We present approximation algorithms for a number of problems of pricing items for sale so as to maximize seller’s revenue in an unlimited supply setting. Our main result is an O(k)approximation for pricing items to single-minded bidders who each want at most k items. For the case k = 2 (where we get a 4-approximation) this can be viewed as the following graph vertex pricing problem: given a gra...

K. pneumoniae is the predominant pathogen isolated from liver abscesses of diabetic patients in Asian countries. Although elevated blood glucose levels cause various immune problems, its effects on K. pneumoniae virulence are unknown. This study investigated the regulation of capsular polysaccharide (CPS) biosynthesis, a major determinant for K. pneumoniae virulence, in response to exogenous gl...

The edges of the complete graph Kn are coloured so that no colour appears no more than k times, k = [n/Alnn], for some sufficiently large A. We show that there is always a Hamiltonian cycle in which each edge is a different colour. The proof technique is probabilistic. 'Supported by NSF grant CCR-89000112

We present the first constant-factor approximation algorithm for the metric k-median problem. The k-median problem is one of the most well-studied clustering problems, i.e., those problems in which the aim is to partition a given set of points into clusters so that the points within a cluster are relatively close with respect to some measure. For the metric k-median problem, we are given n poin...

In this study, we analyzed the brightness temperature characteristics of short-duration heavy rainfall (SDHR) along Chengdu–Chongqing Railway (CCR), an important corridor economic and transportation activity in southwest China. Our findings could prove useful monitoring advance warning SDHR events: (1) predominantly occurred from July to August, with a peak frequency CCR area. terms diurnal var...

Extending a result of the first author and Katsura, we prove that for every UHF algebra [Formula: see text] infinite type, in uncountable cardinality there are nonisomorphic approximately matricial C*-algebras with same group as text]. These algebras “twisted” by prescribed canonical commutation relations (CCR), they can also be considered nonseparable generalizations noncommutative tori.