On polyhedral extension of some LP theorems

McLinden (Mathematical Programming 24 (1982) 162–176) has extended theorems of Tucker (1956) and Williams (1970) on the complementarity behaviour of feasible and optimal solutions to a pair of canonical linear programs to proper convex polyhedral functions. He achieved this by heavily using the well-developed machinery of convex analysis. In this note, we prove most of his results mainly using linear programming theory.     

A Note on Shadow Prices in Linear Programming

Using convex analysis and a characterization of the entire family of optimal solutions to an L.P., we show that in order to obtain shadow prices, one has to solve a much smaller L.P. derived from any optimal tableau. We then show that positive as well as negative shadow prices for any constraint or for any combination of constraints can easily be computed by parametric linear programming. Some examples exhibiting the method are also included.     

Deoxygenation and X-ray photoelectron studies on some quinoxalines and their N-oxides

Deoxygenation results of some quinoxaline dioxides with phosphorous trichloride are presented and compared with previous deoxygenations with other reagents. Differentiation between isomeric quinoxaline oxides using X-ray photoelectron spectroscopy is also discussed.     

Temperature dependence of transport characteristics of wurtzite GaN epilayers

We report electrical transport properties of intentionally and unintentionally doped wurtzite GaN epilayers within the temperature range of 3K up to 340 K. Specifically, temperature dependence of the carrier concentration, mobility and resistivity are investigated. Obtained data could only be explained on the basis of two-band model, namely, high mobility conduction band and low mobility impurity band. The threshold doping concentration for the dominance of the conduction band electrons is estimated to be about 10¹⁸ cm^–3.     

Experimental and theoretical studies on molecular structures and vibrational modes of novel compounds containing silver

The two novel silver containing complexes of N-(pyridin-2-yl)pyridin-2-amine (NDPA) molecule has been synthesized and characterized by elemental analysis, FT-Raman and FT-IR (at far and mid regions) spectroscopies. The optimized geometries of the compounds were obtained by using DFT/B3LYP method with LANL2DZ basis set for the (C₁₀H₉N₃) · AgNO₃ and B3LYP method with DGDZVP basis set for the (C₁₀H₉N₃) · AgClO₄. The vibrational frequencies and their IR and Raman intensities were determined by theoretical methods. In addition, the HOMO-LUMO energies, thermochemical properties and atomic charges for the complexes were obtained in same level of theory. The experimental and theoretical results show that the silver atoms are coordinated to ligands in bidentate fashion. In addition, in the structures of complexes there are intra-molecular interactions. The oxygen atoms of nitrate and perchlorate are bonded to ligand via hydrogen bonds.