Understanding Stability Trends along the Lanthanide Series

The stability trends across the lanthanide series of complexes with the polyaminocarboxylate ligands TETA^4? (H₄TETA=2,2′,2′′,2′′′‐(1,4,8,11‐tetraazacyclotetradecane‐1,4,8,11‐tetrayl)tetraacetic acid), BCAED^4? (H₄BCAED=2,2′,2′′,2′′′‐{[(1,4‐diazepane‐1,4‐diyl)bis(ethane‐2,1‐diyl)]bis(azanetriyl)}tetraacetic acid), and BP18C6^2? (H₂BP18C6=6,6′‐[(1,4,10,13‐tetraoxa‐7,16‐diazacyclooctadecane‐7,16‐diyl)bis(methylene)]dipicolinic acid) were investigated using DFT calculations. Geometry optimizations performed at the TPSSh/6‐31G(d,p) level, and using a 46+4fⁿ ECP for lanthanides, provide bond lengths of the metal coordination environments in good agreement with the experimental values observed in the X‐ray structures. The contractions of the Ln³⁺ coordination spheres follow quadratic trends, as observed previously for different isostructural series of complexes. We show here that the parameters obtained from the quantitative analysis of these data can be used to rationalize the observed stability trends across the 4f period. The stability trends along the lanthanide series were also evaluated by calculating the free energy for the reaction [La( L )]^n+/?_(sol)+Ln³⁺_(sol)→[Ln( L )]^n+/?_(sol)+La³⁺_(sol). A parameterization of the Ln³⁺ radii was performed by minimizing the differences between experimental and calculated standard hydration free energies. The calculated stability trends are in good agreement with the experimental stability constants, which increase markedly across the series for BCAED^4? complexes, increase smoothly for the TETA^4? analogues, and decrease in the case of BP18C6^2? complexes. The resulting stability trend is the result of a subtle balance between the increased binding energies of the ligand across the lanthanide series, which contribute to an increasing complex stability, and the increase in the absolute values of hydration energies along the 4f period.     

Multiobjective routing problems

Summary Many network routing problems, particularly where the transportation of hazardous materials is involved, are multiobjective in nature; that is, it is desired to optimise not only physical path length but other features as well. Several such problems are defined here and a general framework for multiobjective routing problems is proposed. The notion of “efficient solution” is defined and it is demonstrated, by means of an example, that a problem may have very many solutions which are efficient. Next, potentially useful solution methods for multiobjective routing problems are discussed with emphasis being placed on the use of shortest/k-shortest path techniques. Finally, some directions for possible further research are indicated. Invited by B. Pelegrin     

Simultaneous analysis of multiple PCR amplicons enhances capillary SSCP discrimination of MHC alleles

Major histocompatibility complex (MHC) genotyping still remains one of the most challenging issues for evolutionary ecologists. To date, none of the proposed methods have proven to be perfect, and all provide both important pros and cons. Although denaturing capillary electrophoresis has become a popular alternative, allele identification commonly relies upon conformational polymorphisms of two single‐stranded DNA molecules at the most. Using the MHC class II (β chain, exon 2) of the black kite (Aves: Accipitridae) as our model system, we show that the simultaneous analysis of overlapping PCR amplicons from the same target region substantially enhances allele discrimination. To cover this aim, we designed a multiplex PCR capable to generate four differentially sized and labeled amplicons from the same allele. Informative peaks to assist allele calling then fourfold those generated by the analysis of single PCR amplicons. Our approach proved successful to differentiate all the alleles (N=13) isolated from eight unrelated birds at a single optimal run temperature and electrophoretic conditions. In particular, we emphasize that this approach may constitute a straightforward and cost‐effective alternative for the genotyping of single or duplicated MHC genes displaying low to moderate sets of divergent alleles.     

A practical algorithm for decomposing polygonal domains into convex polygons by diagonals

We present algorithms for decomposing a polygon (with holes) into convex polygons by diagonals. The methods are computationally quick, and although the partitions that they produce may not have minimal cardinality they usually have a low number of convex pieces. Thus, the methods are suitable for being used when achieving a modest load on the CPU time is more important than finding optimal decompositions as, for instance, in location problems. Part of the results in this paper are from Fernández (1999), and were presented in Fernández et al. (1998). This work has been supported by the Ministry of Science and Technology of Spain under the research projects BEC2002-01026, SEJ2005-06273/ECON (J. Fernández, B. Tóth and B. Pelegrín) and TIC2003-05982-C05-03 (L. Cánovas), in part financed by the European Regional Development Fund (ERDF).     

Heteroscedastic controlled calibration model applied to analytical chemistry

In chemical analyses performed by laboratories, one faces the problem of determining the concentration of a chemical element in a sample. In practice, one deals with the problem using the so‐called linear calibration model, which considers that the errors associated with the independent variables are negligible compared with the former variable. In this work, a new linear calibration model is proposed assuming that the independent variables are subject to heteroscedastic measurement errors. A simulation study is carried out in order to verify some properties of the estimators derived for the new model and it is also considered the usual calibration model to compare it with the new approach. Three applications are considered to verify the performance of the new approach. Copyright © 2010 John Wiley & Sons, Ltd.     

Solving a Huff-like competitive location and design model for profit maximization in the plane

A chain wants to set up a single new facility in a planar market where similar facilities of competitors, and possibly of its own chain, are already present. Fixed demand points split their demand probabilistically over all facilities in the market proportionally with their attraction to each facility, determined by the different perceived qualities of the facilities and the distances to them, through a gravitational or logit type model. Both the location and the quality (design) of the new facility are to be found so as to maximise the profit obtained for the chain. Several types of constraints and costs are considered.     

On Fractional PI λ Controllers: Some Tuning Rules for Robustness to Plant Uncertainties

The objective of this work is to find out optimum settings for a fractional PI ^λ controller in order to fulfill three different robustness specifications of design for the compensated system, taking advantage of the fractional order, λ. Since this fractional controller has one parameter more than the conventional PI controller, one more specification can be fulfilled, improving the performance of the system and making it more robust to plant uncertainties, such as gain and time constant changes. For the tuning of the controller an iterative optimization method has been used, based on a nonlinear function minimization. Two real examples of application are presented and simulation results are shown to illustrate the effectiveness of this kind of unconventional controllers.