The Webster scalar curvature problem on the three dimensional CR manifolds

In this paper, we prove some existence results for the Webster scalar curvature problem on the three dimensional CR compact manifolds locally conformally CR equivalent to the unit sphere S³ of C². Our methods are based on the techniques related to the theory of critical points at infinity.     

Synthesis, crystal structure and mono-dimensional thallium ion conduction of TlFe0.22Al0.78As2O7

A new solid solution TlFe_0.22Al_0.78As₂O₇ has been synthesized by a solid-state reaction. The structure of the title compound has been determined from a single-crystal X-ray diffraction and refined to final values of the reliability factors: R(F²)=0.030 and wR(F²)=0.081 for 1343 independent reflections with I>2σ(I). It crystallizes in the triclinic space group P-1, with a=6.296(2) Å, b=6.397(2) Å, c=8.242(2) Å, α=96.74(2)°, β=103.78(2)°, γ=102.99(3)°, V=309.0(2) Å³ and Z=2. The structure can be described as a three-dimensional framework containing (Fe/Al)O₆ octahedra connected through As₂O₇ groups. The metallic units and diarsenate groups share oxygen corners to form a three-dimensional framework with interconnected tunnels parallel to the a, b and c directions, where Tl⁺ cations are located. The ionic conductivity measurements are performed on pellets of the polycrystalline powder. At 683 K, The conductivity value is 5.23×10⁻⁶ S cm⁻¹ and the ionic jump activation energy is 0.656 eV. The bond valence analysis reveals that the ionic conductivity is ensured by Tl⁺ along the [001] direction.     

A note on the two-stage hybrid flow shop problem with dedicated machines

In this paper we introduce a new dominance rule for the two-stage hybrid flow shop problem with dedicated machines. The rule is then used to construct a dominating set. The efficiency of the proposed rule is shown through an analysis of the dominating set cardinality.     

Numerical differentiation on scattered data through multivariate polynomial interpolation

BIT Numerical Mathematics - We discuss a pointwise numerical differentiation formula on multivariate scattered data, based on the coefficients of local polynomial interpolation at Discrete Leja...     

Ce-promoted Fe–Cu–ZSM-5 catalyst: SCR-NO activity and hydrothermal stability

Research on Chemical Intermediates - Fe–Cu–ZSM-5 and Ce–Fe–Cu–ZSM-5 solids prepared using solid-state ion exchange method (SSIE) were tested in the NH3–SCR of NO...     

The symmetric D ω -semi-classical orthogonal polynomials of class one

We give the system of Laguerre–Freud equations associated with the D _ω -semi-classical functionals of class one, where D _ω is the divided difference operator. This system is solved in the symmetric case. There are essentially two canonical cases. The corresponding integral representations are given.     

Surface plasmon resonance immunosensor for bacteria detection

This work describes an approach for the development of two bacteria biosensors based on surface plasmon resonance (SPR) technique. The first biosensor was based on functionalized gold substrate and the second one on immobilized gold nanoparticles. For the first biosensor, the gold substrate was functionalized with acid-thiol using the self-assembled monolayer technique, while the second one was functionalized with gold nanoparticles immobilized on modified gold substrate. A polyclonal anti-Escherichia coli antibody was immobilized for specific (E. coli) and non-specific (Lactobacillus) bacteria detection. Detection limit with a good reproducibility of 10⁴ and 10³ cfu mL⁻¹ of E. coli bacteria has been obtained for the first biosensor and for the second one respectively. A refractive index variation below 5 × 10⁻³ due to bacteria adsorption is able to be detected. The refractive index of the multilayer structure and of the E. coli bacteria layer was estimated with a modeling software.     

Evaluation of antileishmanial, cytotoxic and antioxidant activities of essential oils extracted from plants issued from the leishmaniasis-endemic region of Sned (Tunisia)

In this study, we tested 10 essential oils (EOs) extracted from 10 plants issued from Sned region (Tunisia) to evaluate both their leishmanicidal effects against Leishmania major and L. infantum, and their cytotoxicity against murine macrophage cell line RAW 264.7 (ATCC, TIB-71). The antioxidant activity was also monitored by the DDPH method, while the chemical composition of active EO was assessed by GC-MS analysis. The results showed that the EOs obtained from Thymus hirtus sp. algeriensis (rich on monoterpenoids, especially linalool at 17.62% and camphor at 13.82%) is significantly active against both L. major and L. infantum, whereas Ruta chalepensis EO (rich on 2-undecanone at 84.28%) is only active against L. infantum. Both oil extracts showed low cytotoxicity towards murine macrophages. The characteristic ratios (IC?? Raw264.7 cells/IC?? L. infantum and IC?? Raw264.7 cells/IC?? L. major) were, respectively, 2.7 and 1.57 for T. hirtus sp. algeriensis, and 1.34 and 0.19 for R. chalepensis. However, when measuring the antioxidant effects (DDPH method), the two latter EOs presented a moderate 2,2-diphenyl-2-picrylhydrazyl hydrate scavenging effects compared to EOs from Eucaliptus globulus, Pinus halepensis, Pituranthos tortuosus, Rosmarinus officinalis, Tetraclinis articulata or to BHT.     

The Webster scalar curvature revisited: the case of the three dimensional CR sphere

In this paper we consider the problem of prescribing the Webster scalar curvature on the three CR sphere of ${\mathbb{C}^{2}}$ . We use techniques related to the theory of critical points at infinity, and obtain existence results for curvature satisfying an assumption of Bahri?CCoron type.     

q-Extension of generalized Gegenbauer polynomials

We study in detail a q-extension of the generalized Gegenbauer form (functional). We show that it is symmetric H _q -semi-classical of class one. The moments and the integral representations are given.