An Introduction to Hyperbolic Barycentric Coordinates and their Applications

Barycentric coordinates are commonly used in Euclidean geometry. The adaptation of barycentric coordinates for use in hyperbolic geometry gives rise to hyperbolic barycentric coordinates, known as gyrobarycentric coordinates. The aim of this article is to present the road from Einstein's velocity addition law of relativistically admissible velocities to hyperbolic barycentric coordinates along with applications.Comment: 66 pages, 3 figure

Harmonic analysis on the Möbius gyrogroup

In this paper we propose to develop harmonic analysis on the Poincaré ball $B_t^n$, a model of the n-dimensional real hyperbolic space. The Poincaré ball $B_t^n$ is the open ball of the Euclidean n-space $R^n$ with radius $t>0$, centered at the origin of $R^n$ and equipped with Möbius addition, thus forming a Möbius gyrogroup where Möbius addition in the ball plays the role of vector addition in $\mathbb{R}^n$. For any $t>0$ and an arbitrary parameter $\sigma \in R$ we study the $(\sigma,t)$-translation, the $( \sigma,t)$-convolution, the eigenfunctions of the $(\sigma,t)$-Laplace-Beltrami operator, the $(\sigma,t)$-Helgason Fourier transform, its inverse transform and the associated Plancherel's Theorem, which represent counterparts of standard tools, thus, enabling an effective theory of hyperbolic harmonic analysis. Moreover, when $t \rightarrow +\infty$ the resulting hyperbolic harmonic analysis on $B_t^n$ tends to the standard Euclidean harmonic analysis on $R^n$, thus unifying hyperbolic and Euclidean harmonic analysis. As an application we construct diffusive wavelets on $B_t^n$

Evaluation of nonmetallic thermal protection materials for the manned space shuttle. Volume 1, task 1: Assessment of technical risks associated with utilization of nonmetallic thermal protection system

Technical problems of design and flight qualification of the proposed classes of surface insulation materials and leading edge materials were reviewed. A screening test plan, a preliminary design data test plan and a design data test plan were outlined. This program defined the apparent critical differences between the surface insulators and the leading edge materials, structuring specialized screening test plans for each of these two classes of materials. Unique testing techniques were shown to be important in evaluating the structural interaction aspects of the surface insulators and a separate task was defined to validate the test plan. In addition, a compilation was made of available information on proposed material (including metallic TPS), previous shuttle programs, pertinent test procedures, and other national programs of merit. This material was collected and summarized in an informally structured workbook

Evidence of strong stabilizing effects on the evolution of boreoeutherian (Mammalia) dental proportions.

The dentition is an extremely important organ in mammals with variation in timing and sequence of eruption, crown morphology, and tooth size enabling a range of behavioral, dietary, and functional adaptations across the class. Within this suite of variable mammalian dental phenotypes, relative sizes of teeth reflect variation in the underlying genetic and developmental mechanisms. Two ratios of postcanine tooth lengths capture the relative size of premolars to molars (premolar-molar module, PMM), and among the three molars (molar module component, MMC), and are known to be heritable, independent of body size, and to vary significantly across primates. Here, we explore how these dental traits vary across mammals more broadly, focusing on terrestrial taxa in the clade of Boreoeutheria (Euarchontoglires and Laurasiatheria). We measured the postcanine teeth of N = 1,523 boreoeutherian mammals spanning six orders, 14 families, 36 genera, and 49 species to test hypotheses about associations between dental proportions and phylogenetic relatedness, diet, and life history in mammals. Boreoeutherian postcanine dental proportions sampled in this study carry conserved phylogenetic signal and are not associated with variation in diet. The incorporation of paleontological data provides further evidence that dental proportions may be slower to change than is dietary specialization. These results have implications for our understanding of dental variation and dietary adaptation in mammals

Coherent Quantum Engineering of Free-Space Laser Cooling

We perform a quantitative analysis of the cooling dynamics of three-level atomic systems interacting with two distinct lasers. Employing sparse-matrix techniques, we find numerical solutions to the fully quantized master equation in steady state. Our method allows straightforward determination of laser-cooling temperatures without the ambiguity often accompanied by semiclassical calculations, and more quickly than non-sparse techniques. Our calculations allow us to develop an understanding of the regimes of cooling, as well as a qualitative picture of the mechanism, related to the phenomenon of electromagnetically induced transparency. Effects of the induced asymmetric Fano-type lineshapes affect the detunings required for optimum cooling, as well as the predicted minimum temperatures which can be lower than the Doppler limit for either transition.Comment: 5 pages, 3 figure

Thomas rotation and Thomas precession

Exact and simple calculation of Thomas rotation and Thomas precessions along a circular world line is presented in an absolute (coordinate-free) formulation of special relativity. Besides the simplicity of calculations the absolute treatment of spacetime allows us to gain a deeper insight into the phenomena of Thomas rotation and Thomas precession.Comment: 20 pages, to appear in Int. J. Theo. Phy

Geometric observation for the Bures fidelity between two states of a qubit

In this Brief Report, we present a geometric observation for the Bures fidelity between two states of a qubit.Comment: 4 pages, 1 figure, RevTex, Accepted by Phys. Rev.

Cold collisions between atoms in optical lattices

We have simulated binary collisions between atoms in optical lattices during Sisyphus cooling. Our Monte Carlo Wave Function simulations show that the collisions selectively accelerate mainly the hotter atoms in the thermal ensemble, and thus affect the steady state which one would normally expect to reach in Sisyphus cooling without collisions.Comment: 4 pages, 1 figur

Nonlinear Dynamics of Aeolian Sand Ripples

We study the initial instability of flat sand surface and further nonlinear dynamics of wind ripples. The proposed continuous model of ripple formation allowed us to simulate the development of a typical asymmetric ripple shape and the evolution of sand ripple pattern. We suggest that this evolution occurs via ripple merger preceded by several soliton-like interaction of ripples.Comment: 6 pages, 3 figures, corrected 2 typo

Patient-Reported Satisfaction and Study Drug Discontinuation: Post-Hoc Analysis of Findings from ROCKET AF.

IntroductionPatient-reported outcomes (PROs) and satisfaction endpoints are increasingly important in clinical trials and may be associated with treatment adherence. In this post hoc substudy from ROCKET AF, we examined whether patient-reported satisfaction was associated with study drug discontinuation.MethodsROCKET AF (n = 14,264) compared rivaroxaban with warfarin for prevention of stroke and systemic embolism in patients with atrial fibrillation. We analyzed treatment satisfaction scores: the Anti-Clot Treatment Scale (ACTS) and Treatment Satisfaction Questionnaire for Medication version II (TSQM II). We compared satisfaction with study drug between the two treatment arms, and examined the association between satisfaction and patient-driven study drug discontinuation (stopping study drug due to withdrawal of consent, noncompliance, or loss to follow-up).ResultsA total of 1577 (11%) patients participated in the Patient Satisfaction substudy; 1181 (8.3%) completed both the ACTS and TSQM II 4 weeks after starting study drug. Patients receiving rivaroxaban did not experience significant differences in satisfaction compared with those receiving warfarin. During a median follow-up of 1.6 years, 448 premature study drug discontinuations occurred (213 rivaroxaban group; 235 warfarin group), of which 116 (26%) were patient-driven (52 [24%] rivaroxaban group; 64 [27%] warfarin group). No significant differences were observed between satisfaction level and rates of patient-driven study drug discontinuation.ConclusionsStudy drug satisfaction did not predict rate of study drug discontinuation. No significant difference was observed between satisfaction with warfarin and rivaroxaban, as expected given the double-blind trial design. Although these results are negative, the importance of PRO data will only increase, and these analyses may inform future studies that explore the relationship between drug-satisfaction PROs, adherence, and clinical outcomes. CLINICALTRIALS.GOV: NCT00403767.FundingThe ROCKET AF trial was funded by Johnson & Johnson and Bayer