Intersection of paraboloids and application to Minkowski-type problems

In this article, we study the intersection (or union) of the convex hull of N confocal paraboloids (or ellipsoids) of revolution. This study is motivated by a Minkowski-type problem arising in geometric optics. We show that in each of the four cases, the combinatorics is given by the intersection of a power diagram with the unit sphere. We prove the complexity is O(N) for the intersection of paraboloids and Omega(N^2) for the intersection and the union of ellipsoids. We provide an algorithm to compute these intersections using the exact geometric computation paradigm. This algorithm is optimal in the case of the intersection of ellipsoids and is used to solve numerically the far-field reflector problem

The impact of brand gender on consumer-brand engagement and consumer-based brand equity on Facebook

In this research, we investigate how two distinct and universal dimensions of brand personality - brand masculinity and brand femininity - which constitute the two dimensions of brand gender (Grohmann 2009) influence consumer-brand engagement on Facebook. Another critical aim is to investigate the relationship between brand masculinity and brand femininity perceptions and consumer-based brand equity, on Facebook

Coverage of Infertility Treatment and Fertility Outcomes: Do Women Catch Up?

The ageing of first-time mothers and the changes in women's labor market conditions have been accompanied by the introduction and subsequent increase in the use of assisted reproductive therapies (ART) that help extend women's reproductive lives. Considering the financial cost of infertility treatments, policy interventions that increase insurance coverage may significantly affect fertility trends, and ultimately, population age structures. However, policies have ignored the overall impact of ART coverage on fertility. In this paper, long-term effects of insurance coverage for infertility on the timing of first births and on total fertility rates are examined. Variation in the enactment of infertility insurance mandates over time and across U.S. states allows the estimation of both the short-term and long-term effects. We concentrate on the effects of the more demanding mandates enacted in six states in the later 80s and 90s. Our results show that the effect of these mandates to cover infertility treatment is positive on the average age at first birth and increases over time. The long-term estimates of the increase in age of first-time mothers range from 3 to 5 months. Importantly, we also show that these mandates do not increase the total fertility rates of women by the end of their reproductive lives.assisted reproductive technologies, infertility insurance mandates, total fertility, synthetic control methods