Flatness of Gaussian curvature and area of ideal triangles

Let M be aC ^k ,k 4, compact surface of genus greater than two whose curvature is negative in all points but along a simple closed geodesic (t) where the curvature is zero at every point. We show that the area of ideal triangles having a lifting of as an edge is infinite. This provides a family of surfaces having ideal triangles of infinite area whose geodesic flows are equivalent to Anosov flows, in contrast with the well-known examples of surfaces with flat strips which also have ideal triangles of infinite area. By the CAT-comparison theory we can deduce, using these surfaces as models, that aC compact surface of non-positive curvature having one geodesic along which the curvature is zero has ideal triangles of infinite area.Partially supported by CNPq of Brazilian Government     

On Non-hyperbolic Quasi-convex Spaces

We show that if the universal covering of a compact Riemannian manifold with no conjugate points is a quasi-convex metric space then the following assertion holds: Either the universal covering of the manifold is a hyperbolic geodesic space or it contains a quasi-isometric immersion of .

     

Measuring the Elasticity of Poly‐l‐Proline Helices with Terahertz Spectroscopy

The rigidity of poly‐l ‐proline is an important contributor to the stability of many protein secondary structures, where it has been shown to strongly influence bulk flexibility. The experimental Young's moduli of two known poly‐l ‐proline helical forms, right‐handed all‐cis (Form I) and left‐handed all‐trans (Form II), were determined in the crystalline state by using an approach that combines terahertz time‐domain spectroscopy, X‐ray diffraction, and solid‐state density functional theory. Contrary to expectations, the helices were found to be considerably less rigid than many other natural and synthetic polymers, as well as differing greatly from each other, with Young's moduli of 4.9 and 9.6 GPa for Forms I and II, respectively.     

On the measurement of technical efficiency in the public sector

Existing measures of technical inefficiency obtained through linear programming models in the public sector do not properly control for environmental variables that affect production. It will be shown that the consequences of not controlling for these fixed factors are biased estimates of technical efficiency. This paper extends the mathematical programming approach to frontier estimation known as Data Envelopment Analysis to allow for environmental variables. This modified model will be then contrasted with the existing model that purportedly controls for exogeneous factors to measure public sector efficiency with simulated data. The results provide evidence that the existing Data Envelopment Analysis model will overestimate the level of technical inefficiency and that the modified model developed in this paper does a better job controlling for exogenous factors. The modified model is also applied to analyze the technical efficiency of school districts.     

Localization and delocalization of energy in a Peyrard-Bishop chain

This paper studies energy localization conditions in lattices of the type proposed by Peyrard and Bishop. Homogeneous and inhomogeneous lattices are analyzed and the role of interfaces in the latter is emphasized. Simulations allowed us to identify critical energy values for the existence of localization. After a certain energy value, it is possible to observe the loss of energy localization along the chain.     

The Sagnac Phase Shift Suggested by the Aharonov-Bohm Effect for Relativistic Matter Beams

The phase shift due to the Sagnac Effect, for relativistic matter beams counter-propagating in a rotating interferometer, is deduced on the bases of a formal analogy with the Aharonov-Bohm effect. A procedure outlined by Sakurai, in which non relativistic quantum mechanics and Newtonian physics appear together with some intrinsically relativistic elements, is generalized to a fully relativistic context, using the Cattaneo's splitting technique. This approach leads to an exact derivation, in a self-consistently relativistic way, of the Sagnac effect. Sakurai's result is recovered in the first order approximation.     

Synthesis and photochromism of Δ2,2′-BI-(2H-1,4-benzothiazine)

Δ^2,2′-Bi- (2H-1,4-benzothiazine) (4), the parent ring system of a group of amino-acid pigments (trichosiderins) from red hair and feathers, has been synthesized by a simple and novel method involving air oxidation of 2H-1,4-benzothiazine, generated in situ by treatment of 1-(o-aminophenylthio)-2,2-diethoxyethane (1). This procedure yields only the yellow trans-isomer 4, which in solution exhibits marked photochromism, being reversibly converted into the red unstable cis-form 5 on brief irradiation with sunlight.