Estimation of platinum in environmental water samples with solid phase extraction technique using inductively coupled plasma mass spectrometry

A solid phase extraction technique for the determination of platinum(IV) at trace levels by inductively coupled plasma mass spectromA solid phase extraction technique for the determination of platinum(IV) at trace levels by inductively coupled plasma mass spectrometry (ICP-MS) was developed. The method was based on retention of platinum in a sample on silica gel modified with aminepropyl groups. The retention of platinum(IV) from the sample solution and the recovery of platinum with 1.0 mol L⁻¹ thiourea solution were quantitative. The relative standard deviation (RSD) was calculated as 5% (n = 7) at the 10 ng L⁻¹ level. The enrichment factor was found to be (50-fold) for 250 mL of water sample. Under optimum conditions, the method detection limit (MDL) was found to be 1 ng L⁻¹ for platinum in water matrices. Recoveries of Pt from spike addition to atmospheric water samples were quantitative (80–95%). The present method was used for the determination of platinum in precipitation, throughfall and runoff water samples.      

Warmstarting for interior point methods applied to the long-term power planning problem

The long-term planning of electricity generation in a liberalised market using the Bloom and Gallant model can be posed as a quadratic programming (QP) problem with an exponential number of linear inequality constraints called load-matching constraints (LMCs) and several other linear non-LMCs. Direct solution methods are inefficient at handling such problems and a heuristic procedure has been devised to generate only those LMCs that are likely to be active at the optimiser. The problem is then solved as a finite succession of QP problems with an increasing, though still limited, number of LMCs, which can be solved efficiently using a direct method, as would be the case with a QP interior-point algorithm. Warm starting between successive QP solutions helps then in reducing the number of iterations necessary to reach the optimiser.     

Technical diagnostic of a fleet of vehicles using rough set theory

The paper presents a process of technical diagnostic applied to a fleet of vehicles utilized in the delivery system of express mail. It is focused on evaluation of diagnostic capacity of particular characteristics, reduction of a set of initially selected characteristics to a minimal and satisfactory subset, recognition of a technical condition of vehicles resulting in their condition-based classification. In addition, the decision rules facilitating technical diagnostic and management of a fleet of vehicles are generated and utilized. N-fold cross validation is applied to estimate the efficiency of the decision rules. The rough set theory is applied to support the diagnostic process of vehicles. Classical rough set (CRS) theory is compared with the dominance-based rough set (DRS) approach. The results of computational experiments for both approaches are compared.     

A note on a paper of I.D. Arand?elovi? on asymptotic contractions

W.A. Kirk [W.A. Kirk, Fixed points of asymptotic contractions, J. Math. Anal. Appl. 277 (2003) 645-650] defined the notion of an asymptotic contraction on a metric space and using ultrapower techniques he gave a nonconstructive proof of an asymptotic version of the Boyd-Wong fixed point theorem. Subsequently, I.D. Arand?elovi? [I.D. Arand?elovi?, On a fixed point theorem of Kirk, J. Math. Anal. Appl. 301 (2005) 384-385] established somewhat more general version of Kirk's result and he gave an elementary proof of it. However, our purpose is to show that there is an error in this proof and, moreover, Arand?elovi?'s theorem is false. We also explain how to correct this result.     

Interplay between degenerate convergence of semigroups and asymptotic analysis: a study of a singularly perturbed abstract telegraph system

Singularly perturbed evolution equations may be analyzed by various techniques. In this paper, we focus on ideas of asymptotic analysis and those akin to the Trotter–Kato approximation theorems. Using as an example an abstract telegraph-type system, we show how these two approaches intertwine and complement each other. The paper also may be seen as a continuation of Kato’s project (in Turbululence and Navier–Stokes Equations Theory. Proc. Conf. Univ. Paris-Sud, Orsay 1975, Lect. Notes Math., Springer, Berlin, vol 565, pp. 104–112, 1976) taking account of recent results. On leave from Lublin University of Technology.     

A structure-conveying modelling language for mathematical and stochastic programming

We present a structure-conveying algebraic modelling language for mathematical programming. The proposed language extends AMPL with object-oriented features that allows the user to construct models from sub-models, and is implemented as a combination of pre- and post-processing phases for AMPL. Unlike traditional modelling languages, the new approach does not scramble the block structure of the problem, and thus it enables the passing of this structure on to the solver. Interior point solvers that exploit block linear algebra and decomposition-based solvers can therefore directly take advantage of the problem’s structure. The language contains features to conveniently model stochastic programming problems, although it is designed with a much broader application spectrum.     

Radiative correction to the helium dimer interaction energy

The leading-order radiative correction to the helium-helium interaction energy at the equilibrium internuclear distance has been calculated for the first time. The result is -1.27(2) mK. The calculations were performed using a new technique of evaluating expectation values of singular operators in connection with the most accurate wave functions of He(2) available today-the exponentially correlated Gaussian functions.     

New method to measure packing densities of self-assembled thiolipid monolayers

For a monolayer of 2,3-di-phytanyl-sn-glycerol-1-tetraethylene glycol-D,L-a-lipoic acid ester lipid (DPTL) self-assembled (SAM) at a gold electrode surface we propose a new method to determine the charge number per adsorbed molecule and the packing density (area per molecule) in the monolayer. The method relies on chronocoulometry to measure the charge density at the SAM covered gold electrode surface. Two series of measurements have to be performed. In the first series, charge densities are measured for a monolayer transferred from the air-solution to the metal-solution interface using the Langmuir-Blodgett (LB) technique. This series of measurements allows one to determine charge numbers per adsorbed DPTL molecule. The second series is performed using a gold electrode covered with a self-assembled monolayer. The charge densities obtained in this series are then used to calculate the packing density with the help of charge numbers per adsorbed DPTL determined in the first series. The area per adsorbed molecule determined by the new method was compared to the area per molecule determined by the popular reductive desorption method. The molecular area determined with the new method is about 20% larger than the area calculated from the van der Waals model, which is a physically reasonable result. In contrast, the popular reductive desorption method gives an area per molecule 20% lower than the minimum estimated based on a van der Waals model. This is a physically unreasonable result. It is also shown that the charge numbers per adsorbed molecule depend on the electrode potential and may assume values smaller than the number of electrons participating in the reductive desorption step. An explanation of the origin of the "partial charge numbers" is provided. We recommend the new method be used in future studies of thiol adsorption at metal surfaces.     

New macrocycles with planar chirality-synthesis and determination of absolute configurations

A versatile system for preparing macrocyclic compounds with planar chirality is presented. In this system chiral diazacoronands are synthesized readily from lariat-type diesters 13 and 14 and unsymmetrical diamines 7, 8, 12, 15, and 16 under non-high-dilution conditions. The title compounds were subjected to structural analysis by X-ray crystallography and circular dichroism spectroscopy, and absolute configurations for two representative examples (compounds 2 and 3) were assigned by molecular modeling. The correctness of the theoretical approach was verified by the crystallographic results obtained experimentally.     

Porous structure of natural and modified clinoptilolites

The evaluation of the pore-size distribution (PSD) of natural and modified mesoporous zeolites, i.e., clinoptilolites is presented. We demonstrate the SEM results showing that the pores of fracture-type from 25-50 nm to 100 nm in size between clinoptilolite grains, as well as pores between crystal aggregates up to 500 nm in size are present in the studied material. The detailed distribution of pore sizes and tortuosity factor of the above-mentioned materials are determined from the adsorption-desorption isotherms of nitrogen measured volumetrically at 77 K. To obtain the reliable pore size distribution (PSD) of the above-mentioned materials both adsorption and desorption branches of the experimental hysteresis loop are described simultaneously by recently developed corrugated pore structure model (CPSM) of Androutsopoulos and Salmas. Evaluated pore size distributions are characterized by well-defined smooth peaks placed in the region of the mesoporosity. Moreover, the mean pore diameter calculated from the classical static measurement of nitrogen adsorption at 77 K correspond very well to the pore diameters from SEM, showing the applicability of the CPSM for characterization of the porosity of natural zeolites. We conclude that classical static adsorption measurements combined with the proper modeling of the capillary condensation/evaporation phenomena are a powerful method which can be applied for pore structure characterization of natural and modified clinoptilolites.