Orthogonalization in momentum space

Since the overlap integral between two functions in position space is the same as the overlap integral between their counterparts in momentum space, there is an intimate connection between orthonormalization procedures in the two spaces. It is pointed out that in certain cases this situation can be used to simplify the orthogonalization.     

Algebraic families of nonzero elements of Shafarevich-Tate groups

Principal homogeneous spaces under an abelian variety defined over a number field may have rational points in all completions of the number field without having rational points over . Such principal homogeneous spaces represent the nonzero elements of the Shafarevich-Tate group of the abelian variety.

We produce nontrivial, one-parameter families of such principal homogeneous spaces. The total space of these families are counterexamples to the Hasse principle. We show these may be accounted for by the Brauer-Manin obstruction.

     

Grandes valeurs du nombre de factorisations d’un entier en produit ordonné de facteurs premiers

Among various functions used to count the factorizations of an integer n, we consider here the number of ways of writing n as an ordered product of primes, which, if , is equal to the multinomial coefficient . The function P(s)=∑ _{p prime} p ^−s , sometimes called the prime zeta function, plays an important role in the study of the function h. We denote by λ=1.399433… the real number defined by P(λ)=1. The mean value of the function h satisfies . In this paper, we study how large h(n) can be. We prove that there exists a constant C ₁>0 such that, for all n≥3, holds. We also prove that there exists a constant C ₂ such that, for all n≥3, there exists m≤n satisfying . Let us call h-champion an integer N such that M<N implies h(M)<h(N). S. Ramanujan has called highly composite a τ-champion number, where τ(n)=∑ _d∣n 1 is the number of divisors of n. We give several results about the number of prime factors of an h-champion number N, about the exponents in the standard factorization into primes of such an N and about the number Q(X) of h-champion numbers N≤X. At the end of the paper, several open problems are listed. Recherche partiellement financée par le CNRS, Institut Camille Jordan, UMR 5208 et par l’action de coopération franco-algérienne 01 MDU 514, Arithmétique, Géométrie Algébrique et Applications.     

Electrochromatography in poly(dimethyl)siloxane microchips using organic monolithic stationary phases

This paper shows the in situ synthesis of an hexyl acrylate monolith in PDMS microfluidic devices and its subsequent use as stationary phase for electrochromatography on chip. To overcome the ability of PDMS material to absorb organic monomers, surface modification of the enclosed channels was realized by UV-mediated graft polymerization. This grafting procedure is based on the preliminary adsorption of a photoinitiator onto the PDMS surface and polymerization of charged monomers. Next, hexyl acrylate monoliths were cast in situ using photopolymerization process. The chromatographic behavior of the monolithic column was confirmed by the successful separation of derivatized catecholamines in the PDMS device using a 30 mm effective separation length (100 microm x 100 microm section). Efficiencies reached up to 200,000 plates per meter.     

Approximative "one particle" bridge function B(1)(r) for the theory of simple fluids

New properties for the one particle bridge function B(1)(r), which are necessary to the calculation of the excess chemical potential betamue), are derived for the hard sphere fluid. The method, which only requires the knowledge of the bridge function B(2)(r), is based on an investigation of the correlation function dependence on the Kirkwood charging parameter. In this framework, the unavoidable question of topological homotopy is addressed. As far as B(2)(r) is considered as exact, this work provides useful information on B(1)(r) in the well identified dynamical regimes of the hard sphere fluid. Signatures of the transitions between these regimes are identified on the trends of B(1)(r). This approach provides self-consistent results for betamue) that agree very well with simulation data.     

High throughput liquid chromatography with sub-2 microm particles at high pressure and high temperature

In this study, ultra performance liquid chromatography (UPLC) using pressures up to 1,000 bar and columns packed with sub-2 microm particles has been combined with high temperature mobile phase conditions (up to 90 degrees C). By using high temperature ultra performance liquid chromatography (HT-UPLC), it is possible to drastically decrease the analysis time without loss in efficiency. The stability and chromatographic behavior of sub-2 microm particles were evaluated at high temperature and high pressure. The chromatographic support remained stable after 500 injections (equivalent to 7,500 column volumes) and plate height curves demonstrated the capability of HT-UPLC to obtain fast separations. For example, a separation of nine doping agents was performed in less than 1 min with sub-2 microm particles at 90 degrees C. Furthermore, a shorter column (30 mm length) was used and allowed a separation of eight pharmaceutical compounds in only 40s.     

Magnetic interactions in CuII-LnIII cyclic tetranuclear complexes: is it possible to explain the occurrence of SMM behavior in CuII-TbIII and CuII-DyIII complexes?

An extensive series of tetranuclear CuII2LnIII2 complexes [CuIILLnIII(hfac)2]2 (with LnIII being all lanthanide(III) ions except for the radioactive PmIII) has been prepared in order to investigate the nature of the CuII-LnIII magnetic interactions and to try to answer the following question: What makes the CuII2TbIII2 and CuII2DyIII2 complexes single molecule magnets while the other complexes are not? All the complexes within this series possess a similar cyclic tetranuclear structure, in which the CuII and LnIII ions are arrayed alternately via bridges of ligand complex (CuIIL). Regular SQUID magnetometry measurements have been performed on the series. The temperature-dependent magnetic susceptibilities from 2 to 300 K and the field-dependent magnetizations from 0 to 5 T at 2 K have been measured for the CuII2LnIII2 and NiII2LnIII2 complexes, with the NiII2LnIII2 complex containing diamagnetic NiII ions being used as a reference for the evaluation of the CuII-LnIII magnetic interactions. These measurements have revealed that the interactions between CuII and LnIII ions are very weakly antiferromagnetic if Ln=Ce, Nd, Sm, Yb, ferromagnetic if Ln=Gd, Tb, Dy, Ho, Er, Tm, and negligible if Ln=La, Eu, Pr, Lu. With the same goal of better understanding the evolution of the intramolecular magnetic interactions, X-ray magnetic circular dichroism (XMCD) has also been measured on CuII2TbIII2, CuII2DyIII2, and NiII2TbIII2 complexes, either at the L- and M-edges of the metal ions or at the K-edge of the N and O atoms. Last, the CuII2TbIII2 complex exhibiting SMM behavior has received a closer examination of its low temperature magnetic properties down to 0.1 K. These particular measurements have revealed the unusual very slow setting-up of a 3D order below 0.6 K.     

Optimization of in-situ monolithic synthesis for immunopreconcentration in capillary

Poly(glycidyl methacrylate-co-ethylene dimethacrylate) monoliths have been synthetized in fused-silica capillary. The monomer mixture composition, initiation mode and porogen composition were optimized in order to provide a monolith with an homogeneous morphology and able to generate an electroosmotic flow via the incorporation of a small percentage of monomers possessing sulfonate group. Anti-ochratoxin A antibodies were immobilized through a single step on the epoxy groups leading to a miniaturized immunoextraction column. In order to evaluate the specificity of the analyte-antigen interaction on this immunosorbent, the retention of ochratoxin A was examined on this support but also on two complementary sorbents: one constituted by the non-bonded monolith and another one bonded with non-specific antibodies. Only the monolith bonded with anti-ochratoxin A antibodies lead to retention, showing the specificity of the interactions involved. This affinity phase based on a monolithic polymer support exhibits a high potential for specific preconcentration of small molecules.