Extended kac-akhiezer formulae and the fredholm determinant of finite section hilbert-schmidt kernels

This paper deals with some results (known as Kac-Akhiezer formulae) on generalized Fredholm determinants for Hilbert-Schmidt operators on L2-spaces, available in the literature for convolution kernels on intervals. The Kac-Akhiezer formulae have been obtained for kernels which are not necessarily of convolution nature and for domains in R(n).

Chemoselective Schmidt Reaction Mediated by Triflic Acid: Selective Synthesis of Nitriles from Aldehydes

An excellent utility of Schmidt reaction of aldehydes to access corresponding nitriles in an instantaneous reaction is demonstrated. The reaction of aldehydes with NaN3 and TfOH furnishes the corresponding nitriles in near quantitative yields and tolerates a variety of electron-withdrawing and electron-donating substituents on the substrates. Formanilides, a common side product in Schmidt reaction, is not observed in this reaction. Besides these advantages, the salient feature of this reaction is that it exhibits a remarkable chemoselectivity, as acid and ketone functionalities are well tolerated under the reaction conditions. The reaction is easily scalable, high yielding, and nearly instantaneous.

Behaviour of turbulent Prandtl/Schmidt number in compressible mixing layer

The behaviour of turbulent Prandtl/Schmidt number is explored through the model-free simulation results. It has been observed that compressibility affects the Reynolds scalar flux vectors. Reduced peak values are also observed for compressible convective Mach number mixing layer as compared with the incompressible convective Mach number counterpart, indicating a reduction in the mixing of enthalpy and species. Pr-t and Sc-t variations also indicate a reduction in mixing. It is observed that unlike the incompressible case, it is difficult to assign a constant value to these numbers due to their continuous variation in space. Modelling of Pr-t and Sc-t would be necessary to cater for this continuous spatial variation. However, the turbulent Lewis number is evaluated to be near unity for the compressible case, making it necessary to model only one of the Pr-t and Sc-t..