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.     

Thermal parameters associated to micellization of dodecylpyridinium bromide and chloride in aqueous solution

Electrical conductivity of aqueous solutions of dodecylpyridinium chloride and bromide have been determined. From these data the critical micelle concentration (cmc) was determined. The thermal properties as standard Gibbs free energy, enthalpy and entropy of micellization was estimated from a uncharged-phase separation model and enables to obtain another properties like heat capacity of micellization and the relevant parameters in the minimum of temperature dependence of cmc. The enthalpy-entropy compensation was shown for the studied compounds. This revised version was published online in July 2006 with corrections to the Cover Date.     

In solution sensitization of Er(III) luminescence by the 4-tetrathiafulvalene-2,6-pyridinedicarboxylic acid dimethyl antenna ligand

In the [Er(hfac)(3)(L)](2) complex (1) (L = 4-tetrathiafulvalene-2,6-pyridinecarboxylic acid dimethyl ester), the Er(III) ion is bonded to the tridentate coordination site. Electrochemical and photophysical measurements in solution reveal that the tetrathiafulvalene moiety is a versatile antenna for erbium luminescence sensitization at 6540 cm(-1) upon excitation in the low-energy charge transfer transition (donor to acceptor charge transfer) at 16600 cm(-1) assigned via time-dependent density functional theory calculations.     

Scattering from non-overlapping potentials. I. General formulation

The problem of scattering from an assembly of non-overlapping spherical potentials is solved in partial-wave basis for each of the constituent potentials. The resulting scattering operator is a quotient of two infinite matrices and depends on “on-shell” partial wave amplitudes of the individual potentials. It suggests in general a truncation scheme which essentially considers only those partial waves effective for each collision at the given energy. The multiple-scattering series is recovered and limiting cases of low energy and high energy are considered. Applications to high-energy scattering of elementary particles on nuclei are briefly discussed.     

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).     

Overview of \boldsymbol{\bar{K} N} and \boldsymbol{\bar{K}}-nucleus dynamics

The main features of coupled-channel ${\bar K}N$ dynamics near threshold and its repercussions in few-body $\bar K$ -nuclear systems are briefly reviewed highlighting the I?=?1/2 ${\bar K}NN$ system. For heavier nuclei, the extension of mean-field calculations to multi- $\bar K$ nuclear quasibound states is discussed focusing on kaon condensation.     

Bilevel problems over polyhedra with extreme point optimal solutions

Bilevel programming involves two optimization problems where the constraint region of the upper level problem is implicitly determined by another optimization problem. In this paper we focus on bilevel problems over polyhedra with upper level constraints involving lower level variables. On the one hand, under the uniqueness of the optimal solution of the lower level problem, we prove that the fact that the objective functions of both levels are quasiconcave characterizes the property of the existence of an extreme point of the polyhedron defined by the whole set of constraints which is an optimal solution of the bilevel problem. An example is used to show that this property is in general violated if the optimal solution of the lower level problem is not unique. On the other hand, if the lower level objective function is not quasiconcave but convex quadratic, assuming the optimistic approach we prove that the optimal solution is attained at an extreme point of an ??enlarged?? polyhedron.