On a functional equation related to derivations in prime rings

In this paper we prove the following result. Let m ≥ 1, n ≥ 1 be fixed integers and let R be a prime ring with m + n + 1 ≤ char(R) or char(R) = 0. Suppose there exists an additive nonzero mapping D : R → R satisfying the relation 2D(x ^n+m+1) = (m + n + 1)(x ^m D(x)x ⁿ + x ⁿ D(x)x ^m ) for all \({x\in R}\). In this case R is commutative and D is a derivation.     

Tip‐enhanced Raman spectroscopy using single‐crystalline Ag nanowire as tip

We report the surface‐enhanced Raman scattering (SERS) effect from the apex of single‐crystalline Ag nanowires (NWs). We also fabricated tip‐enhanced Raman spectroscopy (TERS) tips by attaching individual Ag NWs to W wires by using the alternating current dielectrophoresis (AC‐DEP) method. The single‐crystalline Ag NW tips could overcome many of the shortcomings of conventional TERS tips. Most importantly, the results obtained from TERS using single‐crystalline metal NWs are very reproducible, and the tips are also reusable. This development represents a significant progress in making TERS a reliable optical characterization technique with nanometer spatial resolution. Copyright © 2010 John Wiley & Sons, Ltd.     

Facile and Rapid Solid Phase Synthesis of Monodisperse Oligo（1, 4-phenyleneethynylene）s

An extremely facile and rapid solid phase route free of column chromatographic purification for the synthesis of the soluble monodisperse oligo(l, 4-phenyleneethynylene)s up to-60A was presented.     

Chemoselective Carbophilic Addition of α‐Diazoesters through Ligand‐Controlled Gold Catalysis

The chemoselective addition of arenes and 1,3‐diketones to α‐aryldiazoesters was achieved through ligand‐controlled gold catalysis. Unlike a dirhodium catalyst (which promotes C? H insertion and cyclopropanation) and a copper catalyst (which catalyzes O? H and N? H insertions), the gold catalyst with an electron‐deficient phosphite as the ancillary ligand exclusively gave the carbophilic addition product, thus representing a new and efficient approach to form “carbophilic carbocations”, which selectively react with carbon nucleophiles.     

Ultrafiltration liquid chromatography combined with high‐speed countercurrent chromatography for screening and isolating potential α‐glucosidase and xanthine oxidase inhibitors from Cortex Phellodendri

Cortex Phellodendri is a typical Chinese herb with a large number of alkaloids existing in all parts of it. The most common methods for screening and isolating alkaloids are mostly labor intensive and time consuming. In this study, a new assay based upon ultrafiltration liquid chromatography was developed for the rapid screening of ligands for α‐glucosidase and xanthine oxidase. The C. Phellodendri extract was found to contain two alkaloids with both α‐glucosidase‐ and xanthine oxidase binding activities and one lactone with α‐glucosidase‐binding activity. Subsequently, with the help of high‐speed countercurrent chromatography, the specific binding ligands including palmatine, berberine, and obaculactone with purities of 97.38, 96.12, and 96.08%, respectively, were successfully separated. An optimized low‐toxicity two‐phase solvent system composed of ethyl acetate/n‐butanol/ethanol/water (3.5:1.7:0.5:5, v/v/v/v) was used to isolate the three compounds mentioned above from C. Phellodendri. The targeted compounds were identified by liquid chromatography coupled with mass spectrometry and NMR spectroscopy. Therefore, ultrafiltration liquid chromatography combined with high‐speed countercurrent chromatography is not only a powerful tool for screening and isolating α‐glucosidase and xanthine oxidase inhibitors in complex samples but is also a useful platform for discovering bioactive compounds for the prevention and treatment of diabetes mellitus and gout.     

A note on local automorphisms

Let H be an infinite-dimensional almost separable Hilbert space. We show that every local automorphism of ℬ(H), the algebra of all bounded linear operators on a Hilbert space H, is an automorphism.     

Numerical Solution of Several Models of Internal Transonic Flow

The paper deals with numerical solution of internal flow problems. It mentions a long tradition of mathematical modeling of internal flow, especially transonic flow at our department. Several models of flow based on potential equation, Euler equations, Navier-Stokes and Reynolds averaged Navier-Stokes equations with proper closure are considered. Some mathematical and numerical properties of the model are mentioned and numerical results achieved by in-house developed methods are presented.     

Asymmetric total synthesis and structural elucidation of NFAT-68

Total synthesis of NFAT-68 (7) has been achieved and its relative stereochemistry has been determined. A key step thereof is the utilization of the chelation-controlled vinylogous Mukaiyama aldol reaction (VMAR) to stereoselectively synthesize the syn-aldol product 8. This developed chemistry is anticipated to have wider application in total syntheses of many other natural products.