Matrix Valued Spherical Functions Associated to the Complex Projective Plane

The main purpose of this paper is to compute all irreducible spherical functions on G=\SU(3) of arbitrary type $\delta\in \hat K$, where $K={\mathrm{S}}(\mathrm{U}(2)\times\mathrm{U}(1))\simeq\mathrm{U}(2)$. This is accomplished by associating to a spherical function $\Phi$ on $G$ a matrix valued function $H$ on the complex projective plane $P_2(\mathbb{C})=G/K$. It is well known that there is a fruitful connection between the hypergeometric function of Euler and Gauss and the spherical functions of trivial type associated to a rank one symmetric pair $(G,K)$. But the relation of spherical functions of types of dimension bigger than one with classical analysis, has not been worked out even in the case of an example of a rank one pair. The entries of $H$ are solutions of two systems of ordinary differential equations. There is no ready made approach to such a pair of systems, or even to a single system of this kind. In our case the situation is very favorable and the solution to this pair of systems can be exhibited explicitely in terms of a special class of generalized hypergeometric functions ${}_{p+1}F_p$.Comment: 70 pages, 1 figur

One-dimensional quantum walks with one defect

The CGMV method allows for the general discussion of localization properties for the states of a one-dimensional quantum walk, both in the case of the integers and in the case of the non negative integers. Using this method we classify, according to such localization properties, all the quantum walks with one defect at the origin, providing explicit expressions for the asymptotic return probabilities at the origin

In Vivo measurement of human body composition

Physiological changes in human beings were studied during a 21 day bed rest regime. Results of blood analyses indicated clearly that major metabolic adjustments occurred during prolonged bed rest. However, urinary metabolic analyses showed variances attributed to specimen collection inaccuracies and the small number of test subjects

Inelastic collapse of a randomly forced particle

We consider a randomly forced particle moving in a finite region, which rebounds inelastically with coefficient of restitution r on collision with the boundaries. We show that there is a transition at a critical value of r, r_c\equiv e^{-\pi/\sqrt{3}}, above which the dynamics is ergodic but beneath which the particle undergoes inelastic collapse, coming to rest after an infinite number of collisions in a finite time. The value of r_c is argued to be independent of the size of the region or the presence of a viscous damping term in the equation of motion.Comment: 4 pages, REVTEX, 2 EPS figures, uses multicol.sty and epsf.st

Tetrachloroethylene (PCE, Perc) Levels in Residential Dry Cleaner Buildings in Diverse Communities in New York City

Fugitive tetrachloroethylene (PCE, perc) emissions from dry cleaners operating in apartment buildings can contaminate residential indoor air. In 1997, New York State and New York City adopted regulations to reduce and contain perc emissions from dry cleaners located in residential and other buildings. As part of a New York State Department of Health (NYSDOH) study, indoor air perc levels were determined in 65 apartments located in 24 buildings in New York City where dry cleaners used perc on site. Sampling occurred during 2001–2003, and sampled buildings were dispersed across minority and nonminority as well as low-income and higher income neighborhoods. For the entire study area, the mean apartment perc level was 34 μg/m(3), 10-fold lower than mean apartment levels of 340–360 μg/m(3) documented before 1997. The maximum detected perc level was 5,000 μg/m(3), 5-fold lower than the maximum of 25,000 μg/m(3) documented before 1997. Despite these accomplishments, perc levels in 17 sampled apartments still exceeded the NYSDOH residential air guideline of 100 μg/m(3), and perc levels in 4 sampled apartments exceeded 1,000 μg/m(3). Moreover, mean indoor air perc levels in minority neighborhoods (75 μg/m(3)) were four times higher than in nonminority households (19 μg/m(3)) and were > 10 times higher in low-income neighborhoods (256 μg/m(3)) than in higher income neighborhoods (23 μg/m(3)). Logistic regression suitable for clustered data (apartments within buildings) indicated that perc levels on floors 1–4 were significantly more likely to exceed 100 μg/m(3) in buildings located in minority neighborhoods (odds ratio = 6.7; 95% confidence interval, 1.5–30.5) than in nonminority neighborhoods. Factors that may be contributing to the elevated perc levels detected, especially in minority and low-income neighborhoods, are being explored

Adolescent obesity, educational attainment, and adult earnings

We estimate the effects of being obese during adolescence on the likelihood of high school graduation, post-secondary educational attainment and labour market earnings as an adult (over 13 years later). We use longitudinal data from the National Longitudinal Survey of Adolescent Health (Add Health), conducted by the Carolina Population Center of the University of North Carolina at Chapel Hill. This is a nationally representative sample of students in grades 7 through 12 for the 1994-1995 first wave survey. Three subsequent waves of follow-up interviews occurred in 1996, 2001-2002 and finally in 2007-2008, when the sample was aged 25-31. Probit and linear regression models with a large set of controls (to minimize any bias that may result from omitting factors related to both adolescent obesity and adult outcomes) are fitted to carry out analyses separately by gender or racial groups. Pathological body weights are most notably present among males, blacks and Hispanics, suggesting possibility that diverging obesity effects may be found across race and gender groups. Unlike some prior research, we find no significant effects of adolescent obesity on high school graduation, but for some demographic groups, negative effects are found on college graduation and future income. Policy implications are discussed. © 2014 Taylor & Francis

Repeatable texture sampling with interchangeable patches

Rendering textures in real-time environments is a key task in computer graphics. This paper presents a new parallel patch-based method which allows repeatable sampling without cache, and does not create visual repetitions. Interchangeable patches of arbitrary shape are prepared in a preprocessing step, such that patches may lie over the boundary of other patches in a repeating tile. This compresses the example texture into an infinite texture map with small memory requirements, suitable for GPU and ray-tracing applications. The quality of textures rendered with this method can be tuned in the offline preprocessing step, and they can then be rendered in times comparable to Wang tiles. Experimental results demonstrate combined benefits in speed, memory requirements, and quality of randomisation when compared to previous methods

Root polytopes and abelian ideals

We study the root polytope $\mathcal P_\Phi$ of a finite irreducible crystallographic root system $\Phi$ using its relation with the abelian ideals of a Borel subalgebra of a simple Lie algebra with root system $\Phi$. We determine the hyperplane arrangement corresponding to the faces of codimension 2 of $\mathcal P_\Phi$ and analyze its relation with the facets of $\mathcal P_\Phi$. For $\Phi$ of type $A_n$ or $C_n$, we show that the orbits of some special subsets of abelian ideals under the action of the Weyl group parametrize a triangulation of $\mathcal P_\Phi$. We show that this triangulation restricts to a triangulation of the positive root polytope $\mathcal P_\Phi^+$.Comment: 41 pages, revised version, accepted for publication in Journal of Algebraic Combinatoric