Iron-promoted elimination of beta-thioalkoxy alcohols. Olefination by coupling of a carbonyl group with a dithioacetal

Treatment of propargylic dithiolanes with nBuLi followed by a carbonyl electrophile yields the corresponding propargylic dithioacetals. Upon treatment with 1 equiv of Fe(acac)3 and excess MeMgI, elimination of SR and OH moieties from 8 affords the corresponding olefins in satisfactory yield. Benzylic dithioacetals behave similarly. The reaction can be considered an alternative of McMurry coupling of two different carbonyl equivalents.     

Elimination of beta-thioalkoxy alcohols under Mitsunobu conditions. A new synthesis of conjugated enynes from propargylic dithioacetals

Treatment of propargylic dithiolanes 1 with (n)BuLi followed by a carbonyl electrophile yields the corresponding homopropargylic alcohol 3. Upon treatment with 2 equiv of PPh3 and DIAD, elimination of SR and OH moieties from 3 affords the corresponding olefins 4 in moderate to good yield. The reaction can be considered an alternative of McMurry coupling of two different carbonyl equivalents.     

The crucial constants in the exponential-type error estimates for Gaussian interpolation

It's well-known that there is a very powerful error bound for Gaussians put forward by Madych and Nelson in 1992.It's of the form|f(x)-s(x)|≤(Cd)c/d‖f‖h where C,c are constants,h is the Gaussian function,s is the interpolating function,and d is called fill distance which,roughly speaking,measures the spacing of the points at which interpolation occurs.This error bound gets small very fast as d→0.The constants C and c are very sensitive.A slight change of them will result in a huge change of the error bound.The number c can be calculated as shown in [9].However,C cannot be calculated,or even approximated.This is a famous question in the theory of radial basis functions.The purpose of this paper is to answer this question.