Conformally equivariant quantization: Existence and uniqueness

We prove the existence and the uniqueness of a conformally equivariant symbol calculus and quantization on any conformally flat pseudo-Riemannian manifold (M,\rg). In other words, we establish a canonical isomorphism between the spaces of polynomials on $T^*M$ and of differential operators on tensor densities over $M$, both viewed as modules over the Lie algebra \so(p+1,q+1) where $p+q=\dim(M)$. This quantization exists for generic values of the weights of the tensor densities and compute the critical values of the weights yielding obstructions to the existence of such an isomorphism. In the particular case of half-densities, we obtain a conformally invariant star-product.Comment: LaTeX document, 32 pages; improved versio

The maison europeenne des procedes innovants (MEPI),an example of piloting and industrial demonstration facility for the green process engineering

Abstract. Economical, energy savings and environmental challenges require an actual technological breakthrough in process engineering, aiming with productivity, product quality, safety and reliability objectives. This explains the present growth of interest in innovative technologies (intensified devices for reaction, mixing and separation) and methods (multifunctionality, hybrid separation, batch to continuous methodology, new media …), the whole being recognized as Process Intensification. Up to now, a few of innovations has been successfully industrialized, probably due to the lack of experience and retrofitting in front of a breakthrough that always represents a technical and financial risk. There is now clearly a need for industrial demonstrations of successful PI experiments avoiding the questions of confidentiality. Consequently, a piloting and demonstration facility has been created in Toulouse in order to accelerate the implementation of PI technology in industry and the development of the Green Process Engineering. The idea is to build a data bank of success stories. The principle of this industrial technical platform lies on the association of 3 types of partners: university, equipment providers and industrial end-users

Decomposition of symmetric tensor fields in the presence of a flat contact projective structure

Let $M$ be an odd-dimensional Euclidean space endowed with a contact 1-form $\alpha$. We investigate the space of symmetric contravariant tensor fields on $M$ as a module over the Lie algebra of contact vector fields, i.e. over the Lie subalgebra made up by those vector fields that preserve the contact structure. If we consider symmetric tensor fields with coefficients in tensor densities, the vertical cotangent lift of contact form $\alpha$ is a contact invariant operator. We also extend the classical contact Hamiltonian to the space of symmetric density valued tensor fields. This generalized Hamiltonian operator on the symbol space is invariant with respect to the action of the projective contact algebra $sp(2n+2)$. The preceding invariant operators lead to a decomposition of the symbol space (expect for some critical density weights), which generalizes a splitting proposed by V. Ovsienko

A hermeneutic inquiry into user-created personas in different Namibian locales

Persona is a tool broadly used in technology design to support communicational interactions between designers and users. Different Persona types and methods have evolved mostly in the Global North, and been partially deployed in the Global South every so often in its original User-Centred Design methodology. We postulate persona conceptualizations are expected to differ across cultures. We demonstrate this with an exploratory-case study on user-created persona co-designed with four Namibian ethnic groups: ovaHerero, Ovambo, ovaHimba and Khoisan. We follow a hermeneutic inquiry approach to discern cultural nuances from diverse human conducts. Findings reveal diverse self-representations whereby for each ethnic group results emerge in unalike fashions, viewpoints, recounts and storylines. This paper ultimately argues User-Created Persona as a potentially valid approach for pursuing cross-cultural depictions of personas that communicate cultural features and user experiences paramount to designing acceptable and gratifying technologies in dissimilar locales

On sl(2)-equivariant quantizations

By computing certain cohomology of Vect(M) of smooth vector fields we prove that on 1-dimensional manifolds M there is no quantization map intertwining the action of non-projective embeddings of the Lie algebra sl(2) into the Lie algebra Vect(M). Contrariwise, for projective embeddings sl(2)-equivariant quantization exists.Comment: 09 pages, LaTeX2e, no figures; to appear in Journal of Nonlinear Mathematical Physic

Natural and projectively equivariant quantizations by means of Cartan Connections

The existence of a natural and projectively equivariant quantization in the sense of Lecomte [20] was proved recently by M. Bordemann [4], using the framework of Thomas-Whitehead connections. We give a new proof of existence using the notion of Cartan projective connections and we obtain an explicit formula in terms of these connections. Our method yields the existence of a projectively equivariant quantization if and only if an \sl(m+1,\R)-equivariant quantization exists in the flat situation in the sense of [18], thus solving one of the problems left open by M. Bordemann.Comment: 13 page

Cohomology of groups of diffeomorphims related to the modules of differential operators on a smooth manifold

Let $M$ be a manifold and $T^*M$ be the cotangent bundle. We introduce a 1-cocycle on the group of diffeomorphisms of $M$ with values in the space of linear differential operators acting on $C^{\infty} (T^*M).$ When $M$ is the $n$-dimensional sphere, $S^n$, we use this 1-cocycle to compute the first-cohomology group of the group of diffeomorphisms of $S^n$, with coefficients in the space of linear differential operators acting on contravariant tensor fields.Comment: arxiv version is already officia

Intracellular mechanism of the action of inhibin on the secretion of follicular stimulating hormone and of luteinizing hormone induced by LH-RH in vitro

The FSH secretion-inhibiting action of inhibin in vitro under basal conditions and also in the presence of LH-RH is suppressed by the addition of MIX, a phosphodiesterase inhibitor. In the presence of LH-RH, inhibin reduces significantly the intracellular level of cAMP in isolated pituitary cells. In contrast, the simultaneous addition of MIX and inhibin raises the cAMP level, and this stimulation is comparable to the increase observed when MIX is added alone. These observations suggest that one mode of action of inhibin could be mediated by a reduction in cAMP within the pituitary gonadotropic cell

Thick films of YSZ electrolytes by dip-coating process

Yttria stabilized zirconia (YSZ, 8% Y2O3) thick films were coated on porous Ni-YSZ substrates using the dip-coating process and a suspension with a new formulation. The suspension was obtained by addition of a polymeric matrix in a stable suspension of a commercial YSZ (Tosoh) powders dispersed in an azeotropic MEK-EtOH mixture. The green layers were densified after an optimization of the suspension composition. YSZ Tosoh particles encapsulated by a zirconium alkoxide sol and added with colloidal alkoxide precursor are used to load the suspension. The in situ growth of these colloids increases significantly the layers density after an appropriated heat treatment. The obtained films are continuous, homogeneous and 20 μm thick. Different microstructures are obtained depending on the synthesis parameters of the suspension