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1.
We establish a self-improving property of the Hardy inequality and an estimate on the size of the boundary of a domain supporting a Hardy inequality.
2.
A Radial Uniqueness Theorem for Sobolev Functions 总被引:1,自引:0,他引:1
We show that continuous functions u in the Sobolev space , 1 < p n, which have the limitzero in a certain weak sense in a set of positive p-capacityon B with
where B is the open unit ball of Rn and
for 0 > > , are identically zero. Conversely, we produce for each 1 > p n and each positive a non-constant function u in , continuous in , and a compact set EB of positive p-capacity such that u = 0 in E and the aboveinequality holds with exponent p l + . 相似文献
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6.
RITVA LINDBERG GORAN SUNDHOLM JOHAN SJö BLOM PETRI AHONEN ESKO I. KAUPPINEN 《Journal of Dispersion Science and Technology》2013,34(1-2):715-722
The zeta-potentials of silica, copper, platinum and gold particles have been measured as a function of pH. The isoelectric points were found to be at pH 3.0, 5.8, 3.0 and 3.5, respectively. In the pH range 3.0 to 5.8 copper and silica particles are oppositely charged and accordingly the coating of silica with copper particles could be demonstrated. In the case of gold and platinum the sign of the charge is such that direct adhesion to silica particles cannot be expected and this was also demonstrated in the case of platinum. 相似文献
7.
We prove an essentially sharp estimate in terms of generalized Hausdorff measures for the images of boundaries of Hölder domains under continuous Sobolev mappings, satisfying suitable Orlicz–Sobolev conditions. This estimate marks a dimension gap, which was first observed in [2] for conformal mappings. 相似文献
8.
Kristopher M. Koskela Stephen J. Quiton Shaama Mallikarjun Sharada Travis J. Williams Richard L. Brutchey 《Chemical science》2022,13(11):3208
Oxide dissolution is important for metal extraction from ores and has become an attractive route for the preparation of inks for thin film solution deposition; however, oxide dissolution is often kinetically challenging. While binary “alkahest” systems comprised of thiols and N-donor species, such as amines, are known to dissolve a wide range of oxides, the mechanism of dissolution and identity of the resulting solute(s) remain unstudied. Here, we demonstrate facile dissolution of both bulk synthetic and natural mineral ZnO samples using an “alkahest” that operates via reaction with thiophenol and 1-methylimidazole (MeIm) to give a single, pseudotetrahedral Zn(SPh)2(MeIm)2 molecular solute identified by X-ray crystallography. The kinetics of ZnO dissolution were measured using solution 1H NMR, and the reaction was found to be zero-order in the presence of excess ligands, with more electron withdrawing para-substituted thiophenols resulting in faster dissolution. A negative entropy of activation was measured by Eyring analysis, indicating associative ligand binding in, or prior to, the rate determining step. Combined experimental and computational surface binding studies on ZnO reveal stronger, irreversible thiophenol binding compared to MeIm, leading to a proposed dissolution mechanism initiated by thiol binding to the ZnO surface with the liberation of water, followed by alternating MeIm and thiolate ligand additions, and ultimately cleavage of the ligated zinc complex from the ZnO surface. Design rules garnered from the mechanistic insight provided by this study should inform the dissolution of other bulk oxides into inks for solution processed thin films.Oxide dissolution is important for metal extraction from ores and has become an attractive route for the preparation of inks for thin film solution deposition; however, oxide dissolution is often kinetically challenging. 相似文献
9.
Koskela H Kilpeläinen I Heikkinen S 《Journal of magnetic resonance (San Diego, Calif. : 1997)》2003,164(2):228-232
A new pulse sequence, long-range CPMG-adjusted heteronuclear single quantum coherence (LR-CAHSQC), is proposed for the determination of long-range JCH coupling constants from a long-range 1H-13C correlation experiment. The long-range heteronuclear coupling constants can be directly extracted from COSY-type antiphase peak patterns. The current approach utilizes CPMG-sequences for polarization transfer, and thus avoids the evolution of homonuclear JHH couplings, which normally may introduce abnormalities into the cross peak pattern. The differences between LR-CAHSQC and normal LR-HSQC are discussed. 相似文献
10.
van Enk SJ 《Physical review letters》2000,84(4):789; author reply 790