Optimality and duality in nonsmooth multiobjective fractional programming problem with constraints

In this paper, we establish some quotient calculus rules in terms of contingent derivatives for the two extended-real-valued functions defined on a Banach space and study a nonsmooth multiobjective fractional programming problem with set, generalized inequality and equality constraints. We define a new parametric problem associated with these problem and introduce some concepts for the (local) weak minimizers to such problems. Some primal and dual necessary optimality conditions in terms of contingent derivatives for the local weak minimizers are provided. Under suitable assumptions, sufficient optimality conditions for the local weak minimizers which are very close to necessary optimality conditions are obtained. An application of the result for establishing three parametric, Mond–Weir and Wolfe dual problems and several various duality theorems for the same is presented. Some examples are also given for our findings.

     

GaP:Mg layers grown on GaN by MOCVD

We have investigated the growth of magnesium-doped GaP (GaP:Mg) layers on GaN by metalorganic chemical vapor deposition. The hole carrier concentration increased linearly from 0.8×10¹⁸ to 4.2×10¹⁸ cm⁻³ as the Bis(cyclopentadienyl) magnesium (Cp₂Mg) mole flow rate increased from 1.2×10⁻⁷ to 3.6×10⁻⁷ mol/min. However, the hole carrier concentration decreased when the CP₂Mg mole flow rate was further increased. The double crystal X-ray diffraction (DCXRD) rocking curves showed that the GaP:Mg layers were single crystalline at low CP₂Mg molar flow. However, the GaP:Mg layers became polycrystalline if the CP₂Mg molar flow was too high. The decrease in hole carrier concentration at high CP₂Mg molar flow was due to crystal quality deterioration of the GaP layer, which also resulted in the low hole mobility of the GaP:Mg layer.     

Quality assessment of Cortex Phellodendri by high‐performance liquid chromatography coupled with electrospray ionization mass spectrometry

A simple method based on liquid chromatography coupled with diode array detection and electrospray ionization mass spectrometry (LC‐DAD‐ESI‐MS) was developed for the quality assessment of Cortex Phellodendri (CP), which was mainly derived from two species of Phellodendron chinense Schneid and Phellodendron amurense Rupr. Total 41 compounds, including 14 phenols, 24 alkaloids and three liminoidal triterpenes were identified or tentatively characterized from the 75% methanol extract of CP samples by online ESI‐MSⁿ fragmentation and UV spectra analysis. Among them, two phenols and six alkaloids were simultaneously quantified using HPLC‐DAD method. The validated HPLC‐DAD method showed a good linearity, precision, repeatability and accuracy for the quantification of eight marker compounds. Furthermore, the plausible fragmentation pathway of the representative compounds were proposed in the present study. The differences of the chemical constituents content and the comprehensive HPLC profiles between the two CP species using LC‐DAD‐ESI‐MS method are reported for the first time, indicating that the CP drugs from different resources should be used separately in the clinic. Copyright © 2009 John Wiley & Sons, Ltd.     

Synthesis of a magnetic micro/nano Fe x O y -CeO2 composite and its application for degradation of hexachlorobenzene

A micrometer-sized nanostructured, magnetic, ball-like Fe _x O _y -CeO₂ composite was synthesized through an ethylene-glycol mediated process. The synthesized samples were characterized by scanning electron microscopy combined with energydisperse X-ray analysis, transmission electron microscopy and X-ray powder diffraction. In the synthesis system, polyethylene glycol (PEG) and urea were found to play significant roles in the formation of the micrometer-sized spherical architecture of the precursor. The details of morphology and particle size could be changed with the initial concentration of Fe(NO₃)₃·9H₂O and Ce(NO₃)₃·6H₂O as the reactants. The magnetic Fe _x O _y -CeO₂ composite with a similar morphology was readily obtained by calcination from the precursor. The characterization of transmission electron microscopy showed the calcined ball-like architecture was a highly porous structure consisting of many nanoparticles. Because of the micrometer-sized nanostructure and the multi-components as well as the magnetism, the as-obtained Fe _x O _y -CeO₂ composite showed better activity and potentially easy recovery for the harmless degradation of hexachlorobenzene (HCB).     

Cascade synthesis of substituted 4-amino-1,2,4-triazol-3-ones from aldehyde hydrazones and azodicarboxylates

Substituted 4-amino-1,2,4-triazol-3-ones were synthesized from aldehyde hydrazones and azodicarboxylates in the presence of triphenylphosphine. The cascade reaction was conducted in a single step and the procedure is general and efficient.     

关于中心原子杂化轨道数的计算方法

对于HmABn型的共价分子（或离子），本文提出用公式G=V／2-3n计算中心原子A的杂化轨道数，并由此确定对应的杂化轨道类型。该方法简单、直接、有效。     

无损贮存及涨罐饱和相热力学模型研究

在低温液体无损贮存及涨罐研究方面,经常采用一种假设容器内气、液相均为饱和相的热力学模型.这种模型比较符合实际,并能够大大简化容器内的热力学状态,是一种比较常用的热力学模型.文中利用一个5m3低温贮罐进行的液氮无损贮存及涨罐试验,对该热力学模型进行了对比研究,讨论了饱和相热力学模型误差产生的原因,对于无损贮存和涨罐研究具...     

Miscible blends of nitro‐substituted polybenzimidazole and polyetherimide

A novel blend system was prepared by blending organosoluble nitro‐substituted polybenzimidazole (NO₂‐PBI) and polyetherimide (PEI) in a cosolvent at a moderate condition. It was shown that the NO₂‐PBI/PEI blends not only possess tractable processability owing to the enhanced solubility of NO₂‐PBI but also retain the desirable features of unmodified PBI/PEI blends. Apparent miscibility in the blends was observed and attributed to hydrogen‐bonding interactions between N? H groups in NO₂‐PBI and carbonyl groups in PEI. It was revealed that the NO₂‐PBI/PEI blends phase‐separate upon heating above the glass‐transition temperatures. The observed mixing of NO₂‐PBI and PEI in a molecular level, although sustainable only in the glassy region, was shown to lend synergy effects to the physical properties of the blends. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 1778–1783, 2001