Grauert’s line bundle convexity,reduction and Riemann domains

We consider a convexity notion for complex spaces X with respect to a holomorphic line bundle L over X. This definition has been introduced by Grauert and, when L is analytically trivial, we recover the standard holomorphic convexity. In this circle of ideas, we prove the counterpart of the classical Remmert’s reduction result for holomorphically convex spaces. In the same vein, we show that if H⁰(X,L) separates each point of X, then X can be realized as a Riemann domain over the complex projective space Pⁿ, where n is the complex dimension of X and L is the pull-back of O(1).     

New O-Aryl-Carbamoyl-Oxymino-Fluorene Derivatives with MI-Crobicidal and Antibiofilm Activity Enhanced by Combination with Iron Oxide Nanoparticles

Antimicrobial resistance is one of the major public health threats at the global level, urging the search for new antimicrobial molecules. The fluorene nucleus is a component of different bioactive compounds, exhibiting diverse pharmacological actions. The present work describes the synthesis, chemical structure elucidation, and bioactivity of new O-aryl-carbamoyl-oxymino-fluorene derivatives and the contribution of iron oxide nanoparticles to enhance the desired biological activity. The antimicrobial activity assessed against three bacterial and fungal strains, in suspension and biofilm growth state, using a quantitative assay, revealed that the nature of substituents on the aryl moiety are determinant for both the spectrum and intensity of the inhibitory effect. The electron-withdrawing inductive effect of chlorine atoms enhanced the activity against planktonic and adhered Staphylococcus aureus, while the +I effect of the methyl group enhanced the anti-fungal activity against Candida albicans strain. The magnetite nanoparticles have substantially improved the antimicrobial activity of the new compounds against planktonic microorganisms. The obtained compounds, as well as the magnetic core@shell nanostructures loaded with these compounds have a promising potential for the development of novel antimicrobial strategies.     

Liquid crystal properties resulting from synergetic effects between non-mesogenic organic molecules and a one nanometre sized octahedral transition metal cluster

This work presents the synthesis and studies of a red-NIR luminescent liquid crystal compound based on an octahedral metallic cluster core orthogonally bounded to six non-mesogenic organic ligands. It evidences synergetic effects between the organic and inorganic parts of the hybrid, resulting in the generation of liquid crystal properties on cooling from the isotropic melt.     

Radiation induced grafting of acrylic acid onto extruded polystyrene surface

Polystyrene materials with good solubility in liquid scintillation cocktails are used to wipe off different types of surfaces in order to determine the tritium removable contamination with the help of a liquid scintillation counter. This paper analyses hydrophilic surface modifications by radiation induced grafting of acrylic groups onto extruded polystyrene plates. Two grafting methods were used: (a) exposure of extruded polystyrene plates, immersed in aqueous acrylic acid solution, to a gamma radiation of a Co-60 source, and (b) exposure of extruded polystyrene plates to a Co-60 source, followed by the immersion of extruded polystyrene plates in aqueous acrylic acid solution. The grafting of acrylic was proved by IR spectrometry and by radiometric methods using acrylic acid labelled with tritium.     

Investigation of thermal decomposition of yttrium–aluminum-based precursors for YAG phosphors

Three types of precursors were prepared using the wet-chemical synthesis route, starting from yttrium?Ceuropium?Caluminum nitrate solution and different precipitating agents (urea, oxalic acid, and ammonium carbonate). The precursors were fired at 1200?°C in nitrogen atmosphere in order to obtain europium-doped yttrium aluminate Y₃Al₅O₁₂:Eu³⁺ phosphor with garnet structure (YAG:Eu). The processes involved in the thermal decomposition of precursors and their composition were put in evidence using thermal analysis (TG?CDTA) and FT-IR spectroscopy. The GA?CDTA curves possess typical features for basic-oxalate, -nitrate, and -carbonates as formed with oxalic acid, urea, and ammonium carbonate, respectively. Correlation between the thermal decomposition steps, mass loss, and composition of gases evolved during the thermal treatment was established using TG?CDTA?CFT-IR coupling. It was found that the different composition of precursors reflects on the luminescent characteristics of the corresponding phosphors. Urea and ammonium carbonate lead to the formation of YAG type phosphors, with garnet structure and specific red emission. As for the oxalic acid, this precipitating agent generates a non-homogeneous powder that contains yttrium oxide as impurity phase. This phosphor is a mixture of Y₂O₃:Eu³⁺, Y₄Al₂O₉:Eu³⁺, and Y₃Al₅O₁₂:Eu³⁺ that explain the relative higher emission intensity.     

Commutator Criteria for Magnetic Pseudodifferential Operators

The gauge covariant magnetic Weyl calculus has been introduced and studied in previous works. We prove criteria in terms of commutators for operators to be magnetic pseudodifferential operators of suitable symbol classes; neither the statements nor the proofs depend on a choice of a vector potential. We apply this criteria to inversion problems, functional calculus, affiliation results and to the study of the evolution group generated by a magnetic pseudodifferential operator.     

A minimum principle for a soap film problem in {\mathbb{R}^{2}}

In this note, we investigate the problem of a thin extensible film (a soap film), under the influence of gravity and surface tension, supported by the contour of a given strictly convex smooth domain Ω. Our main result is a minimum principle for an appropriate combination of u(x) and ${\left\vert \nabla u\left( \mathbf{x}\right) \right\vert }$ , that is, a kind of P-function in the sense of Payne (see the book of Sperb in Maximum Principles and Their Applications. Academic Press, New York, 1981), where u(x) is the solution of our problem. As an application of this minimum principle, we obtain some a priori estimates for the surface represented by the thin extensible film, in terms of the curvature of ${\partial \Omega}$ . The proofs make use of Hopf’s maximum principles, some topological arguments regarding the local behavior of analytic functions and some computations in normal coordinates with respect to the boundary ${\partial \Omega }$ .     

Algebra Structures Arising from Yang–Baxter Systems

Yang–Baxter operators from algebra structures appeared for the first time in [11 D?sc?lescu , S. , Nichita , F. ( 1999 ). Yang–Baxter operators arising from (co)algebra structures . Comm. Algebra 27 : 5833 – 5845 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar], 22 Nichita , F. ( 1999 ). Self-inverse Yang–Baxter operators from (co)algebra structures . J. Algebra 218 : 738 – 759 .[Crossref], [Web of Science ®] , [Google Scholar], 23 Nuss , P. ( 1997 ). Noncommutative descent and non-abelian cohomology . K-Theory 12 ( 1 ): 23 – 74 .[Crossref] , [Google Scholar]]. Later, Yang–Baxter systems from entwining structures were constructed in [8 Brzeziński , T. , Nichita , F. F. ( 2005 ). Yang–Baxter systems and Entwining Structures . Comm. Algebra 33 : 1083 – 1093 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]]. In fact, Yang–Baxter systems are equivalent with braid systems. In this paper we show that braidings and entwinings of various algebraic structures—in particular, algebra factorisations—can be constructed from a braid system, whence from a Yang–Baxter system as well.     

Schatten–von Neumann norm inequalities for two-wavelet localization operators associated with β-Stockwell transforms

In this article we define two-wavelet localization operators corresponding to an irreducible and square-integrable representation of a locally compact Hausdorff group on a Hilbert space. The group structure admitting an irreducible and square-integrable representation which is related to β-Stockwell transform, that we shall use in this article β?∈?R have been introduced in Boggiatto et al. [P. Boggiatto, C. Fernandez, and A. Galbis, A group representation related to the Stockwell transform, Indiana Univ. Math. J. 58(5) (2009), pp. 2277–2296]. The Schatten–von Neumann norm inequalities of these two-wavelet localization operators are established. The traces and the trace class norm inequalities of the trace class two-wavelet localization operators are given.     

Universal Upper Bound for the Growth of Artin Monoids

In this paper we study the growth rates of Artin monoids, and we show that 4 is a universal upper bound. We also show that the generating functions of the associated right-angled Artin monoids are given by families of Chebyshev polynomials. Applications to Artin groups and positive braids are given.