A note on “A LP-based heuristic for a time-constrained routing problem”

In their paper, Avella et al. (2006) investigate a time-constrained routing problem. The core of the proposed solution approach is a large-scale linear program that grows both row- and column-wise when new variables are introduced. Thus, a column-and-row generation algorithm is proposed to solve this linear program optimally, and an optimality condition is presented to terminate the column-and-row generation algorithm. We demonstrate by using Lagrangian duality that this optimality condition is incorrect and may lead to a suboptimal solution at termination.     

PEPPSI-Pd-NHC catalyzed Suzuki-Miyaura cross-coupling reactions in aqueous media

A series of unsymmetrical 1,3-disubstituted benzimidazolium chlorides were synthesized as N-heterocyclic carbene (NHC) precursors. These compounds were used to synthesize of the PEPPSI-type palladium NHC complexes. The structures of all compounds were characterized by ¹H NMR, ¹³C NMR, FT-IR spectroscopy and elemental analyses. The catalytic activity of the PEPPSI-type palladium–NHC complexes has been evaluated with respect to the Suzuki-Miyaura cross-coupling reactions of phenyl boronic acid with various aryl halides in aqueous media.     

Anticancer activities of manganese-based photoactivatable CO-releasing complexes (PhotoCORMs) with benzimidazole derivative ligands

Carbon monoxide is an important signaling molecule which is produced by heme oxygenase-1. CO shows antiproliferative activity against cancer cells; hence, activation of HO-1 is a significant inhibition strategy against tumor formation and survival of cancer cells. In this work, manganese-based CO-releasing molecules (CORMs) were designed and synthesized to inhibit breast cancer cell proliferation. Human invasive ductal breast cancer cells (MCF-7) were treated with the synthesized CORMs to investigate the effect of the complexes on breast cancer survival under UV light. In vitro experiments indicated that the complexes inhibited breast cancer cell proliferation, and further, the antiproliferative effects were increased under UV light. Thus, these novel CORMs may provide a drug template for the treatment of invasive ductal breast cancer.     

Surface wave scattering by a material filled rectangular impedance groove in a reactive plane

The problem of TE-polarized surface wave scattering from a rectangular impedance groove located on an infinite reactive plane which is filled with dielectric material is considered for a rather general case where the impedances of the horizontal and vertical sides of the groove have different values. The multiple interactions up to the second order between the edges of the groove are obtained to yield diffracted field. The diffraction problem is first reduced into a modified Wiener-Hopf equation and then solved approximately. The solution contains branch-cut integrals and two infinite sets of constants satisfying two infinite systems of linear algebraic equations. The approximate analytical evaluations of the corresponding integrals as well as the numerical solutions of the linear algebraic equation systems are obtained for various values of the parameters such as the surface reactance of the guiding plane, the vertical and horizontal wall impedances of the groove, the permittivity of the material loading, the width and the height of the groove which permit one to study the effect of these parameters on the diffraction phenomenon.     

Hot-air drying of purslane (Portulaca oleracea L.)

Drying characteristics of purslane was experimentally studied in a cabinet dryer. The experimental drying data were fitted best to Modified Henderson and Pabis and Midilli et al. models apart from other models to predict the drying kinetics. The effective moisture diffusivity varied from 1.12 × 10^?9 to 3.60 × 10^?9 m²/s over the temperature range studied and activation energy was 53.65 kJ/mol.     

Palladium(II)?NHC complexes containing benzimidazole ligand as a catalyst for C?N bond formation

The reaction of 2‐(2‐bromoethyl)‐1,3‐dioxane with 1‐alkylbenzimidazole derivatives results in the formation of the new benzimidazolium salts (1). The reaction of Pd(OAc)₂ with 1,3‐dialkylbenzimidazolium salts (1a–c) yields palladium N‐heterocyclic carbene (NHC) complexes (2a–c). All synthesized compounds were characterized by ¹H NMR, ¹³ C NMR, IR and elemental analysis techniques which support the proposed structures. As catalysts, these new palladium complexes offer a simple and efficient methodology for the synthesis of triarylamines and secondary amines from anilines and amines and in a single step with potassium tertiary butoxide as a base. Copyright © 2010 John Wiley & Sons, Ltd.     

Tauberian theorems for Abel limitability method

This paper addresses conditions for the Abel method of limitability to imply convergence and subsequential convergence.      

On geometric interpretations of split quaternions

Quaternions are an important tool that provides a convenient and effective mathematical method for representing reflections and rotations in three-dimensional space. A unit timelike split quaternion represents a rotation in the Lorentzian space. In this paper, we give some geometric interpretations of split quaternions for lines and planes in the Minkowski 3-space with the help of mutual pseudo orthogonal planes. We classified mutual planes with respect to the casual character of the normals of the plane as follows; if the normal is timelike, then the mutual plane is isomorphic to the complex plane; if the normal is spacelike, then the plane is isomorphic to the hyperbolic number plane (Lorentzian plane); if the normal is lightlike, then the plane is isomorphic to the dual number plane (Galilean plane).