Statistical approximation theorems by k-positive linear operators

In this paper, using A-statistical convergence we obtain various approximation theorems by means of k-positive linear operators defined on the space of all analytic functions on the unit disk. Received: 17 February 2005     

On the algebraic construction of chemistry from quantum mechanics. A fundamental valency vector field defined on the euclidean 3-space and its relation to the Hilbert space

To obtain from quantum mechanics directly the qualitative deductions of chemistry, a mathematical machinery is set up. A single vector space, and a dyad space relate different molecules or spatial configurations of an isomeric set of atoms to each other. Different electronic Hamiltonians belong to the dyad space and are treated so as to be used directly without the intermediary of orbitals, parameter choices, or variational calculations.     

Problems for Ordinary Differential Equations with Transmission Conditions

We investigate a boundary-functional problem with transmission conditions for ordinary differential-operator equation in Sobolev spaces with a weight. We prove an isomorphism, coerciveness with respect to the spectral parameter, completeness and Abel basis of a system of root functions of the problem. Obtained results in the article are new even in case of Sobolev spaces without the weight.     

Valid inequalities based on simple mixed-integer sets

In this paper we use facets of simple mixed-integer sets with three variables to derive a parametric family of valid inequalities for general mixed-integer sets. We call these inequalities two-step MIR inequalities as they can be derived by applying the simple mixed-integer rounding (MIR) principle of Wolsey (1998) twice. The two-step MIR inequalities define facets of the master cyclic group polyhedron of Gomory (1969). In addition, they dominate the strong fractional cuts of Letchford and Lodi (2002).     

Models for capacitated lot-sizing problem with backlogging,setup carryover and crossover

Setup operations are significant in some production environments. It is mandatory that their production plans consider some features, as setup state conservation across periods through setup carryover and crossover. The modelling of setup crossover allows more flexible decisions and is essential for problems with long setup times. This paper proposes two models for the capacitated lot-sizing problem with backlogging and setup carryover and crossover. The first is in line with other models from the literature, whereas the second considers a disaggregated setup variable, which tracks the starting and completion times of the setup operation. This innovative approach permits a more compact formulation. Computational results show that the proposed models have outperformed other state-of-the-art formulation.     

Selenium speciation in dill (Anethum graveolens L.) by ion pairing reversed phase and cation exchange HPLC with ICP-MS detection

In the present work, speciation of selenium in dill (Anethum graveolens L.), supplemented with sodium selenite during its growth, was performed using ion pairing reversed phase and cation exchange chromatography. Heptafluorobutyric acid (HFBA) was used as the ion-pairing agent in reversed phase chromatography. In cation exchange chromatography, two different gradient programs were employed for the identification of selenospecies using pyridinium formate as the mobile phase. Low molecular weight selenocompounds were extracted from root, stem and dill leaf with 0.1 M HCl. Enzymatic digestion was used for the extraction of selenospecies related to high molecular weight compounds. The chromatograms obtained from different parts of the plant revealed major differences in the type of selenospecies as well as their concentrations. The major selenospecies found in different parts of the plant is Se-methyl-selenocysteine (MeSeCys). Another major Se species identified is Se-methyl-selenomethionine (MeSeMet), which has the highest relative concentration in the root indicating possible Se volatilization from that part of the plant. Selenomethionine (SeMet) is present in minor quantities in all parts of the plant.     

Approximation by nonlinear integral operators via summability process

In this paper, we study the approximation properties of nonlinear integral operators of convolution-type by using summability process. In the approximation, we investigate the convergence with respect to both the variation semi-norm and the classical supremum norm. We also compute the rate of approximation on some appropriate function classes. At the end of the paper, we construct a specific sequence of nonlinear operators, which verifies the summability process. Some graphical illustrations and numerical computations are also provided.