Each compact manifold M of finite dimension k is differentiable and supports an intrinsic probability measure. There then exists a measurable transformation of M to the k-dimensional " surface " of the (k + 1)−dim-ensional ball. 1 Manifolds 1.1 Topologies, coordinates, and measures Let k be a positive integer. By definition, a given compact topological space M is a manifold of k dimensions.if e...

Many medical universitiesaround the world have donestunning changes in the recent years.Some of these changes have been performed with the support of international organizations.They changed the traditionaltrainingprograms based on teacher- centered learning and disciplined approach to the educational course based on community needs responsivity and Student-centered learning. This process is ai...

The degree set of a graph is the set of its degrees. Kapoor et al. [Degree sets for graphs, Fund. Math. 95 (1977) 189-194] proved that for every set of positive integers, there exists a graph of diameter at most two and radius one with that degree set. Furthermore, the minimum order of such a graph is determined. A graph is 2-self- centered if its radius and diameter are two. In this paper for ...

The Tadmor type of entropy conservation formulation for the Euler equations and various skewsymmetric splittings of the inviscid flux derivatives are discussed. Numerical stability of high order central and Padé type (centered compact) spatial discretization is enhanced through the application of these formulations. Numerical test on a 2-D vortex convection problem indicates that the stability ...

Organic solid-state tri-wavelength lasing was demonstrated from dye-doped holographic polymer-dispersed liquid crystal (HPDLC) distributed feedback (DFB) laser with semiconducting polymer poly[-methoxy-5-(2'-ethyl-hexyloxy)-1,4-phenylene-vinylene] (MEH-PPV) and laser dye [4-(dicyanomethylene)-2-methyl-6-(p-dimethylaminostyryl)-4H-pyran] (DCM) by a one-step holography technique, which centered a...

In this paper we present polynomial-time algorithms that translate First-Order Logic (FOL) theories to smaller propositional encodings than achievable before in polynomial time. For example, we can sometimes reduce the number of propositions to O(|P | + |C|), or O(|P | · log |P |), for |P | predicates of arity k and |C| constant symbols. The guarantee depends on availability of some graphical s...

Smectic orders on curved substrates can be described by differential forms of rank one (1-forms), whose geometric meaning is the differential of the local phase field of density modulation. The exterior derivative of the 1-form is the local dislocation density. Elastic deformations are described by superposition of exact differential forms. Applying this formalism to study smectic order on a to...