Existence of conformal metrics with prescribed scalar curvature on the four dimensional half sphere

In this paper, we consider the problem of prescribing the scalar curvature under minimal boundary conditions on the four dimensional half sphere. Using dynamical and topological methods involving the study of the critical points at infinity of the associated variational structure, we prove some existence results like Bahri-Coron theorem. Furthermore, we consider the approximate subcritical problem and we construct some solutions which blow up at two different points, one of them lay on the boundary and the other one is an interior point.     

A Compact Solar Laser Side-Pumping Scheme Using Four Off-Axis Parabolic Mirrors

Journal of Russian Laser Research - Laser side-pumping approach is an extremely attractive configuration for many laser applications. Through this approach, the laser beam can be generated in the...     

On a variational problem involving critical Sobolev growth in dimension three

In this paper we consider the following nonlinear problem: \({{-\Delta u=Ku^{5}}}\), u > 0 in \({{\Omega}}\), u =  0 on \({{\partial \Omega}}\), where K > 0 in \({{\Omega}}\), K =  0 on \({{\partial \Omega}}\) and \({{\Omega}}\) is a bounded domain of \({{\mathbb{R}^{3}}}\). We prove a version of a Morse lemma at infinity for this problem, which allows us to describe the critical points at infinity of the associated variational functional. Using a topological argument, we prove an existence result.     

Ultrasound mediated green synthesis of rhodanine derivatives: Synthesis,chemical behavior,and antibacterial activity

A variety of rhodanine derivatives were synthesized via a three-component reaction of carbon disulfide, amines, and dialkyl acetylenedicarboxylate in polyethylene glycol under conventional stirring or ultrasound irradiation. The sonochemical-assisted procedure provides an improved and accelerated conversion when compared to the conventional reaction, with increased rate of reaction and quality of product obtained. The product formed, 2a, could be readily converted to bis-rhodanine under microwave conditions. Moreover, the pyranothiazoles 9a,b were prepared from the corresponding rhodanines 2a,b and malononitrile. Fifteen compounds were screened for their antibacterial activities against nine human, animal and plant pathogenic Gram-positive and Gram-negative bacteria using the agar well diffusion method. Out of these derivatives, compounds 2g and 2h were the most effective against all tested bacteria.     

Blowing Up of Sign-changing Solutions to an Elliptic Subcritical Equation

This paper is concerned with the following non linear elliptic problem involving nearly critical exponent (P^k_ε): (-Δ)^ku=K(x)|u|^{(4k/(n-1k))-ε}u in Ω, Δ^{k-1}u=…=Δu=u=0 on ∂Ω, where Ω is a bounded smooth domain in R^n, n≥ 2k+2, k≥ 1, ε is a small positive parameter and K is a smooth positive function in Ω. We construct signchanging solutions of (P^k_ε) having two bubbles and blowing up either at two different critical points of K with the same speed or at the same critical point.     

UV-VIS- und Raman-spektroskopische Untersuchungen der grünen Lösungen von Stickstofftriiodid-1-Pyridin in Pyridin

UV-VIS-Spectroscopical Investigations of the Green Solutions of Nitrogen Triiodide-1-Pyridine in Pyridine Solid, crystalline nitrogen triiodide-1-pyridine has a polymeric structure similar to that of nitrogen triiodide-1-ammonia consisting of NI₄ tetrahedra linked to chains by common vertices. The solubility of both compounds in liquid ammonia is accomplished by a degradation of the chains involving protolysis equilibria with monoiodamine. UV-VIS-spectra of the green solutions of NI₃ pyridine in the aprotic solvent pyridine between ?30 and ?16°C and Raman-spectra of these solutions at ?30°C or quenched with liquid nitrogen at ?196°C show, that the chains are retained here at least to some extent. The solutions are instable even at low temperatures and decompose in a first order reaction yielding nitrogen and iodine. The halflife period at ?16°C is 5 hours, at ?30°C 20 hours.     

One-pot synthesis to engineer a Co-KIT-6 catalyst for the ring opening of methylcyclopentane

Co-KIT-6 mesoporous materials with Ia3d symmetry and Si/Co ratios of 50, 25, and 10 were prepared using hydrothermal one-pot synthesis. The Co-KIT-6 mesoporous materials were characterized by X-ray diffraction, N₂ adsorption–desorption isotherms, scanning electron microscopy, transmission electron microscopy, Fourier transform infrared, and X-ray photoelectron spectroscopy. The physicochemical characterization results show that all of the samples have well-ordered cubic mesostructures and that the structural integrity is preserved for n_Si/n_Co ratios as high as 10. It was found that most of the cobalt ions exist as isolated framework species, but for Co-KIT-6 with an n_Si/n_Co ratio of 10, the presence of extra-framework species/small cobalt oxide clusters cannot be excluded. The ability of these catalysts was tested by examining the conversion of the reaction of methylcyclopentane with hydrogen at atmospheric pressure and temperatures between 200 and 450 °C. The catalytic results show that their catalytic activity increases significantly with increasing cobalt content. The active sites, tetrahedrally coordinated Co and isolated atomic Co sites, were responsible for the endocyclic CC bond rupture between substituted secondary–tertiary carbon atoms, whereas the small clusters serve as active sites for the successive CC bond rupture. The ring-opening selectivity can be improved by increasing the density of isolated cobalt atom sites at low reaction temperatures.