The NMR reciprocity theorem for arbitrary probe geometry

It is shown that the NMR reciprocity theorem is a variant of a problem considered by Lorentz in 1895. This formulation is quite general and applies to electric-dipole-based as well as coil-based or resonator-based magnetic resonance probes. The reasoning is related to, but different from, the proof of the reciprocity theorem for radiofrequency networks and for transmit/receive antenna systems in telecommunications. The signal-to-noise ratio of the NMR experiment is also discussed in very general terms.     

Novel cephalosporins synthesized by amination of 2,5-dihydroxybenzoic acid derivatives using fungal laccases II

Sixteen novel cephalosporins were synthesized by amination of 2,5-dihydroxybenzoic acid derivatives with the aminocephalosporins cefadroxil, cefalexin, cefaclor, and the structurally related carbacephem loracarbef using laccases from Trametes sp. or Myceliophthora thermophila. All products inhibited the growth of several Gram positive bacterial strains in the agar diffusion assay, among them methicillin-resistant Staphylococcus aureus and vancomycin-resistant enterococci. The products protected mice against an infection with Staphylococcus aureus lethal to the control animals. Cytotoxicity and acute toxicity of the new compounds were negligible. The results show the usefulness of laccase for the synthesis of potential new antibiotics. The biological activity of the new compounds stimulates intensified pharmacological tests.     

Novel penicillins synthesized by biotransformation using laccase from Trametes spec

Eight novel penicillins were synthesized by heteromolecular reaction of ampicillin or amoxicillin with 2,5-dihydroxybenzoic acid derivatives using a laccase from Trametes spec. All products inhibited the growth of several gram positive bacterial strains in the agar diffusion assay, among them methicillin-resistant Staphylococcus aureus and vancomycin-resistant Enterococci. The products protected mice against an infection with Staphylococcus aureus lethal to the untreated animals. Cytotoxicity and acute toxicity of the new compounds were neglectable. The results show the usefulness of laccase for the synthesis of potential new antibiotics. The biological activity of the new compounds stimulates intensified pharmacological tests.     

Z4-Kerdock Codes, Orthogonal Spreads, and Extremal Euclidean Line-Sets

When m is odd, spreads in an orthogonal vector space of type⁺(2m + 2,2) are related to binary Kerdock codes and extremalline-sets in 2^{m + 1} with prescribed angles. Spreads in a 2m-dimensionalbinary symplectic vector space are related to Kerdock codesover Z₄ and extremal line-sets in with prescribed angles. These connections involve binary, realand complex geometry associated with extraspecial 2-groups.A geometric map from symplectic to orthogonal spreads is shownto induce the Gray map from a corresponding Z₄-Kerdock codeto its binary image. These geometric considerations lead tothe construction, for any odd composite m, of large numbersof Z₄-Kerdock codes. They also produce new Z₄-linear Kerdockand Preparata codes. 1991 Mathematics Subject Classification:primary 94B60; secondary 51M15, 20C99.