Distant perturbation asymptotics in window-coupled waveguides. I. The non-threshold case

We consider a pair of adjacent quantum waveguides, in general of different widths, coupled laterally by a pair of windows in the common boundary, not necessarily of the same length, at a fixed distance. The Hamiltonian is the respective Dirichlet Laplacian. We analyze the asymptotic behavior of the discrete spectrum as the window distance tends to infinity for the generic case, i.e. for eigenvalues of the corresponding one-window problems separated from the threshold

Temperature-induced pair correlations in clusters and nuclei

The pair correlations in mesoscopic systems such as $nm$-size superconducting clusters and nuclei are studied at finite temperature for the canonical ensemble of fermions in model spaces with a fixed particle number: i) a degenerate spherical shell (strong coupling limit), ii) an equidistantly spaced deformed shell (weak coupling limit). It is shown that after the destruction of the pair correlations at T=0 by a strong magnetic field or rapid rotation, heating can bring them back. This phenomenon is a consequence of the fixed number of fermions in the canonical ensemble

PT-symmetric models in curved manifolds

We consider the Laplace-Beltrami operator in tubular neighbourhoods of curves on two-dimensional Riemannian manifolds, subject to non-Hermitian parity and time preserving boundary conditions. We are interested in the interplay between the geometry and spectrum. After introducing a suitable Hilbert space framework in the general situation, which enables us to realize the Laplace-Beltrami operator as an m-sectorial operator, we focus on solvable models defined on manifolds of constant curvature. In some situations, notably for non-Hermitian Robin-type boundary conditions, we are able to prove either the reality of the spectrum or the existence of complex conjugate pairs of eigenvalues, and establish similarity of the non-Hermitian m-sectorial operators to normal or self-adjoint operators. The study is illustrated by numerical computations.Comment: 37 pages, PDFLaTeX with 11 figure

Time dependent partial waves and vortex rings in the dynamics of wave packets

We have found a new class of time dependent partial waves which are solutions of time dependent Schr\"odinger equation for three dimensional harmonic oscillator. We also showed the decomposition of coherent states of harmonic oscillator into these partial waves. This decomposition appears perticularly convenient for a description of the dynamics of a wave packet representing a particle with spin when the spin--orbit interaction is present in the hamiltonian. An example of an evolution of a localized wave packet into a torus and backwards, for a particular initial conditions is analysed in analytical terms and shown with a computer graphics.Comment: 10 pages, LaTeX, 6 postscript figures, submitted to J. Phys. A: Math. Ge

Age features of molecular-biological subtypes of breast cancer

In this article, we analyzed the age-related features of molecular- biological subtypes in 499 patients with invasive breast cancer. All cases were divided into 5 molecular- biological subtypes based on immunohistochemical studies of hormone receptors, Her2, Ki-67. The average age of patients was 53.4 + 0.39 years, the predominant group were patients 50-60 years old (37.2%). The most common molecular biological subtype in our study was the luminal A subtype (35.6%). The hormone receptor positive subtypes of breast cancer (luminal A and B) were more common in all age groups. The triple negative subtype (43.2%) was the most common in the of group younger of 40 years old and the percentage of HER2-positive breast subtypes in groups 51-60 and older was twice as high as the groups 41-50 and younger of 40.В данной работе проведен анализ возрастных особенностей молекулярно-биологических подтипов у 499 больных инвазивным раком молочной железы. Все случаи были разделены на 5 молекулярно-биологических подтипов на основе иммуногистохимического исследования рецепторов к гормонам, Her2, Ki-67. Средний возраст пациенток составлял 53,4 + 0,39 года, самой многочисленной группой были пациентки от 50 до 60 лет (37,2% от общего числа). Наиболее распространенным молекулярно-биологическим подтипом в нашем исследовании был люминальный А подтип (35,6%). Во всех возрастных группах чаще встречались гормон-рецептор позитивные подтипы РМЖ (люминальный А и В), однако в группе до 40 лет самым распространенным оказался тройной негативный подтип РМЖ (43,2%), а доля HER2-позитивных подтипов РМЖ в группах 51-60 и старше оказалась в два раза выше по сравнению с группами 41-50 и до 40 лет

The age structure of molecular-biological subtypes of breast cancer

This article analyzes 516 cases of invasive breast cancer, which were divided into 4 age groups: younger than 40 years, 41-49 years, 50-59 years, older than 60 years. These groups were divided into 5 molecular biological subtypes based on immunohistochemical studies of hormone receptors, HER2/neu, and Ki- 67.The average age of the patients was 53.0 + 0.25 years, the largest group were patients from 50 to 59 years (39.5% of the total number). The most common molecular biological subtype in our study was the luminal A subtype (35.9%).In all age groups, hormone-receptor positive subtypes of breast cancer were more common (luminal A and B), in the group up to 40 years, the triple negative subtype of breast cancer was the most common (45.5%), and the HER2-positive subtype of breast cancer was more common in groups older than 50 years than in groups up to 50.В данной статье проведен анализ 516 случаев инвазивного рака молочной железы, которые были разделены на 4 возрастные группы: пациентки моложе 40 лет, 41-49 лет, 50-59 лет, старше 60 лет. В данных группах произведено разделение на 5 молекулярно-биологических подтипов на основе иммуногистохимического определения рецепторов к гормонам, HER2/neu, Ki-67. Средний возраст пациенток составлял 53,0 + 0,25 года, самой многочисленной группой были пациентки от 50 до 59 лет (39,5% от общего числа). Наиболее распространенным молекулярно-биологическим подтипом в нашем исследовании оказался люминальный А подтип (35,9%). Во всех возрастных группах чаще встречались гормон-рецептор позитивные подтипы РМЖ (люминальный А и В), в группе до 40 лет самым распространенным оказался тройной негативный подтип РМЖ (45,5%), HER2-позитивный подтип РМЖ в группах старше 50 лет встречался чаще, чем в группах до 50

On the similarity of Sturm-Liouville operators with non-Hermitian boundary conditions to self-adjoint and normal operators

We consider one-dimensional Schroedinger-type operators in a bounded interval with non-self-adjoint Robin-type boundary conditions. It is well known that such operators are generically conjugate to normal operators via a similarity transformation. Motivated by recent interests in quasi-Hermitian Hamiltonians in quantum mechanics, we study properties of the transformations in detail. We show that they can be expressed as the sum of the identity and an integral Hilbert-Schmidt operator. In the case of parity and time reversal boundary conditions, we establish closed integral-type formulae for the similarity transformations, derive the similar self-adjoint operator and also find the associated "charge conjugation" operator, which plays the role of fundamental symmetry in a Krein-space reformulation of the problem.Comment: 27 page