Discrete linear regulator revisited
Discrete-time symmetric polynomial equations with complex coefficients
Discrete-time symmetric polynomial equations with complex coefficients are studied in the scalar and matrix case. New theoretical results are derived and several algorithms are proposed and evaluated. Polynomial reduction algorithms are first described to study theoretical properties of the equations. Sylvester matrix algorithms are then developed to solve numerically the equations. The algorithms are implemented in the Polynomial Toolbox for Matlab.
Discriminant algebras and adjoints of quadratic forms.
Displacement Structure of Generalized Inverse At,s(1,2)
Dissident algebras
Given a euclidean vector space V = (V,〈〉) and a linear map η: V ∧ V → V, the anti-commutative algebra (V,η) is called dissident in case η(v ∧ w) ∉ ℝv ⊕ ℝw for each pair of non-proportional vectors (v,w) ∈ . For any dissident algebra (V,η) and any linear form ξ: V ∧ V → ℝ, the vector space ℝ × V, endowed with the multiplication (α,v)(β,w) = (αβ -〈v,w〉+ ξ(v ∧ w), αw + βv + η(v ∧ w)), is a quadratic division algebra. Up to isomorphism, each real quadratic division algebra arises in this way. Vector...
Dissident maps on the seven-dimensional Euclidean space
Our article contributes to the classification of dissident maps on ℝ ⁷, which in turn contributes to the classification of 8-dimensional real division algebras. We study two large classes of dissident maps on ℝ ⁷. The first class is formed by all composed dissident maps, obtained from a vector product on ℝ ⁷ by composition with a definite endomorphism. The second class is formed by all doubled dissident maps, obtained as the purely imaginary parts of the structures of those 8-dimensional...
Distances on the tropical line determined by two points
Let and be points in . Write if is a multiple of . Two different points and in uniquely determine a tropical line passing through them and stable under small perturbations. This line is a balanced unrooted semi-labeled tree on leaves. It is also a metric graph. If some representatives and of and are the first and second columns of some real normal idempotent order matrix , we prove that the tree is described by a matrix , easily obtained from . We also prove that...
Distribution of values of permanent and standard forms of (0,1)-matrices
Distributions homogènes sur des espaces de matrices
Divisible ℤ-modules
In this article, we formalize the definition of divisible ℤ-module and its properties in the Mizar system [3]. We formally prove that any non-trivial divisible ℤ-modules are not finitely-generated.We introduce a divisible ℤ-module, equivalent to a vector space of a torsion-free ℤ-module with a coefficient ring ℚ. ℤ-modules are important for lattice problems, LLL (Lenstra, Lenstra and Lovász) base reduction algorithm [15], cryptographic systems with lattices [16] and coding theory [8].
Dodgon's determinant-evaluation rule proved by TWO-TIMING MEN and WOMEN.
D-optimal and highly D-efficient designs with non-negatively correlated observations
In this paper we consider D-optimal and highly D-efficient chemical balance weighing designs. The errors are assumed to be equally non-negatively correlated and to have equal variances. Some necessary and sufficient conditions under which a design is D*-optimal design (regular D-optimal design) are proved. It is also shown that in many cases D*-optimal design does not exist. In many of those cases the designs constructed by Masaro and Wong (2008) and some new designs are shown to be highly D-efficient....
D-optimal weighing designs for four and five objects.
Dunkl operators and canonical invariants of reflection groups.
Dynamical Systems for Rational Normal Curves.
Dynamics of doubly stochastic quadratic operators on a finite-dimensional simplex
The present paper focuses on the dynamics of doubly stochastic quadratic operators (d.s.q.o) on a finite-dimensional simplex. We prove that if a d.s.q.o. has no periodic points then the trajectory of any initial point inside the simplex is convergent. We show that if d.s.q.o. is not a permutation then it has no periodic points on the interior of the two dimensional (2D) simplex. We also show that this property fails in higher dimensions. In addition, the paper also discusses the dynamics classifications...