A note on the nucleolus for 2-convex TU games

For 2-convex n-person cooperative TU games, the nucleolus is determined as some type of constrained equal award rule. Its proof is based on Maschler, Peleg, and Shapley’s geometrical characterization for the intersection of the prekernel with the core. Pairwise bargaining ranges within the core are required to be in equilibrium. This system of non-linear equations is solved and its unique solution agrees with the nucleolus.     

Facile synthesis of complicated 9,9-diarylfluorenes based on BF3.Et2O-mediated Friedel-Crafts reaction

[reaction: see text] BF3.OEt2-mediated Friedel-Crafts reaction of 9-phenyl-fluoren-9-ol with electron-rich aromatic substrates to prepare a new family of complicated 9,9-diarylfluorenes is described. The 9,9-diarylfluorenes tethered with various functional substituents, e.g., bulky spiro units, hole-transporting moieties, and fluorescent dyes, will be promising building blocks for the construction of optoelectronic materials.     

Markov skeleton process in PERT networks

In this article, we investigate Programming Evaluation and Review Technique networks with independently and generally distributed activity durations. For any path in this network, we select all the activities related to this path such that the completion time of the sub-network (only consisting of all the related activities) is equal to the completion time of this path. We use the elapsed time as the supplementary variables and model this sub-network as a Markov skeleton process, the state space is related to the sub-network structure. Then use the backward equation to compute the distribution of the sub-network's completion time, which is an important rule in project management and scheduling.     

Permanence and periodic solutions for a class of delay Nicholson’s blowflies models

This paper covers the dynamic behaviors for a class of Nicholson’s blowflies models with a nonlinear density-dependent mortality term. By using inequality analyze technique and coincidence degree theory, some sufficient conditions are determined that guarantee the permanence of the model and the existence of positive periodic solutions. Moreover, we give an example to illustrate our main results.     

Observation of the growth of carbon nanotubes prepared at low temperature

Lack of information during the growth of carbon nanotubes has hindered efforts to understand the growth mechanism of these unique nanoscale structures. Here, we report that Multi‐walled carbon nanotubes with bamboo‐shaped structure may be synthesized by solvothermal method at 300°C using benzene as carbon source and Zn as catalyst. We have obtained direct experimental information on the growth under Transmission electron microscopy. It has been shown that all the compartments of bamboo‐like tube successively joined leading to the formation of regularly segmented nanobamboos. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Screening and isolation of cyclooxygenase‐2 inhibitors from Trifolium pratense L. via ultrafiltration,enzyme‐immobilized magnetic beads,semi‐preparative high‐performance liquid chromatography and high‐speed counter‐current chromatography

Nonsteroidal anti‐inflammatory drugs reportedly reduce the risk of developing cancer. One mechanism by which they reduce carcinogenesis involves the inhibition of the activity of cyclooxygenase‐2, an enzyme that is overexpressed in various cancer tissues. Its overexpression increases cell proliferation and inhibits apoptosis. However, selected cyclooxygenase‐2 inhibitors can also act through cyclooxygenase‐independent mechanisms. In this study, using ultrafiltration, enzyme‐immobilized magnetic beads, high‐performance liquid chromatography, and electrospray‐ionization mass spectrometry, several isoflavonoids in Trifolium pratense L. extracts were screened and identified. Semi‐preparative high‐performance liquid chromatography and high‐speed counter‐current chromatography were then applied to separate the active constituents. Using these methods, seven major compounds were identified in Trifolium pratense L. As cyclooxygenase‐2 inhibitors: rothindin, ononin, daidzein, trifoside, pseudobaptigenin, formononetin, and biochanin A, which were then isolated with >92% purity. This is the first report of the presence of potent cyclooxygenase‐2 inhibitors in Trifolium pratense L. extracts. The results of this study demonstrate that the systematic isolation of bioactive components from Trifolium pratense L., by using ultrafiltration, enzyme‐immobilized magnetic beads, semi‐preparative high‐performance liquid chromatography, and high‐speed counter‐current chromatography, represents a feasible and efficient technique that could be extended for the identification and isolation of other enzyme inhibitors.     

High-resolution photorefractive gratings in nematic liquid crystals sandwiched with photoconductive polymer film

Photorefractive gratings with high grating resolution were observed in the 20 μm thick low-molar-mass nematic liquid crystal (NLC) cell with a separate photoconductive (PC) poly(N-vinylcarbazole) layer. An orientational grating with a grating spacing of 1.9 μm was produced. It is believed that a space–charge field with small fringe spacing forms in the PC layer and its evanescent component penetrates into the NLC layer. The penetrated evanescent field drives the NLC to reorient, and consequently the orientational grating forms. The model indicates that the modulated field exists in several hundred nanometers near the surface, and thus the orientational grating is not full of the NLC film, which is consistent with the observed phenomena of the multiple diffractions. Besides, asymmetric two-beam coupling of 11.2% was achieved for the grating with a grating spacing of 1.9 μm, and a net gain coefficient of larger than 62 cm⁻¹ was obtained.     

Transmission property for a one-dimensional photonic crystal containing a subwavelength layer and a nonlinear layer

Using the transfer matrix method, we investigate the transmission property of a one-dimensional photonic crystal doped with a linear subwavelength layer and a Kerr-type nonlinear layer. We find that a thin film of subwavelength layer can significantly modify the characteristic of optical bistability. We also find that the sequence of the thin film and the nonlinear layer has a major impact on the hysteretic behavior. With the investigations to the linear defect mode and the electric field distribution in the nonlinear material, we explain these phenomena. PACS 42.65.Pc; 42.25.Bs; 42.70.Qs; 42.65.-k; 78.66.-w     

Structural change of laser-irradiated Ge2Sb2Te5 films studied by electrical property measurement

Sheet resistance of laser-irradiated Ge₂Sb₂Te₅ thin films prepared by magnetron sputtering was measured by the four-point probe method. With increasing laser power the sheet resistance undergoes an abrupt drop from 10⁷ to 10³ Ω/□ at about 580 mW. The abrupt drop in resistance is due to the structural change from amorphous to crystalline state as revealed by X-ray diffraction (XRD) study of the samples around the abrupt change point. Crystallized dots were also formed in the amorphous Ge₂Sb₂Te₅ films by focused short pulse laser-irradiated, the resistivities at the crystallized dots and the non-crystallized area are 3.375 × 10^?3 and 2.725 Ω m, sheet resistance is 3.37 × 10⁴ and 2.725 × 10⁷ Ω/□ respectively, deduced from the I–V curves that is obtained by conductive atomic force microscope (C-AFM).