Divisibility properties of Smith 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.
Domains of analytic continuation for the top Lyapunov exponent
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.
Doubly stochastic matrices and the Bruhat order
The Bruhat order is defined in terms of an interchange operation on the set of permutation matrices of order which corresponds to the transposition of a pair of elements in a permutation. We introduce an extension of this partial order, which we call the stochastic Bruhat order, for the larger class of doubly stochastic matrices (convex hull of permutation matrices). An alternative description of this partial order is given. We define a class of special faces of induced by permutation matrices,...
Drei-Nachrichten-Probleme in verallgemeinerter Definition.
Dualità e teoria dei grafi per la completa positività di matrici
Duality of real and quaternionic random matrices.
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...
Ecuaciones lineales y anillos conmutativos.
Edge matrices for the fundamental cone.
Editors’ Summary for the Special Issue: Proceedings of the 24th International Workshop on Matrices and Statistics
Eduard Weyr (1852-1903) [Book]
Efficient computation of enclosures for the exact solvents of a quadratic matrix equation.
Efficient measurement of higher-order statistics of stochastic processes
This paper is devoted to analysis of block multi-indexed higher-order covariance matrices, which can be used for the least-squares estimation problem. The formulation of linear and nonlinear least squares estimation problems is proposed, showing that their statements and solutions lead to generalized `normal equations', employing covariance matrices of the underlying processes. Then, we provide a class of efficient algorithms to estimate higher-order statistics (generalized multi-indexed covariance...
Eigenspace decompositions with respect to symmetrized incidence mappings.