Infinitesimal Liouville Distributions for Teichmuller space

We consider an arbitrary Riemann surface X, possibly of infinitehyperbolic area. The Liouville measure of the hyperbolic metricdefines a measure on the space of geodesics of the universal covering of X. As we vary the Riemann surface structure,this gives an embedding from the Teichmuller space of X intothe Fréchet space of Hölder distributions on G. We show that the embedding is continuouslydifferentiable. In particular, we obtain an explicit integralrepresentation of the tangent map. 2000 Mathematics SubjectClassification 30F60, 32G15 (primary), 46F99 (secondary).     

Invariant Metrics on Nilmanifolds with Positive Topological Entropy

Let T _n denote the group of real n × n upper-triangular matrices with 1s on the diagonal. This paper constructs left-invariant Riemannian and sub-Riemannian metrics on T ₃ T ₄ whose geodesic flow has a subsystem that factors onto a suspended horseshoe. As a corollary, left-invariant Riemannian metrics with positive topological entropy are constructed on all quotients DT _n where D is a discrete subgroup of T _n and n 7.     

Nanomaterials for Ocular Drug Delivery

Efficient drug delivery to the eye remains a challenging task for pharmaceutical scientists. Due to the various anatomical barriers and the clearance mechanisms prevailing in the eye, conventional drug delivery systems, such as eye drop solutions, suffer from low bioavailability. More invasive methods, such as intravitreal injections and implants, cause adverse effects in the eye. Recently, an increasing number of scientists have turned to nanomaterial‐based drug delivery systems to address the challenges faced by conventional methods. This paper highlights recent applications of various nanomaterials, such as polymeric micelles, hydrogels, liposomes, niosomes, dendrimers, and cyclodextrins as ocular drug delivery systems to enhance the bioavailability of ocular therapeutic agents.

     

Application of Phosphorus-31 Nuclear Magnetic Resonance Spectrosocopy for the Study of Human Diabetic Cataractogenesis

Intact human Senses incubated at 5.5 mM (normal) and 35.5 mM glucose were examined by phosphorus-31 nuclear magnetic resonance (31P NMR) spectroscopy. Lense in 35.5 mM glucose showed an altered metabolic steady-state characterized by a lowered adenosine triphosphate/inorganic orthophosphate ratio. ³¹P NMR spectroscopy can be used to measure metabolic changes in the lens. This model offers an important means to study dynamic metabolism in the human lens in the setting of diabetic cataractogenesis.     

Absolute continuity of Wasserstein geodesics in the Heisenberg group

In this paper we answer to a question raised by Ambrosio and Rigot [L. Ambrosio, S. Rigot, Optimal mass transportation in the Heisenberg group, J. Funct. Anal. 208 (2) (2004) 261-301] proving that any interior point of a Wasserstein geodesic in the Heisenberg group is absolutely continuous if one of the end-points is. Since our proof relies on the validity of the so-called Measure Contraction Property and on the fact that the optimal transport map exists and the Wasserstein geodesic is unique, the absolute continuity of Wasserstein geodesic also holds for Alexandrov spaces with curvature bounded from below.     

Geodesic flows on path spaces

On the path space over a compact Riemannian manifold, the global existence and the global uniqueness of the quasi-invariant geodesic flows with respect to a negative Markov connection are obtained in this paper. The results answer affirmatively a left problem of Li.     

Métriques de révolution d'un disque et invariance par rotation de la longueur des géodésiques

We give a geometrical proof of a Muhometov type inequality, for a single Riemannian metric defined on a closed disc in the plane. We mainly study the case of equality which is achieved if and only if the distance between points on the boundary is invariant under rotation along the boundary. We show that this implies that the metric itself must be invariant under rotation, at least when the metric is analytic or of nonpositive curvature.     

Equation of Motion of a Spinning Test Particle in Gravitational Field

Based on the coupfing between the spin of a particle and gravitoelectromagnetic field, the equation of motion of a spinning test particle in gravitational field is deduced. From this equation of motion, it is found that the motion of a spinning particle deviates from the geodesic trajectory, and this deviation originates from the coupling between the spin of the particle and gravitoelectromagnetic field, which is also the origin of Lense-Thirring effects. In post-Newtonian approximations, this equation gives the same results as those of Mathisson-Papapetrou equation. Effect of the deviation of geodesic trajectory is detectable.     

集值Superpramart的上鞅逼近

文中讨论了可积随机集条件期望的若干性质,在此基础上,给出了集值Superpramart的上鞅逼近.同时,证明了集值Superpramart在Kuratowski-Mosco意义下的收敛定理.     

Third-order design of aspheric spectacle lenses

The theory of third-order aberrations for a system of rotationally symmetric aspheric thin lenses and relations for calculation of the shape of rotationally symmetric aspheric spectacle lenses with zero astigmatism are described. A comparison of aspheric and spherical spectacle lens design is presented. Possible applications of aspheric lens surfaces are proposed including the design of a spectacle lens with two types of primary aberrations corrected, an anastigmatic spectacle lens with minimum weight and a spectacle lens with the desired aesthetic shape. Our work performs a complex analysis of the third-order design of spectacle lenses considering not only astigmatism but all types of primary aberrations and their combinations.