Positive evanescent solutions of nonlinear elliptic equations

In this note we investigate the existence of positive solutions vanishing at +∞ to the elliptic equation Δu+f(x,u)+g(|x|)x⋅∇u=0, |x|>A>0, in Rn (n?3) under mild restrictions on the functions f, g.     

Enhanced fibroblast cell adhesion on Al/Al2O3 nanowires

Biological cells stick together via transmembrane proteins, which are linked to receptor molecules of the extracellular matrix (ECM). This specific biochemical adhesion plays a leading role in many cellular processes, among them cell differentiation, morphogenesis, and wound healing. Various medical applications require endogen cells to bind to an exogene substrate as in the case of an implant. Coatings with proteins that naturally belong to the ECM are known to enhance the cell adhesion. However, the choice of inorganic materials, which promote cell adhesion, is limited. Here, we report on a new engineered surface composed of Al/Al₂O₃ bi-phasic nanowires (NWs), which promotes the adhesion of fibroblast cells. Fibroblasts grow well on this inorganic layer and keep proliferating. Using the cell monolayer rheology (CMR) technique, we show that the adhesion of fibroblasts on Al/Al₂O₃ NWs is comparable to fibronectin coated surfaces. To our knowledge, this is one of the strongest cell adhesions on an inorganic surface, which has been reported on so far, since it compares to bio-organic layers such as fibronectin.     

Linkage isomerism in coordination polymers

The use of the recently prepared polynitrile ligand tcnopr3OH(-) ([(NC)(2)CC(OCH(2)CH(2)CH(2)OH)C(CN)(2)](-)) with different salts of Fe(II), Co(II), and Ni(II) has led to a very rare example of linkage isomerism in a coordination chain. These pairs of linkage isomers can be formulated as [M(tcnopr3OH-κN,κO)(2)(H(2)O)(2)]; M = Fe (1), Co (3), and Ni(5) and [M(tcnopr3OH-κN,κN')(2)(H(2)O)(2)]; M = Fe (2), Co (4), and Ni (6). Compounds 1-2, 3-4, and 5-6 are three pairs of linkage isomers since they present the same formula and chain structure and they only differ in the connectivity of the polynitrile ligand bridging the metal ions in the chain: through a N and an O atom (1κN:2κO-isomer) or through two N atoms (1κN:2κN'-isomer). The magnetic properties show, as expected, very similar behaviors for both isomers.     

Fourth-Order p-Laplacian Nonlinear Systems via the Vector Version of Krasnosel’skiĭ’s Fixed Point Theorem

In this paper, existence results for a fourth-order nonlinear system are obtained. Both classical and vector versions of the Krasnosel’skiĭ’s fixed point theorem are used and a comparison of the obtained results to those from the literature is provided.     

Transient Optical Regime of Two Level Atom in Laser Light

An extended analytic approach is considered for optical Bloch equations in the two level atom interacting with laser light. The separation approach of coupled differential equations is always possible with a sequence of special transformation into the Riccati nonlinear differential equation. The conditions that permit an exact solutions of three coupled system are extracted in a natural manner. The case of sodium atom moving along the axis of a monochromatic wave is treated in some details including a discussion on the radiation pressure forces exerted by laser light in the transient regime. PACS numbers: 32.80.Pj, 42.50.Vk, 42.50.Hz, 42.50.Lc.     

AgNi3(PO4)(HPO4)2: an alluaudite‐like structure

The new title phosphate, silver trinickel phosphate bis(hydrogenphosphate), has been synthesized by the hydro­thermal method. It has an alluaudite‐like structure but shows some differences owing to the presence of the H atoms. The structure is isomorphous with the compounds of general formula AM₃(XO₄)(HXO₄)₂ (A is Na or Ag, M is Co, Zn or Mn, and X is As or P), with the Ag atom, one Ni atom and one P atom lying on twofold axes.     

Reactivity of [(Ph2Si)2O3]4[Al(OH)]4 and [(Ph2Si)2O3]4[Al(OLi)]4 towards NaOEt and LiOH. Synthesis of New Twelve‐membered Alumopolysiloxane Rings

The reaction between [(Ph₂Si)₂O₃]₄[Al(OH)]₄ ( 1 ) or [(Ph₂Si)₂O₃]₄[Al(OLi)]₄ ( 2 ) with sodium ethoxide, or lithium hydroxide in presence of CuI·H₂O leads to the formation of new alumopolysiloxane compounds. Indeed, transformations of 1 under the partial incorporation of the reactants are found giving rise to new heteroleptic inorganic macrocycles. The molecular structure of [(Ph₂Si)₂O₃]₄[Al(ONa)]₂[Al(OH)(NaOEt)]₂·2Et₂O ( 3 ) and [(Ph₂Si)₂O₃]₄[Al(OLi)]₂[Al(OH)(LiOH)]₂·2Et₂O·2THF ( 4 ) have been determined by single‐X‐ray diffraction analysis. Both alumosiloxanes 3 and 4 are constituted by a twelve‐membered ring.     

Photocatalytic degradation of ammonia and butyric acid in plug-flow reactor: Degradation kinetic modeling with contribution of mass transfer

Photocatalytic treatment of polluted air by odorous contaminants – ammonia and butyric acid – is investigated in a plug-flow reactor covered by non-woven fiber textile coated with TiO₂. For the first time, the single-component degradation pathway of ammonia by photocatalysis at ambient condition is highlighted. It appears fundamentally different compared to the butyric acid degradation pathway. The ammonia degradation pathway highlights a possible auto-accelerated behavior of the reaction. The chemical degradation kinetics follows the Langmuir–Hinshelwood model, though observed oxidation rates depend upon flow conditions in the reactor. Thus, interpretation of degradation results through a model considering the Langmuir–Hinshelwood approach and mass transfer phenomenon is presented. This model succeeds with a pair of determined kinetic constants and mass transfer coefficients to describe experimental results for different flow rates and for both pollutants, though they present wide dissimilarities in their degradation pathways.     

ZN-Graded Noncommutative Differential Calculus

We consider the algebra M _N (C) ofN × N matrices as a cyclic quantum plane.We also analyze the coaction of the quantum group F and the action of its dualquantum algebra H on it. Then we study the decomposition ofM _N (C) in termsof the quantum algebra representations. Finally, we develop the differential algebraof the cyclic group Z _N with d ^N = 0, where Z _N is viewed as the the subalgebraof diagonal N × N complex matrices, and treat the particularcase N = 3.