Let S be a given set of positive rational primes. Assume that the value of the Dedekind zeta function ζK of a number field K is less than or equal to zero at some real point β in the range 1 2 < β < 1. We give explicit lower bounds on the residue at s = 1 of this Dedekind zeta function which depend on β, the absolute value dK of the discriminant of K and the behavior in K of the rational primes...

Represented as graphs, real networks are intricate combinations of order and disorder. Fixing some of the structural properties of network models to their values observed in real networks, many other properties appear as statistical consequences of these fixed observables, plus randomness in other respects. Here we employ the dk-series, a complete set of basic characteristics of the network str...

Take N sites distributed randomly and uniformly on a smooth closed surface. We express the expected distance ŒDkN‘ from an arbitrary point on the surface to its kth-nearest neighboring site, in terms of the function Al‘ giving the area of a disc of radius l about that point. We then find two universalities. First, for a flat surface, where Al‘ = πl2, ŒDkN‘ is separable in k and N . All kt...

Along with using geometric information to define spatial terms such as “in”, Coventry and Garrod (2004) have proposed the use of dynamic-kinematic (DK) routines which relate to how two objects interact (kinematic) over time (dynamic). For the spatial description, “The penny is in the bowl,” the penny is contained by a bounding box around the bowl as well as the DK location-control routine that ...

We examined the extent to which young Hong Kong Chinese children, taught to read English as a second language via a logographic "look and say" method used information about letter names and letter sounds to learn English words. Forty children from each of three kindergarten grade levels (mean ages 3.8, 5.0, and 5.9 years old, respectively) were taught to pronounce novel English spellings that w...