Using bright ellipticals as dark energy cosmic clocks

The age of the Universe has been increasingly constrained by different techniques, such as the observations of type Ia supernovae (SNIa) at high redshift or dating the stellar populations of globular clusters. In this paper, we present a complementary approach using the colours of the brightest elliptical galaxies in clusters over a wide redshift range  ( z ≲ 1)  . We put new and independent bounds on the dark energy equation of state parametrized by a constant pressure-to-density ratio   w _Q  and by a parameter (ξ) which determines the scaling between the matter and dark energy densities. We find that accurate estimates of the metallicities of the stellar populations in moderate and high-redshift cluster galaxies can pose stringent constraints on the parameters that describe dark energy. Our results are in good agreement with the analysis of dark energy models using SNIa data as a constraint. Accurate estimates of the metallicities of stellar populations in cluster galaxies at   z ≲ 2  will make this approach a powerful complement to studies of cosmological parameters using high-redshift SNIa.     

The Expansion of the Distance Between Two Arbitrary Gravitating Points as Applied to Specific Models of Celestial Bodies

For the complete system of biharmonic functions a suitable representation in spheroidal coordinates is found. It is used for expanding the distance between two arbitrary gravitating points and its inverse quantity in appropriate series. Such expansions can be of interest and useful in a number of problems of celestial mechanics and stellar dynamics.     

Models for the magnitude‐distribution of brightest cluster galaxies

The brightest, or first-ranked, galaxies (BCGs) in rich clusters show a very small dispersion in luminosity, making them excellent standard candles. This small dispersion raises questions about the nature of BCGs. Are they simply the extremes of normal galaxies formed via a stochastic process, or do they belong to a special class of atypical objects? If they do, are all BCGs special, or do normal galaxies compete for the first rank? To answer these questions, we undertake a statistical study of BCG magnitudes using results from extreme value theory. Two-population models do better than one-population models. A simple scenario where a random boost in the magnitude of a fraction of bright normal galaxies forms a class of atypical galaxies best describes the observed distribution of BCG magnitudes.     

Formation of Concentric Rings Around Sources

Zones of increased concentration formed by a solvent flowing from a source are considered. A matehmatical model for forming such zones is proposed. It takes into account that such a zone is composed of a set of independent particles. Hence the distribution of a substance around the source can be explained by movement of an individual particle. In the model this movement is a continuous semi-Markov process with terminal stopping at some random point in space. Parameters of the process depend on the velocity field of the flow. Forward and backward partial differential equations for the distribution density of a random stopping point of the process are derived. The forward equation is investigated for the centrally symmetric case. Solutions of the equation demonstrate either a maximum or a local minimum at the source location. In the latter case a concentric ring around the source is formed. If different substances vary in their absorption rates, they can form separable concentration zones as a family of concentric rings.     

华南石炭纪岩关-大塘界线期牙形石地层分带

系统采集不同沉积相区和连续沉积的剖面，即浅海台地相广西柳江龙殿山剖面、台缘缓坡相云南施甸鱼硐剖面和台内盆地相广西柳州碰冲剖面，运用数理统计方法，研究了华南岩关一大塘界线过渡期牙形石的产出丰度和相分布，在恢复生物演化序列的基础上，对各剖面首先详细分带，再进一步综合成系统的5个牙形石带，即Gnathodus typicus—G．cuneiformis带、Gnathodus typicus—Protognathodus cordiformis带、Scaliognathus anchoralis—Gnathodus pseu-dosemiglaber带、Gnathodus praebilineatus带和Paragnathodus horrtopunctatus带。以生物系统发生为标准，严格限定各带的界线，并与北美、西欧同期地层进行精确对比，为建立杜内阶一维宪阶界线的全球层型(GSSP)提供可靠依据。     

转动物台椭圆偏光运动轨迹分析

本文研究了转动物台椭圆偏光的运动规律,并用公式和图解表示椭圆偏光运动轨迹,导出的椭圆偏光方程式集中反映了各公式之间的关系。为解决椭圆偏光长轴运动轨迹,推导出计算椭圆长轴(a)和视旋转角(Ar)两个新公式,使最大视旋转角所对应的物台转角的研究有新的进展。本文重点讨论不透明矿物反射光的椭圆偏光的性质,但对透明矿物透射光的椭圆偏光也有一定意义。     

被动椭圆形标志物应变分析的计算机模拟

本文采用计算机数学模拟的方法更深入地探讨了椭圆形标志物应变分析技术(R_f/Φ去应变法、Shimamoto等提出的代数法、调和平均值法和算术平均值法)的适用条件。一共形成了十一组有代表性的应变前数组,四种变形路径:纯剪、单剪、纯剪加单剪和体变。当应变前数组在(-90°,90°)内均匀分布或随机分布时,无论变形路径是哪一种(共轴的还是非共轴的),上述的所有方法都是适用有,且以代数法最佳。当应变前数组具有优选方位(单峰分布)且变形路径为共轴递进变形时,在一定条件下,R_f/Φ法能用来估计应变。经分析发现当应变足够大时,调和平均值法是一种简单快速的应变计算法。