Solving a class of generalized fractional programming problems using the feasibility of linear programs

Abstract This article presents a new approximation algorithm for globally solving a class of generalized fractional programming problems (P) whose objective functions are defined as an appropriate composition of ratios of affine functions. To solve this problem, the algorithm solves an equivalent optimization problem (Q) via an exploration of a suitably defined nonuniform grid. The main work of the algorithm involves checking the feasibility of linear programs associated with the interesting grid points. It is proved that the proposed algorithm is a fully polynomial time approximation scheme as the ratio terms are fixed in the objective function to problem (P), based on the computational complexity result. In contrast to existing results in literature, the algorithm does not require the assumptions on quasi-concavity or low-rank of the objective function to problem (P). Numerical results are given to illustrate the feasibility and effectiveness of the proposed algorithm

Effect Of Nd-Doping On The Optical Properties Of Yttrium Aluminum Garnet Nanopowders

Nd-doped and Nd/Si-codoped yttrium aluminum garnet powders were synthesized via a solvothermal method using ethanol as the solvent. The photoluminescence spectra of the powders revealed that the intensity of the emission increased with Nd-doping concentration initially and then decreased with further increase in Nd concentration. The powder containing 3.5 atm% Nd exhibited the highest light emission intensity. The fluorescence lifetime of the yttrium aluminum garnet powders was also measured as a function of Nd-doping concentration. The results were fitted with an empirical equation. Copyright © 2008 American Scientific Publishers All rights reserved

Hydrothermal Synthesis of 1T-MoS2/Pelagic Clay Composite and Its Application in the Catalytic Reduction of 4-Nitrophenol

Pelagic clay is an emerging marine resource with strong hydrophilicity, fine particles and a large specific surface area. In this work, a 1T-MoS2/pelagic clay composite was fabricated by hydrothermal synthesis. In the composite, 1T-MoS2 nanosheets are evenly dispersed on the surface of the clay minerals, significantly reducing the agglomeration of MoS2. Compared with pure 1T-MoS2, the 1T-MoS2 nanosheets generated on the surface of pelagic clay have significantly smaller lateral dimensions and thicknesses. Moreover, the specific surface area is much larger than that of the pure 1T-MoS2 nanosheets fabricated by the same method, indicating that the active sites of the MoS2 sheets are fully exposed. In addition, the composite exhibited excellent hydrophilicity, leading to a high dispersibility in aqueous solutions. In this work, the composite was used as a catalyst in the reduction of 4-nitrophenol (4-NP), and the conversion of 4-NP reached up to 96.7%. This result shows that the 1T-MoS2/pelagic clay composite is a promising catalyst in a variety of reactions

Synthesis Of Nd/Si Codoped Yag Powders Via A Solvothermal Method

We report the synthesis of single-phased Nd/Si-doped yttrium aluminum garnet powder via a solvothermal method by using ethanol as the solvent. The obtained powder exhibits a spherical shape, no agglomeration, and an average particle size of ∼300 nm, suitable for conventional powder processing. The effect of heat treatment on the lattice parameter and optical properties of the powder is also studied. The results are discussed in terms of Nd/Si solubility. © 2006 The American Ceramic Society

A method for material decomposition and quantification with grating based phase CT.

Material decomposition (MD) is an important application of computer tomography (CT). For phase contrast imaging, conventional MD methods are categorized into two types with respect to different operation sequences, i.e., "before" or "after" image reconstruction. Both categories come down to two-step methods, which have the problem of noise amplification. In this study, we incorporate both phase and absorption (PA) information into MD process, and correspondingly develop a simultaneous algebraic reconstruction technique (SART). The proposed method is referred to as phase & absorption material decomposition-SART (PAMD-SART). By iteratively solving an optimization problem, material composition and substance quantification are reconstructed directly from absorption and differential phase projections. Comparing with two-step MD, the proposed one-step method is superior in noise suppression and accurate decomposition. Numerical simulations and synchrotron radiation based experiments show that PAMD-SART outperforms the classical MD method (image-based and dual-energy CT iterative method), especially for the quantitative accuracy of material equivalent atomic number