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.     

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.     

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.     

Vibrations Action of the Trilling Machine MA750 on the Human Operator Hand

The Work includes identifying and analyzing vibrations produced by a trilling machine MA750 within space work. To identify vibration is used a special method, which has not been used so far in identifying vibrations, with the action on the human body. For obtaining a very good identification of the human body vibrations has been used the Moiré projection method. General conditions were applied to human hand operator during working hours on a trilling machine, with different speeds of main shaft. In the paper are presented successively two methods of measuring the vibrations: the Moiré projection method and conventional method of measuring the vibrometer. The results in the booth situation (classical measurements and Moiré projection method) were in the same order of the unit scale, and the optical method named Moiré projection method can be considered a valid method for the human vibrations measurements without touch of the surface. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)