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     

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.     

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.     

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.     

Reversible Immobilization of Urease by Using Bacterial Cellulose Nanofibers

In this work, bacterial cellulose nanofibers were produced by using the Gluconacetobacter hansenii HE1 strain. These nanofibers were derivatized with dye affinity ligand Reactive Green 5, and these newly synthesized dye-attached nanofibers were used for affinity adsorption of urease. Reactive Green 5-attached nanofibers were characterized by Fourier transform infrared spectroscopy, SEM, and energy-dispersive x-ray spectroscopy analysis. Some adsorption conditions which significantly affect the adsorption efficiency were investigated. The maximum urease adsorption capacity was found to be 240 mg/g nanofiber in pH 6.0 and at room temperature. Dye-free plain nanofibers also used for studying nonspecific urease adsorption onto plain nanofibers and nonspecific adsorption were found to be negligible (3.5 mg/g nanofiber). Prepared dye-attached nanofibers can be used in five successive adsorption/desorption steps without any decrease in their urease adsorption capacity. The desorption rate of the adsorbed urease was found to be 98.9 %. The activity of the urease was also investigated, and it was found that free and desorbed urease from the dye-attached nanofibers showed similar specific activity.     

Two-dimensional agnor evaluation as a prognostic variable in urinary bladder carcinoma: a different approach via total agnor area/nucleus area per cell

Traditional criterions are not sufficient to predict accurately the recurrence of transitional cell carcinoma of the urinary bladder. Therefore, we aimed to evaluate the AgNORs via total AgNOR area/nucleus area (TAA/NA) for each cell as a prognostic parameter, in TCC of urinary bladder. Tumor tissues of 20 consecutive cases of male bladder cancer patients were divided into two groups as middle differentiated (LG) and high grade (HG). The extra-tumoral tissue (ETT) samples of 10 males served as control group. A second control group (HC) consisted of five healthy and normal bladder tissue samples. The 3 microm of sections from each paraffin embedded tumoral, extra-tumoral and normal tissue samples served as patient and control groups. After deparaffinization and rehydratation steps, silver (AgNO(3)) staining of nucleolar organizer regions-associated proteins (AgNORs) was performed. Instead of Giemsa stain, we used Hematoxylin for contra staining. The images of the 100 analyzable nuclei from each tissue sample, transferred by means of a video camera and video capture card from microscope and recorded onto a computer. Software was prepared in Delphi language for analysis. Mean (E+02) TAA/NA values of HC, ETT, LG and HG groups were 6.97+2.80, 5.70+1.82, 7.80+3.22 and 9.24+3.88, respectively. Statistical comparisons have shown significant differences between all groups.In conclusion, mean TAA/NA per cell has a potential to be a prognostic parameter. Therefore, further evaluation of big patient series will be useful.     

Quantum Computational Investigation of (E)-1-(4-methoxyphenyl)-5-methyl-N′-(3-phenoxybenzylidene)-1H-1,2,3-triazole-4-carbohydrazide

The title compound was synthesized and structurally characterized. Theoretical IR, NMR (with the GIAO technique), UV, and nonlinear optical properties (NLO) in four different solvents were calculated for the compound. The calculated HOMO–LUMO energies using time-dependent (TD) DFT revealed that charge transfer occurs within the molecule, and probable transitions in the four solvents were identified. The in silico absorption, distribution, metabolism, and excretion (ADME) analysis was performed in order to determine some physicochemical, lipophilicity, water solubility, pharmacokinetics, drug-likeness, and medicinal properties of the molecule. Finally, molecular docking calculation was performed, and the results were evaluated in detail.