Automatic continuity of operational calculi on algebras of differentiable functions
On Choquet's theory
Automatic continuity of translation - invariant linear operators
Flows in infinite networks
An application of fixed-point theory to equilibrium analysis
On a strong form of a conjecture of Boyle and Handelman.
Bounds for graph expansions via elasticity.
A note on Newton and Newton-like inequalities for -matrices and for Drazin inverses of -matrices.
A parallel algorithm for computing the group inverse via Perron complementation.
On the derivatives of the Perron vector
An improvement of an inequality of Fiedler leading to a new conjecture on nonnegative matrices
Suppose that is an nonnegative matrix whose eigenvalues are . Fiedler and others have shown that , for all , with equality for any such if and only if is the simple cycle matrix. Let be the signed sum of the determinants of the principal submatrices of of order , . We use similar techniques to Fiedler to show that Fiedler’s inequality can be strengthened to: , for all . We use this inequality to derive the inequality that: . In the spirit of a celebrated conjecture due to Boyle-Handelman,...
The algebraic connectivity of two trees connected by an edge of infinite weight.
Alternating projected Barzilai-Borwein methods for nonnegative matrix factorization.
The notion of -weak dependence and its applications to bootstrapping time series.
Continuity of sublinear operators on F-spaces.
Tight bounds on the algebraic connectivity of a balanced binary tree.
On a bound on algebraic connectivity: the case of equality
In a recent paper the authors proposed a lower bound on , where , , is an eigenvalue of a transition matrix of an ergodic Markov chain. The bound, which involved the group inverse of , was derived from a more general bound, due to Bauer, Deutsch, and Stoer, on the eigenvalues of a stochastic matrix other than its constant row sum. Here we adapt the bound to give a lower bound on the algebraic connectivity of an undirected graph, but principally consider the case of equality in the bound when...
Bounds on the subdominant eigenvalue involving group inverses with applications to graphs
Let be an symmetric, irreducible, and nonnegative matrix whose eigenvalues are . In this paper we derive several lower and upper bounds, in particular on and , but also, indirectly, on . The bounds are in terms of the diagonal entries of the group generalized inverse, , of the singular and irreducible M-matrix . Our starting point is a spectral resolution for . We consider the case of equality in some of these inequalities and we apply our results to the algebraic connectivity of undirected...
A central limit theorem for triangular arrays of weakly dependent random variables, with applications in statistics
We derive a central limit theorem for triangular arrays of possibly nonstationary random variables satisfying a condition of weak dependence in the sense of Doukhan and Louhichi [84 (1999) 313–342]. The proof uses a new variant of the Lindeberg method: the behavior of the partial sums is compared to that of partial sums of Gaussian random variables. We also discuss a few applications in statistics which show that our central limit theorem is tailor-made for statistics of different type.
On the Mazur-Orlicz theorem
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