A new trigonometric method of summation and its application to the degree of approximation

The object of the present investigation is to introduce a new trigonometric method of summation which is both regular and Fourier effective and determine its status with reference to other methods of summation (see §2-§4) and also give an application of this method to determine the degree of approximation in a new Banach space of functions conceived as a generalized Holder metric (see §5).     

基于Web的图书馆管理系统访问控制策略

针对基于Web的图书馆管理系统资源访问控制的动态性问题，提出了一种基于角色的访问控制策略描述方案．通过对基于Web的图书馆管理系统访问控制管理影响因素和访问控制需求的分析，结合NIST基于角色的访问控制统一模型标准，构造了一种基于角色的访问控制元模型．并在这一元模型的基础上，提出了一种紧凑的基于角色的访问控制XML策略描述语言框架．结果表明该访问控制策略描述语言框架适合表述动态环境下对图书馆资源的访问策略，提高了基于Web的图书馆管理系统资源访问的安全性．     

Ribaucour Transformations for Hypersurfaces in Space Forms

The theory of Ribaucour transformations for hypersurfaces in space forms is established. For any such hypersurface M, that admits orthonormal principal vector fields, it was shown the existence of a totally umbilic hypersurface locally associated to M by a Ribaucour transformation. A method of obtaining linear Weingarten surfaces in a three-dimensional space form is provided. By applying the theory, a new one-parameter family of complete constant mean curvature (cmc) surfaces in the unit sphere, locally associated to the flat torus, is obtained. The family contains a class of complete cmc cylinders in the sphere. In particular, one gets a family of complete minimal surfaces and minimal cylinders, locally associated to the Clifford torus.Mathematics Subject Classifications (2000): 53C20.     

Quotient probabilistic normed spaces and completeness results

We introduce the concept of quotient in PN spaces and give some examples. We prove some theorems with regard to the completeness of a quotient.     

Singlet versus triplet dynamics of β-carotene studied by quantum control spectroscopy

Biomolecules very often present complex energy deactivation networks with overlapping electronic absorption bands, making their study a difficult task. This can be especially true in transient absorption spectroscopy when signals from bleach, excited state absorption and stimulated emission contribute to the signal. However, quantum control spectroscopy can be used to discriminate specific electronic states of interest by applying specifically designed laser pulses. Recently, we have shown the control of energy flow in bacterial light-harvesting using shaped pump pulses in the visible and the selective population of pathways in carotenoids using an additional depletion pulse in the transient absorption technique. Here, we apply a closed-loop optimization approach to β-carotene using a spatial light modulator to decipher the energy flow network after a multiphoton excitation with a shaped ultrashort pulse in the near-IR. After excitation, two overlapping bands were detected and identified as the S₁ state and the first triplet state T₁. Using the transient absorption signal at a specific probe delay as feedback, the triplet signal could be optimized over the singlet contribution.     

Generic Transport Aft-body Drag Reduction using Active Flow Control

Active flow-separation control is an effective and efficient mean for drag reduction and unsteady load alleviation resulting from locally or massively separated flow. Such a situation occurs in configurations where the aerodynamic performance is of secondary importance to functionality. The performance of heavy transport helicopters and aeroplanes, having a large, and almost flat, aft loading ramp suffer from the poor aerodynamics of the aft body. Hence, a combined experimental and numerical investigation was undertaken on a generic transport aeroplane/helicopter configuration. The experimental study provided surface pressures, direct drag measurements, surface and smoke flow visualization. The baseline flow was numerically analyzed, using finite volume solutions of the RANS equations. The baseline flow around the model was insensitive to the Reynolds number in the range it was tested. The flow separating from the aft body was characterized by two main sources of drag and unsteadiness. The first is a separation bubble residing at the lower ramp corner and the second is a pair of vortex systems developing and separating from the sides of the ramp. As the model incidence is decreased, the pair of vortex systems also penetrates deeper towards the centerline of the ramp, decreasing the pressure and increasing the drag. As expected, the ramp lower corner bubble was highly receptive to periodic excitation introduced from four addressable piezo-fluidic actuators situated at the ramp lower corner. Total drag was reduced by 3–11%, depending on the model incidence. There are indications that the flow in the wake of the model is also significantly steadier when the bubble at the lower ramp corner is eliminated. The vortex system is tighter and steadier when the ramp-corner bubble is eliminated.     

Sobolev-Type Classes of Functions with Values in a Metric Space. II

We prove equivalence of the definitions by the author and by Korevaar and Schoen of the Sobolev classes of mappings of a domain of an arithmetic n-dimensional space to a metric space.     

Fixed point theorems for multivalued nonexpansive mappings satisfying inwardness conditions

Let X be a Banach space whose characteristic of noncompact convexity is less than 1 and satisfies the nonstrict Opial condition. Let C be a bounded closed convex subset of X, KC(X) the family of all compact convex subsets of X and T a nonexpansive mapping from C into KC(X) with bounded range. We prove that T has a fixed point. The nonstrict Opial condition can be removed if, in addition, T is an 1-χ-contractive mapping.     

Stratifiable Families of Extremals and Sufficient Conditions for Optimality in Optimal Control Problems

It is shown that, if a parametrized fämily of extremals F can be stratified in a way compatible with the flow map generated by F, then those trajectories of the family which realize the minimal values of the cost in F are indeed optimal in comparison with all trajectories which lie in the region R covered by the trajectories of F. It is not assumed that F is a field covering the state space injectively. As illustration, an optimal synthesis is constructed for a system where the flow of extremals exhibits a simple cusp singularity.     

Optimal Control of Magnetohydrodynamic Equations with State Constraint

This work is concerned with the maximum principle for optimal control problem governed by magnetohydrodynamic equations, which describe the motion of a viscous incompressible conducting fluid in a magnetic field and consist of a subtle coupling of the Navier-Stokes equation of viscous incompressible fluid flow and the Maxwell equation of electromagnetic field. An integral type state constraint is considered.