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We consider the nth eigenvalue as a function on the space of self-adjoint regular Sturm Liouville problems with positive leading coefficient and weight functions. The discontinuity of the nth eigenvalue is completely characterized. Academic Press

SUMMARYMecA, a structural gene located on the chromosome of Staphylococcus aureus, characterizes methicillin-resistant S. aureus (MRSA), and femA and femB(fem) genes encode proteins which influence the level of methicillin resistance of S. aureus. In order to examine effectiveness of detecting mecA and fem genes in identification of MRSA, the presence of these genes in 237 clinically isolated strains of staphylococci was investigated by polymerase chain reaction (PCR). An amplified mecA DNA fragment of 533 base pairs (bp) was detected in 100 % of oxacillin-resistant S. aureus, in 16'7 % of oxacillin-sensitive S. aureus, in 81-5 % of S. epidermidis, and in 58'3 % of other coagulase-negative staphylococci (CNS). While the PCR product of femA (509 bp) or femB (651 bp) was obtained from almost all the S. aureus strains except for five oxacillin-resistant strains (2'5%), neither of these genes were detected in CNS. Therefore, the detection offemA and femB together with mecA by PCR was considered to be a more reliable indicator to identify MRSA by differentiating it from mecA-positive CNS than single detection of mecA.

SUMMARYThe presence of six gene 4 alleles (or VP4 genotypes) in human rotaviruses has been recognized. Using 16 representative cultivable human rotavirus strains, we confirmed the specificity of VP4 genotyping by polymerase chain reaction (PCR) using the nested oligonucleotides specific to each of the four representative gene 4 alleles. Using the PCR. we surveyed the gene 4 alleles of 199 human rotaviruses in stools collected in Japan and Thailand. Strains with the gene 4 allele, corresponding to P1A serotype. were shown to be the most prevalent, but two strains with P2 gene 4 allele and one strain with P3 gene 4 allele were detected in Thailand and in Japan, respectively.

There are well-known inequalities among the eigenvalues of Sturm-Liouville problems with periodic, semi-periodic, Dirichlet and Neumann boundary conditions. In this paper, for an arbitrary coupled self-adjoint boundary condition, we identify two separated boundary conditions corresponding to the Dirichlet and Neumann conditions in the classical case, and establish analogous inequalities. It is also well-known that the lowest periodic eigenvalue is simple; here we prove a similar result for the general case. Moreover, we show that the algebraic and geometric multiplicities of the eigenvalues of self-adjoint regular Sturm-Liouville problems with coupled boundary conditions are the same. An important step in our approach is to obtain a representation of the fundamental solutions for sufficiently negative values of the spectral parameter. Our approach yields the existence and boundedness from below of the eigenvalues of arbitrary self-adjoint regular Sturm-Liouville problems without using operator theory.