Diels-Alder-Reaktionen mit 3-Cyclopropylidenprop-1-enyl-ethyl-ether als 1,3-Dien

Diels-Alder Reactions with 3-Cyclopropylideneprop-1-enyl Ethyl Ether as 1,3-Diene The title compound undergoes readily Diels-Alder reactions with various dienophiles, especially with quinones. The resulting adducts constitute key intermediates in the synthesis of labdane diterpenoids.     

Fluid percolation in bond-site size-correlated three-dimensional networks

A treatment of sites appropriate to fluid percolation in bond controlled processes results in sensitivity of breakup of the defender to the degree of size-correlation for three-dimensional networks. In strongly correlated lattices network control of invasion yields to a statistical treatment as a result of improved accessibility.     

Enumeration results for Runge–Kutta methods for index 2 DAEs

Recursive formulas are presented that give the number of order conditions for single-step Runge–Kutta methods for index 2 DAEs.     

The rate of convergence for the cyclic projections algorithm III: Regularity of convex sets

The cyclic projections algorithm is an important method for determining a point in the intersection of a finite number of closed convex sets in a Hilbert space. That is, for determining a solution to the “convex feasibility” problem. This is the third paper in a series on a study of the rate of convergence for the cyclic projections algorithm. In the first of these papers, we showed that the rate could be described in terms of the “angles” between the convex sets involved. In the second, we showed that these angles often had a more tractable formulation in terms of the “norm” of the product of the (nonlinear) metric projections onto related convex sets.In this paper, we show that the rate of convergence of the cyclic projections algorithm is also intimately related to the “linear regularity property” of Bauschke and Borwein, the “normal property” of Jameson (as well as Bakan, Deutsch, and Li’s generalization of Jameson’s normal property), the “strong conical hull intersection property” of Deutsch, Li, and Ward, and the rate of convergence of iterated parallel projections. Such properties have already been shown to be important in various other contexts as well.