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.     

Doppler cooling a single Ca+ ion with a violet extended-cavity diode laser

We present a scheme for employing a violet extended-cavity diode laser in experiments with single, trapped ions. For this the grating-stabilised laser is spatially and spectrally filtered and referenced to a Fabry–Pérot cavity. We measure an upper limit to the line width by observing a 305-kHz FWHM beat note with the second harmonic of a titanium sapphire laser. The laser is subsequently used to optically cool a single ⁴⁰Ca⁺ ion close to the Doppler limit. PACS 03.67.Lx; 32.80.Pj; 42.55.Px     

Bestmögliche innere Schalengleichungen für schubweiche Werkstoffe unter Berücksichtigung von Dickenänderungen

Übersicht Konsistente Schalentheorien lassen sich in einer besonders anschaulichen Weise durch lineare Approximation der Erhaltungssätze eines als Multi-Direktor-Körper beschriebenen, dreidimensionalen Kontinuums herleiten. Im vorliegenden Beitrag entstchen auf diesem Wege bestmögliche, in Geschwindigkeiten formulierte innere Schalengleichungen für beliebig große Deformationen und willkürliche, in eine Leistungsaussage einpaßbare Materialgesetze. Dabei finden Schub- und Querdeformationen Berücksichtigung. Der optimale Charakter der Schalentheorie mit gleichen Unschärfen in allen Einzelbeziehungen wird durch den Herleitungsgang sichergestellt und durch Einschrankungen mittels lokaler Tensornormen bewiesen.

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Best interior shell equations including transverse shear deformations and thickness changes

Summary Consistent shell theories can be derived in a particular correct manner by linear approximation of conservation laws of a three-dimensional continuum, described as a multi-director-body. In the present paper best interior shell equations-formulated in velocities—are developed, valid for arbitrarily large deformations and rather optional material laws, incorporating shear distorsions and thickness changes. The optimal character of the theory is guaranteed by the derivation process and proven by bounding techniques using tensor norms.

     

Influence of cultivation conditions on the production of cellulolytic enzymes withTrichoderma reesei Rutgers C30 in aqueous two-phase systems

Cellulolytic enzyme production in aqueous two-phase systems withTrichoderma reesei Rutgers C30 has been investigated. The influ ence of different phase systems, as well as addition of media compo nents and substrate on enzyme production have been studied. Extractive enzyme production in fed-batch cultivations was per formed in a phase system composed of PEG 8000 5%-Dextran T500 7% with 1% Solka-Floc BW 200 as substrate. The cellulolytic enzyme system was intermittently withdrawn with the top phase. Addition of media components every 24 h and cellulose every 72 h gave an aver age enzyme activity in the withdrawn top phase of 2.2 FPU/mL dur ing 170 h cultivation. The corresponding productivity was 18 FPU/lh. The productivity was increased to 24 FPU/l.h when media compo nents and cellulose were added every 72 h. The average enzyme con centration was then 1.6 FPU/mL. The results are discussed in relation to methods for cellulolytic enzyme production involving immobiliza tion and cell recycling.     

Optical spectra and laser-induced dissociation of supported Na particles

This paper reports new results on the optical spectra of Na particles and on laser-induced photodissociation of Na atoms from the surface of these particles. In continuation of our earlier studies we have performed experiments to elucidate the mechanism of thenonthermal dissociation process. Furthermore, theoretical calculations have been carried out with the goal to correlate the wavelength dependence of the photodissociation yield with the optical absorption spectra of the metal particles. In addition, manipulation of the size distribution of metal particles on supports is outlined as an application of the effect. This allows for the preparation of very special surfaces with novel physical and chemical properties.     

On Nodal Sets for Dirac and Laplace Operators

We prove that the nodal set (zero set) of a solution of a generalized Dirac equation on a Riemannian manifold has codimension 2 at least. If the underlying manifold is a surface, then the nodal set is discrete. We obtain a quick proof of the fact that the nodal set of an eigenfunction for the Laplace-Beltrami operator on a Riemannian manifold consists of a smooth hypersurface and a singular set of lower dimension. We also see that the nodal set of a Δ-harmonic differential form on a closed manifold has codimension 2 at least; a fact which is not true if the manifold is not closed. Examples show that all bounds are optimal. Received: 28 October 1996 / Accepted: 3 March 1997