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     

Asymptotic expansions for Markov processes with lévy generators

This paper considers a deterministic flow inn-dimensional space, perturbed by a Markov jump process with small variance. Asymptotic expansions are obtained for certain functionals of Feynman—Kac type, in powers of a small parameter representing a noise intensity. The methods are analytical rather than probabilistic.The research of the first author was partly supported by AFOSR under Contract No. 91-0116-0, by ONR under Contract No. N0014-83-K-0542, and by the Institute for Mathematics and Its Applications with funds provided by the NSF and ONR. The second author's research was partly supported by NSF under Contract No. DMS-8702537, and by the Institute for Mathematics and Its Applications with funds provided by the NSF and ONR.     

Random walks generated by affine mappings

This article is concerned with Markov chains on ^m constructed by randomly choosing an affine map at each stage, and then making the transition from the current point to its image under this map. The distribution of the random affine map can depend on the current point (i.e., state of the chain). Sufficient conditions are given under which this chain is ergodic.     

N,N‐Diethyl‐2,6,6‐trimethyl‐4‐(3‐nitrophenyl)‐5‐oxo‐1,4,5,6,7,8‐hexahydroquinoline‐3‐carboxamide

The title compound, C₂₃H₂₉N₃O₄, has potential calcium modulatory properties. The conformation of the 1,4‐di­hydro­pyridine ring is unusual in that it is planar, instead of the usual shallow boat. The 3‐nitro­phenyl substituent is in the synperiplanar orientation with respect to the di­hydro­pyridine ring plane. The oxo­cyclo­hexene ring has a distorted envelope conformation, with the out‐of‐plane atom being disordered on opposite sides of the ring plane. The mol­ecules are linked into chains by intermolecular hydrogen bonds.     

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.     

The exponentiated generalized power Lindley distribution: Properties and applications

In this paper, we introduce a new extension of the power Lindley distribution, called the exponentiated generalized power Lindley distribution. Several mathematical properties of the new model such as the shapes of the density and hazard rate functions, the quantile function, moments, mean deviations, Bonferroni and Lorenz curves and order statistics are derived.Moreover, we discuss the parameter estimation of the new distribution using the maximum likelihood and diagonally weighted least squares methods. A simulation study is performed to evaluate the estimators. We use two real data sets to illustrate the applicability of the new model. Empirical findings show that the proposed model provides better fits than some other well-known extensions of Lindley distributions.     

Metallo Phthalocyanines bearing 2‐Isopropyl‐6‐methylpyrimidin‐4‐yloxy Substituents: Synthesis,Characterization, Aggregation Behavior,Antioxidant and Antibacterial Activity,and Electronic Properties

A novel phthalonitrile derivative bearing 2‐isopropyl‐6‐methylpyrimidin‐4‐yloxy substituents at peripheral positions was synthesized by a nucleophilic substitution reaction. Metallophthalocyanines were obtained from the reaction of the novel phthalonitrile with metal Zn, Cu, Co, and Ni salts. The characterization of the compounds was performed using elemental analysis as well as UV/Vis, FT‐IR, and ¹H‐NMR spectroscopy. The aggregation behaviors of phthalocyanine complexes were also investigated. These metallophthalocyanines do not show any aggregation behavior between 10^–4–10^–6 M concentration range in THF. The antioxidant activities of the synthesized compounds were evaluated using three different tests: 2, 2‐diphenyl‐1‐picrylhydrazyl (DPPH) radical scavenging, metal chelating activity, and reducing power assays. All the compounds exhibited various antioxidant activities. In addition, antimicrobial activity of the compounds was tested over four gram positive and two gram negative bacteria. Moreover, the ground‐state geometries of the complexes were optimized using density functional theory (DFT) methods at B3LYP/6‐31G(d, p) level in order to obtain information about the 3D arrangements and electronic structure.     

Heterograft copolymers via double click reactions using one‐pot technique

The double click reactions (Cu catalyzed Huisgen and Diels–Alder reactions) were used as a new strategy for the preparation of well‐defined heterograft copolymers in one‐pot technique. The synthetic strategy to the various stages of this work is outlined: (i) preparing random copolymers of styrene (St) and p‐chloromethylstyrene (CMS) (which is a functionalizable monomer) via nitroxide mediated radical polymerization (NMP); (ii) attachment of anthracene functionality to the preformed copolymer by the o‐etherification procedure and then conversion of the remaining ? CH₂Cl into azide functionality; (iii) by using double click reactions in one‐pot technique, maleimide end‐functionalized poly(methyl methacrylate) (PMMA‐MI) via atom transfer radical polymerization (ATRP) of MMA and alkyne end‐functionalized poly (ethylene glycol) (PEG‐alkyne) were introduced onto the copolymer bearing pendant anthryl and azide moieties. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 6969–6977, 2008     

High sensitivity and high selectivity terahertz biomedical imaging

We demonstrate two distinct emerging terahertz (THz) biomedical imaging techniques.One is based on the use of a new single frequency THz quantum cascade laser and the other is based on broadband THz time domain spectrocopy.The first method is employed to derive a metastasis lung tissue imaging at 3.7 THz with clear contrast between cancerous and healthy areas.The second approach is used to study an osseous tissue under several imaging modalities and achieve full THz spectroscopic imaging based on the freque...