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

Approximate resonance states in the semigroup decomposition of resonance evolution

The semigroup decomposition formalism makes use of the functional model for $C_{.0}$ class contractive semigroups for the description of the time evolution of resonances. For a given scattering problem the formalism allows for the association of a definite Hilbert space state with a scattering resonance. This state defines a decomposition of matrix elements of the evolution into a term evolving according to a semigroup law and a background term. We discuss the case of multiple resonances and give a bound on the size of the background term. As an example we treat a simple problem of scattering from a square barrier potential on the half-line.Comment: LaTex 22 pages 3 figure

On operators of transition in Krein spaces

Abstract. The paper is devoted to investigation of operators of transition and the corresponding decompositions of Krein spaces. The obtained results are applied to the study of relationship between solutions of operator Riccati equations and properties of the associated operator matrix L. In this way, we complete the known result (see Theorem 5.2 in the paper of S. Albeverio, A. Motovilov, A. Skhalikov, Integral Equ. Oper. Theory 6

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

Arrhythmic Mitral Valve Prolapse: New Menaces of the Known Disease

Mitral  valve prolapse  (MVP) has  long  been  the subject  of intense  discussions regarding the prognosis and  follow-up tactics.  In most  cases,  this condition has a benign prognosis. However, recent autopsy and follow-up studies have shown risks of developing  sudden cardiac death (SCD) in some subgroups of patients who have this clinical phenomenon. The proposed  literature review uses the population  of patients with MVP with the highest probability  of developing  life-threatening ventricular tachyarrhythmias. Patients with the presence of a complex  of changes, including  bicuspid  MVP, negative T waves in the inferior and lateral leads on a standard  12-lead electrocardiogram (ECG), and a special anatomical  phenomenon called mitral annular  disjunction  (MAD), are at high  risk of developing  ventricular  ectopias  and VSS.  A reflection  of the high  risk of SCD  in such patients  is the increase of ventricular ectopy according to Holter monitoring. The presence of a bicuspid  MVP and the MAD  phenomenon, which is a separation  of the line of attachment  of the posterior mitral leaflet from the basal inferior wall segment  towards  the atrial wall, determines the presence of a special form of MVP,  the so-called  arrhythmogenic MVP.  Hence,  in most cases MVP has a benign  prognosis. However, patients with the aforementioned ar- rhythmic  MVP  signs  must  be given  particular  attention  and  annual  follow-up including  ECG  control,  Holter  monitoring and  echocardiographic examination of the heart to reduce the risk of ventricular tachyarrhythmias and SCD development

SAFETY OF AMIODARONE USAGE IN PATIENTS WITH WOLFF-PARKINSON-WHITE SYNDROME AND ATRIAL FIBRILLATION

Amiodarone is one of the basic antiarrhytmic drugs for atrial fibrillation treatment. However application of amiodarone in patients with atrial fibrillation and Wolff-Parkinson-White syndrome can induce ventricular fibrillation. Amiodarone usage in these patients should be accompanied by readiness for performance of resuscitation. This is confirmed by clinical case presentation

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

Клинико-экономическая оценка эффективности и безопасности существующей практики проведения периоперационной антибиотикопрофилактики на оcнове фармакоэпидемиологического исследования в многопрофильных стационарах Санкт-Петербурга

A survey conducted in four hospitals located in the city of St. Petersburg revealed that the commonly used perioperative antibiotic prophylaxis (PAP) did not follow (in 88% of cases) the guidelines approved for national clinical practice.Aim. To perform a cost-effectiveness analysis of the commonly practiced PAP among patients with clean, clean-contaminated and contaminated surgical wounds in a multidisciplinary hospital.Materials and methods. The PAP cost-effectiveness analysis was performed using the data from a multicenter epidemiological survey and previously conducted studies. The Markov model was used to compare the effectiveness and safety of the commonly used PAP with that recommended by the clinical practice guidelines. The rate of surgical site infection (SSI) and antibiotic-associated diarrhea (AAD) were chosen for the endpoints.Results. The costs associated with a single case of PAP according to the clinical practice guidelines was 3.5 times less than that associated with the PAP used in the common practice (RUB 4913,67 and 17837,71 respectively). The present analysis demonstrates that the PAP recommended by the clinical practice guidelines was more cost-effective as compared with the commonly practiced PAP.Conclusion. Regular epidemiological monitoring is required to improve effectiveness and safety of the existing PAP practice. Целью исследования является клинико-экономическая оценка эффективности и безопасности существующей практики назначения периоперационной антибиотикопрофилактики.Материалы и методы. На основании данных фармакоэпидемиологического исследования, проведенного в четырех многопрофильных стационарах г. Санкт-Петербурга, оценена реальная практика проведения периоперационной антибиотикопрофилактики (ПАП) инфекций области хирургического вмешательства (ИОХВ), которая в абсолютном большинстве случаев (88%) не соответствовала клиническим рекомендациям. Построена модель анализа решений относительно эффективности и безопасности ПАП в реальной практике в сравнении с ПАП в соответствии с клиническими рекомендациями. В качестве критериев эффективности выбраны частота ИОХВ и число случаев предотвращенной антибиотик-ассоциированной диареи (ААД). Проведен анализ «затраты-эффективность».Результаты. Стоимость одного случая ПАП, проведенной по протоколу, с учетом прямых и непрямых затрат меньше таковой, используемой в реальной практике, более чем в 3,5 раза (4913,67 руб. и 17837,71 руб., соответственно). Анализ «затраты-эффективность» показал, что стратегия применения ПАП по протоколу доминировала перед стратегией проведения ПАП в реальной практике: при меньших затратах она имела наибольший прирост эффективности.Выводы. Для оптимизации потребления АМП с целью ПАП в каждом стационаре необходим периодический фармакоэпидемиологический мониторинг существующей практики проведения ПАП. Соблюдение основных принципов ПАП наряду с мерами инфекционного контроля является одной из возможностей минимизировать затраты, связанные с ее неэффективностью.