Multipole Gravitational Lensing and High-order Perturbations on the Quadrupole Lens

An arbitrary surface mass density of gravitational lens can be decomposed into multipole components. We simulate the ray-tracing for the multipolar mass distribution of generalized SIS (Singular Isothermal Sphere) model, based on the deflection angles which are analytically calculated. The magnification patterns in the source plane are then derived from inverse shooting technique. As have been found, the caustics of odd mode lenses are composed of two overlapping layers for some lens models. When a point source traverses such kind of overlapping caustics, the image numbers change by \pm 4, rather than \pm 2. There are two kinds of images for the caustics. One is the critical curve and the other is the transition locus. It is found that the image number of the fold is exactly the average value of image numbers on two sides of the fold, while the image number of the cusp is equal to the smaller one. We also focus on the magnification patterns of the quadrupole (m = 2) lenses under the perturbations of m = 3, 4 and 5 mode components, and found that one, two, and three butterfly or swallowtail singularities can be produced respectively. With the increasing intensity of the high-order perturbations, the singularities grow up to bring sixfold image regions. If these perturbations are large enough to let two or three of the butterflies or swallowtails contact, eightfold or tenfold image regions can be produced as well. The possible astronomical applications are discussed.Comment: 24 pages, 6 figure

Testing mechanisms of compensatory fitness of dioecy in a cosexual world

Questions: All else being equal, populations of dioecious species with a 50:50 sex ratio have only half the effective reproductive population size of bisexual species of equal abundance. Consequently, there is a need to explain how dioecious and bisexual species coexist. Increased mean individual seed mass, fecundity, and population density have all been proposed as attributes of unisexual individuals or populations that may contribute to the persistence or resilience of dioecious species. To date, no studies have compared sympatric dioecious and cosexual species with respect to all three components of fitness. In this study, we sought evidence for these compensatory advantages (higher seed mass, greater seed production per unit basal area, and higher population density) in dioecious species. Location: Five 20–25 ha forest dynamic plots spanning a latitudinal gradient in China, including two temperate, two subtropical, and one tropical forest. Methods: We used a phylogenetically corrected generalized linear modelling approach to assess the phylogenetic dependence and joint evolution of sexual system, seed mass and production, and ecological abundances among 48–333 species and 32,568–136,237 individuals per forest. Results: Across all five forests, we detected no consistent advantage for dioecious relative to sympatric cosexual species with respect to mean individual seed mass, seed production or the density of stems in any size class. Conclusions: Our study suggests that seed traits may provide compensatory mechanisms in some forests, but most often the coexistence of sexual systems cannot be explained by advantages of dioecy related to seed quality and demographic parameters. Future investigations of the factors that promote coexistence may increase our understanding by expanding the search to include attributes such as lifespan and tolerance or resistance to herbivores

The images of foreign versus domestic retailer brands in China: A model of corporate brand image and store image

Both foreign and domestic retailers are competing for the newly emerged affluent consumers in China, yet little is known about how these retailer brands are perceived by the Chinese consumers. The corporate branding literature often considers retailer’s store image as corporate image, which neglects the nuance between these two interrelated but distinctive constructs. Drawing upon cognitive associative network and categorisation theories, this study investigates the interrelations of retailer corporate brand image and store image and their differential effects on consumer patronage intention, with corporate brand origin (foreign versus domestic) as a moderator. Our sample was from a survey of 338 department store customers in Beijing, China. The empirical results show that both corporate brand image and store image have a positive effect on patronage intention, but the effect of store image is stronger. Brands of foreign origin have a more positive corporate brand image than their local counterparts, yet there is no significant difference in store image by corporate brand origin. Corporate branding recommendations for both foreign and domestic retailers operating in China are provided