Rhodium(I)-catalyzed silylation of aryl halides with triethoxysilane: practical synthetic route to aryltriethoxysilanes

[reaction: see text] The specific silylation of aryl iodides and bromides with triethoxysilane (EtO)(3)SiH in the presence of NEt(3) and a catalytic amount of [Rh(cod)(MeCN)(2)]BF(4) provides the corresponding aryltriethoxysilanes in high yield.     

Trudinger type inequalities in and their best exponents

We study Trudinger type inequalities in and their best exponents . We show for , ( is the surface area of the unit sphere in ), there exists a constant such that

for all . Here is defined by

It is also shown that with is false, which is different from the usual Trudinger's inequalities in bounded domains.

     

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.