A formal finite element approach for open boundaries in transport and diffusion ground-water problems

In the application of the finite element method to diffusion and convection-dispersion equations over a ground-water domain, the Galerkin technique was used to incorporate Neumann (or second-type) and Cauchy (or third-type) boundary conditions. While mass movement through open boundaries is a priori unknown, these boundaries are usually treated as a zero Neumann condition at some far distance from the domain of interest. Nevertheless, cheaper and better solutions can be obtained if these unknown conditions are adequately incorporated in the weak formulation and in the transient solution schemes (open boundary condition). Theoretical and numerical proofs are given of the equivalences between this approach and a ‘well-posed’ problem in a semi-infinite domain with a zero Neumann condition at a boundary placed at infinity. Transport and diffusion equations were applied in one dimension to show the numerical performances and limitations of this procedure for some linear and non-linear problems. No a priori limitations are foreseen in order to find similar solutions in two or three dimensions. Thus the spatial discretization in the proximity of open boundaries could be drastically reduced to the domain of interest.     

Phototoxicity of Some Bromine-Substituted Rhodamine Dyes: Synthesis, Photophysical Properties and Application as Photosensitizers

Abstract— The synthesis of some bromine-substituted rhodamine derivatives viz. , 4,5-dibromorhodamine methyl ester (dye 2) and 4,5-dibromorhodamine n -butyl ester (dye 3) are reported. These dyes were synthesized to promote a more efficient cancer cell photosensitizer for potential use in in vitro bone marrow purging in preparation for autologous bone marrow transplantation. Spectroscopic and photo-physical characterization of these dyes together with rhodamine 123 (dye 1) are reported in water, methanol, eth-anol and also in a microheterogeneous system, sodium dodecyl sulfate. The possible mechanism of photosensi-tization is characterized in terms of singlet oxygen efficiency of these dyes. Singlet oxygen quantum yields for bromine-substituted dyes are in the range of 0.3-0.5 depending on the solvent. For dye 1 no singlet oxygen production is found. The photodynamic actions of these dyes in different cell lines are tested. It was found that dye 2 and dye 3 are efficient photosensitizers and mediate eradication of K562, EM2, myeloid cell lines (CML) and the SMF-AI rhabdomyosarcoma line.     

Ruthenium-catalyzed [2 + 2] cycloadditions of ynamides

Ruthenium-catalyzed [2 + 2] cycloadditions between norbornene and ynamides were investigated. The ynamide moiety was found to be compatible with the ruthenium-catalyzed cycloaddition conditions, giving the corresponding cyclobutene cycloadducts in moderate to good yields (up to 97%). [reaction: see text]     

Scheduling the flying squad nurses of a hospital using a multi-objective programming model

In this paper, we address the problem of scheduling nurses working on the flying squad of a hospital. Considering the large number of constraints, many of them being conflicting, the problem is formulated as a multi-objective programming problem with binary variables, where the objective function consists of a vector of objectives and penalty variables (deviation measures) provided by the soft constraints. Two approaches are considered to solve the problem: the weighted method and the sequential method. The best results are obtained with a mix of the two solving methods. Numerical results are presented. This revised version was published online in June 2006 with corrections to the Cover Date.     

On Compact Formulations for Integer Programs Solved by Column Generation

Column generation has become a powerful tool in solving large scale integer programs. It is well known that most of the often reported compatibility issues between pricing subproblem and branching rule disappear when branching decisions are based on imposing constraints on the subproblem's variables. This can be generalized to branching on variables of a so-called compact formulation. We constructively show that such a formulation always exists under mild assumptions. It has a block diagonal structure with identical subproblems, each of which contributes only one column in an integer solution. This construction has an interpretation as reversing a Dantzig-Wolfe decomposition. Our proposal opens the way for the development of branching rules adapted to the subproblem's structure and to the linking constraints.     

Adsorption of polyprotic acid at the water/air interface

A rigorous thermodynamic treatment appropriate for surface adsorption from mixed aqueous solution of alkali and polyprotic acid was derived. Those equations were applied to mixed aqueous solution/air systems of alkali metal hydroxide and Fe^III complex with ethylenediamine- N, N, N′,N′-tetraacetate (Fe-EDTA). Surface density of each species arising from Fe-EDTA was separately evaluated, and thus, surface activity of Fe-EDTA was studied, especially its dependence on pH and how it is influenced by the counter cations. Fe-EDTA was positively adsorbed at the water/air interface at very low pHs and negatively at high pHs. The pH range of positive adsorption of Fe-EDTA with potassium ion, as a counter ion, was wider than that with sodium ion. Thus, potassium ion, a structure breaker, tended to smooth surface adsorption of Fe-EDTA at the water/air interface, whereas sodium ion, a structure maker, tended to withdraw Fe-EDTA from the interfacial region.