Simultaneous pairs of dual integral equations

A fruitful method of attack in the solution of mixed boundary value problems is the utilization of integral transform techniques. Satisfaction of the mixed boundary conditions then leads to consideration of one or more pairs of dual integral equations. Oftentimes the solution of these dual integral equations only follows from laborious and complex manipulations. An exception to this is the work of Copson [1] and Lowengrub, Sneddon [2] in which the general solution to the pair of dual integral equations (1a) ∫_(0)^(∞)ψ(ξ)J_(v)(ξr) dξ = f1(r), 1<r<∞, (1b) ∫_(0)^(∞)ψ(ξ)ξ^(2a)J_(v)(ξr) dξ=f2(r), 0<r<1, is obtained in a simple and straightforward manner. It is the purpose of this article to demonstrate that the solution techniques in [1], [2] are equally applicable for the simultaneous pairs of dual integral equations ∫_(0)^(∞) [aψ1(ξ)+ψ2(ξ)]J(v+2)(ξr)dξ=f1(r), 1<r<∞, ∫_(0)^(∞) [bψ1(ξ)+ψ2(ξ)]ξ^(2a)J_(v+2)(ξr)dξ=f2(r), 0<r<1, ∫_(0)^(∞) [cψ1(ξ)+ψ2(ξ)]J(v+2)(ξr)dξ=f3(r), 1<r<∞, ∫_(0)^(∞) [ψ1(ξ)+ψ2(ξ)]ξ^(2a)J_(v)(ξr)dξ=f4(r), 0<r<1

Mining Novel Constitutive Promoter Elements in Soil Metagenomic Libraries in Escherichia coli

Although functional metagenomics has been widely employed for the discovery of genes relevant to biotechnology and biomedicine, its potential for assessing the diversity of transcriptional regulatory elements of microbial communities has remained poorly explored. Here, we experimentally mined novel constitutive promoter sequences in metagenomic libraries by combining a bi-directional reporter vector, high-throughput fluorescence assays and predictive computational methods. Through the expression profiling of fluorescent clones from two independent soil sample libraries, we have analyzed the regulatory dynamics of 260 clones with candidate promoters as a set of active metagenomic promoters in the host Escherichia coli. Through an in-depth analysis of selected clones, we were able to further explore the architecture of metagenomic fragments and to report the presence of multiple promoters per fragment with a dominant promoter driving the expression profile. These approaches resulted in the identification of 33 novel active promoters from metagenomic DNA originated from very diverse phylogenetic groups. The in silico and in vivo analysis of these individual promoters allowed the generation of a constitutive promoter consensus for exogenous sequences recognizable by E. coli in metagenomic studies. The results presented here demonstrates the potential of functional metagenomics for exploring environmental bacterial communities as a source of novel regulatory genetic parts to expand the toolbox for microbial engineering

Un élément fini de poutre fissurée application à la dynamique des arbres tournants

International audienceDans ce travail on présente une méthode originale de construction d'un élément fini de poutre affectée de fissurations. La souplesse additionnelle due à la présence des fissures est identifiée à partir de calculs éléments finis tridimensionnels tenant compte des conditions de contact unilatéral entre les lèvres. Cette souplesse est répartie sur toute la longueur de l'élément dont on se propose de construire la matrice de rigidité. La démarche permet un gain considérable en temps de calcul par rapport à la représentation nodale de la section fissurée lors de l'intégration temporelle de systèmes différentiels en dynamique des structures

Elastic properties of hollow-sphere-reinforced composites

This paper is concerned with determining the elastic properties of a composite material composed of hollow spherical inclusions em-bedded in a matrix. Both inclusions and surrounding material are taken to be isotropic and elastic. As the result of a straightforward extension of Hashin’s work, upper and lower bounds have been developed for the gross shear modulus of the composite. In addition, a closed form expression is presented for the gross bulk modulus of the material. Numerical results have been presented illustrating the effect of wall thickness of the inclusion upon the elastic constants of the composite. As illus-trated by example, control of the properties and geometry of the inclusions permits &quot;design &quot; of a material with prescribed elastic behavior. I