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.     

Synthesis of C 2-Symmetric Chiral Amino Alcohols: Their Usage as Organocatalysts for Enantioselective Opening of Epoxide Ring

A series of β-amino alcohols derivatives were synthesized from (R)-2-amino-1-butanol and (S)-1,2-propanediol, and they have been used as organocatalaysts in the racemic ring opening of epoxide in good yields with high enantiomeric excess (up to 97%).     

Responsive microgrooves for the formation of harvestable tissue constructs

Given its biocompatibility, elasticity, and gas permeability, poly(dimethylsiloxane) (PDMS) is widely used to fabricate microgrooves and microfluidic devices for three-dimensional (3D) cell culture studies. However, conformal coating of complex PDMS devices prepared by standard microfabrication techniques with desired chemical functionality is challenging. This study describes the conformal coating of PDMS microgrooves with poly(N-isopropylacrylamide) (PNIPAAm) by using initiated chemical vapor deposition (iCVD). These microgrooves guided the formation of tissue constructs from NIH-3T3 fibroblasts that could be retrieved by the temperature-dependent swelling property and hydrophilicity change of the PNIPAAm. The thickness of swollen PNIPAAm films at 24 °C was approximately 3 times greater than at 37 °C. Furthermore, PNIPAAm-coated microgroove surfaces exhibit increased hydrophilicity at 24 °C (contact angle θ = 30° ± 2) compared to 37 °C (θ = 50° ± 1). Thus PNIPAAm film on the microgrooves exhibits responsive swelling with higher hydrophilicity at room temperature, which could be used to retrieve tissue constructs. The resulting tissue constructs were the same size as the grooves and could be used as modules in tissue fabrication. Given its ability to form and retrieve cell aggregates and its integration with standard microfabrication, PNIPAAm-coated PDMS templates may become useful for 3D cell culture applications in tissue engineering and drug discovery.     

Crystal structure,spectroscopic characterization,DFT computations and molecular docking study of a synthesized Zn(II) complex

The Zn(II) complex, dichloro[N-hydroxy-1,1-di(2-pyridinyl)methanimine]zinc(II), was synthesized from the reaction between ZnCl₂ and di-2-pyridylketone oxime. The structural and spectral characterizations were performed by using single crystal X-ray diffraction, FT-IR, Laser-Raman, NMR and UV–Vis spectroscopic techniques. To support experimental evidences, computational results were obtained with the DFT/B3LYP method using the 6-311++G(d,p)+LanL2DZ mixed basis set. Theoretical analyses of some structural and spectroscopic results of effects of intermolecular Cl···H interactions in the crystal packing of the Zn(II) complex were investigated with the mentioned computational level. The non-bonding interactions in the experimental crystal packing of the complex were examined by Hirshfeld surface analysis. The HOMO and LUMO analyses were used for investigation of electronic transitions obtained with UV–Vis spectroscopy. NBO analyses were used to investigate the hyperconjugation interactions between donor and acceptor groups, coordination environment, electronic configuration and electron numbers of the Zn(II) metal ion and the natural atomic charges of the complex. The nucleophilic and electrophilic reactive sites of the complex were studied by MEP surface analysis. The static polarizabilities (α) and static hyperpolarizabilities (β) were analyzed theoretically to characterize NLO profile of the complex. The interaction with A-DNA (PDB ID: 1ZF6) of the Zn(II) complex was investigated with a molecular docking study.     

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.