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.     

Mathematical assessment of a fractional-order vector–host disease model with the Caputo–Fabrizio derivative

Vector–host diseases outbreak is a major public health concern, and it has greatly affected human health and economy in various regions around the globe. Different approaches have been adopted to investigate the dynamical behavior and possible control of these diseases. In this study, we present a compartmental transmission model in order to explore the dynamics of vector–host infectious diseases. The saturated incidence rate instead of bilinear (or standard) and saturated treatment function is considered in model formulation which enhance the biological suitability of the proposed model. We first formulate the model based on nonlinear classical integer-order differential equations. Then, the proposed integer-order model is reformulated using the fractional-order operator in Caputo–Fabrizio sense with nonsingular kernel. We investigate the model equilibria and evaluate the expression for the most important threshold parameter known as the basic reproduction number. Furthermore, the existence and uniqueness are presented via the fixed point approach. Additionally, using an efficient numerical scheme, the iterative solution of the model is obtained. Finally, we present the model simulations to illustrate the impact of arbitrary fractional order and some of other important parameters involved in the model on the disease dynamics and minimization.     

A high accuracy minimally invasive regularization technique for navier–stokes equations at high reynolds number

A method is presented, that combines the defect and deferred correction approaches to approximate solutions of Navier–Stokes equations at high Reynolds number. The method is of high accuracy in both space and time, and it allows for the usage of legacy codes a frequent requirement in the simulation of turbulent flows in complex geometries. The two‐step method is considered here; to obtain a regularization that is second order accurate in space and time, the method computes a low‐order accurate, stable, and computationally inexpensive approximation (Backward Euler with artificial viscosity) twice. The results are readily extendable to the higher order accuracy cases by adding more correction steps. Both the theoretical results and the numerical tests provided demonstrate that the computed solution is stable and the accuracy in both space and time is improved after the correction step. We also perform a qualitative test to demonstrate that the method is capable of capturing qualitative features of a turbulent flow, even on a very coarse mesh. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 814–839, 2017     

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.     

Hille’s non-oscillation theorem and the decay of solutions to a class of semi-linear PDE’s

With a change of perspective in Hille’s paper on oscillation [Trans. Amer. Math. Soc. 64 (1948), 234–252], we provide optimal integral conditions for an application of the method of sub-solutions and super-solutions to investigating the existence of solutions for the semi-linear elliptic equation in the euclidean space , n ≥ 3, that decay to zero as . Received: 26 October 2006     

Modification of Crosslinked Poly(styrene) Based Polymers for Boron-Specific Extraction

A new polymeric resin with glucose sulfonamide functions has been prepared for the extraction of boric acid. This poly (styryl sulfonamide) based resin has been demonstrated to be an efficient sorbent for the removal of boron. The resin had a boron loading capacity of 2.365 mmol.g⁻¹ and showed reasonably rapid sorption ability. Splitting of sorbed boron can be achieved by simple acid leaching (2M H₂SO₄).