition to offering a concise guide to their properties, operations and applications, it discusses some of their advantages with regard to classical fuzzy numbers, and describes the most important operations together with a set of interesting applications in e.g.
Felix Mora-Camino +1 more
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This is the first book focusing exclusively on fuzzy dual numbers. In addition to offering a concise guide to their properties, operations and applications, it discusses some of their advantages with regard to classical fuzzy numbers, and describes the most important operations together with a set of interesting applications in e.g.
Felix Mora-Camino +1 more
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n-Dimensional dual complex numbers
Advances in Applied Clifford Algebras, 1998The authors consider an \(n\)-dimensional generalization of the quadric algebra \(Q_{0,0}=\{z\mid z=x+qy\), \(q^2=0\), \(q\not\in {\mathbb{R}}\}= {\mathbb{R}}[x]/x^2\) of dual complex numbers. They introduce various basic algebraic and analytic notions, investigate the analyticity property and establish analogues to several classical results such as ...
Fjelstad, Paul, Gal, Sorin G.
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Investigation of Dual-Complex Fibonacci, Dual-Complex Lucas Numbers and Their Properties
Advances in Applied Clifford Algebras, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Güngör, Mehmet Ali, Azak, Ayşe Zeynep
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Computations of Dual Numbers in the Extended Finite Dual Plane
19th Design Automation Conference: Volume 2 — Design Optimization; Geometric Modeling and Tolerance Analysis; Mechanism Synthesis and Analysis; Decomposition and Design Optimization, 1993Abstract 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.
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Subdiagrams equal in number to their duals
Algebra Universalis, 1986A subdiagram S of an ordered set P is a cover-preserving ordered subset of P. If S is finite, \(\ell (S)\neq 2\) and S is, as a down set, embedded in a selfdual lattice of subspaces of a projective geometry then the authors prove that S is a ''dual subdiagram invariant'' which means: For any modular lattice M, the number of subdiagrams of M isomorphic ...
Reuter, Klaus, Rival, Ivan
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Martin's Axiom and the Dual Distributivity Number
MLQ, 2000Let \(\kappa\) be a regular uncountable cardinal. The author proves the consistency of: MA holds, \(\mathfrak c = \kappa\) and \(\mathfrak H = \omega_1\). \(\mathfrak H\) is the dual distributivity number, (i.e., dual to \(\mathfrak h\)) defined by the following string of definitions: Let \(X, Y\) be partitions of \(\omega\).
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Dual Numbers and Topological Hjelmslev Planes
Canadian Mathematical Bulletin, 1983AbstractIn 1929 J. Hjelmslev introduced a geometry over the dual numbers ℝ+tℝ with t2 = Q. The dual numbers form a Hjelmslev ring, that is a local ring whose (unique) maximal ideal is equal to the set of 2 sided zero divisors and whose ideals are totally ordered by inclusion.
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Coxeter and dual coxeter numbers
Communications in Algebra, 1998(1998). Coxeter and dual coxeter numbers. Communications in Algebra: Vol. 26, No. 1, pp. 147-153.
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Dual numbers and supersymmetric mechanics
Czechoslovak Journal of Physics, 2005We show that dual numbers, apart from the known practical applications to the description of a rigid body movements in three dimensional space and natural presence in abstract differential algebra, play a role in field theory and are related to supersymmetry as well. Relevant models are considered.
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