直觉Menger空间中的广义压缩映射原理及其在微分方程中的应用

利用Atanassov的思路,将直觉Menger空间定义为由Menger提出的Menger空间的自然推广.同时也得出一个新广义压缩映射,并运用该压缩映射证明了直觉Menger空间中微分方程解的存在性定理.     

Shear deformation plate continua of large double layered space structures

A simple method is presented to model large rigid-jointed lattice structures as continuous elastic media with couple stresses using energy equivalence. In our analysis the transition from the discrete system to the continuous media is achieved by expanding the displacements and the rotations of the nodal points in a Taylor series about a suitable chosen origin. The strain energy of the continuous media with couple stresses is then specialized to obtain shear deformation plate continua. Equivalent continua for single layered grids, double layered grids and three-dimensional lattices are then obtained.     

Sonochemical Synthesis of Gold Nanoparticles by Using High Intensity Focused Ultrasound

The sonochemical synthesis of gold nanoparticles (GNPs) with different shapes and size distributions by using high‐intensity focused ultrasound (HIFU) operating at 463 kHz is reported. GNP formation proceeds through the reduction of Au³⁺ to Au⁰ by radicals generated by acoustic cavitation. TEM images reveal that GNPs show irregular shapes at 30 W, are primarily icosahedral at 50 W and form a significant amount of nanorods at 70 W. The size of GNPs decreases with increasing acoustic power with a narrower size distribution. Sonochemiluminescence images help in the understanding of the effect of HIFU in controlling the size and shapes of GNPs. The number of radicals that form and the mechanical forces that are generated control the shape and size of the GNPs. UV/Vis spectra and TEM images are used to propose a possible mechanism for the observed effects. The results presented demonstrate, for the first time, that the HIFU system can be used to synthesise size‐ and shape‐controlled metal nanoparticles.     

Rapid preparative isolation of erythrocentaurin from Enicostemma littorale by medium‐pressure liquid chromatography,its estimation by high‐pressure thin‐layer chromatography,and its α‐amylase inhibitory activity

Erythrocentaurin is a relatively simple natural product present among the members of Gentianaceae. A preparative method for the isolation of erythrocentaurin from the ethyl acetate fraction of Enicostemma littorale using medium‐pressure liquid chromatography has been reported. The method consisted of a simple step gradient from 10 to 20% ethyl acetate in n‐hexane. Using a 70 × 460 mm Si60 column, this method is capable of processing 20 g of material in <3 h (purity ≈ 97%). The recovery of erythrocentaurin was 87.77%. Estimation of erythrocentaurin in extracts and fractions based on high‐pressure thin‐layer chromatography was carried out on silica gel 60 F₂₅₄ plates with toluene/ethyl acetate/formic acid (80:18:2 v/v/v) as the mobile phase. The densitometric analysis was performed at 230 nm. A well‐separated compact band of erythrocentaurin appeared at R_f 0.54 ± 0.04. The analytical method showed good linearity in the concentration range of 200–1500 ng/band with a correlation coefficient of 0.99417. The limits of detection and quantification were found to be ≈60 and ≈180 ng/band, respectively. Erythrocentaurin exhibited a concentration‐dependent α‐amylase inhibition (IC₅₀ 1.67 ± 0.28 mg/mL). The outcome of the study should be considered for pharmacokinetic and biotransformation studies involving E. littorale.     

Asymmetric Transfer Hydrogenation Catalyzed by Mesoporous MCM‐41‐Supported Chiral Ru‐Complex

Chiral N‐sulfonyldiamine was successfully anchored on mesoporous MCM‐41 silica. The MCM‐41‐supported chiral N‐sulfonyldiamine was used as an efficient heterogeneous chiral ligand in the asymmetric transfer hydrogenation of ketones. This heterogeneous system offered satisfactory enantioselectivities up to 94 % with excellent conversions.     

Liquid Chromatographic Determination of NSAIDs in Urine After Dispersive Liquid–Liquid Microextraction Based on Solidification of Floating Organic Droplets

An environmentally benign method of sample preparation based on dispersive liquid–liquid microextraction and solidification of floating organic droplets (DLLME-SFO) coupled with high-performance liquid chromatography with ultraviolet detection has been developed for analysis of non-steroidal anti-inflammatory drugs (NSAIDs) in biological fluids. A low-toxicity solvent was used to replace the chlorinated solvents commonly used in conventional DLLME. Seven conditions were investigated and optimized: type and volume of extraction solvent and dispersive solvent, extraction time, effect of addition of salt, and sample pH. Under the optimum conditions, good linearity was obtained in the range 0.01–10 µg mL⁻¹, with coefficients of determination (r ²) >0.9949. Detection limits were in the range 0.0034–0.0052 µg mL⁻¹ with good reproducibility (RSD) and satisfactory inter-day and intra-day recovery (95.7–115.6 %). The method was successfully used for analysis of diclofenac, mefenamic acid, and ketoprofen in human urine. Analysis of urine samples from a patient 2 and 4 h after administration of diclofenac revealed concentrations of 1.20 and 0.34 µg mL⁻¹, respectively.

     

Theoretical and experimental studies of ion imprinted polymer for nitrate detection

Molecular imprinting is an approach to synthesize receptors with specific molecular recognition properties. A computational method was carried out to study interaction between template and monomer in prepolymerization mixture. The functional monomer and template complexes were optimized, at the minimum energy confirmation using Austin Model 1 semi empirical method within Restricted Hartree Fock formalism. The theoretical results showed that allylthiourea (functional monomer) has the largest interaction energy towards template (sodium nitrate) with the mole ratio of 4 : 1; functional monomer : template. The resulting polymers were characterized using Fourier Transform infrared spectroscopy, thermogravimetry analysis and field emission scanning electron microscopy. Rebinding experiments were carried out to evaluate binding capacity of the polymer. The adsorption data of ion imprinted polymer (IIP) were fitted with Langmuir-Freundlich isotherm model. Pseudo-second order kinetic model was used to describe the kinetic adsorption behavior of IIP. The experimental binding result showed good agreement with theoretical computation and the IIP was further used for nitrate ion detection. The results of membrane optimization indicated that the sensor, which composed of 30% polyvinylchloride, 60% nitrophenyl octyl ether as a plasticizer, 2% sodium tetraphenyl borate, and 10% IIP as ionophore exhibited an almost Nernstian slope with the limit of detection 3.9 × 10^-6 M. The fabricated sensor had shown good potential in nitrate detection with wide linear range, low limit of detection and found to have good selectivity towards nitrate ion over other anion.     

Stochastic upscaling of random microstructures

In this work we present an upscaling technique for multi-scale computations based on random microstructures modelled as realisations of lognormally distributed random fields, or described by randomly distributed inclusions in a homogeneous matrix. Their corresponding coarse-scale model parameters are considered as uncertain, and are approximated by random variables, the distributions of which are obtained via polynomial chaos based Bayesian procedures in which the fine-scale energy is used as an observation. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Large Time Asymptotics with Error Estimates to Solutions of a Forced Burgers Equation

This article deals with a forced Burgers equation (FBE) subject to the initial function, which is continuous and summable on . Large time asymptotic behavior of solutions to the FBE is determined with precise error estimates. To achieve this, we construct solutions for the FBE with a different initial class of functions using the method of separation of variables and Cole–Hopf like transformation. These solutions are constructed in terms of Hermite polynomials with the help of similarity variables. The constructed solutions would help us to pick up an asymptotic approximation and to show that the magnitude of the difference function of the true and approximate solutions decays algebraically to 0 for large time.