Results 271 to 280 of about 30,859 (297)

Roots of algebraic equations and Clifford algebra

Advances in Applied Clifford Algebras, 1999
The author investigates roots of real polynomials inside the real two-dimensional Clifford algebra with generator \(\varepsilon\), \(\varepsilon^2=1\), calling the elements of this algebra hyperbolic. The corresponding numbers of real and hyperbolic roots of a polynomial are calculated.
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Spinor Equation and Operator Algebra

Journal of Geometry and Symmetry in Physics, 2023
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The Riccati algebraic equation in a locallyC ⋆-algebra

Integral Equations and Operator Theory, 1993
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Differential Equations in Banach Algebras

Doklady Mathematics, 2020
In a complex Banach algebra \(\mathbb{B}\) the ordinary linear differential equation \[ \mathbf{x}^{(n)} + \mathbf{p}_1\mathbf{x}^{(n-1)} + \dots + \mathbf{p}_{n-1}\dot{\mathbf{x}} + \mathbf{p}_ n \mathbf{x} = 0 \tag{1} \] with constant coefficients is considered.
Perov, A. I., Kostrub, I. D.
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An equation algebra

Soviet Physics Journal, 1977
A generalization of the theory of algebraic properties is proposed for an equation of general form, providing a tool for the acquisition of new results with regard to the symmetry of certain nondifferential equations of theoretical physics.
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The Algebraic Riccati Equation for Quaternions

Advances in Applied Clifford Algebras, 2013
The paper studies a Riccati equation \[ p(x):=a+bx+xc+xdx=0,\qquad a,b,c,d,x \in \mathbb{H}, \] where \(p\) is a quaternionic polynomial, which is shown to be reducible to a one-sided type. The set of quaternions \( \mathbb{H}\) can be seen as the four-dimensional vector space \( \mathbb{R}^4\) equipped with a special multiplication rule.
Janovská, Drahoslava, Opfer, Gerhard
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Injectivity in Equational Classes of Algebras

Canadian Journal of Mathematics, 1972
The concept of injectivity in classes of algebras can be traced back to Baer's initial results for Abelian groups and modules in [1]. The first results in non-module types of algebras appeared when Halmos [14] described the injective Boolean algebras using Sikorski's lemma on extensions of Boolean homomorphisms [19].
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On the Dirac equation in the algebraic approximation

Theoretica Chimica Acta, 1986
It is shown that the restrictive conditions of Wood et al. [1] are not necessary to reach the conclusion that the Dirac hamiltonian, projected onto the space of the large component, exhibits variational properties. The eigenvalue spectrum of matrix approximations to the partitioned hamiltonian (obtained by matrix partitioning) converges to the exact ...
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Polynomials and equations in arabic algebra

Archive for History of Exact Sciences, 2008
The paper has two parts. In the first part, the author explains the Arabic way of expressing algebraic problems. Since everything is done in sentences, not formulas, equality as a statement is expressed differently from equality as assignment or problem.
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On the Roots of Algebraic Equations

Journal of Mathematics and Physics, 1951
Luke, Yudell L., Ufford, Dolores
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