Generalizations of the Liouville theorem

The purpose of this paper is to generalize the Liouville theorem for functions which are defined on the complete Riemannian manifolds. Then, we apply it to the isometric immersions between complete Riemannian manifolds in order to obtain an estimate for the size of the image of immersions in terms of the supremum of the length of their mean curvature vector in a quite general setting. The proofs are based on the Calabi's generalization of maximum principle for functions which are not necessarily differentiable.     

A meshless approach for solution of Burgers’ equation

A new meshless method called gradient reproducing kernel particle method (GRKPM) is proposed for numerical solutions of one-dimensional Burgers’ equation with various values of viscosity and different initial and boundary conditions. Discretization is first done in the space via GRKPM, and subsequently, the reduced system of nonlinear ordinary differential equations is discretized in time by the Gear's method. Comparison with the exact solutions, which are only available for restricted initial conditions and values of viscosity, approves the efficacy of the proposed method. For challenging cases involving small viscosities, comparison with the results obtained using other numerical schemes in the literature further attests the desirable features of the presented methodology.     

Study of the vibrational characteristics of the homonuclear diatomic nuclear schrödinger equation with a numerov method using a number of empirical potential functions

Many empirical potential energy functions have been modeled to represent the potential energy function of a diatomic molecule along whole range of internuclear distance coordinate, whereby one can determine certain molecular constants. Here we employ various potential functions such as Morse, Rydberg, Varshni(II), Varshni(III), Varshni(VI), Pöschl-Teller, Hulburt-Hirschfelder, Lippincott, Frost-Musulin, Linnet, and Rosen-Morse, and the Numerov method to solve the nuclear Schrödinger equation for F2, as an example of a homonuclear diatomic molecule. Herewith, the vibrational and vibration-rotation energy levels are obtained and excellent accuracy is achieved. The potential of employing the Numerov method in engineering physics computations is emphasized.     

Trichloroisocyanuric Acid (TCCA) and N-Chlorosuccinimide (NCS) as Efficient Reagents for the Direct Oxidative Conversion of Thiols and Disulfides to Sulfonyl Chlorides

Abstract

Trichloroisocyanuric acid (TCCA) and N-chlorosuccinimide (NCS) were found to be mild and efficient reagents for the direct oxidative conversion of sulfur compounds to the corresponding arenesulfonyl chlorides in good-to-excellent yields through the oxidative chlorination. The overall process is simple and practical, and it provides convenient access to a variety of aryl or heteroarylsulfonyl chlorides. The mild reaction conditions and the broad substrate scope render this method attractive and complementary to existing syntheses of aryl or heteroarylsulfonyl chlorides.     

Chemoselective Synthesis of Fused Phosphorus Compound with 2-Hydropyrimidine-2-Thione Derivatives in Mixture of Water/Acetone as a Green Solvent

Abstract

3,4-Dihydropyrimidin-2(1H)-thione derivatives undergo a chemoselective reaction with dialkylacetylenedicarboxylate in the presence of triphenylphosphine lead to the corresponding stable heterocyclic phosphorus ylides in good yield. In this method, a mixture of water/acetone as a green solvent was used.

[Supplemental materials are available for this article. Go to the publisher's online edition of Phosphorus, Sulfur, and Silicon and the Related Elements to view the following free supplemental files: Additional figures]     

Quinolinium Fluorochromate: An Efficient and Convenient Reagent for Oxidative Cleavage of Thioacetals to Their Parent Carbonyl Compounds

Deprotection of thioacetals to their parent carbonyl compounds in high yields has been carried out using quinolinium fluorochromate under mild conditions.     

Catalyst-free synthesis of 3-hydroxyimidazo[1,2-a]pyridine zwitterion derivatives via the three-component reaction of ethyl glyoxalate, 2‑aminopyridines and cyclic 1,3-dicarbonyls

The three-component reaction of ethyl glyoxalate, 2-aminopyridines, and cyclic 1,3-dicarbonyl compounds such as 4-hydroxycoumarin, N,N-dimethylbarbituric acid and 4-hydroxy-6-methyl-2H-pyran-2-one is described for the synthesis of 3-hydroxyimidazo[1,2-a]pyridine zwitterion derivatives.     

Effect of synthesis method on physicochemical and catalytic properties of Cu–Zn-based mesoporous nanocatalysts for water-gas shift reaction

Two new mesoporous nanocatalysts based on CuO–ZnO/MgO were synthesized by using a modified liquid-phase method. Due to use of this method, the nanocatalysts contained an efficient ZnO/MgO phase in which MgO is incorporated into ZnO phase. The structural and catalytic properties of the nanocatalysts in the water-gas shift reaction were investigated compared with samples prepared by conventional sol–gel and liquid-phase methods as references, as well as a commercial catalyst. The results reveal that the new nanocatalysts exhibited higher surface area, lower degree of agglomeration, and higher activity than the reference samples, indicating the influence of both the synthesis method and phase composition.