On higher order computations in strong coupling

An algorithm which simplifies manipulation of higher order graphs in strong coupling is presented.     

The Bloch theorem in several complex variables

The background theory for the Bloch theorem is generalized to several complex variables. This work involves study of the Bergman kernel functions in order to extend work of Landau and Bonk. The main conclusion is an estimate for Bloch’s constant for mappings of domains of the first classical type. In the special case of then-dimensional ball, the estimate of Bloch’s constant coincides with that of Liu.     

A fast minimal residual algorithm for shifted unitary matrices

A new iterative scheme is described for the solution of large linear systems of equations with a matrix of the form A = ρU + ζI, where ρ and ζ are constants, U is a unitary matrix and I is the identity matrix. We show that for such matrices a Krylov subspace basis can be generated by recursion formulas with few terms. This leads to a minimal residual algorithm that requires little storage and makes it possible to determine each iterate with fairly little arithmetic work. This algorithm provides a model for iterative methods for non-Hermitian linear systems of equations, in a similar way to the conjugate gradient and conjugate residual algorithms. Our iterative scheme illustrates that results by Faber and Manteuffel [3,4] on the existence of conjugate gradient algorithms with short recurrence relations, and related results by Joubert and Young [13], can be extended.     

New classes of self-complementary codes and quasi-symmetric designs

We present a new technique for constructing binary error correcting codes and give some examples of codes that can be constructed via this method. Among the examples is an infinite family of self-complementary codes with parameters (2u ²−u, 8u ², u ²−u) that can be constructed whenever there exists a u × u Hadamard Matrix. These codes meet the Grey–Rankin bound and imply the existence of quasi-symmetric designs on 2u ²−u points.     

The exact condition of the B-spline basis may be hard to determine

The author's conjecture concerning the knot sequence whose associated B-spline sequence has maximum max-norm condition number is disproved. Related condition numbers are explored and the corresponding conjecture concerning the “worst” knot sequence for them is further supported by numerical results.     

Regioselective organocadmium alkylations of substituted quinones.

A series of substituted quinones was alkylated with diethylcadmium. Regiochemistry of addition shifted from quinol formation to conjugate addition as a function of the steric and electronic effects of the substituents.     

N,S-dimethyl-s-phenylsulfoximine: A reagent for the optical resolution of ketones

The addition of the α-lithio derivative of (+)- or (-)-N,S-dimethyl-S-phenylsulfoximine to selected dl-ketones was carried out at -78° in tetrahydrofuran followed by acid quench at that temperature to produce mixtures of diastereomeric β-hydroxysulfoximines. The optically-active diastereomers were chromatographically separated on sil recycled.