Vectorial penalization for generalized functional constrained problems

In this paper we use a double penalization procedure in order to reduce a set-valued optimization problem with functional constraints to an unconstrained one. The penalization results are given in several cases: for weak and strong solutions, in global and local settings, and considering two kinds of epigraphical mappings of the set-valued map that defines the constraints. Then necessary and sufficient conditions are obtained separately in terms of Bouligand derivatives of the objective and constraint mappings.     

Carbon and diamond paste microelectrodes based on Mn(III) porphyrins for the determination of dopamine

Three Mn(III) porphyrins were used for the design of carbon paste and diamond paste based microelectrodes, which were employed for the determination of dopamine in pharmaceutical and biological samples using differential pulse voltammetry (DPV). The limits of detection lie between 1.6 × 10⁻¹³ and 2.0 × 10⁻⁶ mol L⁻¹ while the sensitivities were between 230 pA μmol L⁻¹ and 3.24 μA mol L⁻¹. Dopamine was recovered reliable from pharmaceutical and biological samples in percentages higher than 91.00% and 92.00%, respectively. The surface of the microelectrodes can easily be renewed by simple polishing, obtaining a fresh surface ready for use in a new assay.     

Comparison of luminescence ADP production assay and radiometric scintillation proximity assay for Cdc7 kinase

Several assay technologies have been successfully adapted and used in HTS to screen for protein kinase inhibitors; however, emerging comparative analysis studies report very low hit overlap between the different technologies, which challenges the working assumption that hit identification is not dependent on the assay method of choice. To help address this issue, we performed two screens on the cancer target, Cdc7-Dbf4 heterodimeric protein kinase, using a direct assay detection method measuring [(33)P]-phosphate incorporation into the substrate and an indirect method measuring residual ADP production using luminescence. We conducted the two screens under similar conditions, where in one, we measured [(33)P]-phosphate incorporation using scintillation proximity assay (SPA), and in the other, we detected luminescence signal of the ATP-dependent luciferase after regenerating ATP from residual ADP (LUM). Surprisingly, little or no correlation were observed between the positives identified by the two methods; at a threshold of 30% inhibition, 25 positives were identified in the LUM screen whereas the SPA screen only identified two positives, Tannic acid and Gentian violet, with Tannic acid being common to both. We tested 20 out of the 25 positive compounds in secondary confirmatory study and confirmed 12 compounds including Tannic acid as Cdc7-Dbf4 kinase inhibitors. Gentian violet, which was only positive in the SPA screen, inhibited luminescence detection and categorized as a false positive. This report demonstrates the strong impact in detection format on the success of a screening campaign and the importance of carefully designed confirmatory assays to eliminate those compounds that target the detection part of the assay.     

Influence of Phytochemical Reductive Capacity on Ultraviolet–visible Spectroscopic Behavior of Silver Nanoparticles

ABSTRACT

A widely used method for obtaining silver nanoparticles uses plant extracts for reduction because of the presence of phytochemicals such as terpenoids, tannins, and flavonoids. Extracts of Flores sambuci, Hypericum perforatum, Lavandula angustifolia, Origanum vulgare, Rosmarinus officinalis, and Salvia officinalis were used for generating silver nanoparticles. The ultraviolet–visible spectra of silver nanoparticle solutions were correlated with variations of phytochemical characteristics to evaluate the plant extracts. These parameters were the antioxidant activity, total flavonoids, total tannins, total terpenoids, and total phenolics. Correlations between measurements of extracts’ phytoreductive characteristics were explained using Pearson coefficients. The results showed medium linear positive correlations for total tannins with the spectra of silver nanoparticle solutions. The antioxidant activity and total terpenoids presented medium linear negative correlations. Pearson coefficients between total phenolics and relative areas from ultraviolet–visible spectra from 350 to 600?nm were close to zero indicating no linear correlation.     

The Geometry of Systems of Third Order Differential Equations Induced by Second Order Regular Lagrangians

A system of third order differential equations, whose coefficients do not depend explicitly on time, can be viewed as a third order vector field, which is called a semispray, and lives on the second order tangent bundle. We prove that a regular second order Lagrangian induces such a semispray, which is uniquely determined by two associated Poincaré-Cartan one-forms. To study the geometry of this semispray, we construct a horizontal distribution, which is a Lagrangian subbundle for an associated Poincaré-Cartan two-form. Using this semispray and the associated nonlinear connection we define dynamical covariant derivatives of first and second order. With respect to this, the second order dynamical derivative of the Lagrangian metric tensor vanishes.     

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.     

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.