A Sufficient Condition for Interolation by Functions in A~P(φ) (1

肖杰  赵大蕻 《数学季刊》1992,(4)

Normal Vietoris Implies Compactness: A Short Proof

One of the most celebrated results in the theory of hyperspaces says that if the Vietoris topology on the family of all nonempty closed subsets of a given space is normal, then the space is compact (Ivanova-Keesling-Velichko). The known proofs use cardinality arguments and are long. In this paper we present a short proof using known results concerning Hausdorff uniformities.     

Formation of highly substituted chiral cyclohexanone derivatives using a tandem conjugate addition/cyclisation

A tandem conjugate addition/cyclisation approach, that allows the synthesis of chiral highly substituted cyclohexanones and cyclohexenones, which is applicable to natural product syntheses has been developed.     

Acceleration of the DABCO-promoted Baylis-Hillman reaction using a recoverable H-bonding organocatalyst

It has been shown that catalytic amounts (20-40 mol %) of bis-aryl (thio)ureas greatly accelerate the DABCO-promoted Baylis-Hillman reaction between a range of aromatic aldehydes and methyl acrylate in the absence of solvent. These robust organocatalysts are superior mole per mole promoters of the reaction than either methanol or water and are recoverable in high yield after the reaction by column chromatography.     

Eikonal Approximation to 5D Wave Equations and the 4D Space-Time Metric

We apply a method analogous to the eikonal approximation to the Maxwell wave equations in an inhomogeneous anisotropic medium and geodesic motion in a three dimensional Riemannian manifold, using a method which identifies the symplectic structure of the corresponding mechanics, to the five dimensional generalization of Maxwell theory required by the gauge invariance of Stueckelberg's covariant classical and quantum dynamics. In this way, we demonstrate, in the eikonal approximation, the existence of geodesic motion for the flow of mass in a four dimensional pseudo-Riemannian manifold. These results provide a foundation for the geometrical optics of the five dimensional radiation theory and establish a model in which there is mass flow along geodesics. We then discuss the interesting case of relativistic quantum theory in an anisotropic medium as well. In this case the eikonal approximation to the relativistic quantum mechanical current coincides with the geodesic flow governed by the pseudo-Riemannian metric obtained from the eikonal approximation to solutions of the Stueckelberg–Schrödinger equation. The locally symplectic structure which emerges is that of a generally covariant form of Stueckelberg's mechanics on this manifold.     

Variation Preserving Extensions and Generalized Essential Variation

A mapping from a subset of the real axis to a metric space with finite generalized variation is shown to admit extension to a mapping of the whole real axis with the same variation. This result leads to characterization of the generalized essential variation of a mapping.     

Henry Reaction in Aqueous Media：Chemoselective Addition of Aldehydes

The chemoselective addition of aldehydes in aquoues medium was obtained under mild condition using improved Henry reaction.     

Monofunctionalised resorcinarenes

A convenient methodology for introducing single functional groups to the lower rim of resorcinarenes is described. The methodology allows for very convenient differential protection or derivatisation of the upper and lower rims, and a wide range of functional groups (alcohol, carboxylic acid, thiol, amine, carbamate, alkyl halide) can be incorporated as a single unit at the lower rim, opening up the way to further modification at this point and generally widening the scope for further utilising resorcinarenes. Furthermore, our approach has enabled us to link two resorcinarenes together to form novel resorcinarene dimers.     

Vinyl‐type polymerization of norbornene by nickel(II) bisbenzimidazole catalysts

Novel nickel(II) bisbenzimidazole complexes were prepared via a three‐step synthetic procedure consisting of aniline/diacid condensation, ligand N‐alkylation, and metal complexation. The complexes were characterized by X‐ray crystallography and found to possess a pseudotetrahedral geometry. Upon activation with methylaluminoxane, these nickel bisbenzimidazoles did not polymerize simple olefins (e.g., ethylene, propylene, and 1‐butene) but were found to carry out the rapid and efficient polymerization of norbornene. The polynorbornene products were characterized by gel permeation chromatography/light scattering, ¹³C NMR, and IR, and their Mark–Houwink and dn/dc parameters were determined. The molecular weights of the polynorbornenes were very high (weight‐average molecular weight = 587,000–797,000 g/mol). ¹³C NMR suggested that the polymerization occurred via vinyl addition (i.e., a 2,3‐linked polymer); no ring‐opened product was observed. Thermogravimetric analysis indicated that the polynorbornenes were stable up to 400 °C under nitrogen. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 2095–2106, 2003     

A Possibility for Studying Gravitational Properties of the Neutrino

We consider the effect that the gravitational field of a neutrino pulse radiated in the collapse of presupernova nuclei has on the observable optical radiation spectra of atoms at the supernova surface. We show that at the modern level of development of experimental methods, neutrino monitoring supplemented by optical monitoring of supernova candidates provides a unique possibility to check whether the Einstein equivalence principle is satisfied for neutrinos of each of the three types (electron, muon, and tau-lepton) and their antiparticles, to estimate the change of the gravitational potential at the surface of the star at the instant of the neutrino radiation pulse, and to obtain upper limits on the mass values of these neutrinos in a new way.