On the graph of a function in two variables over a finite field

We show that if the number of directions not determined by a pointset of , of size q² is at least p^e q then every plane intersects in 0 modulo p^e+1 points and apply the result to ovoids of the generalised quadrangles and .     

Two strong convergence theorems for Bregman strongly nonexpansive operators in reflexive Banach spaces

We study the convergence of two iterative algorithms for finding common fixed points of finitely many Bregman strongly nonexpansive operators in reflexive Banach spaces. Both algorithms take into account possible computational errors. We establish two strong convergence theorems and then apply them to the solution of convex feasibility, variational inequality and equilibrium problems.     

An approximation theory for the identification of nonlinear volterra equations

An abstract approximation framework and convergence theory for Galerkin approximations to inverse problems involving nonlinear Volterra integral equations is developed. The approach relies on the theory of m-accretive operators in Banach spaces. An application to heat flow in materials with memory is also discussed.     

Two Strong Convergence Theorems for a Proximal Method in Reflexive Banach Spaces

Two strong convergence theorems for a proximal method for finding common zeroes of maximal monotone operators in reflexive Banach spaces are established. Both theorems take into account possible computational errors.     

Two Projection Algorithms for Solving the Split Common Fixed Point Problem

Journal of Optimization Theory and Applications - We study the split common fixed point problem for Bregman relatively nonexpansive operators in real reflexive Banach spaces. Using Bregman...     

An easier proof of the maximal arcs conjecture

It was a long-standing conjecture in finite geometry that a Desarguesian plane of odd order contains no maximal arcs. A rather inaccessible and long proof was given recently by the authors in collaboration with Mazzocca. In this paper a new observation leads to a greatly simplified proof of the conjecture.

     

Quantification of atrazine and its metabolites in urine by on-line solid-phase extraction–high-performance liquid chromatography–tandem mass spectrometry

We have developed a method using on-line solid-phase extraction–high-performance liquid chromatography–tandem mass spectrometry (SPE-HPLC-MS/MS) and isotope dilution quantification to measure atrazine and seven atrazine metabolites in urine. The metabolites measured were hydroxyatrazine, diaminochloroatrazine, desisopropylatrazine, desethylatrazine, desethylatrazine mercapturate, atrazine mercaturate and atrazine itself. Our method has good precision (relative standard deviations ranging from 4 to 20% at 5, 10 and 50 ng/mL), extraction efficiencies of 67 to 102% at 5 and 25 ng/mL, relative recoveries of 87 to 112% at 5, 25, 50 and 100 ng/mL limits of detection (LOD) ranging from 0.03 to 2.80 ng/mL. The linear range of our method spans from the analyte LOD to 100 ng/mL (40 ng/mL for atrazine and atrazine mercapturate) with R ² values of greater than 0.999 and errors about the slope of less than 3%. Our method is rapid, cost-effective and suitable for large-scale sample analyses and is easily adaptable to other biological matrices. More importantly, this method will allow us to better assess human exposure to atrazine-related chemicals. Figure A schematic representation showing the elution of the analytes from the solid-phase extraction cartridge onto the analytical column for chromatographic separation prior to MS/MS analysis