The Pure Adaptive Search (PAS) algorithm for global optimization yields a sequence of points, each of which is uniformly distributed in the level set corresponding to its predecessor. This algorithm has the highly desirable property of solving a large class of global optimization problems using a number of iterations that increases at most linearly in the dimension of the problem. Unfortunately...

We classify n-point extensions of ergodic Z-actions up to relative orbit equivalence and establish criteria under which one n-point extension of an ergodic Z-action can be sped up to be relatively isomorphic to an n-point extension of another ergodic Z-action. Both results are characterized in terms of an algebraic object associated to each n-point extension which is a conjugacy class of subgro...

in this paper we enumerate fuzzy subgroups, up to a natural equivalence, of some finite abelian p-groups of rank two where p is any prime number. after obtaining the number of maximal chains of subgroups, we count fuzzy subgroups using inductive arguments. the number of such fuzzy subgroups forms a polynomial in p with pleasing combinatorial coefficients. by exploiting the order, we label the s...

in this paper we classify fuzzy subgroups of a rank-3 abelian group $g = mathbb{z}_{p^n} + mathbb{z}_p + mathbb{z}_p$ for any fixed prime $p$ and any positive integer $n$, using a natural equivalence relation given in cite{mur:01}. we present and prove explicit polynomial formulae for the number of (i) subgroups, (ii) maximal chains of subgroups, (iii) distinct fuzzy subgroups, (iv) non-isomorp...

We classify n-point extensions of ergodic Z-actions up to relative orbit equivalence and establish criteria under which one n-point extension of an ergodic Z-action can be sped up to be relatively isomorphic to an n-point extension of another ergodic Z-action. Both results are characterized in terms of an algebraic object associated to each n-point extension which is a conjugacy class of subgro...

BACKGROUND In studying the therapeutic evidence of innovative drug treatments, increasing attention is being devoted to differentiating between results that indicate no significant differences among the treatments under examination ("no proof of difference") and results that demonstrate the therapeutic equivalence among the treatments ("proof of no difference"). AIM Our analysis was aimed at ...