On Erdélyi–Kober Quadratic Functional-Integral Equation in Banach Algebra

Using the technique of a suitable measure of noncompactness in Banach algebra, we prove an existence theorem for some functional-integral equations in Banach algebra, namely Erdélyi–Kober quadratic functional-integral equation. This equation contains as particular cases a lot of integral equations that appear in many branches of nonlinear analysis and its applications. The obtained result is illustrated by an example.     

Molecular and crystal structures of 2-amino-5-benzoyl-4-(2-nitrophenyl)-3-cyano-4,5-dihydrothiophene

The crystal structure of 2-amino-5-benzoyl-4-(2-nitrophenyl)-3-cyano-4,5-dihydrothiophene is determined by X-ray diffraction analysis. The unit cell parameters are as follows: a = 10.878(2) Å, b = 12.890(3) Å, c = 13.539(4) Å, α = 108.15(2)°, β = 99.26(2)°, γ = 107.13(2)°, V = 1656(2) ų, d _calcd = 1.410 g/cm³, Z = 4, and space group P1ˉ. The molecules occupy two systems of independent positions in the crystal. Similar to the compounds studied earlier in this series, the o-nitrophenyl substituent has a synperiplanar orientation relative to the hydrogen atom at the C(4) atom of the heterocycle. __________ Translated from Kristallografiya, Vol. 45, No. 2, 2000, pp. 282–285. Original Russian Text Copyright ? 2000 by Nesterov, Kuleshova, Samet, Shestopalov.     

Efficient synthesis of 3,4-diarylpyrrole-2-carboxylates,the key fragments of natural antimitotic agents

Russian Chemical Bulletin - Barton-Zard reaction of nitrostilbenes with ethyl isocyanoacetate carried out in EtOH in the presence of K2CO3 allowed us to minimize the formation of side products and...     

Role of Stone–Wales defects on the functionalization of (8,0) single wall carbon nanotubes by the amine group: Ab initio study

Using first-principle calculations, we have investigated the chemical functionalization of (8,0) zigzag single wall carbon nanotubes (SWNTs) by the amine group on Stone–Wales (SW) defects. The binding of NH₂ with the defective (8,0) nanotube was explored and the preferential grafting sites have been identified. On the other hand, the modifications induced by SW defect and functional groups in the structural and electronic properties of (8,0) SWNT have also been investigated. The role of SW defects in the chemical reactivity of carbon nanotubes was well identified.     

Berinde mappings in orbitally complete metric spaces

We give a fixed point theorem for a self-mapping satisfying a general contractive condition of integral type in orbitally complete metric spaces. Some examples are given to illustrate our obtained result.     

On the growth of Betti numbers of locally symmetric spaces

We announce new results concerning the asymptotic behavior of the Betti numbers of higher rank locally symmetric spaces as their volumes tend to infinity. Our main theorem is a uniform version of the Lück Approximation Theorem (Lück, 1994 [10]) which is much stronger than the linear upper bounds on Betti numbers given by Gromov in Ballmann et al. (1985) [3].The basic idea is to adapt the theory of local convergence, originally introduced for sequences of graphs of bounded degree by Benjamini and Schramm, to sequences of Riemannian manifolds. Using rigidity theory we are able to show that when the volume tends to infinity, the manifolds locally converge to the universal cover in a sufficiently strong manner that allows us to derive the convergence of the normalized Betti numbers.     

Electronic structure calculations and optical properties of a new organic-inorganic luminescent perovskite: (C9H19NH3)2PbI2Br2

(C₉H₁₉NH₃)₂PbI₂Br₂ compound is a new crystal belonging to the large hybrid organic-inorganic perovskites compounds family. Optical properties are investigated by optical absorption UV-visible and photoluminescence (PL) techniques. Bands to band absorption peak at 2.44 eV as well as an extremely strong yellow-green photoluminescence emission at 2.17 eV is observed at room temperature. First principle calculations based on the DFT and FLAPW methods combined with LDA approximation are performed as well. Density of state close to the gap is presented and discussed in terms of optical absorption and photoluminescence experimental results. The perfect agreement between experimental data and electronic structure calculations is highlighted.     

Towards a Sustainable Synthesis of Formate Salts: Combined Catalytic Methanol Dehydrogenation and Bicarbonate Hydrogenation

Formate salts are important chemicals widely used in everyday products. The current industrial‐scale manufacture of formates requires CO at high pressure and harsh reaction conditions. Herein, we describe a new process for these products without the utilization of hazardous gases and chemicals. By application of ruthenium pincer complexes, a simultaneous methanol dehydrogenation and bicarbonate hydrogenation reaction proceeds, which provides a green synthesis of formate salts with excellent TON (>18 000), TOF (>1300 h^?1), and yield (>90 %).