A Facile Reaction of Unactivated Imines with Telluronium Allylide . Highly Stereoselective Synthesis of Vinylaziridines
Supporting Information General methods. Infrared spectra were recorded on a Nicolet AVATAR-360 spectrometer. H NMR and C NMR spectra were recorded at Bruker AM-300 instruments. Low resolution mass spectra (m/z) were recorded on HP5989A. High-resolution mass spectra were recorded on Concept 1H or MALDI/DHB. Microanalyses were performed using a Elemantar Vario EL. All reaction flasks were dried by flame. And all reactions were carried out under argon unless otherwise noted. THF and toluene were dried by distilled over sodium-benzophenone ketyl prior to use. N-aryl imines and -amidoalkyl-p-tolyl sulfones were prepared according to literature methods.
The Wittig Rearrangement
In 1942 Wittig and Lohmann described the isomerization of α-lithiated ethers (2; R = Me or CH2Ph) to skeletally rearranged lithio alkoxides (3; equation 1).1 Subsequent work by Wittig and others established that a variety of ethers undergo the Wittig rearrangement, provided the α-anion is stabilized by an aryl substituent. Of the several mechanisms proposed for this reaction a sequence involving homolysis of the anion intermediate (5), followed by recombination of the radical and radical anion fragments (equation 2) best accommodates the experimental findings.1–4
DIFFERENTIAL CALCULUS OF SEVERAL VARIABLES WITH MATHEMATICA OR MAPLE
The use of Computer Algebra Systems (CAS) in Mathematical Laboratories at Engineering Schools is increasing. Therefore, it has become necessary to undertake a new educational approach in the teaching of many mathematical topics. Obviously it is not possible to give the same lectures as in the 1950,s. The CAS allows us to experiment and teach in “a different way”. The students' mathematical knowledge at the beginning of their studies in the University is completely different. Moreover we have fewer credits assigned to Mathematical topics in engineering curriculum. The objective of he authors, professors of different Spanish Universities, is to try to demonstrate a new way to use the CAS, concretely Maple and Mathematica, as a support in the teaching of Differential Calculus of Several Variables. They take advantage of the computer's graphical capacities to sketch the graphs of surfaces defined in explicit, parametric or implicit form. They survey the general topics: limits, partial derivatives, differentiability, chain rule, implicit functions and extreme values. For each topic, they give a few basic instructions of the CAS used; afterwards they give several examples, in increasing order of difficulty, and finally the students must solve exercises and try to establish a general procedure for a quite general problem. In this paper we have included several examples used in this survey.