lorentz characterized the almost convergence through the concept of uniform convergence of de lavallée-poussin mean. in this paper, we generalize the notion of almost convergence by using the concept ofinvariant mean and the generalized de la vallée-poussin mean. we determine the bounded linear operators forthe generalized σ-conservative, σ-regular and σ-coercive matrices.

We study a cooperation structure in which the feasible coalitions are those belonging to a partition closure system. First, we develop the relation between the dividends of Harsanyi in the restricted game and the worth function in the original game. Next, we obtain an method for computing the Shapley and Banzhaf values of the closure-restricted games using the dividends formula. Finally, we ana...

Suppose that we have the unit Euclidean ball in R and construct new bodies using three operations linear transformations, closure in the radial metric and multiplicative summation defined by ‖x‖K+0L = p ‖x‖K‖x‖L. We prove that in dimension 3 this procedure gives all origin symmetric convex bodies, while this is no longer true in dimensions 4 and higher. We introduce the concept of embedding of ...

Suppose that we have the unit Euclidean ball in R and construct new bodies using three operations linear transformations, closure in the radial metric and multiplicative summation defined by ‖x‖K+0L = p ‖x‖K‖x‖L. We prove that in dimension 3 this procedure gives all origin symmetric convex bodies, while this is no longer true in dimensions 4 and higher. We introduce the concept of embedding of ...

When closure operators are deened over gures in the plane, they are normally deened with respect to convex closure in the Euclidean plane. This report concentrates on discrete closure operators deened over the discrete, rectilinear plane. Basic to geometric convexity is the concept of a geodesic, or shortest path. Such geodesics can be regarded as the closure of two points. But, given the usual...

Let N be a ...nite set. By a closure space we mean the family of the closed sets of a closure operator on 2 satisfying the additional condition ; = ;. A simple game on a closure space L is a function v : L ! f0; 1g such that v(;) = 0 and v (N) = 1. We assume simple games are monotonic. The coalitions are the closed sets of L and the players are the elements i 2 N . We will give results concerni...

hadamard (or complete $cat(0)$) spaces are complete, non-positive curvature, metric spaces. here, we prove a nonlinear ergodic theorem for continuous non-expansive semigroup in these spaces as well as a strong convergence theorem for the commutative case. our results extend the standard non-linear ergodic theorems for non-expansive maps on real hilbert spaces, to non-expansive maps on had...

We pursue the principles of duality and symmetry building upon Pratt’s idea of the Stone Gamut and Abramsky’s representations of quantum systems. In the first part of the paper, we first observe that the Chu space representation of quantum systems leads us to an operational form of state-observable duality, and then show via the Chu space formalism enriched with a generic concept of closure con...

Formal Concept Analysis is based on the occurrence of symbolic attributes in individual objects, or observations. But, when the attribute is numeric, treatment has been awkward. In this paper, we show how one can derive logical implications in which the atoms can be not only boolean symbolic attributes, but also ordinal inequalities, such as x ≤ 9. This extension to ordinal values is new. It em...