Formation of novel photoadducts from irradiation of 5(S)-5-O-tert-butyldimethylsiloxymethylfuran-2(5H)-one

Irradiation of 5S-5-O-tert-butyldimethylsiloxymethylfuran-2(5H)-one 1 in acetonitrile yields the C2-symmetric bis(lactone), 1S,2S,6S,7S-[3S,10S]-bis-tert-butyldimethylsiloxymethyl-4,9-dioxatricyclo[5.3.0.02,6]deca-5,8-dione 6, and a 3-substituted intramolecular product resulting from an apparent 8-endo-trig cyclisation.

Numerical Methods for Stiff Two-Point Boundary Value Problems

We consider the two-point boundary value problem for stiff systems of ordinary differential equations. For systems that can be transformed to essentially diagonally dominant form with appropriate smoothness conditions, a priori estimates are obtained. Problems with turning points can be treated with this theory, and we discuss this in detail. We give robust difference approximations and present error estimates for these schemes. In particular we give a detailed description of how to transform a general system to essentially diagonally dominant form and then stretch the independent variable so that the system will satisfy the correct smoothness conditions. Numerical examples are presented for both linear and nonlinear problems.

Free People of Color: expulsion and enslavement in the Antebellum South

This chapter explores the expulsion and enslavement of free People of Color in the southern states of the USA before the Civil War.