When testing that a sample of n points in the unit hypercube [0, 1] comes from a uniform distribution, the Kolmogorov–Smirnov and the Cramér–von Mises statistics are simple and well-known procedures. To encompass these measures of uniformity, Hickernell introduced the so-called generalized Lp-discrepancies. These discrepancies can be used in numerical integration through Monte Carlo and quasi–M...

We introduce and study the notions of a strongly completable and of a strongly complete quasi-uniform space. A quasi-uniform space (X,U) is said to be strongly complete if every Cauchy filter (in the sense of Sieber and Pervin) clusters in the uniform space (X,U ∨ U−1). An interesting motivation for the study of this notion of completeness is the fact, proved here, that the quasi-uniformity ind...

Two-dimensional (2-D) photo-count mapping on CMOS single photon avalanche diodes (SPADs) has been demonstrated. Together with the varied incident wavelengths, the depth-dependent electric field distribution in active region has been investigated on two SPADs with different structures. Clear but different non-uniformity of photo-response have been observed for the two studied devices. With the h...

We demonstrate a one-to-one correspondence between idempotent closure operators and the so-called saturated quasi-uniform structures on category C. Not only this result allows to obtain categorical counterpart P of Császár-Pervin quasi-uniformity P, that we characterize as transitive compatible with an interior operator, but also permits describe those topogenous orders are induced by The P⁎ P−...

Quasi-random (also called low discrepancy) sequences are a deterministic alternative to random sequences for use in Monte Carlo methods, such as integration and particle simulations of transport processes. The error in uniformity for such a sequence of N points in the s-dimensional unit cube is measured by its discrepancy, which is of size (log N) N-Ifor large N, as opposed to discrepancy of si...

For a T3.s-ordered space, certain families of maps are designated as "defining families." For each such defining family we construct the smallest T=-ordered compactification such that each member of the family can be extended to the compactification space. Each defining family also generates a quasi-uniformity on the space whose bicompletion produces the same T=-ordered

We show that for even quasi-concave objective functions the worst-case distribution, with respect to a family of unimodal distributions, of a stochastic programming problem is a uniform distribution. This extends the so-called “Uniformity Principle” of Barmish and Lagoa (1997) where the objective function is the indicator function of a convex symmetric set.