In particular, (6) implies that the functions/i, • • • , /„ are all regular in the domain (7) a > 0, i wi\ < r, • • • ,| to„| < r. In these notations, the following theorem will be proved: Theorem. In the domain (7), let fx, • ■ • ,fnbe regular functions of the form (1) with uniformly almost periodic coefficient functions defined on (2) having Fourier expansions of the type (3), satisfying (4)....

We show that a completely multiplicative automatic function, which dos not have 0 as value, is almost periodic.

This paper studies some sufficient conditions for the existence and uniqueness of a pseudo almost periodic mild solution to abstract hyperbolic differential equations with infinite delay. Applications include the existence and uniqueness of a pseudo almost periodic mild solution to the heat equation.

Pairwise testing has become an indispensable tool in a software tester’s toolbox. The technique has been known for almost twenty years [22] but it is the last five years that we have seen a tremendous increase in its popularity. Information on at least 19 tools that can generate pairwise test cases, have so far been published [1]. Most tools, however, lack practical features necessary for them ...

Comorbidity patterns have become a major source of information to explore shared mechanisms of pathogenesis between disorders. In hypothesis-free exploration of comorbid conditions, disease-disease networks are usually identified by pairwise methods. However, interpretation of the results is hindered by several confounders. In particular a very large number of pairwise associations can arise in...

This paper examines the problem of ranking a collection of objects using pairwise comparisons (rankings of two objects). In general, the ranking of n objects can be identified by standard sorting methods using n log2 n pairwise comparisons. We are interested in natural situations in which relationships among the objects may allow for ranking using far fewer pairwise comparisons. Specifically, w...

For a countable, weakly minimal theory T , we show that the SchröderBernstein property (any two elementarily bi-embeddable models are isomorphic) is equivalent to each of the following: 1. For any U -rank-1 type q ∈ S(acl(∅)) and any automorphism f of the monster model C, there is some n < ω such that f(q) is not almost orthogonal to q ⊗ f(q)⊗ . . .⊗ fn−1(q); 2. T has no infinite collection of ...

For a sequence of pairwise negative quadrant dependent random variables {Xn, n ≥ 1}, conditions are given under which normed and centered partial sums converge to 0 almost certainly. As special cases, new results are obtained for weighted sums { ∑n j=1 ajXj , n ≥ 1} where {an, n ≥ 1} is a sequence of positive constants and the {Xn, n ≥ 1} are also identically distributed. A result of Matu la [1...

Large systems of particles interacting pairwise in d dimensions give rise to extraordinarily rich patterns. These patterns generally occur in two types. On one hand, the particles may concentrate on a co-dimension one manifold such as a sphere (in 3D) or a ring (in 2D). Localized, space-filling, co-dimension zero patterns can occur as well. In this paper, we utilize a dynamical systems approach...