Hydroxyalkylation of alpha-C-H bonds of tetrahydrofuran with aldehydes in the presence of triethylborane and tert-butyl hydroperoxide

The alpha-hydroxyalkylation of tetrahydrofuran with aldehydes via radical C-H abstraction was conducted using triethylborane in the presence of tert-butyl hydroperoxide. This study presents a rare instance of direct intermolecular radical addition of unactivated cyclic ether to aldehydes.     

Functionalization on silica gel with allylsilanes. A new method of covalent attachment of organic functional groups on silica gel

Treatment of an (allyl)organosilane with silica gel in refluxing toluene brought about deallylation forming an Si-O-Si bond with the silicon on the silica gel. This Si-O-Si bond formation provides us with a new reliable method for the functionalization of a silica gel surface.     

A primal—dual infeasible-interior-point algorithm for linear programming

As in many primal—dual interior-point algorithms, a primal—dual infeasible-interior-point algorithm chooses a new point along the Newton direction towards a point on the central trajectory, but it does not confine the iterates within the feasible region. This paper proposes a step length rule with which the algorithm takes large distinct step lengths in the primal and dual spaces and enjoys the global convergence.Part of this research was done when M. Kojima and S. Mizuno visited at the IBM Almaden Research Center. Partial support from the Office of Naval Research under Contract N00014-91-C-0026 is acknowledged.Supported by Grant-in-Aids for Co-operative Research (03832017) of The Japan Ministry of Education, Science and Culture.Supported by Grant-in-Aids for Encouragement of Young Scientist (03740125) and Co-operative Research (03832017) of The Japan Ministry of Education, Science and Culture.     

A chaotic map with a flat segment can produce a noise-induced order

Matsumoto and Tsuda studied the effects of noise on chaos in a one-dimensional Belousov-Zhabotinsky (BZ) map and found noise-induced order, that is, an external noise destroys a chaotic behavior and produces some kind of order (periodicities). This phenomenon is very interesting in understanding the relation between chaos and natural phenomena. The present paper proposes a unimodal piecewise linear map which has a flat segment. It is shown numerically that the noise-induced order can be observed in this simple map in the same way as the BZ map. These numerical results clarify the mechanism of noise-induced order.     

Computational aspects of general minimax optimization

With an optimization problem of minimax type, we associate another problem which is, in turn, of maxmin type. We show that both the problems are equivalent in a sense and they have the same optimal value. The results obtained here are intimately related to Chebyshev (or uniform) approximation theory.