The lunar surface progressively darkens and reddens as a result of sputtering from solar wind particles and bombardment of micrometeoroids. The extent of exposure to these space weathering agents is frequently calculated as the location in a diagram of reflectance at 750 nm vs. 950 nm/750 nm color (R-C). Sim & Kim (2018) examined the R-C trends of pixels within ∼3,500 craters, and revealed that the length (L) and skewness (s) of R-C trends can be employed as a secondary age or maturity indicator. We broaden this research to general lunar surface areas (3,400 tiles of 0.25◦ × 0.25◦ size) in 218 mare basalt units, whose ages have been derived from the size-frequency distribution analysis by Hiesinger et al. (2011). We discover that L and s rise with age until ∼3.2 Gyr and reduce rather rapidly afterward, while the optical maturity, OMAT, reduces monotonically with time. We show that in some situations, when not only OMAT but also L and s are incorporated in the estimation utilizing 750 & 950 nm photometry, the age estimation becomes considerably more reliable. We also observed that OMAT and the lunar cratering chronology function (cumulative number of craters larger than a certain diameter as a function of time) have a relatively linear relationship.

Because English grammar consists of a long list of features, it is impractical to include all of them in a single grammar test. It would be useful to identify among all those features the best indicators of students’ grammatical knowledge and ability so that we could focus on what were the most representative knowledge and skills and simplify grammar assessment. This study is a preliminary, small-scale attempt to do just that. It surveyed 72 high school teachers and 129 Grade 12 students on their opinions of which features of grammar best represented grammatical knowledge and ability. They were asked to choose five indicators, including the best one, and provide reasons for thinking so. The relative pronoun was selected most frequently as the best indicator of grammatical knowledge and ability, followed by subject-verb agreement, the subjunctive, to-infinitives, and participles. This paper does not claim these five features to definitively represent the best indicators; further research should be conducted.

We study the dynamical evolution of the M87 globular cluster (GC) system using the most advanced and realistic Fokker-Planck (FP) model.By comparing our FP models with both mass function (MF) and radial distribution (RD) of the observed GC system, we find the best-fit initial (at M87's age of 2-3 Gyr) MF and RD for three GC groups: all GCs, blue GCs, and red GCs. We estimate the initial total mass in GCs to be 1.8+0.3-0.2 X 1010⊙, which is about 100 times larger than that of the Milky Way GC system. We also find that the fraction of the total mass currently in GCs is 34%. When blue and red GCs are fitted separately, blue GCs initially have a larger total mass and a shallower radial distribution than red GCs. If one assumes that most of the significant major merger events of M87 have ended by the age of 2-3 Gyr, our finding that blue (metal-poor) GCs initially had a shallower radial distribution supports the major merger scenario for the origin of metallicity bimodality.

We have analyzed H and Ks -band images of the Arches cluster obtained using the NIRC2 instrument on Keck with the laser guide star adaptive optics (LGS AO) system. With the help of the LGS AO system, we were able to obtain the deepest ever photometry for this cluster and its neighborhood, and derive the background-subtracted present-day mass function (PDMF) down to 1.3M⊙ for the 5"-9" annulus of the cluster. We find that the previously reported turnover at 6M⊙ is simply due to a local bump in the mass function (MF), and that the MF continues to increase down to our 50 % completeness limit (1.3M⊙) with a power-law exponent of Γ= -0.91 for the mass range of 1.3 < M/M⊙ < 50. Our numerical calculations for the evolution of the Arches cluster show that the Γ values for our annulus increase by 0.1-0.2 during the lifetime of the cluster, and thus suggest that the Arches cluster initially had Γ of -1.0~-1.1 which is only slightly shallower than the Salpeter value.