Language and communication difficulties may occur in the elderly population. This is the case of the tip-of-the-tongue phenomenon and receptive and auditory comprehension difficulties. Few studies have focused on examining the effects of social exposure on maintaining communication in the aging process. OBJECTIVES [1] To describe the communication map of healthy elderly subjects; [2] To searc...

We consider the problem of locating a spherical circle with respect to existing facilities on a sphere, such that the sum of distances between the circle and the facilities is minimized, or such that the maximum distance is minimized. The problem properties are analyzed, and we give solution procedures. When the circle to be located is restricted to be a great circle, some simplifications are p...

The Descartes circle theorem states that if four circles are mutually tangent in the plane, with disjoint interiors, then their curvatures (or “bends”) bi = 1 ri satisfy the relation (b1 + b2 + b3 + b4) 2 = 2(b1 + b 2 2 + b 2 3 + b 2 4). We show that similar relations hold involving the centers of the four circles in such a configuration, coordinatized as complex numbers, yielding a complex Des...

We give a complete and explicit characterization of the connected graphs which admit a continuous 3-to-1 map onto the circle, and of the connected graphs which admit a continuous 2-to-l map onto the circle. This generalizes earlier work of Heath and Hilton who considered the mappings of trees onto the circle.

The importance of infrastructure for growth is well established in the macroeconomic literature. Previous research has treated public investment in infrastructure as exogenous. We remedy this shortcoming by providing a political economy analysis of infrastructure choice based upon consumer preferences derived from spatial competition models. In this setting, infrastructure investment has two po...