One-dimensional point interaction with three complex parameters

For a pair of non-Hermitian Hamiltonian H and its Hermitian adjoint H(dagger), there are situations in which their eigenfunctions form a biorthogonal system. We illustrate such a situation by means of a one-particle system with a one-dimensional point interaction in the form of the Fermi pseudo-potential. The interaction consists of three terms with three strength parameters g(i) (i = 1, 2 and 3), which are all complex. This complex point interaction is neither Hermitian nor PT-invariant in general. The S-matrix for the transmission reflection problem constructed with H (or with H(dagger)) in the usual manner is not unitary, but it conforms to the pseudo-unitarity that we define. The pseudounitarity is closely related to the biorthogonality of the eigenfunctions. The eigenvalue spectrum of H with the complex interaction is generally complex but there are cases where the spectrum is real. In such a case H and H(dagger) form a pseudo-Hermitian pair.

Application of Real-Time PCR Stool Assay for Helicobacter pylori Detection and Clarithromycin Susceptibility Testing in Brazilian Children

Background: Helicobacter pylori ClariRes assay is a novel commercially available real-time PCR assay allowing H. pylori detection and clarithromycin susceptibility testing in either gastric biopsy or stool specimens. Objective: The aim of this study was to validate the novel biprobe real-time assay in stool specimens from 217 dyspeptic children. Methods: DNA from gastric biopsies and stool specimens were obtained and submitted to the biprobe real time assay for H. pylori detection and clarithromycin susceptibility testing. Results: The sensitivity, specificity, and test accuracy were 69, 100 and 93.9% for the detection of H. pylori infection and 83.3, 100 and 95.6%, for detection of clarithromycin resistance. Conclusion: This assay proved to be appropriate for H. pylori clarithromycin susceptibility testing, particularly in children populations where a high prevalence of clarithromycin-resistant strains is suspected.