Sulfonic acid supported on magnetic nanoparticle as an eco‐friendly,durable and robust catalyst for the synthesis of β‐amino carbonyl compounds through solvent free Mannich reaction

A simple, efficient and environmentally benign solid acid catalyst was prepared by anchoring a propyl sulfonic acid on the surface of silica‐coated magnetic nanoparticles by low cost precursors. The catalyst has been then engaged in the efficient β‐amino carbonyl compounds production via three component Mannich reaction under solvent free reaction condition at room temperature. After the completing the reaction, the catalyst was readily separated by external magnet and reused for 10 successive rounds of reaction, without any significant loss in catalytic efficiency. The solid acidic system presented reusable strategy for the efficient synthesis of β‐amino carbonyl compounds, simplicity in operation, and green aspects by avoiding toxic conventional catalysts under solvent‐free condition.     

On the flow of chemically reacting gaseous mixture

We consider the Cauchy problem for the system of equations governing flow of isothermal reactive mixture of compressible gases. Our main contribution is to prove sequential stability of weak solutions when the state equation essentially depends on the species concentration and the viscosity coefficients vanish on vacuum. Moreover, under additional assumption on the “cold” component of the pressure in the regions of small density, we prove the existence of weak solutions for arbitrary large initial data.     

Convergence of approximate deconvolution models to the mean Navier–Stokes equations

We consider a 3D Approximate Deconvolution Model ADM which belongs to the class of Large Eddy Simulation (LES) models. We aim at proving that the solution of the ADM converges towards a dissipative solution of the mean Navier–Stokes equations. The study holds for periodic boundary conditions. The convolution filter we first consider is the Helmholtz filter. We next consider generalized convolution filters for which the convergence property still holds.     

Studies of magnetite nanoparticles synthesized by thermal decomposition of iron (III) acetylacetonate in tri(ethylene glycol)

In this paper, water-soluble magnetite nanoparticles have been directly synthesized by thermal decomposition of iron (III) acetylacetonate, Fe(acac)₃ in tri(ethyleneglycol). Size and morphology of the nanoparticles are determined by transmission electron microscopy (TEM) and dynamic light scattering (DLS) measurements while the crystal structure is identified using X-ray diffraction (XRD). Surface charge and surface coating of the nanoparticles are recognized using Fourier transform infrared spectroscopy (FTIR), X-ray photoelectron spectra (XPS) and zeta potential measurements. Magnetic properties are determined using vibrating sample magnetometer (VSM) and superconducting quantum interference device (SQUID) measurements. The results show that as-prepared magnetite nanoparticles are relatively monodisperse, single crystalline and superparamagnetic in nature with the blocking temperature at around 100 K. The magnetite nanoparticles are found to be highly soluble in water due to steric and electrostatic interactions between the particles arising by the surface adsorbed tri(ethyleneglycol) molecules and associated positive charges, respectively. Cytotoxicity studies on human cervical (SiHa), mouse melanoma (B16F10) and mouse primary fibroblast cells demonstrate that up to a dose of 80 μg/ml, the magnetic nanoparticles are nontoxic to the cells. Specific absorption rate (SAR) value has been calculated to be 885 and 539 W/gm for samples with the iron concentration of 1 and 0.5 mg/ml, respectively. The high SAR value upon exposure to 20 MHz radiofrequency signifies the applicability of as-prepared magnetite nanoparticles for a feasible magnetic hyperthermia treatment.     

Chiral symmetry breaking and vacuum structure in QCD

The solution of the axial U(1) problem, the role of the topology of the gauge group in forcing the breaking of axial symmetry in any irreducible representation of the observable algebra and the θ vacua structure are revisited in the temporal gauge with attention to the mathematical consistency of the derivations. Both realizations with strong and weak Gauss law are discussed; the control of the general mechanisms and structures is obtained on the basis of the localization of the (large) gauge transformations and the local generation of the chiral symmetry. The Schwinger model in the temporal gauge exactly reproduces the general results.     

1H and 13C NMR Determination of the Enantiomeric Purity of Substituted 4-Amino-3- (thien-2-Yl)-Butyric Acids and 4-Amino-3-(Benzo[b]Furan-2-yl)-Butyric Acids,Ligands of the GabaB Receptor.

The enantiomeric composition and absolute configuration of 4-Amino-3-(benzo[b]furan-2-yl)-Butanoic Acids and of 4-Amino-3-(thien-2-yl)-Butanoic Acids 1 may be accurately determined by ¹H and ¹³C nuclear magnetic resonance analysis of the corresponding derivatives 3 prepared by reaction with chiral reagents. Correlation with HPLC is signaled.     

Taylor Expansions of Distributions

Classical Taylor expansions of holomorphic functions in the complex plane are extended to distributions in Rⁿand in domains