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.     

Anodic voltammetric behavior of ascorbic acid and its selective determination in pharmaceutical dosage forms and some Rosa species of Turkey

Ascorbic acid is the most common electroactive biological compound found in some plant species (e.g., Citrus species, Rosa species). The electrochemical oxidation of ascorbic acid was investigated by cyclic, linear sweep, differential pulse (DPV), and square wave (SWV) voltammetry. For analytical purposes, a very well-resolved diffusion-controlled voltammetric peak was obtained in acetate buffer at pH 3.50 for DPV and SWV. The linear response was obtained in the range of 3.52–176.1 μg/mL with a detection limit of 0.88 μg/mL for DPV and 0.52 μg/mL for SWV. Based on this study, simple, rapid, selective, and sensitive voltammetric methods were developed for the determination of ascorbic acid in pharmaceutical dosage forms and Rosa species (R. dumalis ssp. boissieri var. boissieri, R. canina, R. pulverulenta, R. heckeliana ssp. vanheurckiana, and R. montana subsp. woronowii). The results obtained are compared with the HPLC data. The developed methods enable the extracts to be analyzed without the necessity of any time-consuming separation. The text was submitted by the authors in English.     

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.     

Surface characterization and radical decay studies of oxygen plasma‐treated PMMA films

Polymethylmethacrylate (PMMA) films were modified by RF oxygen plasma with various powers applied for different periods, and the effects of these parameters on the surface properties such as hydrophilicity, surface free energy (SFE), chemistry, and topography were investigated by water contact angle, goniometer, X‐ray photoelectron spectroscopy (XPS), and atomic force microscopy, and the types of the created free radicals and their decay were detected by electron spin resonance spectroscopy (ESR). SFE and contact angle results varied depending on the plasma parameters. Oxygen plasma treatment (100 W–30 min) enhanced the hydrophilicity of PMMA surface as shown by decreasing the water contact angle from 70° to 26°. XPS analysis showed the change in the amounts of the present functionalities as well as formation of new groups as free carbonyl and carbonate groups. The roughness of the surface increased considerably from ~2 nm to ~75 nm after 100 W–30 min oxygen plasma treatment. ESR analysis indicated the introduction of peroxy radicals by oxygen plasma treatment, and the intensity of the radicals increased with increasing the applied power. Significant decrease in radical concentration was observed especially for the samples treated with higher powers when the samples were kept under the atmospheric conditions. As a conclusion, RF plasma, causes changes in the chemical and physical properties of the materials depending on the applied parameters, and can be used for the creation of specific groups or radicals to link or immobilize active molecules onto the surface of a material. Copyright © 2012 John Wiley & Sons, Ltd.     

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...     

Hedging with temporary price impact

We consider the problem of hedging a European contingent claim in a Bachelier model with temporary price impact as proposed by Almgren and Chriss (J Risk 3:5–39, 2001). Following the approach of Rogers and Singh (Math Financ 20:597–615, 2010) and Naujokat and Westray (Math Financ Econ 4(4):299–335, 2011), the hedging problem can be regarded as a cost optimal tracking problem of the frictionless hedging strategy. We solve this problem explicitly for general predictable target hedging strategies. It turns out that, rather than towards the current target position, the optimal policy trades towards a weighted average of expected future target positions. This generalizes an observation of Gârleanu and Pedersen (Dynamic portfolio choice with frictions. Preprint, 2013b) from their homogenous Markovian optimal investment problem to a general hedging problem. Our findings complement a number of previous studies in the literature on optimal strategies in illiquid markets as, e.g., Gârleanu and Pedersen (Dynamic portfolio choice with frictions. Preprint, 2013b), Naujokat and Westray (Math Financ Econ 4(4):299–335, 2011), Rogers and Singh (Math Financ 20:597–615, 2010), Almgren and Li (Option hedging with smooth market impact. Preprint, 2015), Moreau et al. (Math Financ. doi: 10.1111/mafi.12098, 2015), Kallsen and Muhle-Karbe (High-resilience limits of block-shaped order books. Preprint, 2014), Guasoni and Weber (Mathematical Financ. doi: 10.1111/mafi.12099, 2015a; Nonlinear price impact and portfolio choice. Preprint, 2015b), where the frictionless hedging strategy is confined to diffusions. The consideration of general predictable reference strategies is made possible by the use of a convex analysis approach instead of the more common dynamic programming methods.     

Secondary metabolites from the roots of Paronychia chionaea

Two novel secondary metabolites, compounds (1-2) were isolated from the roots of Paronychia chionaea. On the basis of spectroscopic data including 1D and 2D NMR experiments (COSY, TOCSY, HSQC, and HMBC), and mass spectroscopy, their structures were established as 6-C-[alpha-L-arabinopyranosyl-( 1 --> 2)-beta-D-glucopyranosyl]-7-O-[beta-D-glucopyranosyl]-luteolin 3'-methyl ether (1), and 2-(methoxy)-2-(3,5-dimethoxy 4-hydroxyphenyl)-ethane-1,2-diol 1-O-beta-D-glucopyranoside (2).