We study the following question: for given d ⩾ 2 , n and k ⩽ what is largest value c ( ) such that from any set of unit vectors in R we may select with corresponding signs ±1 so their signed sum has norm at least ? The problem dual to classical vector minimization balancing questions, which have been studied over a century. give asymptotically sharp estimates general case. In several special ca...

The Inequality Process (IP) has been tested and confirmed against data on incomes that are approximately gamma distributed. IP’s pdf (probability density function) model expresses statistics of IP particle wealth algebraically in terms parameters for the subset generate distributions wealth, a serious limitation, one leaving many empirical income with heavier-than-gamma distribution right tails...

BACKGROUND Lymphocyte subsets enumeration is considered prominent in the management of primary and acquired immunodeficiency disorders. Because of local variations due to race, age, gender, and environmental conditions on lymphocyte subsets, and to improve the accuracy of interpretation of laboratory findings, reference intervals must be determined in every population. OBJECTIVE To establish ...

Let n be a large number. A subset A of Zn is complete if SA = Zn, where SA is the collection of the subset sums of A. Olson proved that if n is prime and |A| > 2n1/2, then SA is complete. We show that a similar result for the case when n is a composite number, using a different approach.

Consider the following problem which we call Maximum k-Subset Intersection (MSI): Given a collection C = {S1, . . . , Sm} of m subsets over a finite set of elements E = {e1, . . . , en}, and a positive integer k, the objective is to select exactly k subsets Sj1 , . . . , Sjk whose intersection size |Sj1 ∩ . . . ∩ Sjk | is maximum. In [2], Clifford and Popa studied a related problem and left as ...

A set S of positive integers has distinct subset sums if there are 2|S| distinct elements of the set {∑ x∈X x : X ⊂ S } . Let f(n) = min{maxS : |S| = n and S has distinct subset sums}. Erdős conjectured f(n) ≥ c2n for some constant c. We give a construction that yields f(n) < 0.22002 · 2n for n sufficiently large. This now stands as the best known upper bound on f(n).