Задача Римана на системе концентрических колец и дискретные уравнения типа свертки (Riemann problem on the concentrated circles and discrete equations of convolution type)

Theory of one-sided invertibility for the operator R of Riemann’s boundary value problem in Lebesgue spaces Lp(Γ), where Γ is a union of 2n concentric circles, in terms of matrix operators is described. Constructions of inverse operators are obtained and subspaces Ker R and Im R are described. As application to this theory we consider system of discrete equations of convolution type generated by the operator R.На основе матричного операторного исчисления порядка 2n построена теория односторонней обратимости оператора R, по форме аналогичная классической теории краевой задачи Римана на замкнутом контуре, указаны конструкции обратных операторов и описаны подпространства Ker R и Im R. В качестве приложения рассмотрена система дискретных уравнений типа свертки в пространстве последовательностей, суммируемых с показательными весами, порождаемая оператором R.

Оператор краевой задачи Римана на системе концентрических окружностей и его приложения к одному классу систем уравнений в дискретных свертках (Operator of Riemann’s boundary value problem on the system of concentric circumferences and its application for one class of discrete convolution systems)

Theory of one-sided invertibility for the operator R of Riemann’s boundary value problem in Lebesgue spaces Lp(Γ), where Γ is a union of 2n concentric circles, in terms of matrix operators is described. We obtain constructions of inverse operators and describe subspaces Ker R and Im R. As application to this theory we consider system of discrete equations of convolution type generated by the operator R.На основе матричного операторного исчисления порядка 2n построена теория односторонней обратимости оператора R краевой задачи Римана в пространстве Лебега на составном контуре, который является объединением 2n концентрических окружностей, указаны конструкции обратных операторов и описаны подпространства Ker R и Im R. В качестве приложения рассмотрена система дискретных уравнений типа свертки в пространстве последовательностей, суммируемых с показательными весами, порождаемая оператором R. Для этой системы построена теория односторонней обратимости, найдены обратные операторы, описаны дефектные подпространства.

Оператор краевой задачи Римана на кольце и его приложения к одному классу систем уравнений в дискретных свертках (Operator of Riemann’s boundary value problem on the circle and its applications to one class of systems of equations in discrete convolutions)

Theory of one-sided invertibility for the operator R of Riemann’s boundary value problem in Lebesgue spaces Lp(Γ), where Γ is a union of two concentric circles, in terms of matrix operators is described. We obtain constructions of inverse operators and describe subspaces Ker R and Im R. As application to this theory we consider system of discrete equations of convolution type generated by the operator R.На основе матричного операторного исчисления порядка 2 построена теория односторонней обратимости оператора R краевой задачи Римана в пространстве Лебега на кольце, указаны конструкции обратных операторов и описаны подпространства Ker R и Im R. В качестве приложения рассмотрена система дискретных уравнений типа свертки в пространстве последовательностей, суммируемых с показательными весами, порождаемая оператором R. ISBN för värdpublikation: 978-5-9275-0750-4</p

Effects of hypertensive heart disease on the quality of life of military personnel under the conditions of the Far north

Aim: To assess the relationship between the presence of hypertension and the quality of life of contracted military personnel in the Far North, as well as to establish a correlation between the military rank and body mass index.Materials and methods. A medical and sociological study was conducted using a questionnaire survey of 613 military personnel serving on a contract basis in the Far North. The main research tool was a short version of the World Health Organization questionnaire developed for estimating the subjective quality of life. Additionally, questions were asked regarding the health status, as well as the conditions of service and life of military personnel.Results. A positive answer to the question about the presence of a hypertension diagnosis was given by 52 (8.5%) of the respondents. 135 (22%) of the respondents confirmed episodes of increased blood pressure. According to the scale, the quality of life of the military personnel with hypertension comprised 94 points (95% CI: 90.25–97.75), whereas this value equaled 95.33 points (95% CI: 93.10–97.57) and 99.99 points (95% CI: 98.91–101.06) for people experiencing episodes of increased blood pressure and for healthy individuals, respectively. A statistically significant difference in the general assessment of the quality of life was noted between the group of healthy individuals and the group of the personnel suffering from hypertension (U = 10861, p ˂ 0.01), as well as from the group of healthy individuals and people experiencing episodes of increased blood pressure (U = 17185, p ˂ 0.05). In terms of the military rank, statistically significant differences were noted in the hypertension group — between unranked military personnel and warrant officers (U = 78.5, p ˂ 0.05), and in the group experiencing episodes of increased blood pressure — unranked military personnel and warrant officers (U = 587.5, p ˂ 0.05) and warrant officers and junior officers (U = 620, p ˂ 0.05). Spearman correlation criterion values were obtained for the relationship between the body mass index and both hypertension (rs = –0.212, p ˂ 0.001) and high blood pressure (rs = –0.231, p ˂ 0.001).Conclusion. The obtained data confirm the negative impact of conditions associated with increased blood pressure on such aspects as the physical and mental well-being, self-perception, self-assessment of the quality of life and the state of health, general assessment of the quality of life. A correlation between the overall quality of life, the body mass index and the military rank of military personnel was established

Local administration of autologous platelet-rich plasma in a female patient with skin ulcer defect

The paper describes a clinical observation of the efficiency of local therapy with autologous platelet-rich plasma for .skin ulcer defect in a female with chronic lymphocytic leukemi