Second Eigenvalue of Schrödinger Operators¶and Mean Curvature

Let $M$ be a compact immersed submanifold of the Euclidean space, the hyperbolic space or the standard sphere. For any continuous potential q on M, we give a sharp upper bound for the second eigenvalue of the operator −Δ+q in terms of the total mean curvature of M and the mean value of q. Moreover, we analyze the case where this bound is achieved. As a consequence of this result we obtain an alternative proof for the Alikakos–Fusco conjecture concerning the stability of the interface in the Allen–Cahn reaction diffusion model. Received: 18 June 1999 / Accepted: 6 July 1999     

Multi-objective time–cost trade-off in dynamic PERT networks using an interactive approach

We develop a multi-objective model for the time–cost trade-off problem in a dynamic PERT network using an interactive approach. The activity durations are exponentially distributed random variables and the new projects are generated according to a renewal process and share the same facilities. Thus, these projects cannot be analyzed independently. This dynamic PERT network is represented as a network of queues, where the service times represent the durations of the corresponding activities and the arrival stream to each node follows a renewal process. At the first stage, we transform the dynamic PERT network into a proper stochastic network and then compute the project completion time distribution by constructing a continuous-time Markov chain. At the second stage, the time–cost trade-off problem is formulated as a multi-objective optimal control problem that involves four conflicting objective functions. Then, the STEM method is used to solve a discrete-time approximation of the original problem. Finally, the proposed methodology is extended to the generalized Erlang activity durations.     

Combination of MCDM and covering techniques in a hierarchical model for facility location: A case study

In this paper, locating some warehouses as distribution centers (DCs) in a real-world military logistics system will be investigated. There are two objectives: finding the least number of DCs and locating them in the best possible locations. The first objective implies the minimum cost of locating the facilities and the latter expresses the quality of the DCs locations, which is evaluated by studying the value of appropriate attributes affecting the quality of a location. Quality of a location depends on a number of attributes; so the value of each location is determined by using Multi Attribute Decision Making models, by considering the feasible alternatives, the related attributes and their weights according to decision maker’s (DM) point of view. Then, regarding the obtained values and the minimum number of DCs, the two objective functions are formed. Constraints imposed on these two objectives cover all centers, which must be supported by the DCs. Using Multiple Objective Decision Making techniques, the locations of DCs are determined. In the final phase, we use a simple set partitioning model to assign each supported center to only one of the located DCs.     

Regioselective Synthesis of Para‐Bromo Aromatic Compounds

Reaction of substituted benzene rings with N‐bromophthalimide, under neutral conditions, gave the corresponding bromo derivatives with a preference for the formation of the para bromo isomer over the ortho isomer. The simple work‐up procedure minimizes loss of product and the yields are good.     

Calixarene Dimers as Host Molecules for Biologically Important Di‐ and Oligophosphates

A dimeric calixarene, with an aliphatic C₆‐bridge and six anilinium head groups at its upper rim, preferably complexes diphosphates and oligonucleotides with more than 10 bonds between both anionic moieties. Free binding energies correlate with the length of the aliphatic bridge in a roughly linear fashion. The binding event, which is monitored by fluorescence titrations and competition experiments, relies on Coulomb interactions, as opposed to a nonpolar variant with tert‐butyl instead of ammonium groups; here, hydrophobic forces prevail, rendering the calixarene dimer selective for less polar cofactors such as FAD. The best guest for the hexaanilinium dimer is found in ssDNA, which carries multiple copies of the optimal trinucleotide for maximum attraction towards the extended cationic host. The recognition event is also observed in the environment of a lipid monolayer, and provides a means to quantify dimer diphosphate interactions by measuring p/A shifts.     

Crystallographic report: Chlorodiphenyltin(IV) piperidine‐1‐carbodithioate

A trigonal bipyramidal C₂ClS₂ coordination geometry for tin is found in Ph₂Sn(S₂CN(CH₂)₅)Cl. Copyright © 2005 John Wiley & Sons, Ltd.     

Few-valence-particle excitations around doubly magic 132Sn

Prompt γ-ray cascades in neutron-rich nuclei around doubly-magic ¹³²Sn have been studied using a ²⁴⁸Cm fission source. Yrast states located in the N = 82 isotones ¹³⁴Te and ¹³⁵I are interpreted as valence proton and neutron particle-hole core excitations with the help of shell model calculations employing empirical nucleon-nucleon interactions from both ¹³²Sn and ²⁰⁸Pb regions.     

Steps, ledges and kinks on the surfaces of platinum nanoparticles of different shapes

Platinum nanoparticles with a high percentage of cubic-, tetrahedral- and octahedral-like shapes, respectively, have been synthesized by a shape-controlling technique that we developed recently [Ahmadi et al., Science 272 (June 1996) 1924]. High resolution transmission electron microscopy (HRTEM) is used here to directly image the atomic scale structures of the surfaces of these particles with different shapes. The truncated shapes of these particles are mainly defined by the {100}, {111}, and {110} facets, on which numerous atom-high surface steps, ledges and kinds have been observed. This atomic-scale fine structure of the surfaces of these particles is expected to play a critical role in their catalytic activity and selectivity.