Existence and mapping properties of the wave operator for the Schrödinger equation with singular potential

We consider the Schrödinger equation in three-dimensional space with small potential in the Lorentz space and we prove Strichartz-type estimates for the solution to this equation. Moreover, using Cook's method, we prove the existence of the wave operator. In the last section we prove the equivalence between the homogeneous Sobolev spaces and in the case .

     

Local and global existence of solutions for a class of integro-differential equations with delay

In this article we consider a class of first order nonlinear integro-differential equations with delay. We propose new approach for investigating local and global existence of the solutions of its Cauchy problem. This approach gives new results.     

Biomimetic Synthesis of Nor-Cedrene and Nor-Isozizaene Sesquiterpenoids and Exploration of Their Olfactive Properties

We report the preparation of nor-bisabolyl epoxide 13 and its use as a common biomimetic intermediate for the synthesis of nor-sesquiterpenoids. Through a cationic cyclization cascade pathway, we prepared nor-isozizaenol 25 , ultimately constituting an eight-step access to this complex sesquiterpenoid from inexpensive and abundant starting materials. Using a radical cyclization cascade pathway, we prepared nor-cedryl alcohol 26 from the same intermediate. Derivatization of these two products led to the discovery of two potent woody odorants of interest in perfumery.     

Porosity and differentiability in smooth Banach spaces

We improve a result of Preiss, Phelps and Namioka, showing that every submonotone mapping in a Gateaux smooth Banach space is single-valued on the complement of a -cone porous subset. If a Banach space has a uniformly -differentiable Lipschitz bump function (with respect to some bornology ), then we show with a much simpler argument (localization of -minimum of a perturbed function) that every continuous convex function on is -differentiable on the complement of a -uniformly porous set.

     

Synthesis and antibacterial activity of hydroxylated 2-arylbenzothiazole derivatives

Abstract

N-acyliminium reagents formed in situ from benzothiazole and alkyl chloroformates react with hydroxyarenes in a Friedel-Crafts manner, providing access to 2-(hydroxyaryl)-benzothiazolines with antibacterial properties.     

Mazur Intersection Properties and Differentiability of Convex Functions in Banach Spaces

It is proved that the dual of a Banach space with the Mazurintersection property is almost weak* Asplund. Analogously,the predual of a dual space with the weak* Mazur intersectionproperty is almost Asplund. Through the use of these arguments,it is found that, in particular, almost all (in the Baire sense)equivalent norms on l₁() and l() are Fréchet differentiableon a dense G subset. Necessary conditions for Mazur intersectionproperties in terms of convex sets satisfying a Krein–Milmantype condition are also discussed. It is also shown that, ifa Banach space has the Mazur intersection property, then everysubspace of countable codimension can be equivalently renormedto satisfy this property.     

Amorphous and crystalline IrO2 thin films as potential stimulation electrode coatings

Amorphous and crystalline iridium oxide thin films with potential use as coating materials for stimulation electrodes were studied. Characterization of these films by cyclic voltammetry and impedance spectroscopy has revealed a considerable decrease in impedance and an increase in charge capacity of iridium oxide thin films after an electrochemical activation process in 0.9% NaCl solution. The surface morphology of these films was studied by scanning electron microscopy. The two types of IrO₂ films were also compared under conditions relevant to applications as stimulation electrodes. The results indicate that amorphous IrO₂ films have significantly higher charge storage capacity and lower impedance than crystalline IrO₂ films. This makes the amorphous films a preferable coating material for stimulation applications.     

Extraction of chlorides of some lanthanoides by tricaprylylmethylammonium pelargonate

Summary The extraction of some lanthanoides by tricaprylylmethylammonium pelargonate has been investigated in the system ofLnCl₃-Na(H)Cl-R ₄NB-CCl₄ at constant ionic strength =0.1. A mechanism of the extraction process is suggested, which explains the simultaneous extraction of HCl andLnCl₃.

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Extraktion von Chloriden einiger Lanthanoiden mittels Tricaprylylethylmammonium-Pelargonat

Zusammenfassung Es wurde die Extraktion von Lanthanoiden mittels Tricaprylylmethylammonium-Pelargonat in dem SystemLnCl₃-Na(H)Cl-R ₄NB-CCl₄ bei konstanter Ionenstärke =0.1 untersucht. Ein Mechanismus des Extraktionsprozesses wird vorgeschlagen, der die gemeinsame Extraktion von HCl undLnCl₃ erklärt.