一类极限为1的未定式

对于一类00型或∞0型未定式，给出其极限为1的一个充分条件，并通过实例展示其应用。     

关于全国大学生数学竞赛决赛试题的解析与思考

本文对二道全国大学生数学竞赛决赛试题(数学类)给予了诠释与解析.     

Side-lobeless far-field spectrum of a short pulse from a circular aperture with Gaussian form of transmittance

The spectrum change of a Gaussian pulse in the far field is studied with the Fresnel diffraction integral when it is incident on an aperture with Gaussian form transmittance. It is found that the side-lobes of the diffracted spectral intensity, which exist in a normal circular aperture with unit transmittance, can be eliminated completely under such a condition. Also, the red shift and blue shift of the spectral intensity maximum of the incident pulse are presented.     

Associating divisors with quadratic differentials on Klein surfaces

We extend the notion and basic properties of quadratic differential divisors to a Klein surface, using the corresponding form’s divisors from the double cover of the Klein surface.     

Challenge to ultra-trace analytical techniques of nuclear materials in environmental samples for safeguards at JAERI: methodologies for physical and chemical form estimation

From a viewpoint of physical and chemical form estimation, ultra-trace analytical techniques of nuclear materials in environmental samples for safeguards have been investigated at Japan Atomic Energy Research Institute. This article deals with (1) an outline of the developed techniques for bulk and particle analyses of uranium and plutonium in the safeguards environmental samples; (2) current R&D on techniques relating to estimation of the physical and chemical form, such as SEM images and EDX spectra for fine particles of nuclear materials and fission track observation applicable to fissile materials; and (3) possible analytical methodologies, as future works, applicable to ultra-trace amounts of nuclear materials in environmental samples.     

Bifurcation analysis of a diffusive predator–prey system with a herd behavior and quadratic mortality

In this paper, a diffusive predator–prey system, in which the prey species exhibits herd behavior and the predator species with quadratic mortality, has been studied. The stability of positive constant equilibrium, Hopf bifurcations, and diffusion‐driven Turing instability are investigated under the Neumann boundary condition. The explicit condition for the occurrence of the diffusion‐driven Turing instability is derived, which is determined by the relationship of the diffusion rates of two species. The formulas determining the direction and the stability of Hopf bifurcations depending on the parameters of the system are derived. Finally, numerical simulations are carried out to verify and extend the theoretical results and show the existence of spatially homogeneous periodic solutions and nonconstant steady states. Copyright © 2014 John Wiley & Sons, Ltd.     

Transition-metal-free synthesis of (Z)-3-ylidenephthalides from 2-acyl-benzoic acids

We report a highly efficient method for the synthesis of (Z)-3-ylidenephthalides via intramolecular cyclization of readily available 2-acyl-benzoic acids mediated by TSTU at room temperature. Using this method, diversely substituted (Z)-3-ylidenephthalides have been generated in good to excellent yields. The application of the method is highlighted by gram-scale preparation of the antiplatelet drug n-butylphthalide.     

Rhenium complex-catalyzed coupling reaction of enol acetates with alcohols

The reaction of enol acetates with alcohols in the presence of a catalytic amount of a rhenium complex, such as ReBr(CO)₅, produced the corresponding ketones and aldehydes in moderate to good yields. It was suggested that the preparation of an ether, an intermolecular dehydrated product, was the first step of the reaction.     

A Novel Solid Nanocrystals Self-Stabilized Pickering Emulsion Prepared by Spray-Drying with Hydroxypropyl-β-cyclodextrin as Carriers

A drug nanocrystals self-stabilized Pickering emulsion (NSSPE) with a unique composition and microstructure has been proven to significantly increase the bioavailability of poorly soluble drugs. This study aimed to develop a new solid NSSPE of puerarin preserving the original microstructure of NSSPE by spray-drying. A series of water-soluble solid carriers were compared and then Box-Behnken design was used to optimize the parameters of spray-drying. The drug release and stability of the optimized solid NSSPE in vitro were also investigated. The results showed that hydroxypropyl-β-cyclodextrin (HP-β-CD), rather than solid carriers commonly used in solidification of traditional Pickering emulsions, was suitable for the solid NSSPE to retain the original appearance and size of emulsion droplets after reconstitution. The amount of HP-β-CD had more influences on the solid NSSPE than the feed rate and the inlet air temperature. Fluorescence microscopy, confocal laser scanning microscopy and scanning electron microscopy showed that the reconstituted emulsion of the solid NSSPE prepared with HP-β-CD had the same core-shell structure with a core of oil and a shell of puerarin nanocrystals as the liquid NSSPE. The particle size of puerarin nanocrystal sand interfacial adsorption rate also did not change significantly. The cumulative amount of released puerarin from the solid NSSPE had no significant difference compared with the liquid NSSPE, which were both significantly higher than that of puerarin crude material. The solid NSSPE was stable for 3 months under the accelerated condition of 75% relative humidity and 40 °C. Thus, it is possible todevelop the solid NSSPE preserving the unique microstructure and the superior properties in vitro of the liquid NSSPE for poorly soluble drugs.