Voronovskaja-Type Results in Compact Disks for Quaternion q-Bernstein Operators, q ≥ 1

Attaching to a compact disk [`(\mathbbD<sub>r</sub>)]{\overline{\mathbb{D}_{r}}} in the quaternion field \mathbbH{\mathbb{H}} and to some analytic function in Weierstrass sense on [`(\mathbbD_r)]{\overline{\mathbb{D}_{r}}} the so-called q-Bernstein operators with q ≥ 1, Voronovskaja-type results with quantitative upper estimates are proved. As applications, the exact orders of approximation in [`(\mathbbD_r)]{\overline{\mathbb{D}_{r}}} for these operators, namely \frac1n{\frac{1}{n}} if q = 1 and \frac1qⁿ{\frac{1}{q^{n}}} if q > 1, are obtained. The results extend those in the case of approximation of analytic functions of a complex variable in disks by q-Bernstein operators of complex variable in Gal (Mediterr J Math 5(3):253–272, 2008) and complete the upper estimates obtained for q-Bernstein operators of quaternionic variable in Gal (Approximation by Complex Bernstein and Convolution-Type Operators, 2009; Adv Appl Clifford Alg, doi:, 2011).     

Ultrasound influence upon calcium carbonate precipitation on bacterial cellulose membranes

The effect of ultrasonic irradiation (40 kHz) on the calcium carbonate deposition on bacterial cellulose membranes was investigated using calcium chloride (CaCl₂) and sodium carbonate (Na₂CO₃) as starting reactants. The composite materials containing bacterial cellulose-calcium carbonate were characterized by means of scanning electron microscopy (SEM), X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FTIR) and color measurements. The polymorphs of calcium carbonate that were deposited on bacterial cellulose membranes in the presence or in the absence of ultrasonic irradiation were calcite and vaterite. The morphology of the obtained crystals was influenced by the concentration of starting solutions and by the presence of ultrasonic irradiation. In the presence of ultrasonic irradiation the obtained crystals were bigger and in a larger variety of shapes than in the absence of ultrasounds: from cubes of calcite to spherical and flower-like vaterite particles. Bacterial cellulose could be a good matrix for obtaining different types of calcium carbonate crystals.     

Transfer of actinide ion at the interface between aqueous and nitrobenzene solutions studied by controlled-potential electrolysis at the interface

A novel electrochemical method based on controlled-potential electrolysis has been developed for the elucidation of the ion transfer at the interface between two immiscible electrolyte solutions (ITIES). A relationship between the applied interfacial potential (E_app) and the amount of the ion transferred (A_tr) was investigated after an electrolytic equilibrium was attained by controlled-potential electrolysis. The A_tr was determined chemically or radiometrically instead of by current measurement. It was found that (i) controlled-potential electrolysis was applicable to the study of the transfer of such hydrophilic ions as transition metal ions which gave no appreciable current within the potential window in voltammetry or polarography at ITIES, (ii) controlled-potential electrolysis in combination with a sensitive analytical method enabled a study of the transfer reaction of an ion of very dilute concentration, and (iii) even when the transfer reaction of an ion was irreversible or quasi-reversible, a standard ion transfer potential could be determined by controlled-potential electrolysis without using a kinetic parameter. The controlled-potential electrolysis method developed was applied to the transfer reactions of actinide ions such as UO₂ ²⁺ and Am³⁺ from aqueous solution to nitrobenzene solution in the absence or presence of an ionophore facilitating the transfer. The Gibbs energy for the transfer of actinide ion and a stability constant of the complex between an actinide ion and the ionophore in nitrobenzene solution were determined from log D versus E_app plots (D the ratio of the concentration of the ion in nitrobenzene solution to that in aqueous solution). The feasibility of controlled-potential electrolysis as a method for electrolytic separation of actinide ions is discussed.     

Symmetries of Taub-NUT Dual Metrics

In this paper we study the symmetries of thedual Taub-nut metrics. Generic and non-genericsymmetries of dual Taub-nut metrics are investigated.The existence of the Runge-Lenz type symmetry isanalyzed for dual Taub-nut metrics. We find that in somecases the symmetries of the dual metrics are the samewith the symmetries of Taub-nut metric.     

A note on the value of zero-sum sequential repeated games with incomplete information

We consider repeated two-person zero-sum games with lack of information on both sides. If the one shot game is played sequentially, it is proved that the sequencev _n is monotonic,v _n being the value of then shot game. Moreover the speed of convergence is bounded byK/n, and this is the best bound.     

Riemannian submersions from almost contact metric manifolds

In this paper we obtain the structure equation of a contact-complex Riemannian submersion and give some applications of this equation in the study of almost cosymplectic manifolds with Kähler fibres.     

Kropina metrics and Zermelo navigation on Riemannian manifolds

The present paper studies globally defined Kropina metrics as solutions of the Zermelo’s navigation problem. Moreover, we characterize the Kropina metrics of constant flag curvature showing that up to local isometry, there are only two model spaces of them: the Euclidean space and the odd-dimensional spheres.     

Approximation by a Durrmeyer-type operator in compact disks

In this paper, the exact order of simultaneous approximation and Voronovskaja kind results with quantitative estimate for a new type of complex Durrmeyer polynomials, attached to analytic functions in compact disks are obtained. In this way, we put in evidence the overconvergence phenomenon for this kind of Durrmeyer polynomials, namely the extensions of approximation properties with exact quantitative estimates, from the real interval [0, 1] to compact disks in the complex plane.     

Inflation and integrable one‐field cosmologies embedded in rheonomic supergravity

In this paper we show that the new approach to the embedding of the inflationary potentials into supergravity, presented in a quite recent paper [11] of Ferrara, Kallosh, Linde and Porrati can be formulated within the framework of standard matter coupled supergravity, without the use of the new minimal auxiliary set and of conformal compensators. The only condition is the existence of a translational Peccei Quinn isometry of the scalar Kähler manifold. We suggest that this embedding strategy based on a nilpotent gauging amounts to a profound Copernican Revolution. The properties of the inflaton potential are encoded in the geometry of some homogeneous one‐dimensional Kähler manifolds that now should be regarded as the primary object, possibly providing a link with microscopic physics. We present a simple and elegant formula for the curvature of the Kähler manifold in terms of the potential. Most relevant consequence of the new strategy is that all the integrable potentials quite recently classified in a paper [7] that we have coauthored, are automatically embedded into supergravity and their associated Kähler manifolds demand urgent study. In particular one integrable potential that provides the best fit to PLANCK data seems to have inspiring geometrical properties deserving further study.     

Nanotopography Engineering on Homopolymeric Surfaces Using Cold Plasma Generated Charges

Summary : Cold plasma as source for charged particles was used to induce nanotopographies on homopolymeric surfaces (nylon 12, PMMA, PMA, etc.). Hydrogen and helium plasmas were successfully used for surface nanoengineering of polymers using inductively coupled or atmospheric pressure non-equilibrium barrier discharge reactors. AFM analyses reveal the presence of nanotopographies on the treated surfaces. Physical factors control the process below the T_g and chemical factors dominate the process above T_g. Pyrolysis GC/MS analyses have been performed in order to obtain more information about the plasma processes. Cold plasma chemical processes, including charges effects are discussed as tools that open-up new ways for nanoengineering of the polymers' surfaces with specific functionalities and / or topography. Future nanomanufacturing techniques can generate anti-scratch, superhydrophobic or superhydrophilic properties on surface of every day use polymeric products by simple and convenient plasma enhanced processes.