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     

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.     

A short synthesis of 4-amino-3-hydroxybutyric acid (GABOB) via allyl cyanide

4-Amino-3-hydroxybutyric acid was synthesized from allyl cyanide in four steps in an overall yield of 38%. Ultrasonically promoted epoxidation of allyl cyanide with m-chloroperoxybenzoic acid giving oxiranylacetonitrile was used as a key step.     

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.     

Studies of kidney stones using INAA,EDXRF and XRD techniques

Four kidney stones collected from patients being treated in the Advance Urology Centre of PGIMR, Chandigarh were characterized using instrumental neutron activation analysis (INAA), energy dispersive X-ray fluorescence (EDXRF) and X-ray diffraction (XRD) techniques. For INAA, samples were irradiated in tray rod facility of Dhruva reactor, Mumbai and pneumatic fast transfer system of KAMINI reactor, IGCAR, Kalpakkam. Radioactive assay was carried out using HPGe detector coupled to 8k channel analyzer. Elements determined in the samples by INAA are Zn, Sr, Co, Fe, Cr, Sc, Se, Na and Mn. EDXRF was used for the quantification of Ca. XRD patterns showed that three of the kidney stones are calcium oxalate stone and the other one is uric acid stone. The concentrations of trace elements in general were found to be higher in calcium oxalate stones and positive correlation was observed in the concentrations of Ca with Sr and Zn.     

Kinetik des Wachstums von Calciumhydroxid-Kristallen aus L?sung

Ohne Zusammenfassung     

Rotational barrier height for diatomic molecular impurities in alkali halides

A general expression for the coupling constants according to Devonshire's model for the hindered rotation of diatomic molecules in cubic crystals is derived. The treatment is confined to alkali halides with polarizable point ions. The results are applied to the librational modes of OH^? and OD^? impurities in KCl-, KBr- and KI-lattices.     

Resonant filtering of compositional waves in multicellular networks

Theoretically predicting the stationary and traveling compositional wave patterns observed over trivial multicellular topologies is common place in biology. Systematic methods are needed to find the relationships between the forms of such waves and the underlying network topologies. Here, we introduce one such method based on the Interface Response Theory (IRT) that combines models of intracellular biochemical reactions with those of intercellular networks to analytically track time variations of concentration profiles across nontrivial cellular network topologies. Cellular chains of infinite length are shown to sustain traveling planar waves under certain conditions among the coefficients of the intracellular chemical reactions. A non-trivial cellular network composed of a finite length side chain attached to the infinite backbone leads to the formation of a standing wave pattern upstream from the site of attachment. Downstream, the wave proceeds although a limited number of frequency bands are filtered out of the original content with that number being equal to the number of cells in the side chain.     

Oxidative decarboxylation of arylacetic acids in water: One-pot transition-metal-free synthesis of aldehydes and ketones

One-pot transition-metal-free synthesis of aromatic aldehydes and ketones via oxidative decarboxylation of arylacetic acids in water is developed. Protocol relies on the direct decarboxylation of sp³-hybridized carbon in water without any over oxidation into carboxylic acids with minimal waste. Reaction mechanism is investigated and application of this protocol is demonstrated on a gram scale.     

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.