A note on sub-Riemannian structures associated with complex Hopf fibrations

Sub-Riemannian structures on odd-dimensional spheres respecting the Hopf fibration naturally appear in quantum mechanics. We study the curvature maps for such a sub-Riemannian structure and express them using the Riemannian curvature tensor of the Fubini-Study metric of the complex projective space and the curvature form of the Hopf fibration. We also estimate the number of conjugate points of a sub-Riemannian extremal in terms of the bounds of the sectional curvature and the curvature form. It presents a typical example for the study of curvature maps and comparison theorms for a general corank 1 sub-Riemannian structure with symmetries done by C.Li and I.Zelenko.Comment: 6 pages. arXiv admin note: substantial text overlap with arXiv:0908.439

Some existence, uniqueness results on positive solutions for a fractional differential equation with infinite-point boundary conditions

We investigate a class of Riemann–Liouville's fractional differential equation with infinite-point boundary conditions. We give some new properties of the Green's function associated with the fractional differential equation boundary value problem. Based upon these new properties and by using Schauder's fixed point theorem, we establish some existence results on positive solutions for the boundary value problem. Further, by using a fixed point theorem of general concave operators, we also present an existence and uniqueness result on positive solutions for the boundary value problem

Green retailing practices: An exploratory comparison between Chinese and British retailers

Constituting the link between supply and demand, retailers can play an important role in a supply chain's green operations and logistics activities, which are one of the key contemporary concerns of governments and the general public. China, as a huge, fast-developing and opening marketplace has been attractive to British and other international retailers. However, the competition facing these retailers in the Chinese marketplace is intensifying. Research shows that British retailers began greening their business operations earlier than Chinese businesses that are still at an early stage. British retailers thus have an early-mover advantage with green operations as a characteristic competitive strength. The comparative study presented in this paper on the current green status/approaches of both Chinese and British retailers will be valuable to managers who are developing green strategies to enhance their competitiveness in the Chinese retail sector; the paper also enriches green theories in relation to this particular marketplace. </jats:p

An efficient algorithm for total variation regularization with applications to the single pixel camera and compressive sensing

In this thesis, I propose and study an efficient algorithm for solving a class of compressive sensing problems with total variation regularization. This research is motivated by the need for efficient solvers capable of restoring images to a high quality captured by the single pixel camera developed in the ECE department of Rice University. Based on the ideas of the augmented Lagrangian method and alternating minimization to solve subproblems, I develop an efficient and robust algorithm called TVAL3. TVAL3 is compared favorably with other widely used algorithms in terms of reconstruction speed and quality. Convincing numerical results are presented to show that TVAL3 is suitable for the single pixel camera as well as many other applications