The Jacobian and the Ginzburg-Landau energy

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     

Simple Analytical Model Predicting Some Features of the Electrolytic Steel-Pickling Process

Electrolytic pickling of steel with neutral solutions, to remove the surface scale, reduces the need for the use of strong acids as needed in conventional pickling. This study is a step towards a more in-depth understanding of the factors affecting the former process. A theoretical model, sufficiently simplified to allow analytical solution, is developed and evaluated to provide a first approximation of the potential and current distributions in the electrolyte and steel band. To gain knowledge and validate the model, a small electrolytic pickling cell is constructed, and experiments, including bubble generation and motion observation, are conducted. The experimental work has shown the remarkable bubble production and adherence to the surfaces, and its effects on reducing pickling efficiency and uniformity. The pickling efficiency is about 30%, confirming other researchers" results. The analytical model shows trends very similar to those observed in the experiments, and provides very valuable guidance. It shows, for example, that the current efficiency decreases as the electrode–band distance increases, and it increases with the band thickness and the band-to-electrolyte conductivity ratio. The energy efficiency decreases by orders of magnitude faster than the current efficiency with all of the above-mentioned parameters, because of the correspondingly strong drop in the band–surface potential. A large amount of current is lost due to interelectrode short circuiting.     

Sodium p‐nitro­benzoxasulfamate monohydrate

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.     

Ultrafast dynamics of resonance energy transfer in cryptochrome

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.     

All-Solid-State PVC Membrane Ag+-Selective Electrodes Based on Diaza-18-Crown-6 Compounds

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.     

A boundary-value problem for Hamilton-Jacobi equations in hilbert spaces

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.     

Comparison of NMR Water Proton T1 Measurements in Healthy and Pathological Blood

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.     

Thermal,mechanical, and topographical evaluation of nonstoichiometric α-cyclodextrin/poly(ε-caprolactone) pseudorotaxane nucleated poly(ε-caprolactone) composite films

Three pseudorotaxanes (PpR) comprised of poly (ε-caprolactone) (PCL) and α-cyclodextrin (α-CD) with varying stoichiometric ratios were synthesized and characterized. Wide-angle X-ray diffraction (WAXD) and thermogravimetric (TGA) analyses provided conclusive evidence for complexation between the guest PCL and host α-CD. The as-synthesized and characterized PpRs were used at 10 and 20% concentrations as nucleants to promote the bulk PCL crystallization in composite films. Both WAXD and TGA provided evidence for intact PpR structures in the composite films. Isothermal differential scanning calorimetric (I-DSC) analyses, performed at various crystallization temperatures demonstrated significant differences in the crystallization patterns among the composite films. In addition, I-DSC analyses showed higher Avrami constant values (n) in the PpR-nucleated composite PCL films (n ~ 3), indicating 3-dimensional crystal growth. In the case of neat PCL films, however, lower n values indicated crystal growth in 1-dimensions or 2-dimensions. Moreover, atomic force microscopic analyses showed large crests and pits in PpR-nucleated PCL composites, with irregular morphologies leading to higher surface roughness. To the contrary, the crests and pits were much smaller in the neat PCL films, resulting in lower surface roughness values. Finally, mechanical testing revealed higher tensile strength for PpR-nucleated PCL composites films, demonstrating larger load bearing capabilities. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 1529–1537     

Acid-Catalysed Hydrolysis of Some Aromatic Cyclic Sulfamates

The acid catalysed hydrolysis of some cyclic sulfamates, X-3-(p-tolylsulfonyl)-1,2,3-benzoxathiazole 2,2-dioxides ( 1a , X = Me; 1b , X = H; 1c , X = Cl; 1d , X = NO 2 ) have been studied in concentrated aqueous sulfuric and perchloric acid solutions. Analysis of the data by the Excess Acidity Method, activation parameters, substituent, solvent deuterium isotope effect and order of the catalytic effects of the acids are all in agreement with an A-1 mechanism in the studied range.