A priori error estimates for a mixed finite element discretization of the Richards’ equation

Summary. A mixed finite element discretization is applied to Richards equation, a nonlinear, possibly degenerate parabolic partial differential equation modeling water flow through porous medium. The equation is considered in its pressure formulation and includes both variably and fully saturated flow regime. Characteristic for such problems is the lack in regularity of the solution. To handle this we use a time-integrated scheme. We analyze the scheme and present error estimates showing its convergence.Mathematics Subject Classification (2000): 65M12, 65M60, 76S05, 35K65Acknowledgments. We would like to thank Markus Bause for very useful discussions and suggestions.     

Three-dimensional tracking of fluorescent nanoparticles with subnanometer precision by use of off-focus imaging

We show that the position of a fluorescent nanoparticle can be measured in three dimensions with subnanometer precision and 100-ms temporal resolution by use of standard epifluorescence video imaging in off-focus mode. The particle can be tracked without feedback in a volume of at least 40 microm x 60 microm x 3 microm. With the technique presented, the structure-mobility relationship of 216-nm latex particle in a porous polymer network was studied in three dimensions.     

The Statistics of the Trajectory of a Certain Billiard in a Flat Two-Torus

We consider a billiard in the punctured torus obtained by removing a small disk of radius >0 from the flat torus ², with trajectory starting from the center of the puncture. In this case the phase space is given by the range of the velocity only. Let (), and respectively R(), denote the first exit time (length of the trajectory), and respectively the number of collisions with the side cushions when ² is being identified with [0,1)². We prove that the probability measures on [0, ) associated with the random variables and R are weakly convergent as 0⁺ and explicitly compute the densities of the limits. Research partially supported by ANSTI grant C6189/2000.     

A hybrid optimization technique coupling an evolutionary and a local search algorithm

Evolutionary algorithms are robust and powerful global optimization techniques for solving large-scale problems that have many local optima. However, they require high CPU times, and they are very poor in terms of convergence performance. On the other hand, local search algorithms can converge in a few iterations but lack a global perspective. The combination of global and local search procedures should offer the advantages of both optimization methods while offsetting their disadvantages. This paper proposes a new hybrid optimization technique that merges a genetic algorithm with a local search strategy based on the interior point method. The efficiency of this hybrid approach is demonstrated by solving a constrained multi-objective mathematical test-case.     

Decomposition of Methylene Blue in Water by Corona Discharges

The decomposition of methylene blue (MB) in aqueous solution was investigated using a pulsed corona discharge. The discharge was ignited in the gas bubbled in the solution through several needle electrodes. The influence of treatment time, volume of the treated solution and initial concentration of the dye in solution on MB degradation was studied. The effect of the nature of the gas introduced was also investigated. For the same energy input, MB conversion increased in the order air < argon < oxygen. When using oxygen, the decomposition of MB exceeded 95% after ~20 min plasma treatment. Higher efficiency was obtained for higher treated volume and higher initial concentration. At 90% conversion the yield obtained with oxygen was ~5 g/kWh for an initial concentration of 150 mg/l and a treated volume of solution of 100 ml.     

A two-dimensional ruin problem on the positive quadrant

In this paper we study the joint ruin problem for two insurance companies that divide between them both claims and premia in some specified proportions (modeling two branches of the same insurance company or an insurance and re-insurance company). Modeling the risk processes of the insurance companies by Cramér-Lundberg processes we obtain the Laplace transform in space of the probability that either of the insurance companies is ruined in finite time. Subsequently, for exponentially distributed claims, we derive an explicit analytical expression for this joint ruin probability by explicitly inverting this Laplace transform. We also provide a characterization of the Laplace transform of the joint ruin time.     

Assay of free captopril in human plasma as monobromobimane derivative,using RPLC/(+)ESI/MS/MS: validation aspects and bioequivalence evaluation

A sensitive method for determination of free captopril as monobromobimane derivative in plasma samples is discussed. The internal standard (IS) was 5‐methoxy‐1H‐benzimidazole‐2‐thiol. Derivatization with monobromobimane immediately after blood collection and plasma preparation prevents oxidation of captopril to the corresponding disulfide compound and enhances the ionization yield. Consequently, derivatization enhances sample stability and detection sensitivity. Addition of the internal standard was made immediately after plasma preparation. The internal standard was also derivatized by monobromobimane, as it contains a thiol functional group. Preparation of plasma samples containing captopril and IS derivatives was based upon protein precipitation through addition of acetonitrile, in a volumetric ratio 1:2. The reversed‐phase liquid chromatographic separation was achieved on a rapid resolution cartridge Zorbax SB‐C₁₈, monitored through positive electrospray ionization and tandem MS detection using the multiple‐reaction monitoring mode. Transitions were 408–362 amu for the captopril derivative and 371–260 amu for the internal standard derivative. The kinetics of captopril oxidation to the corresponding disulfide compound in plasma matrix was also studied using the proposed method. A linear log–log calibration was obtained over the concentration interval 2.5–750 ng/mL. A low limit of quantitation in the 2.5 ng/mL range was obtained. The analytical method was fully validated and successfully applied in a three‐way, three‐period, single‐dose (50 mg), block‐randomized bioequivalence study for two pharmaceutical formulations (captopril LPH 25 and 50 mg) against the comparator Capoten 50 mg. Copyright © 2009 John Wiley & Sons, Ltd.     

<Emphasis Type="Italic">N</Emphasis>-Alkoxy-3,5-dinitro-4-aminobenzoic acid derivatives with controlled physico-chemical properties

Starting from 4-chloro-3,5-dinitrobenzoic acid 1, compounds 2–10 (N-alkoxy-3,5-dinitro-4-aminobenzoic acid esters where alkoxy stands for methoxy, carboxymethoxy, triphenylmethoxy, or corresponding amides) have been obtained, from which compounds 3–5 and 7–10 are new, and for the known compounds 2 and 6 the synthetic procedure has been improved. The new derivatives have been characterized by appropriate means (IR, UV–Vis, ¹H- and ¹³C-NMR, fluorescence) and their properties were studied. Thus, depending on their structure, the compounds have acid properties, fluorescence and complexing properties with alkaline cations.     

New N-aryloxy-phthalimide derivatives. Synthesis,physico-chemical properties,and QSPR studies

Starting from N-hydroxyphthalimide 1 and the reactive fluoro- or chloro-nitroaryl derivatives 2, 3 and 4a-e (2-chloro-3,5-dinitropyridine; 3, NBD-chloride; 4a, 1-fluoro-2,4-dinitrobenzene; 4b, picryl chloride; 4c, 4-chloro-3,5-dinitrobenzotrifluoride; 4d, 2-chloro-3,5- dinitrobenzotrifluoride; 4e, 4-chloro-3,5-dinitrobenzoic acid) the corresponding N-(2-nitroaryloxy)-phthalimide derivatives 5a-e, or 6 and 7 were obtained and characterized by IR, UV-Vis ¹H-NMR and ¹³C-NMR spectroscopy. The TLC behavior and the hydrophobicity of these derivatives have been experimentally evaluated by R_M0 parameters (using RP-TLC). The experimental R_M0 parameters were compared with the calculated partition coefficient, log P. A QSPR study was also performed to establish possible correlations between the structure and physical properties (λ_max and R_M0) of compounds 5a-e, 6, and 7.