A GENERALIZATION OF THE 0-NUMERICAL RANGE
Let H be a complex Hilbert space. Given a bounded linear operator A on H, we describe the set R n (A) = fV AW : V;W : C n ! H;V V = W W = In;V W = 0g. It is shown that the closed matricial convex hull of R n (A) is a closed ball of radius minfkA I k : 2 Cg centered at the origin.
Wigner's theorem in Hilbert C^*-modules over C^*-algebras of compact operators
Let W be a Hilbert C ⁄ -module over the C ⁄ - algebra A 6 C of all compact operators on a Hilbert space. It is proved that any function T : W ! W which pre- serves the absolute value of the A-valued inner product is of the form Tv = '(v)Uv; v 2 W, where ' is a phase func- tion and U is an A-linear isometry. The result generalizes Molnar's extension of Wigner's classical unitary-antiunitary theorem.
Genotypic diversity in field isolates of Babesia bovis from cattle with babesiosis after vaccination.
OBJECTIVE
To determine whether particular genotypes of Babesia bovis were common to field isolates obtained from cattle properties in Queensland where the B bovis vaccine had apparently failed.


DESIGN
A comparative study of polymerase chain reaction genotypes in different populations of B bovis.


PROCEDURE
Two polymerase chain reaction assays were applied to analyse DNA extracts of B bovis vaccine (K, T and Dixie strains) and 27 field isolates from 24 properties where disease outbreaks had occurred despite the use of the vaccine. To evaluate the stability of the genotypes identified, 11 of the field isolates were inoculated into experimental cattle that had either been previously vaccinated with T strain or not vaccinated.


RESULTS
No particular genotype of B bovis was responsible for the problems observed in previously vaccinated herds. None of the isolates had genotypes identical to the vaccine strains used. No geographic trends among the genotypes were observed. Isolates that originated from the same property also had different genotypes. Blood passage of the 11 field isolates in either previously vaccinated or nonvaccinated cattle did not alter the original genotype.


CONCLUSION
No particular genotypes identified by the Bv80 and BvVA1 polymerase chain reaction assays could be associated with vaccine failures.