Infinite propagation speed of a weakly dissipative modified two-component Dullin–Gottwald–Holm system

We consider the infinite propagation speed of a weakly dissipative modified two-component Dullin–Gottwald–Holm (mDGH2) system. The infinite propagation speed is derived for the corresponding solution with compactly supported initial data that does not have compact support any longer in its lifespan.     

富里叶级数的收敛速度

对正弦和余弦富立叶级数,通过合并相邻同号项,使其重排成交错级数.讨论了重排形成的交错级数的敛散性.指出根据自变量x的不同取值,该交错级数可能是单调递减或周期递减的级数.按照莱布尼茨判定法提出了不同精度要求的级数项数的计算公式.选取一到三阶收敛的富立叶级数计算了不同比值精度及差值精度要求的级数项数.计算表明,在x的取值为2π的等分点时,富立叶级数的部分和随项数的增加单调地逼近其收敛值.在x的取值为其它点时,富立叶级数的部分和随项数的增加围绕收敛值上下变动,周期地逼近其收敛值.低收敛阶富立叶级数的收敛速度较慢.要达到0.01%的精度,一收敛阶富立叶级数需要数万项,二收敛阶富立叶级数也需要数百项.在不同计算点处,要达到相同的计算精度,需要的级数项数差别较大.     

ELECTRO-OPTICAL DETERMINATION OF α-FeOOH PARTICLE SIZES

Electric light scattering method is used for revealing the presence of aggregates in very diluted aqueous α-FeOOH suspensions. Three theoretical models are used for the geometrical form of aggregates. The comparison between the electro-optical results -theoretical and experimental - shows that even in the most diluted suspensions exist aggregates with irregular form. Using the comparison between electron microscopy and electro-optical results the geometric shape of the aggregates is determined.     

Mobile relays for enhanced broadband connectivity in high speed train systems

With the introduction of wireless modems and smart phones, the passenger transport industry is witnessing a high demand to ensure not only the safety of the trains, but also to provide users with Internet access all the time inside the train. When the Mobile Terminal (MT) communicates directly with the Base Station (BS), it will experience a severe degradation in the Quality of Service due to the path loss and shadowing effects as the wireless signal is traveling through the train. In this paper, we study the performance in the case of relays placed on top of each train car. In the proposed approach, these relays communicate with the cellular BS on one hand, and with the MTs inside the train cars on the other hand, using the Long Term Evolution (LTE) cellular technology. A low complexity heuristic LTE radio resource management approach is proposed and compared to the Hungarian algorithm, both in the presence and absence of the relays. The presence of the relays is shown to lead to significant enhancements in the effective data rates of the MTs. In addition, the proposed resource management approach is shown to reach a performance close to the optimal Hungarian algorithm.     

An asynchronous high‐speed synchrotron shutter

A high‐repetition‐rate mechanical shutter with asynchronous control and sub‐millisecond operation has been developed and tested for specialist X‐ray systems in the field of medical diagnostics and radiation therapy. Capacitor‐coupled linear voice coil actuators are utilized to achieve opening and closing speeds as fast as 700 µs for an aperture height of 4 mm. The design allows for asynchronous control, permitting slave operation of the shutter, a feature that is distinctly suitable for a number of applications including particle image velocimetry, where high‐frame‐rate operation must be accurately synchronized and triggered by the image acquisition sequence of the detector or timing device. The design and construction of the shutter also makes it ideal, with simple and limited modifications, for applications requiring larger apertures, in particular wide beams as found in many synchrotron beamlines.     

Green ultra‐fast high‐performance liquid chromatographic method using a short narrow‐bore column packed with fully porous sub‐2 μm particles for the simultaneous determination of selected pharmaceuticals as surface water and wastewater pollutants

Fast separations are very desirable in laboratories that analyze large numbers of samples per day or those needing short turn‐around times. Traditional HPLC methods using conventional stationary phases and standard column dimensions require significant amounts of organic solvents and generate large volumes of waste. With growing awareness about the environment, the development of green technologies has been receiving increasing attention. In this work, a very fast green analytical method based on LC‐UV using a short narrow bore column packed with fully porous sub‐2 μm particles has been developed for simultaneous determination of nine pharmaceuticals in wastewater and surface water. The chromatographic separation was optimized in order to achieve short analysis time and good resolution for all analytes in a single run. All analytes could be separated in 1 min with good resolution. Sample preparation was executed by solid phase extraction using Oasis HLB cartridges. The method developed was validated based on parameters such as linearity, precision, accuracy, detection, and quantification limits. The recovery ranged from 70.9 to 92.5% with SDs not higher than 5.4%, except for acetaminophen and sulphanilamide. LODs ranged from 0.6–2.5 μg/L, while the LOQs were in the range 2–8 μg/L.     

An efficient strategy for the extraction and purification of lignans from Schisandra chinensis by a combination of supercritical fluid extraction and high‐speed counter‐current chromatography

An efficient strategy for extracting and separating five lignans from Schisandra chinensis (Turcz.) Baill has been developed using supercritical fluid extraction (SFE) and high‐speed counter‐current chromatography (HSCCC) in the present study. First, the extraction was performed by a preparative SFE system under 15 MPa of pressure at 36°C for 4 h. Then, the SFE extract was successfully separated and purified by HSCCC with a two‐phase solvent system composed of n‐hexane/ethyl acetate/methanol/water (6:4:5:5, 6:4:6:4, 6:4:8:2, v/v) in a stepwise elution mode. The fractions were analyzed by HPLC, and the chemical structures of the products were identified by ESI‐MS and ¹H NMR spectroscopy. As a result, a total of 12.5 mg of schisandrin at 98.0% purity, 7.1 mg of gomisin A at 98.1% purity, 1.8 mg of schisantherin B at 93.3% purity, 4.4 mg of deoxyschisandrin at 92.9% purity, and 6.8 mg of γ‐schisandrin at 89.1% purity were obtained from 300 mg crude extract in a one‐step purification.     

Application of supercritical fluid extraction coupled with counter–current chromatography for extraction and online isolation of unstable chemical components from Rosa damascena

Supercritical fluid extraction (SFE) coupled with high‐speed counter‐current chromatography (HSCCC) was successfully used for the extraction and online isolation of the unstable compounds from Rosa damascene in a single extraction and separation operation in two stages. The solvent systems of SFE/HSCCC were optimized with the help of multiexponential function model. At the first stage, the upper phase of the solvent system of n‐butanol–tert‐butyl methyl ether–acetonitrile–0.1% aqueous TFA (1.7:1.0:0.8:4.0, v/v/v/v) was used as both the SFE entrainer and the HSCCC stationary phase, and the target compounds were eluted with the corresponding lower phase to separate the hydrophobic compounds. At the second stage, the upper phase of the solvent system of n‐hexane–ethyl acetate–methanol–water (3.2:1.0:2.8:2.6, v/v/v/v) was used as both the SFE entrainer and the HSCCC stationary phase, followed by elution with the corresponding lower phase to separate the moderate hydrophobic compounds. Six compounds including formononetin, delphinidin, cyaniding, 5,6,4′‐trihydroxy‐7,8‐dimethoxy flavone, 5,3′‐dihydroxy‐7,8‐dimethoxy flavone, and 5‐hydroxy‐6,7,8,3′,4′‐pentamethoxy flavone were successfully separated in one extraction–separation operation within 300 min. The targeted compounds were identified by MS and NMR spectroscopy. This research has opened up great prospects for industrial application of SFE/HSCCC to the extraction and separation of unstable compounds.     

Solvent‐Free Reactions of Fullerenes with Diethyl Bromomalonate in the Presence of Inorganic Bases Under High‐Speed Vibration Milling Conditions

Abstract

Solvent‐free reactions of C₆₀ and C₇₀ with diethyl bromomalonate in the presence of various inorganic bases were investigated under the high‐speed vibration milling (HSVM) conditions, and are shown to give methanofullerenes 1 and 2 in good to excellent yields based on consumed fullerenes. Several weak inorganic bases were found to be quite effective in promoting the solvent‐free mechanochemical Bingel reactions of C₆₀ and C₇₀ under the HSVM conditions. Among the studied bases, sodium acetate gave the highest yield of monoadducts, while potassium carbonate afforded a considerable amount of bisadducts for both C₆₀ and C₇₀.     

A simple fabrication method for tapered capillary tip and its applications in high‐speed CE and ESI‐MS

Fabrication of capillaries with tapered tips is an important technique that is required in many analytical chemistry areas, such as ESI‐MS, CE, electrochemical analysis, and microinjection. This paper describes a simple and effective grinding‐based fabrication method for capillaries with tapered tips. A novel grinding mode utilizing the combination of rotation and precession of an elastic capillary was developed, which significantly improved the controllability to the grinding process as well as the capillary tip shape. The capillary was fabricated by fixing it in an electric drill installed perpendicularly, and grind the capillary tip rotated around its own axis as well as the drill axis on sandpapers. Compared with conventional fabrication techniques for capillary tips, the present method is easy to control the capillary tip shape in routine laboratories without the requirement of expensive equipments or poisonous reagent (e.g. hydrofluoric acid (HF) solution). Various capillaries with different tip diameters and tip taper angles could be fabricated using the present method with good controllability and reproducibility. These capillaries were applied in high‐speed CE and ESI‐MS analysis to demonstrate the feasibility and potential of this fabrication method.