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Stellar evolution calculations with variable abundance ratios were used to gauge the effects on temperatures, luminosities, and lifetimes in various phases. Individual elements C, N, O, Mg, Si, and Fe were included. Most of the effect relevant to integrated light models is contained in the temperature variable, as opposed to the timescale or luminosity. We derive a recipe for including abundance-sensitive temperature effects that is applicable to existing isochrone grids. The resultant enhanced isochrones are incorporated into composite stellar population models and compared with galaxy data from the Sloan Digital Sky Survey. A severe oxygen-age degeneracy is apparent, 2 - 3 Gyr per 0.1 dex in [O/R], where R represents a heavy element such as Fe. Over the range of early-type galaxy velocity dispersion, the spans of all abundance ratios are reduced but the age range increases, systematically older. Allowing Fe-peak elements the freedom to vary accentuates this increase of age span. Overall, these results sharpen the age-mass correlation known as downsizing but decrease the steepness of abundance ratio gradients. Both of these observations, in turn, imply a more robust contribution from gas free mergers in the histories of typical elliptical galaxies., Comment: 10 pages, 12 figures, 4 tables, accepted to MNRAS, 2022 Jan 26

The tip of the red giant branch is one of the widely used distance measurement methods for the relatively nearby galaxies where the bright individual stars are resolved. Most of the earlier works have used the Photometry in the I-band such as HST ACS/WFC F814W or F850LP for the RGB tip method. Here we look into the RGB tip magnitudes in J-band such as HST WFC3/IR F110W and JWST NIRCam/WF F115W for a wide range of age and metallicity. We find that the J-band (HST WFC3/IR F110W and JWST NIRCam/WF F115W) RGB tip magnitudes do not significantly change compared to that of the I-band (HST ACS/WFC F814W, F850LP) for a wide range of metallicity at given age. Moreover, HST WFC3/IR F110W RGB tip magnitudes stay constant within 0.005 magnitudes for stellar populations with old ages (age > 5 Gyr) at given metallicity., Comment: 4 pages, 3 figures, to appear in the Research Notes of the AAS

We study the inner-most stable circular orbit(ISCO) of Kerr black hole in MOdified gravity(Kerr-MOG black hole) which is one of the exact solution of the field equation of modified gravity in strong gravity regime. Kerr-MOG black hole is constructed commonly known kerr metric in Boyer-Lindquist coordinate by adding repulsive parameter like Yukawa force which explained in quantum gravity. We explore what is some differences of the ISCOs of Kerr-MOG black hole and kerr black hole., Comment: 5pages, 5figures

Embedded diagrams are drawn for investigating the black hole of Kerr and non-Kerr metric. Kerr black holes are characterized by masses $M$ and spin parameters $a$. Non-Kerr black holes also are characterized by the deformation parameters $\epsilon$, which is related to shape of the black hole, in addition to their masses and spins. In this paper, we investigate the behavior of non-Kerr black holes compared with Kerr black holes in the parameter space of ($a$,$\epsilon$) using embedded diagrams. The event horizons and the naked singularity of non-Kerr BHs are discussed in detail., Comment: 4 pages, 6 figures

We present new calibrations of the near-infrared surface brightness fluctuation (SBF) distance method for the F110W (J) and F160W (H) bandpasses of the Wide Field Camera 3 Infrared Channel (WFC3/IR) on the Hubble Space Telescope. The calibrations are based on data for 16 early-type galaxies in the Virgo and Fornax clusters observed with WFC3/IR and are provided as functions of both the optical (g-z) and near-infrared (J-H) colors. The scatter about the linear calibration relations for the luminous red galaxies in the sample is approximately 0.10 mag, corresponding to a statistical error of 5% in distance. Our results imply that the distance to any suitably bright elliptical galaxy can be measured with this precision out to about 80 Mpc in a single-orbit observation with WFC3/IR, making this a remarkably powerful instrument for extragalactic distances. The calibration sample also includes much bluer and lower-luminosity galaxies than previously used for IR SBF studies, revealing interesting population differences that cause the calibration scatter to increase for dwarf galaxies., Comment: 19 pages, 11 figures; version accepted for publication in the Astrophysical Journal; revised version contains a number of clarifications and additional references

The remarkable scientific return and legacy of LSST, in the era that it will define, will not only be realized in the breakthrough science that will be achieved with catalog data. This Big Data survey will shape the way the entire astronomical community advances -- or fails to embrace -- new ways of approaching astronomical research and data. In this white paper, we address the NRC template questions 4,5,6,8 and 9, with a focus on the unique challenges for smaller, and often under-resourced, institutions, including institutions dedicated to underserved minority populations, in the efficient and effective use of LSST data products to maximize LSST's scientific return., Comment: White paper submitted to the National Research Council Committee on a Strategy Optimize the U.S. OIR System in the Era of the LSST, 3 pages

Result diversification is an important aspect in web-based search, document summarization, facility location, portfolio management and other applications. Given a set of ranked results for a set of objects (e.g. web documents, facilities, etc.) with a distance between any pair, the goal is to select a subset $S$ satisfying the following three criteria: (a) the subset $S$ satisfies some constraint (e.g. bounded cardinality); (b) the subset contains results of high "quality"; and (c) the subset contains results that are "diverse" relative to the distance measure. The goal of result diversification is to produce a diversified subset while maintaining high quality as much as possible. We study a broad class of problems where the distances are a metric, where the constraint is given by independence in a matroid, where quality is determined by a monotone submodular function, and diversity is defined as the sum of distances between objects in $S$. Our problem is a generalization of the {\em max sum diversification} problem studied in \cite{GoSh09} which in turn is a generaliztion of the {\em max sum $p$-dispersion problem} studied extensively in location theory. It is NP-hard even with the triangle inequality. We propose two simple and natural algorithms: a greedy algorithm for a cardinality constraint and a local search algorithm for an arbitary matroid constraint. We prove that both algorithms achieve constant approximation ratios.

We introduce a new regression problem which we call the Sum-Based Hierarchical Smoothing problem. Given a directed acyclic graph and a non-negative value, called target value, for each vertex in the graph, we wish to find non-negative values for the vertices satisfying a certain constraint while minimizing the distance of these assigned values and the target values in the lp-norm. The constraint is that the value assigned to each vertex should be no less than the sum of the values assigned to its children. We motivate this problem with applications in information retrieval and web mining. While our problem can be solved in polynomial time using linear programming, given the input size in these applications such a solution might be too slow. We mainly study the \ell_1-norm case restricting the underlying graphs to rooted trees. For this case we provide an efficient algorithm, running in O(n^2) time. While the algorithm is purely combinatorial, its proof of correctness is an elegant use of linear programming duality. We believe that our approach may be applicable to similar problems, where comparable hierarchical constraints are involved, e.g. considering the average of the values assigned to the children of each vertex. While similar in flavor to other smoothing problems like Isotonic Regression (see for example [Angelov et al. SODA'06]), our problem is arguably richer and theoretically more challenging.

Spectral feature index diagrams with integrated globular clusters and simple stellar population models often show that some clusters have weak H beta, so weak that even the oldest models cannot match the observed feature depths. In this work, we rule out the possibility that abundance mixture effects are responsible for the weak indices unless such changes operate to cool the entire isochrone. We discuss this result in the context of other explanations, including horizontal branch morphology, blue straggler populations, and nebular or stellar emission fill-in, finding a preference for flaring in M giants as an explanation for the H beta anomaly., Comment: Submitted to the AJ