Approximation of functions by means of a new generalized Bernstein operator

In this paper we first use a probabilistic method to construct a linear positive polynomial operatorL _{m, r} ^α,β Bernstein type, depending on a non-negative integer parameterr and on two real parameters α and β, such that 0≤α≤β. Then we investigate the approximation properties of this operator mapping into itself the Banach spaceC[0,1] of real-valued continuous functions on [0,1]. A special attention is accorded to the case of the operatorL _m,r=L _m,r ^0,0 . We prove that the remainder of the approximation formula of a functionfεC[0,1] byL _m,r f can be represented either by means of divided differences, or in an integral form, obtained by using a classical theorem of Peano. We give also an asymptotic estimate for this remainder. The operatorL _m,r enjoys the variation diminishing property—in the sense of I. J. Schoenberg [15]. By extending the known inequalities of T. Popoviciu [12] and G. G. Lorentz [7], we evaluate the orders of approximation in terms of the modulus of continuity of the functionf or of its derivative. In the last section of this paper we determine the point spectrum of the operatorL _m,r and , finally, we present a quadrature formula which can be constructed by means of this operator. Dedicated to Professor Aldo Ghizzetti on his 75th birthday     

Electrical Properties of Polyethylene Composites with Low Content of Neodymium

The effects of Neodymium (Nd) on the electrical properties of low density polyethylene in relation with morphological aspects are reported in this article. Scanning electron microscopy and optical microscopy revealed a quasi-uniform dispersion of Nd particles in polyethylene, both individual particles and clusters being observed. Contact angle measurements showed a decrease of contact angle values and, thus, of surface hydrophobicity, with the increase of Nd content. The addition of Nd in polyethylene determined the increase of electric permittivity and conductivity. The variation of permittivity was explained considering the influence of polar species (additives, oxidation products, neodymium oxide), highlighted by Fourier transform infrared analysis.     

Transverse susceptibility method in nanoparticulate magnetic media

Transverse susceptibility (TS) method is a reliable method for the determination of anisotropy in nanoparticulate media. To correctly evaluate the value of anisotropy in various modern nanostructured materials, a number of theoretical problems related to the method have to be well understood to avoid significant systematic errors. This paper presents the state of the art in the TS method which includes the expression for single domain particles with any type of anisotropy, the theoretical and micromagnetic, using Landau-Lifshitz-Gilbert (LLG) equation and stochastic LLG equation studies of the effects of ac field amplitude, inter-particle interactions, and magnetic relaxation. The problem of both real and imaginary parts of the TS signal is also discussed.     

OES monitoring of sequential deposition of C/W layers by PECVD/magnetron sputtering techniques

An innovative sequential plasma deposition method suitable for deposition of carbon/metal nanocomposite or multilayer films is presented. The method is based on cyclic exposure of a substrate, for predefined time intervals, to two totally independent plasma deposition sources, working in alternative sequences: magnetron sputtering (MS) for metal deposition and Plasma Enhanced Chemical Vapor Deposition (PECVD) for hydrogenated amorphous carbon (a-C:H) deposition. This paper presents a study of the a-C:H/W nanocomposite deposition method by optical emission spectroscopy (OES), focusing on identifying the useful wavelengths for optical monitoring of the process. On the basis of optical monitoring, the optimal pumping out and precursor gas admission conditions are established.     

Poly(2-hydroxyethyl methacrylate-co-dodecyl methacrylate-co-acrylic acid): synthesis,physico-chemical characterisation and nafcillin carrier

In the present study polymeric microbeads of poly(2-hydroxyethyl methacrylate-co-dodecyl methacrylate-co-acrylic acid) or p(HEMA-co-dDMA-co-AA) were synthesised and characterized through FT-IR and scanning electron microscopy (SEM); their swelling behavior against saline solution was explored and their in vitro cytotoxicity was evaluated. Further, in order to elucidate kinetic aspects regarding the ternary system p(HEMA-co-dDMA-co-AA), a mathematical model of the reactivity ratios of the comonomers in the terpolymer has been conceived and analyzed. An intensified tendency of AA units accumulation in the copolymer has been noticed, in spite of HEMA units, while dDMA conserves in the copolymer the fraction from the feed. Three compositions have been selected for nafcillin-loading and their in vitro release capacity was evaluated. The compositions of 80:10:10 and 75:10:15 M ratios appear suitable for further in vivo testing, in order to be used as drug delivery systems in the treatment of different osseous diseases.