Lax-Phillips scattering theory for PT-symmetric \rho-perturbed operators

The S-matrices corresponding to PT-symmetric \rho-perturbed operators are defined and calculated by means of an approach based on an operator-theoretical interpretation of the Lax-Phillips scattering theory

On elements of the Lax-Phillips scattering scheme for PT-symmetric operators

Generalized PT-symmetric operators acting an a Hilbert space $\mathfrak{H}$ are defined and investigated. The case of PT-symmetric extensions of a symmetric operator $S$ is investigated in detail. The possible application of the Lax-Phillips scattering methods to the investigation of PT-symmetric operators is illustrated by considering the case of 0-perturbed operators

JJ-self-adjoint operators with C\mathcal{C}-symmetries: extension theory approach

A well known tool in conventional (von Neumann) quantum mechanics is the self-adjoint extension technique for symmetric operators. It is used, e.g., for the construction of Dirac-Hermitian Hamiltonians with point-interaction potentials. Here we reshape this technique to allow for the construction of pseudo-Hermitian ($J$-self-adjoint) Hamiltonians with complex point-interactions. We demonstrate that the resulting Hamiltonians are bijectively related with so called hypermaximal neutral subspaces of the defect Krein space of the symmetric operator. This symmetric operator is allowed to have arbitrary but equal deficiency indices . General properties of the $\cC$ operators for these Hamiltonians are derived. A detailed study of $\cC$-operator parametrizations and Krein type resolvent formulas is provided for $J$-self-adjoint extensions of symmetric operators with deficiency indices . The technique is exemplified on 1D pseudo-Hermitian Schr\"odinger and Dirac Hamiltonians with complex point-interaction potentials

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

Physical-mechanical image of the cell surface on the base of AFM data in contact mode

Изучены физико-механические образы поверхности фибробластов и раковых эпителиальных клеток человека, созданные на основе данных атомно-силовой микроскопии в контактном режиме по средним значениям сил трения, упругости и адгезии и параметров пространственного распределения механических свойств клеточной поверхности.Physical-mechanical images of the cell surface of human fibroblasts and cancerous epithelial cells that were formed using the average values of the parameters of friction, elastic and adhesive forces and the spatial distribution parameters of mechanical properties obtained by atomic force microscopy in contact mode were studied

Исследование влияния температуры культивирования на морфологию, механические и адгезионные свойства раковых клеток легких человека линии А549

The results of study the effect of temperature on the culture surface topography and mechanical properties of human lung cancer cell line A549 by atomic force microscopy are presented. It is shown that lowering the temperature of cultivation does not lead to significant changes in the mechanical properties of A549 cells, but the cells under the influence of low temperatures tend to increase the adhesive force between the probe tip to the membrane surface.Представлены результаты исследования методом атомно-силовой микроскопии влияния температуры культивирования на топографию поверхности и механические свойства раковых клеток легких человека линии А549. Показано, что понижение температуры культивирования не приводит к достоверным изменениям механических свойств данных клеток, однако увеличивает силу адгезии острия зонда к поверхности мембраны

Исследование методом атомно-силовой микроскопии влияния наночастиц на структурные и механические свойства клеток почки быка линии MDBK

The effect of copper and silver nanoparticles Cu+Ag, silver nitrite AgNO3 and zinc oxide ZnO on morphology and mechanical properties of immunocompetent cells bovine kidney line MDBK is investigated by atomic force microscopy. The results of calculation of the local elastic modulus, strength, surface cell adhesion, adhesion work, and the three-dimensional image analysis of cells in control and after incubation with the nanoparticles bioelements for 20 min are presented.Методом атомно-силовой микроскопии (АСМ) исследовано влияние наночастиц меди и серебра Cu+Ag, нитрита серебра AgNO3 и оксида цинка ZnO на морфологию и механические свойства иммунокомпетентных клеток почки быка линии MDBK. Представлены результаты расчетов локального модуля упругости, силы поверхностной адгезии клеток, работы адгезии, а также анализа трехмерных изображений клеток в контроле и после инкубации с наночастицами биоэлементов в течение 20 мин

LEFT VENTRICLE TORSION IN AN IDIOPATHIC HIS LEFT BUNDLE BRANCH BLOCK

The role of left His bundle branch block (LBBB) in normal systolic function of the left ventricle (LV) remains under investigated for the global deformation and torsion.Aim. To investigate on the global deformity of the LV in longitudinal direction by circumference, and its torsion, in patients with idiopathic LBBB with saved LV ejection fraction (EF).Material and methods. Totally, 50 persons with idiopathic LBBB studied, with the mean duration of QRS 153±24,5 ms. Comparison group included 18 persons with no LBBB. All patients underwent echocardiography (Echo) with assessment of intracardiac hemodynamics, deformity measurement by Speckle tracking imaging, with evaluation of torsion and rotation dynamics of the LV. Results. There were no significant differences in idiopathic LBBB group comparing to the controls, by the value of end-diastolic volume (respectively, 110,5±33,5 mL vs 95,3±23,5 mL, р=0,1) and EF LV (61,3±9,5% vs 64,4±9,4%, р=0,2). In idiopathic LBBB group comparing to controls, there was decrease of global LV deformation in longitudinal direction (respectively, -14,6±3,98% vs -8,4±3,10%, р=0,0006) and by circumference at basal segments (-7,02±4,40)% vs -10,6±4,18%, р=0,0075). It was found that in idiopathic LBBB there is disordered rotation at basal segments level (-2,95±4,36º vs -6,10±3,01º, р=0,019) and the torsion of LV as well (7,52±5,48º vs 13,1±5,18º, р=0,001).Conclusion. Disordered conduction in LBBB is followed by impaired rotation and torsion, regardless of the saved systolic function

Heart failure with preserved ejection fraction: the role of diastolic stress test in diagnostic algorithms

Heart failure (HF) with preserved ejection fraction (HFpEF) is currently the most common type of this condition, especially among elderly patients. Despite the preserved left ventricular (LV) and a moderate increase in natriuretic peptide, patients  with HFpEF have the same out-of-hospital mortality as those with HF with reduced ejection fraction (HFrEF). Diagnosis of HFpEF is difficult due to nonspecific symptoms, expensive blood tests, and questionable rest echocardiographic data on diastolic function. In addition, the reason for poor diagnosis of HfpEF in clinical practice may be old age and comorbidities, which can also cause nonspecific symptoms of moderate chronic shortness of breath, weakness, and palpitations. The consequence is the detection of HFpEF only in every fourth patient with an acute or chronic heart failure. The use of simplified clinical diagnostic protocols along with a non-invasive ultrasound stress test can help overcome the existing problems in the diagnosis of HFpEF