Synthesis of β-aminovinylphosphonates by organocatalytic nucleophilic displacement of acetate with amines

The synthesis of diethyl β-aminovinylphosphonates 2 from acetoxy phosphonate 1 is described. The reaction entails an organocatalyzed substitution of the acetoxy group by primary or secondary amines. The use of a catalytic amount of DABCO is necessary if the amine is not nucleophilic enough, otherwise a strong nucleophilic amine can react without organocatalyst. The reaction led to a series of functionalized title compounds in good to excellent yields.     

Photocatalytic degradation of an azo reactive dye,Reactive Yellow 84, in water using an industrial titanium dioxide coated media

The photocatalytic degradation of an azo reactive dye, Reactive Yellow 84 (RY84), in aqueous solutions using industrial titanium dioxide coated non-woven paper was studied. The experiments were carried out to investigate the factors that influence the dye photocatalytic degradation, such as adsorption, initial concentration of dye, temperature, and solution pH. The experimental results show that adsorption is an important parameter controlling the apparent kinetics constant of degradation. The photocatalytic degradation rate was favored by a high concentration of solution in respect to Langmuir–Hinshelwood model. The degradation was enhanced by the temperature and was favored in acidic pH range.     

The CH3D absorption spectrum in the 1.58 μm transparency window of methane: Empirical line lists at 81 K and 294 K and temperature dependence

In spite of its low isotopic abundance in methane (about 5×10⁻⁴), CH₃D contributes greatly to the very weak absorption in the 1.58 μm methane transparency window. This methane window deserves to be characterized in details because it is important for planetary applications in particular for Titan and the giant planets. In this work, we recorded the CH₃D spectrum by high sensitivity differential absorption spectroscopy (α_min≈5×10⁻⁸ cm⁻¹) both at room temperature and at 81 K. A list of more than 9000 lines was constructed from the 81 K spectrum for the 6099–6530 cm⁻¹ region. In order to get the temperature dependence of the line intensities, the low energy values have to be determined. The rovibrational assignments available in the literature provide low energy values for about 380 strong transitions of the region. This is insufficient to characterize the temperature dependence of the CH₃D absorption between 6200 and 6400 cm⁻¹. In this interval, a list of 5500 lines was constructed from the room temperature spectrum. The empirical energy values of the transitions were derived from the ratio of the intensities at 81 K and 294 K. The exact and empirical lower state energies included in the final line lists provided as Supplementary Material, allow for accounting for the temperature dependence of the CH₃D spectrum in the entire 6099–6530 cm⁻¹ region.Our measurements have been compared to the spectroscopic parameters and assignments available in the literature in particular those adopted in the HITRAN database. Improvements and corrections are proposed for the wavenumber calibration and for some lower state energies.     

ON THE SUPERSTABILITY OF THE PEXIDER TYPE GENERALIZED TRIGONOMETRIC FUNCTIONAL EQUATIONS

The aim of this paper is to investigate the superstability problem for the pexiderized trigonometric functional equation∑ v∈Φ∫Kf(xkv(y)k-1)dwK(k)= Φ g(x)h(y), x, y ∈ G,where G is any topological group, K is a compact subgroup of G, ωK is the normalized Haar measure of K, Φ is a finite group of K-invariant morphisms of G and f, g, h are continuous complex-valued functions.Consequently, we have generalized the results of stability for d'Alembert's and Wilson's equations by R. Badora, J. Baker, B. Bouikhalene, P. Gavruta, S. Kabbaj, Pl. Kannappan, G. H.Kim, J.M. Rassias, A. Roukbi, L. Sz′ekelyhidi, D. Zeglami, etc.     

Characterization of Function Spaces for the Dunkl Type Operator on the Real Line

In this work we consider the Dunkl operator on the real line, defined by $$ {\cal D}_kf(x):=f'(x)+k\dfrac{f(x)-f(-x)}{x},\,\,k\geq0. $$ We define and study Dunkl–Sobolev spaces \(L^p_{n,k}(\mathbb{R})\) , Dunkl–Sobolev spaces \({\cal L}^p_{\alpha,k}(\mathbb{R})\) of positive fractional order and generalized Dunkl–Lipschitz spaces \(\wedge^k_{\alpha,p,q}(\mathbb{R})\) . We provide characterizations of these spaces and we give some connection between them.     

An expeditious construction of 9-membered rings

9-Membered rings are readily constructed through a radical addition-cyclisation sequence on a 1,6-dien-3-ol system followed by a Grob-type fragmentation.     

A divergent approach to highly substituted benzothiepinones and to 2,3-dihydrothieno[2,3-b]thiopyran-4-ones

The radical addition-transfer of S-(2-fluoro-phenacyl)xanthates can be used to construct rapidly benzothiepinones, including libraries of complex aza-bridged derivatives, and highly functionalized 2,3-dihydrothieno[2,3-b]thiopyran-4-ones.     

Membrane paradigm realized?

Are there any degrees of freedom on the black hole horizon? Using the ‘membrane paradigm’ we can reproduce coarse-grained physics outside the hole by assuming a fictitious membrane just outside the horizon. But to solve the information puzzle we need ‘real’ degrees of freedom at the horizon, which can modify Hawking’s evolution of quantum modes. We argue that recent results on gravitational microstates imply a set of real degrees of freedom just outside the horizon; the state of the hole is a linear combination of rapidly oscillating gravitational solutions with support concentrated just outside the horizon radius. The collective behavior of these microstate solutions may give a realization of the membrane paradigm, with the fictitious membrane now replaced by real, explicit degrees of freedom.     

Stable numerical schemes for a partly convolutional partial integro-differential equation

A model partial integro-differential operator (PIDO) that contains both local and nonlocal diffusion operators is considered in this article. This type of operators come in modeling various scientific and financial engineering problems. In most cases, people use finite difference schemes to generate solutions of such model problems. We compare and analyze stability and accuracy of two such finite difference schemes. We first present a discrete analogue of the PIDO and then approximate the semi-discrete time dependent problem using two different one step methods and show the stability conditions and the accuracy of the schemes. We use the Fourier transforms throughout our analysis.