A remark on analytic Fredholm alternative

We apply a recent result of Borichev–Golinskii–Kupin on the Blaschke-type conditions for zeros of analytic functions on the complex plane with a cut along the positive semi-axis to the problem of the eigenvalues distribution of the Fredholm-type analytic operator-valued functions.     

Comparison between preparative methodologies of nanostructured carbon nitride and their use as selective photocatalysts in water suspension

Carbon nitride photocatalysts have been prepared by different methodologies, such as chemical ultrasonic irradiation (sonochemical treatment), hydrothermal and ball milling and thermoexfoliation, and have been used for the selective oxidation of 5-hydroxymethyl-2-furaldehyde (HMF) to form 2,5-furandicarboxyaldehyde (FDC) in water suspension both under UV and natural solar irradiation. The physico-chemical features of the photocatalysts have been studied by X-ray diffraction, infrared spectroscopy, UV–Vis diffuse reflectance spectroscopy, photoluminescence spectroscopy, scanning electron microscopy, and specific surface area measurements. The results indicate that exfoliation of carbon nitrides can increase the conversion of HMF and the selectivity to FDC. In particular, samples exfoliated by both thermal and acidic ultrasonic irradiation treatments showed the best photocatalytic performance.     

Spectral and Mechanistic Investigation of Oxidation of Rizatriptan by Silver Third Periodate Complex in Aqueous Alkaline Medium

The oxidation of Rizatriptan by diperiodatoargentate(III) has been studied by spectrophotometry at neutral pH. The kinetics of the reaction of Rizatriptan has been shown to principle of non-complementary oxidation steps. The initial step involves the deprotonated of the diperiodatoargentate(III) with the alkali; this rearranges during the displacement of a ligand to give free periodate and takes up another ligand monoperiodateargentate(III), combines with a substrate to endow with an intermediate complex which decomposes within a slow step to provide the final product in the following step with a first-order rate constant. The main product was identified by spot test, Fourier- transform infrared spectroscopy, Nuclear magnetic resonance and Liquid chromatography-mass spectrometry spectrum. A conceivable mechanism including pre equilibrium of adducts development between the complex and reductant was planned from the kinetics study. The rate conditions got from system can clarify all exploratory phenomena, and the activation parameters alongside rate constants of the rate determining step were ascertained.     

Non-singular space-times with a negative cosmological constant: V. Boson stars

We prove existence of large families of solutions of Einstein-complex scalar field equations with a negative cosmological constant, with a stationary or static metric and a time-periodic complex scalar field.     

The Mystery of Gabor Frames

This is a survey about the theory of Gabor frames. We review the structural results about Gabor frames over a lattice and then discuss the few known results about the fine structure of Gabor frames. We add a new result about the relation between properties of the window and properties of the frame set and conclude with a vision of how a more complete theory of the fine structure might look like.     

The small index property for homogeneous models in AEC’s

We prove a version of a small index property theorem for strong amalgamation classes. Our result builds on an earlier theorem by Lascar and Shelah (in their case, for saturated models of uncountable first-order theories). We then study versions of the small index property for various non-elementary classes. In particular, we obtain the small index property for quasiminimal pregeometry structures.