La somme des chiffres des carrés

In this article we answer a question proposed by Gelfond in 1968. We prove that the sum of digits of squares written in a basis q ⩾ 2 is equidistributed in arithmetic progressions.     

Microbial screening methods for detection of antibiotic residues in slaughter animals

Monitoring of food products from animal origin for the presence of antimicrobial residues is preferably done using microbial screening methods because of their high cost-effectiveness. Traditionally applied methods fail to detect the maximum residue limits which were established when EU Council Regulation 2377/90 came into effect. Consequently, during the last decade this has led to the development of improved microbial screening methods. This review provides an overview of the efforts expended to bring antibiotic screening methods into compliance with EU legislation. It can be concluded that the current situation is still far from satisfactory.     

On the correlation of pseudorandom numbers generated by inversive methods

We introduce two new types of inversive generators for pseudorandom numbers. These new methods offer several advantages over the conventional inversive generator. For instance, we establish good correlation properties of our generators that cannot be obtained for the conventional inversive generator with current methods. A new bound on character sums for finite fields is the essential technical tool for this work. Authors’ addresses: Harald Niederreiter, Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543, Republic of Singapore; Jo?l Rivat, Institut de Mathématiques de Luminy, Université de la Méditerranée, CNRS-UMR 6206, 163 avenue de Luminy, Case 907, 13288 Marseille Cedex 9, France     

Polymorphism in PbBiOXO4 compounds (X=V, P, As): Part II—PbBiOPO4 and PbBiOAsO4 structures and characterization of related solid solutions

Reinvestigation of PbBiOXO₄ (X=V, P, As) thermal behaviour revealed a phase transition for V- and P-compounds, but no transition for the As-compound. As shown by single-crystal X-ray diffraction and high-resolution neutron powder diffraction, α-PbBiOVO₄ transforms to β-PbBiOVO₄ at 550 °C. The two PbBiOPO₄ varieties are isomorph to the vanadate forms, while PbBiOAsO₄ adopts the β-type structure whatever the temperature. PbBiP_1−xOAs_xO₄ and PbBiV_1−xOM_xO₄ (M=As, P, Cr, Mn) solid solutions display both triclinic and monoclinic domains, and the α→β transition temperature is a function of the substitution rate. The ionic conductivity of these compounds was investigated by impedance spectroscopy. The analysis of free space in the β-PbBiOVO₄ structure allows to propose a one-dimensional oxygen diffusion pathway along [010] when the temperature increases.     

Comparative study of the effect of various electrode membranes on biofouling and electrochemical measurements

Stability of sensors in biosamples is a critical issue and can be mitigated by membranes. The effect of different membranes (Nafion, cellulose acetate, chitosan, fibronectin, PSS/PL) on the electrochemistry of an outer-sphere redox couple (ruthenium II/III hexaammine) and on the electrocatalytic reduction of dissolved oxygen are described. Biofouling has been induced by albumin solutions. Results demonstrate good performances of fibronectin in all situations investigated. Other membranes do not provide a satisfactory protection from biofouling and some of them, PSS/PL in particular, seriously disturb electrochemical mechanisms.     

Lie symmetries and CR geometry

This paper is divided into three parts. Part I develops a general, new theory (inspired by modern CR geometry) of Lie symmetries of completely integrable pde systems, viewed from their associated submanifolds of solutions. Part II constructs general combinatorial formulas for the prolongations of vector fields to jet spaces. Part III explicitly characterizes the flatness of some systems of the second order. The results presented here are original and were not published elsewhere; most formulas of Parts II and III were verified by means of Maple Release 7. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 47, Complex Analysis, 2007.     

Mössbauer study of amorphous and crystallized Fe1-xCx alloys

Fe_1?xC_x amorphous alloys have been studied with Mössbauer Spectroscopy for 0.19<-x<-0.31. For x>-0.286, new carbides are formed by crystallization of such alloys. The chemical twinning model allows describing their structures.     

Bismuth (III) coordination to cyclen and cyclam bearing four appended groups

The synthesis of new cyclam and cyclen derivatives (respectively L₁ and L₂), able to efficiently coordinate to Bi(III) are presented here. The two ligands bearing two different pendant arms (two-pycolyl and two (2-(2-hydroxyethoxy)ethyl)-2-aminoacetamide in trans position) were synthesized in the aim to obtain stable and water soluble complexes. The thermodynamic and kinetic of the formation of the corresponding complexes in aqueous solution were studied by means of NMR and potentiometric investigations. The fast kinetic of complexation and the high stability of the complexes are encouraging for further application with the alpha-emitting ²¹³Bi isotope.