一类矩阵多项式的秩特征

给出了一类矩阵多项式的秩特征定理及它的多种证法.     

Multilinear interpolation between adjoint operators

Multilinear interpolation is a powerful tool used in obtaining strong-type boundedness for a variety of operators assuming only a finite set of restricted weak-type estimates. A typical situation occurs when one knows that a multilinear operator satisfies a weak L^q estimate for a single index q (which may be less than one) and that all the adjoints of the multilinear operator are of similar nature, and thus they also satisfy the same weak L^q estimate. Under this assumption, in this note we give a general multilinear interpolation theorem which allows one to obtain strong-type boundedness for the operator (and all of its adjoints) for a large set of exponents. The key point in the applications we discuss is that the interpolation theorem can handle the case q?1. When q>1, weak L^q has a predual, and such strong-type boundedness can be easily obtained by duality and multilinear interpolation (cf. Interpolation Spaces, An Introduction, Springer, New York, 1976; Math. Ann. 319 (2001) 151; in: Function Spaces and Applications (Lund, 1986), Lecture Notes in Mathematics, Vol. 1302, Springer, Berlin, New York, 1988; J. Amer. Math. Soc. 15 (2002) 469; Proc. Amer. Math. Soc. 21 (1969) 441).     

A novel synthesis of 5-perfluorophenyl 4,5-dihydro-1H-pyrazoles in THF or water

5-Perfluorophenyl 4,5-dihydro-1H-pyrazoles were synthesized from 1,3-dipolar cycloaddition reaction of perfluorobenyl 2,4,6-triisopropylbenzenesulfonylhydrazone and α,β-unsaturated carbonyl compounds or acrylonitrile in THF or water. It was worthy to note that better results were obtained when water was employed as the solvent, which was considered as an effective, economic and environmentally friendly method to synthesize these pyrazole derivatives.     

Estimation of growth rate in unidirectionally solidified multicrystalline silicon by the growth-induced striation method

Multicrystalline silicon was grown by unidirectional solidification method using the accelerated crucible rotation technique. The application of the accelerated crucible rotation technique in unidirectional solidification method induced growth striations across the axial direction of the grown crystal. This striation pattern was observed from carbon concentration distribution, obtained by using Fourier transform infrared spectroscopy. The generated striation pattern was found to be weak and discontinuous. Some striations were absent, probably due to back melting, caused during each crucible rotation. From the growth striations and applied time period in crucible rotation, the growth rate was estimated by using Fourier transformation analysis.     

Eu- and Yb-induced reconstructions on a vicinal Si(1 0 0) surface

Early stages of rare-earth metal (Yb and Eu) growth on a vicinal, single-domain Si(1 0 0)2 × 1 surface have been studied in the coverage range of 0.1-0.3 monolayer (ML) by low energy electron diffraction, scanning tunneling microscopy, and synchrotron radiation photoemission spectroscopy. We show that Yb induces the 2 × 3 periodicity in the whole range of coverage studied. The 2 × 3 reconstruction coexists with the local 3 × 2/4 × 2 structure at about 0.2 ML of Yb. In contrast, Eu forms the 3 × 2 periodicity at 0.1-0.2 ML, whereas this structure is converted into the 2 × 3 phase at about 0.3 ML. The atomic arrangement and electronic properties of these reconstructions and the adsorbate-mediated modification of surface morphology are investigated.     

Gorenstein代数上的Hopf代数作用

令H是有限维Hopf代数，A是左H-模代数。本文证明了A是Gorenstein代数的充分必要条件。A^H也是Gorenstein代数的条件。它是Enochs EE,GarciaJJ和del RioA关于群作用相应的理论的推广，同时给出A/A^H是Frobenius扩张的条件。     

Stationary entanglement between macroscopic mechanical oscillators

We show that the optomechanical coupling between an optical cavity mode and two movable cavity mirrors is able to entangle two different macroscopic oscillation modes of the mirrors. This continuous variable entanglement is maintained by the light bouncing between the mirrors and is robust against thermal noise. In fact, it could be experimentally demonstrated using present technology. Received 2 September 2002 / Received in final form 10 October 2002 Published online 7 January 2003     

Synthesis and conformational investigation of tetrapeptide analogues of the fragment B23-B26 of insulin

Tetrapeptides containing one of a set of four different α,α-dialkyl glycines at the C-terminus were synthesized by conventional methods in solution and their conformational behavior investigated by ¹H NMR spectroscopy in connection with molecular mechanics calculations. The results were consistent with conformations stabilized by a γ-turn in the case of compounds with alkyl groups larger than methyl, while the corresponding Aib derivative did not exhibit intramolecular hydrogen bonding.     

The glow curve structure for the LiF:Mg,Cu,Na,Si TL detector with dopants concentrations and sintering temperatures

The glow curve structures for LiF:Mg,Cu,Na,Si TL detectors with various dopant concentrations and sintering temperatures were investigated for the improvement of the glow curve structure and sensitivity of the TL detector. The dopant concentrations were varied over the following ranges: Mg (0–0.25 mol%), Cu (0–0.07 mol%), Na and Si (0–1.5 mol%). With increasing Cu concentration, the intensity of the main peak was intensified and reached a maximum at a concentration of 0.05 mol%. The high-temperature peak was reduced. The dependency of the main peak intensity on the Mg concentration exhibits a sharp maximum at 0.2 mol%. The intensity of the high-temperature peak tends to rise slightly with increasing Mg concentration. It was found that the optimum concentrations of the dopants in the LiF:Mg,Cu,Na,Si TL material are Mg: 0.2 mol%, Cu: 0.05 mol%, Na and Si: 0.9 mol%. The dependency of the main peak intensity on sintering temperature exhibits a very sharp maximum at 830°C. The high-temperature peak was rapidly reduced after 825°C.     

Synthesis and association of poly(N,N‐dimethylacrylamide) copolymers with perfluorocarbon pendent groups connected through polyethylene‐glycol tethers

The synthesis is reported of copolymers of N,N‐dimethylacrylamide (DMA) and methacrylates containing 2,2′‐dihydroperfluorodecanoyl (RF) groups separated from the methacrylate by long polyethylene glycol (PEG) tether groups (between 1000 and 14,000 Da). At concentrations of between 1 and 8 wt % the copolymers with macromonomer contents of 1 mol % or less give gels in organic solvents such as dioxane, THF, or methanol, as well as in water. Given the low molecular weights, this indicates very efficient association of very low numbers of RF groups. Association and gel formation is enormously enhanced in the presence of longer PEG tethers. This is consistent with smaller poly(N,N,‐dimethylacrylamide) (PDMA) intermolecular excluded volume effects that are mediated by the longer PEG tethers and possibly by the incompatibility of PEG and PDMA that may lead to the formation of PEG microdomains. This increases the local concentrations of the RF groups in the PEO domains that are not diluted by the PDMA chains, as would be the case in the absence of PEG tethers. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 360–373, 2004