Inverse scattering problem for Sturm–Liouville operator with nonlinear dependence on the spectral parameter in the boundary condition

The inverse problem of the scattering theory for Sturm–Liouville operator on the half line with boundary condition depending quadratic on the spectral parameter is considered. Scattering data are defined, some properties of the scattering data are examined, the main equation is obtained, solvability of the integral equation is proved and uniqueness of algorithm to the potential with given scattering data is studied. Copyright © 2010 John Wiley & Sons, Ltd.     

Evaluation of the mechanism,regio-, and diastereoselectivity of aza-Diels–Alder reactions of 2H-azirine under a Lewis acid catalyst

Structural Chemistry - The molecular mechanism of the cycloaddition reactions of 2H-azirine with 1-methoxybutadiene and cyclohexadiene has been studied at the M06-2X/cc-pVDZ level of theory....     

Supported palladium oxide nanoparticles in Al-SBA-15 as an efficient and reusable catalyst for the synthesis of pyranopyrazole and benzylpyrazolyl coumarin derivatives via multicomponent reactions

An eco-friendly method for diversity-oriented synthesis of substituted dihydropyrano[2,3-c]pyrazole and benzylpyrazolyl coumarin derivatives has been achieved via one-pot and multicomponent reaction in the presence of PdO/Al-SBA-15 as an efficient and recyclable catalyst in H₂O/EtOH under reflux conditions. The significant merits of this method are wide scope, high yields of the desired products, short reaction times and simple workup procedure. In addition, this nanocatalyst was simply recovered and reused five times without significant loss in catalytic activity and also performance.

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Crosslinking of an unsaturated polyester resin in the mould: Modelling and heat transfer studies

The crosslinking of unsaturated polyester was studied by using an experiment and a mathematical model of the process. Temperature–time profiles were recorded in the centre of the sample inside the mould at the outer wall of the cylindrical copper mould, and in the bulk of the heated air bath. A numerical model was constructed by taking into account the heat transferred by convection from the air to the mould surface and the heat transferred by conduction through the resin, as well as the heat generated by the crosslinking reaction. The convection heat transfer coefficient was determined in independent experiments with the empty copper mould. Introduction of the carbon base filler reduced the amount of heat generated in the composite due to the less reactive component in the composite. As a result, it lowered the temperature of the resin. By recording the temperature-time and the degree of crosslinking time profiles developed within the sample extensive knowledge of the process can be obtained. The effects of the convection heat transfer on the rate of mould heating, and the conduction heat transfer through the mould as well as the internal heat generated by the crosslinking reaction are visibly shown, despite a complexity of the process.     

Continuity of the scattering function and Levinson‐type formula of Klein–Gordon equation

We considered the inverse problem of scattering theory for a boundary value problem on the half line generated by Klein–Gordon differential equation with a nonlinear spectral parameter‐dependent boundary condition. We defined the scattering data, and we proved the continuity of the scattering function S(λ); in a special case, the relation for the difference of the logarithm of the scattering function, which is called the Levinson‐type formula, was obtained. Copyright © 2012 John Wiley & Sons, Ltd.     

Structural determination of prunusins A and B,new C‐alkylated flavonoids from Prunus domestica,by 1D and 2D NMR spectroscopy

Prunusins A (1) and B (2), the new C‐alkylated flavonoids, have been isolated from the seed kernels of Prunus domestica. Their structures were assigned from ¹H and ¹³C nuclear magnetic resonating spectra, DEPT and by correlation spectroscopy, HMQC and HMBC experiments. 3, 5, 7, 4′‐Tetrahydroxyflavone (3) and 3, 5, 7‐trihydroxy‐8, 4′‐dimethoxyflavone (4) have also been reported from this species. Both compounds (1) and (2) showed significant antifungal activity against pathogenic fungus Trichophyton simmi. Copyright © 2009 John Wiley & Sons, Ltd.