Hermite Interpolation of Data Sets by Minimal Spline Spaces

Hermite interpolation of 2n + k data by spline spaces of order k with n variable knots counting multiplicities is studied. A characterization of the minimal spline spaces which admit a solution of the interpolation problem is obtained. A sufficient condition on uniqueness of interpolating spline functions is given.     

Mathematical modelling and analytical solution for workpiece temperature in grinding

This paper deals with modelling the workpiece temperature field produced during the grinding process. The proposed model is given in terms of a two-dimensional boundary-value problem where the interdependence among the grinding wheel, the workpiece and the coolant is described by two variable functions in the boundary condition. An explicit integral form solution is constructed using the Laplace and Fourier transforms and the Green’s function method.     

Iterative variable aggregation and disaggregation in IP: An application

This paper, using the Unconstrained Shape Matrix Optimization Problem as a test bed, we investigate various aspects of variable aggregation and disaggregation for a class of integer programs that contains binary expansion. We present theoretical and numerical results, and propose an iterative algorithm for exact solutions.     

Using the gradients of temperature and internal parameters in Continuum ThermodynamicsIntroduction des gradients de température et de paramètres internes en Thermodynamique des Milieux Continus

In this paper, the possibility of using the gradients of the temperature and of the internal parameters as additional state variables in Continuum Thermodynamics is considered. The expressions of the two principles are discussed and Clausius–Duhem inequality is derived under an appropriate statement of the internal entropy production. Several formulations are proposed and compared to existing results in the literature. To cite this article: P. Ireman, Q.S. Nguyen, C. R. Mecanique 332 (2004).     

A Variable Neighborhood Search for the Multi Depot Vehicle Routing Problem with Time Windows

The aim of this paper is to propose an algorithm based on the philosophy of the Variable Neighborhood Search (VNS) to solve Multi Depot Vehicle Routing Problems with Time Windows. The paper has two main contributions. First, from a technical point of view, it presents the first application of a VNS for this problem and several design issues of VNS algorithms are discussed. Second, from a problem oriented point of view the computational results show that the approach is competitive with an existing Tabu Search algorithm with respect to both solution quality and computation times.     

Design and fabrication of fluid controlled dynamic optical lens system

A novel small fluid controlled optical lens system that is capable of displaying dynamic variation of its focal length and field-of-view (FOV) is designed and fabricated. In this active lens system, appropriate volume of the optical fluid can be pumped into or out of the lens chamber to provide double-convex (DCX) or double-concave (DCV) lens effect. Simple optical imaging experiments were performed using different sets of glass lenses with fixed focal lengths to determine the optimum lens configuration required for designing a dynamic optical lens system. The experimental results obtained from the glass lenses demonstrate that a combination of a single DCX lens with three DCV lenses provides a wider FOV. The flexible membranes for fluid controlled lenses were fabricated using polydimethylsiloxane polymer material, which has good optical transparency and elasticity. A simple fluid injection system is used to vary the radius of curvature of the lenses, and thereby to change the focal length. A dynamic optical lens system with a combination of one DCX and multiple variable focal length DCV lenses as designed here can image an object with a wide range of focal length and FOV. With this fluid controlled optical system, the FOV and focal length could be continuously varied and a maximum FOV of 118.3° could be achieved. The smallest f-number (f_/#) for this fluid controlled single lens system was found to be 1.3, which corresponds to the numerical aperture value of 0.35.     

Evaluating the financial performance of bank branches

We evaluate the financial performance of most of the branch offices of a large European savings bank for a recent accounting period. We employ a complementary pair of nonparametric techniques to evaluate their financial performance, in terms of their ability to conserve on the expenses they incur in building their customer bases and providing customer services. We find variation in the ability of branch offices to perform this task, and agreement on the identity of the laggard branches. We then employ parametric techniques to determine that the list of indicators on which their financial performance is evaluated can be reduced without statistically significant loss of information to bank management. Both findings suggest ways in which the bank can increase the profitability of its branch network. A previous version of this paper was presented at CORE, Université Catholique de Louvain, Louvain-la-Neuve, Belgium, where we received many helpful comments from the audience. We are grateful to three referees for their helpful comments as well.