Let f s : R R a be a real-valued scalar field, and let x x x s T s = ... ∈ R ( , , ) 1 be partitioned into t subsets of non-overlapping variables as x X X t T = ... ( , , ) 1 , with X i p i ∈ R , for i = 1, ...,

There is no simple formula for developing and implementing successful business strategies across national borders. A popular approach to this challenge is to “think global, act local.” Some argue, however, that maximum consistency across global markets is critical, citing examples such as CocaCola, whose emphasis on quality, brand recognition, and a small world theme has been successful in a nu...

For given integers a, b and j ≥ 1 we determine the set R a,b of integers n for which an − bn is divisible by nj . For j = 1, 2, this set is usually infinite; we determine explicitly the exceptional cases for which a, b the set R a,b (j = 1, 2) is finite. For j = 2, we use Zsigmondy’s Theorem for this. For j ≥ 3 and gcd(a, b) = 1, R a,b is probably always finite; this seems difficult to prove, h...

Settling depth of apple was determined by a water column and a digital camera. The depth was experimentally modeled using multivariate regression using a coded program in MATLAB software. The best models were based on the density, dropping height volume/mass with coefficient of determination and mean square error of 0.90 and 4.08, respectively.

We give a characterization theorem for non-degenerate plane foliations of degree different from 1 having a rational first integral. Moreover, we prove that the degree r of a non-degenerate foliation as above provides the minimum number, r+ 1, of points in the projective plane through which pass infinitely many algebraic leaves of the foliation.

It is shown that associated with each metric space (X, d) there is a compactification udX of X that can be characterized as the smallest compactification of X to which each bounded uniformly continuous real-valued continuous function with domain X can be extended. Other characterizations of udX are presented, and a detailed study of the structure of udX is undertaken. This culminates in a topol...