We study the Ginzburg-Landau functional
for , where U is a bounded, open subset of . We show that if a sequence of functions satisfies , then their Jacobians are precompact in the dual of for every . Moreover, any limiting measure is a sum of point masses. We also characterize the -limit of the functionals , in terms of the function space B2V introduced by the authors in [16,17]: we show that I(u) is finite if and only if , and for is equal to the total variation of the Jacobian measure Ju. When the domain U has dimension greater than two, we prove if then the Jacobians are again precompact in for all , and moreover we show that any limiting measure must be integer multiplicity rectifiable. We also show that the total variation
of the Jacobian measure is a lower bound for the limit of the Ginzburg-Landau functional.
Received: 15 December 2000 / Accepted: 23 January 2001 / Published online: 25 June 2001 相似文献
The title compound, alternatively named sodium 6‐nitro‐3H‐1,2,3‐benzoxathiazole 2,2‐dioxide monohydrate, Na+·C6H3N2O5S?·H2O, consists of chains of NaO7 units, with the seven donor‐O atoms coming from two water molecules and five p‐nitrobenzoxasulfamate anions. The seven‐coordinate geometry around the Na+ ion is described as monocapped trigonal prismatic, but with a large distortion from ideal geometry. Each triangular face is defined by one O atom each from a water molecule, a nitro group and a sulfonyl group. An O atom from a sulfonyl group caps one of the square faces of the trigonal prism in an unsymmetrical fashion. The water molecules and one sulfonyl O atom are involved in bridging adjacent units, as is the nitro group of the anion. The sulfamate ions adopt an antiparallel alignment between the NaO7 units and are connected to each other by C—H?O and π–π interactions. The three‐dimensional crystal structure is stabilized by a network of strong O—H?N hydrogen bonds. 相似文献
In this communication, we report the ultrafast dynamics of resonance energy transfer in a blue-light photoreceptor, Vibrio cholerae cryptochrome. The transfer was observed to occur in 60 ps. We also studied the local rigidity and solvation around the binding site of the photoantenna molecule. The results for the first time show energy transfer in cryptochrome suggesting some mechanistic similarities between photolyase that repairs damaged DNA and cryptochrome that mediates blue-light signaling. 相似文献
Two diaza-crown ether compounds were synthesized and evaluated as Ag+-selective carriers in polyvinylchloride (PVC) membrane electrodes of solid-state type. The all-solid-state PVC membrane electrode based on N,N-Dibenzyl-dibenzo-diaza-18-crown-6 exhibited a super-Nernstian response (75±10mV per decade) over the concentration range of 1×10–1 to 7×10–6M of Ag+ ion and a detection limit of 3×10–6M, at a wide range of pH (pH 4–7). The response time of the electrode was fast (less than 10s), and it can be used for three months without any significant deviation in potential. The proposed all-solid-state PVC membrane electrodes revealed high selectivity toward Ag+ ion with respect to alkali, alkaline earth, heavy and transition metal ions. A flow-through cell of all-solid-state PVC membrane Ag+-selective electrode based on N,N-Dibenzyl-dibenzo-diaza-18-crown-6 has also been prepared and applied for flow-injection analysis of Ag+ ion in solution. 相似文献
We study a Hamilton-Jacobi equation in infinite dimensions arising in optimal control theory for problems involving both exit times and state-space constraints. The corresponding boundary conditions for the Hamilton-Jacobi equation, of mixed nature, have been derived and investigated in [19], [2], [5], and [15] in the finite-dimensional case. We obtain a uniqueness result for viscosity solutions of such a problem and then prove the existence of a solution by showing that the value function is continuous.The work of P. Cannarsa was partially supported by the Italian National Project Equazioni Differenziali e Calcolo delle Variazioni. H. M. Soner's work was supported by National Science Foundation Grant DMS-90-02249. 相似文献
water proton T1 in blood from healthy volunteers and patients with acute leukaemia, lymphoma; iron deficiency anaemia, post hepatitic cirrhosis and tuberculosis, was measured by a FT-NMR spectrometer. Relaxation measurements were performed at 60MHz frequency and a temperature of (20 ± 0.5)C. The T1 measured for each disease correlates strongly with hemoglobin content. The spin-lattice relaxation time in each abnormal group was signaficantly (p < 0.001) elevated over normal group. There is little overlap between the healthy and abnormal groups. On the contrast, T1 ranges obtained for malignant groups and non-malignant diseases do overlap. 相似文献
In the study, fluorescent imaging of live cells was performed using fluorescent carbon quantum dots derived from edible mushrooms species; Agaricus bisporus, Pleurotus ostreatus, and Suillus luteus as a fluorophore agent. Carbon quantum dots were synthesized through a facile and low-cost method based on microwave irradiation of dried mushroom samples in hydrogen peroxide solution under optimized conditions (microwave energy, solution type, duration of microwave treatment, amount of mushroom). Upon purification with centrifugation, microfiltration, and dialysis, the lyophilized carbon quantum dots were identified through UV–visible, fluorescence and FT-IR, X-ray photoelectron spectroscopy, X-ray diffraction, high-resolution transmission electron microscopy, and quantum yield calculation. Cell viability assessment of the carbon quantum dots was evaluated against human epithelial cell line PNT1A using the Alamar Blue Assay. In vitro fluorescence cell imaging studies demonstrated that the carbon dots could dynamically penetrate the cell membrane and nuclear membrane and localize in both the cytoplasm and the nucleus.