Semigroup and Riesz transform for the Dunkl–Schrödinger operators

Semigroup Forum - Let $$L_k=-\Delta _k+V$$ be the Dunkl–Schrödinger operators, where $$\Delta _k=\sum _{j=1}^dT_j^2$$ is the Dunkl Laplace operator associated to the Dunkl operators...     

A characterization of be-critical trees

The b-chromatic number of a graph G is the largest integer k such that G admits a proper coloring with k colors for which each color class contains a vertex that has at least one neighbor in all the other $k?1$ color classes. A graph G is called $b_e$-critical if the contraction of any edge e of G decreases the b-chromatic number of G. The purpose of this paper is the characterization of all $b_e$-critical trees.     

Synthesis,characterization and optical properties of ZnO nanoparticles with controlled size and morphology

Zinc oxide monodispersed nanoparticles were synthesized using a modified polyol process without any requirement to use a catalyst or calcination step at high temperature. The morphology and the size of the resulting oxide particles were adjusted by using several synthesis parameters (temperature, alkaline ratio, hydrolysis ratio, etc.). The increasing of the alkaline ratio results in a great change of the elaborated particles morphology that evolved from irregular and anisotropic forms (conical, nanorod-like and elliptical) to spherical one. A growth mechanism of these particles was proposed on the basis of zincite crystal structure and the morphology evolution as a function of the synthesis parameters. The photoluminescence spectra show UV-excitonic and visible emission bands. The strongest intensity of the visible emission was observed in nanorod-like particles, which implies an increased fraction of oxygen vacancies in this sample. The rod-like particles with 1 μm length show the dominant UV-emission, which evidences their improved stoichiometry.     

Data completion via an energy error functional

We propose, in this Note, a new procedure for data completion based on the minimization of an energy like error functional. The efficiency of the proposed method is illustrated by a thermostatic application. To cite this article: S. Andrieux et al., C. R. Mecanique 333 (2005).     

Polypyrrole-coated poly(vinyl chloride) powder particles: surface chemical and morphological characterisation by means of X-ray photoelectron spectroscopy and scanning electron microscopy

Polypyrrole (PPy)-coated poly(vinyl chloride) (PVC) powder particles were prepared by the in situ chemical polymerisation of pyrrole in aqueous solutions in the presence of PVC powder particles. The PVC particles in suspension served as a hydrophobic substrate for the in situ polymerisation of pyrrole using iron chloride as the oxidising agent and sodium p-toluene sulfonate. In these conditions, tosylate-doped PPy (PPyTS) was obtained and chlorides were inserted as minor codoping species. In some cases, the pyrrole was polymerised after incubating the PVC particles with poly(N-vinyl pyrrolidone). Scanning electron microscope (SEM) micrographs showed that the PVC particles retained their initial, quasispherical shape after coating by PPy. At low magnification, the coated PVC particles appeared smooth, but at high magnification, they exhibited a decoration by elementary nanoparticles of about 200-nm size due to PPy bulk powder grains. Elemental analysis indicated a mass loading of PPy in the range 1–58% w/w. Specific surface analysis by X-ray photoelectron spectroscopy (XPS) resulted in the spectra of the PPy-coated PVC particles resembling those of bulk powder PPyTS even for low PPy mass loading. The surface fraction of PPy repeat units was found to vary in the 55–91% range. This result is consistent with the SEM observation of the PPy nanoparticles at the surface of PVC powder grains. However, despite the important loading of PPy, the XPS estimation of the overlayer thickness is in favour of a patchy coating rather than continuous coatings of PPy.     

Study of cascade showers generated by near-horizontal muons in the water Cherenkov detector with a dense array of optical modules

The method for reconstructing the cascade curve by the Cherenkov radiation in water of the NEVOD detector with a dense spatial array of optical modules is discussed. Cascades are generated by near-horizontal muons which are separated by the DECOR coordinate detector. The cascade curves and the cascade energy spectrum measured in an ～8000-hour measurement series are presented.     

Cyclosulfamides as Constraint Dipeptides: The Synthesis and Structure of Chiral Substituted 1,2,5-Thiadiazolidine 1,1-Dioxides: Evaluation of the Toxicity

A general synthesis for the preparation of chiral N-N′ substituted 1,2,5-thiadiazolidine 1,1-dioxides has been developed beginning with proteogenic amino acid, sulfuryl chloride, and dibromoethane. The selected chemistry and spectral properties of these compounds are examined. Overall, routes described are applicable to the synthesis of a variety of constrained dipeptidal sulfamides representing novel peptidomimetic scaffolds.     

Electron-deficient adduct site in the ring opening of methylcyclopentane (MCP) on tungsten-oxide-supported Pt,Ir and Pt–Ir catalysts

The activities of Pt/WO₂, Ir/WO₂ and Pt–Ir/WO₂ toward the conversion of methylcyclopentane (MCP) were investigated. The catalysts were prepared using impregnation and co-impregnation methods and were characterized by SEM, XRD, N₂-sorption and TEM investigations. The most active catalyst toward the conversion of MCP, irrespective of the temperature, was Ir/WO₂. The order of the reactivity was Ir/WO₂ > Pt–Ir/WO₂ > Pt/WO₂. Strong metal–support interactions (SMSI) were observed for all the catalysts over the entire investigated temperature range. At 400 °C, the Pt and Pt–Ir showed 100% selectivity toward ring-enlargement reactions associated with the presence of electron-deficient adduct sites on the reducible acidic WO₂ support. Ring opening occurred over all the catalysts in three positions, resulting in the formation of 2-methylpentane (2-MP), 3-methylpentane (3-MP), and n-hexane (n-H). Difficulty in breaking the secondary – tertiary carbon bonds was observed predominantly on the Ir catalyst, which opens the MCP ring via a selective mechanism.     

Bifurcation analysis of the HIV‐1 within host model

In this paper, a bifurcation solution's analysis is proposed for an HIV‐1 within the host model around its chronic equilibrium point, this is carried out based on Lyapunov–Schmidt approach. It is shown that the coefficient b, which represents the healthy CD4⁺ T‐cells growth rate, is a bifurcation parameter; this means that the rate of multiplication of healthy cells can have serious effects on the qualitative dynamical properties and structural stability of the infection evolution dynamics. Copyright © 2015 John Wiley & Sons, Ltd.     

Function vector synchronization based on fuzzy control for uncertain chaotic systems with dead‐zone nonlinearities

In this article, a fuzzy adaptive control scheme is designed to achieve a function vector synchronization behavior between two identical or different chaotic (or hyperchaotic) systems in the presence of unknown dynamic disturbances and input nonlinearities (dead‐zone and sector nonlinearities). This proposed synchronization scheme can be considered as a generalization of many existing projective synchronization schemes (namely the function projective synchronization, the modified projective synchronization, generalized projective synchronization, and so forth) in the sense that the master and slave outputs are assumed to be some general function vectors. To practically deal with the input nonlinearities, the adaptive fuzzy control system is designed in a variable‐structure framework. The fuzzy systems are used to appropriately approximate the uncertain nonlinear functions. A Lyapunov approach is used to prove the boundedness of all signals of the closed‐loop control system as well as the exponential convergence of the corresponding synchronization errors to an adjustable region. The synchronization between two identical systems (chaotic satellite systems) and two different systems (chaotic Chen and Lü systems) are taken as two illustrative examples to show the effectiveness of the proposed method. © 2015 Wiley Periodicals, Inc. Complexity 21: 234–249, 2016