Fuzzy Study on the Winning Rate of Football Game Betting

This study aims to find variables that affect the winning rate of the football team before a match. Qualitative variables such as venue, match importance, performance, and atmosphere of both teams are suggested to predict the outcome. Regression analysis is used to select proper variables. In this study, the performance of the football team is based on the opinions of experts, and the team atmosphere can be calculated with the results of the previous five games. ELO rating represents the state of the opponent. Also, the selected qualitative variables are expressed in fuzzy numbers using fuzzy partitions. A fuzzy regression model for the winning rate of the football team can be estimated by using the least squares method and the least absolute method. It is concluded that the stadium environment, ELO rating, team performance, and importance of the match have effects on the winning rate of Korean National Football (KNF) team from the data on 118 matches

The Presence of Two Distinct Red Giant Branches in the Globular Cluster NGC 1851

There is a growing body of evidence for the presence of multiple stellar populations in some globular clusters, including NGC 1851. For most of these peculiar globular clusters, however, the evidence for the multiple red giant-branches (RGBs) having different heavy elemental abundances as observed in Omega Centauri is hitherto lacking, although spreads in some lighter elements are reported. It is therefore not clear whether they also share the suggested dwarf galaxy origin of Omega Cen or not. Here we show from the CTIO 4m UVI photometry of the globular cluster NGC 1851 that its RGB is clearly split into two in the U - I color. The two distinct RGB populations are also clearly separated in the abundance of heavy elements as traced by Calcium, suggesting that the type II supernovae enrichment is also responsible, in addition to the pollutions of lighter elements by intermediate mass asymptotic giant branch stars or fast-rotating massive stars. The RGB split, however, is not shown in the V - I color, as indicated by previous observations. Our stellar population models show that this and the presence of bimodal horizontal-branch distribution in NGC 1851 can be naturally reproduced if the metal-rich second generation stars are also enhanced in helium.Comment: 13 pages, 4 figures, accepted for publication in the Astrophysical Journal Letter