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     

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.     

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.     

Molecular structure, spectroscopic properties and DFT calculations of 2-(methylthio)nicotinic acid

The analyses of possible conformations, molecular structures, vibrational and electronic properties of 2-(methylthio)nicotinic acid molecule, C₇H₇NO₂S, with the synonym 2-(methylsulfanyl)nicotinic acid have been first presented theoretically. At the same time, FT-IR and micro-Raman spectra of 2-(methylthio)nicotinic acid were recorded in the regions 400–4000 cm^?1 and 100–4000 cm^?1, respectively. In our calculations, the DFTB3LYP method with 6–311G(d, p) basis set was used to have the structural and spectroscopic data about the mentioned molecule in the ground state and the results obtained were compared with experimental values. Furthermore, gauge invariant atomic orbital (GIAO) ¹H and ¹³C NMR chemical shifts in different solvents, UV-vis TD-DFT calculations, the highest occupied molecular orbitals (HOMO-2, HOMO-1, HOMO), lowest unoccupied molecular orbital (LUMO), molecular electrostatic potantial (MEP) surface, atomic charges and thermodynamic properties of molecule have been theoretically verified and simulated at the mentioned level. The energetic behavior of title molecule in different solvent media was investigated by using DFT/B3LYP method with 6–311G(d, p) basis set in terms of integral equation formalism polarizable continuum model (IEFPCM). In addition, the calculated infrared intensities, Raman activities, reduce masses and force constants of the compound under study have been also reported.     

Propagation factors of Hermite–Gaussian beams in turbulent atmosphere

Based on the extended Huygens–Fresnel integral and the second-order moments of the Wigner distribution function, an analytical formulae for the propagation factors (M²-factors) of coherent and partially coherent one-dimensional Hermite–Gaussian beams in a turbulent atmosphere are derived. Evolution properties of the M²-factor of the Hermite–Gaussian beam in a turbulent atmosphere are studied numerically in detail. Our results show that the M²-factor of the Hermite–Gaussian beam increases upon propagation in a turbulent atmosphere. The M²-factor of the Hermite–Gaussian beam with larger beam order (or lower coherence) increases slower that of the Hermite–Gaussian beam with smaller beam order (or higher coherence) in a turbulent atmosphere, which means that the Hermite–Gaussian beam with a larger beam order and lower coherence is less affected by a turbulent atmosphere. Our results will be useful in long-distance free-space optical communications.     

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.     

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.