Results 241 to 250 of about 3,505,093 (295)

Second‐order design sensitivity analysis using diagonal hyper‐dual numbers

International Journal for Numerical Methods in Engineering, 2021
Although sensitivity analysis provides valuable information for structural optimization, it is often difficult to use the Hessian in large models since many methods still suffer from inaccuracy, inefficiency, or limitation issues.
Vitor Takashi Endo, E. Fancello, P. Muñoz-Rojas   +2 more
semanticscholar   +1 more source

Space Kinematics and Projective Differential Geometry over the Ring of Dual Numbers

, 2020
We study an isomorphism between the group of rigid body displacements and the group of dual quaternions modulo the dual number multiplicative group from the viewpoint of differential geometry in a projective space over the dual numbers.
Hans-Peter Schrocker, M. Pfurner, Johannes Siegele   +2 more
semanticscholar   +1 more source

Martin's Axiom and the Dual Distributivity Number

MLQ, 2000
Let \(\kappa\) 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 \(\omega\).
openaire   +2 more sources

Principle of transference – An extension to hyper-dual numbers

Mechanism and Machine Theory, 2017
The algebra of hyper-dual numbers and hyper-dual vectors of order n, developed in this paper, follows the same rules as those of dual numbers and dual vectors.
A. Cohen, M. Shoham
semanticscholar   +1 more source

The Groups of Two by Two Matrices in Double and Dual Numbers, and Associated Möbius Transformations

Advances in Applied Clifford Algebras, 2017
Möbius transformations have been studied over the field of complex numbers. In this paper, we investigate Möbius transformations over two rings which are not fields: the ring of double numbers and the ring of dual numbers. We give types of continuous one-
Khawlah A. Mustafa
semanticscholar   +1 more source

Elliptic complex numbers with dual multiplication

Applied Mathematics and Computation, 2010
Abstract Investigated is a number system in which the square of a basis number: (w)2, and the square of its additive inverse: (−w)2, are not equal. Termed W space, a vector space over the reals, this number system will be introduced by restating defining relations for complex space C , then changing a defining conjugacy relation from conj(z) + 
John A. Shuster, Jens Köplinger
openaire   +1 more source

n-Dimensional dual complex numbers

Advances in Applied Clifford Algebras, 1998
The 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.
openaire   +1 more source

Variational updates for thermomechanically coupled gradient-enhanced elastoplasticity — Implementation based on hyper-dual numbers

Computer Methods in Applied Mechanics and Engineering, 2018
This paper deals with the implementation of thermomechanically coupled gradient-enhanced elastoplasticity at finite strains. The presented algorithmic formulation heavily relies on the variational structure of the considered initial boundary value ...
Volker Fohrmeister, A. Bartels, J. Mosler   +2 more
semanticscholar   +1 more source

Investigation of Dual-Complex Fibonacci, Dual-Complex Lucas Numbers and Their Properties

Advances in Applied Clifford Algebras, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Güngör, Mehmet Ali, Azak, Ayşe Zeynep
openaire   +4 more sources

Solving Three Systems of Functional Equations Associated with Complex, Double, and Dual Numbers

Russian Mathematics (Izvestiya VUZ. Matematika), 2023
V. A. Kyrov, G. G. Mikhaîlichenko
semanticscholar   +1 more source