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...     

Structural and optical characterizations of rare earth pentaphosphates LnP5O14 (Ln = La, Gd) synthesized by the sol–gel process

The sol–gel chemistry route has successfully been used to prepare samples of LnP₅O₁₄ (Ln = La, Gd) pentaphosphates from lanthanides chlorides and phosphorous pentoxide dissolved in isopropanol. Crystallized powders of single phase were obtained after calcination of gels at 350 °C. The structural characterizations of materials were investigated by means of X-ray diffraction as well as infrared and Raman spectroscopies, whereas their thermal behavior has been studied by differential thermal analyse and thermogravimetric analyses. Powders morphology was analyzed by means of scanning electron microscopy and laser granulometry. The photoluminescence properties of the Eu³⁺ ions in sol–gel derived LaP₅O₁₄ and GdP₅O₁₄ samples were investigated and compared with homologous samples synthesized by the conventional solid state reaction.     

On fractional quantum Hall solitons in ABJM-like theory

Using D-brane physics, we study fractional quantum Hall solitons (FQHS) in ABJM-like theory in terms of type IIA dual geometries. In particular, we discuss a class of Chern-Simons (CS) quivers describing FQHS systems at low energy. These CS quivers come from R-R gauge fields interacting with D6-branes wrapped on 4-cycles, which reside within a blown up CP³ projective space. Based on the CS quiver method and mimicking the construction of del Pezzo surfaces in terms of CP², we first give a model which corresponds to a single layer model of FQHS system, then we propose a multi-layer system generalizing the doubled CS field theory, which is used in the study of topological defect in graphene.     

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.     

On Hexagonal Structures in Higher Dimensional Theories

We analyze the geometrical background under which many Lie groups relevant to particle physics are endowed with a (possibly multiple) hexagonal structure. There are several groups appearing, either as special holonomy groups on the compactification process from higher dimensions, or as dynamical string gauge groups; this includes groups like SU(2), SU(3), G ₂, Spin(7), O(8) as well as E ₈ and O(32). We emphasize also the relation of these hexagonal structures with the octonion division algebra, as we expect as well eventually some role for octonions in the interpretation of symmetries in High Energy Physics.     

Combined static electromagnetic radiation and plant extract contribute to the biosynthesis of instable nanosilver responsible for the growth of microstructures

The instant biosynthesis of silver nanoparticles under static electromagnetic induction, its antibacterial activity and its post exposure monitoring were reported here. A mix of silver nitrate solution and Ruta chalepensis leaf extract was irradiated by a static electromagnetic field (SMF) of 200 mT. The characteristics and stability of the biosynthesized silver nanoparticles (Ag NPs) were determined. Compared to the non-irradiated exposure, the morphology and state of the obtained material change once the exposition to SMF is turned off. Shifting from 453 to 473 nm, the percentage of the needles shaped silver nanoparticles increased and continue to win and dominate the biomixture toward the spherical silver nanoparticles. TEM microscopy showed a wide range of silver materials designed in different nanoscale morphology and beyond where they undergo major changes affecting mainly the size, shape and form (dispersity) of nanosilver.