We prove that every rational angled hyperbolic triangle has transcendental side lengths and that every rational angled hyperbolic quadrilateral has at least one transcendental side length. Thus, there does not exist a rational angled hyperbolic triangle or quadrilateral with algebraic side lengths. We conjecture that there does not exist a rational angled hyperbolic polygon with algebraic side ...

This study evaluated the efficacy of a combination tablet formulation of buprenorphine containing 8 mg of buprenorphine and 2 mg of naloxone for every other day treatment and whether increasing the daily maintenance dose was essential for maintaining an efficacious alternate-day treatment. Twenty-six opioid-dependent outpatients completing a 16-day baseline entered a double-blind, placebo-contr...

It is shown that quadratic constraints are compatible with the geometric integrability scheme of the multidimensional quadrilateral lattice equation. The corresponding Ribaucour-type reduction of the fundamental transformation of quadrilateral lattices is found as well, and superposition of the Ribaucour transformations is presented in the vectorial framework. Finally, the quadratic reduction a...

We present a simple and practical technique for seamlessly texturing quadrilateral meshes. Using our technique any image can be converted to an isotropic texture that can be mapped to any quadrilateral mesh without any discontinuity or singularity. Using our technique, we can make any abstract painter like Miro to seamlessly paint any smooth manifold surface. The surface can have any number of ...

A quadrilateral is a bordered surface homeomorphic to the closed disc, with 4 marked boundary points called vertices, and equipped with a Riemannian metric of constant curvature K ∈ {0, 1,−1}, such that the sides (the arcs between the vertices) are geodesic. So the metric has the so-called conic singularities at the vertices. Let παj > 0 be the interior angles at the vertices. When K = 0, we kn...

Cutaneous fungal infections occurred in four captive brown tree snakes (Boiga irregularis). The ventral scales were most commonly affected, and lesions began as areas of erythema and edema with vesicle formation, followed by development of caseous brown plaques. Lesions usually started where ventral scales overlapped and spread rapidly. All snakes died within 14 days after clinical signs were f...