59 research outputs found
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 -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
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