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A sequence of positive integers w1, w2, . . . , wn is called an ascending wave if wi+1 − wi ≥ wi − wi−1 for 2 ≤ i ≤ n − 1. For integers k, r ≥ 1, let AW (k; r) be the least positive integer such that under any r-coloring of [1, AW (k; r)] there exists a k-term monochromatic ascending wave. The existence of AW (k; r) is guaranteed by van der Waerden’s theorem on arithmetic progressions since an ...

Frequent sub-graph mining entails two significant overheads. The first is concerned with candidate set generation. The second with isomorphism checking. These are also issues with respect to other forms of frequent pattern mining but are exacerbated in the context of frequent sub-graph mining. To reduced the search space, and address these twin overheads, a weighted approach to sub-graph mining...

The conjoint influence of welding and artificial aging on mechanical properties were investigated for extrusions of aluminum alloy 6063, 6061, and 6005A. Uniaxial tensile tests were conducted on the aluminum alloys 6063-T4, 6061-T4, and 6005A-T1 in both the as-received (AR) and as-welded (AW) conditions. Tensile tests were also conducted on the AR and AW alloys, subsequent to artificial aging. ...

Background: There have been some studies of common primary care diseases in Japan, but no reports on which diseases it is difficult for general physicians to diagnose in daily practice. In this study, we identified diseases that provided a diagnostic challenge for Japanese general physicians in daily practice. Methods: The subjects were new undiagnosed patients referred to the General Outpatien...