ON REPRESENTATION OF ONE CLASS OF SCHMIDT OPERATORS

In this paper, unitary symmetrizers are considered. It is well known that using Newton operatoralgorithm, similar to the usual Newton algorithm, for extracting the square root, one can provethat for every Hermitian operator T 0, there exists a unique Hermitian operator S 0 suchthat T = S2. Moreover, S commutes with every bounded operator R with which commutes T. Theoperator S is called a square root of the operator T and is denoted by T1=2. The existence of thesquare root allows one to determine the absolute value jTj = (TT)1=2 of the bounded operator T.For every bounded linear operator T : H ! H there exists a unique partially isometric operatorU : H ! H such that T = UjTj, KerU = KerT. Such an equality is called a polar expansionof the operator T. The Schmidt operator is understood as the unitary multiplier of the polarexpansion of a compact inverse operator, with the help of which E. Schmidt was the rst to obtainthe expansion of a compact and not-self-adjoint operator and introduced so-called s-numbers.This paper shows that the unitary symmetrizer of an operator diers only in sign from the adjointSchmidt operator. The main result of the paper: if A is an invertible and compact operator, andS is a unitary operator such that the operator SA is self-adjoint, then the operator AS is alsoself-adjoint and the formula S = U holds, where U is the Schmidt operator

On one problem for restoring the density of sources of the fractional heat conductivity process with respect to initial and final temperatures

In this paper we consider inverse problems for a fractional heat equation, where the fractional time derivative is taken into account in Riemann-Liouville sense. For the solution of this equation, we have to find an unknown right - hand side depending only on a spatial variable. The problem modeling the process of determining the temperature and density of sources in the process of fractional heat conductivity with respect to given initial and final temperatures is considered. Problems with general boundary conditions with respect to the spatial variable that are not strongly regular are investigated. The existence and uniqueness of classical solution to the problem are proved. The problem is considered independent from a corresponding spectral problem for an operator of multiple differentiation with not strongly regular boundary conditions has the basis property of root functions

Vitamin D3 (Cholecalciferol) and Pelvic Pain Caused by Ovarian Endometriosis

Статья посвящена изучению взаимосвязи концентрации витамина D с наличием и интенсивностью тазовой боли у женщин, страдающих эндометриозом яичников. Цель исследования: установить взаимосвязь уровня витамина D и интенсивности тазовой боли у женщин, страдающих эндометриозом яичников. В исследование были включены 190 женщин репродуктивного возраста с верифицированным диагнозом эндометриоз яичников, в возрасте от 20 до 41 года (средний возраст – 29,1±3,3 года). Для определения интенсивности тазовой боли использовали визуальную аналоговую шкалу (ВАШ). Всем пациенткам (n=190) исходно оценку уровня витамина D проводили путем определения уровня общего 25(ОН)D в сыворотке крови методом масс-спектрометрии, адаптированным к клинической практике, согласно международным стандартам, на тандемном масс-спектрометре AB SCIEX QTRAP 5500.The article studies the relation between vitamin D concentration and the presence and intensity of pelvic pain in women suffering from ovarian endometriosis. The aim of the study is to examine the relation between vitamin D levels and intensity of pelvic pain in women with ovarian endometriosis. Study design: cohort, prospective, non-comparative study. The study included 190 women of reproductive age suffering from ovarian endometriosis (OE), aged 20 to 41 years (mean age 29.1±3.3 years). Visual analogue scale (VAS) was used to determine the intensity of pelvic pain.The evaluation of vitamin D level in all patients (n=190) was initially performed by determining the level of total 25 (OH) D in blood serum by the method of mass spectrometry. Study Results: The average vitamin D level in the study was 23.98±6.82 ng/ml. The average concentration of vitamin D in the blood of the patients with low-intensity pelvic pain was 26.7±5.92 ng/ml, with moderate-intensity – 23.06±of 5.55 ng/ml, with high pain intensity – 19.26±6,01 ng/ml. The content of vitamin D in the blood of the patients in the control group was 28.83±6.15 ng/ml, which met the criteria of insufficiency. Аn inverse correlation between the severity of pain based on VAS and vitamin D in women with endometriosis of the main group was established in the study, it amounted to 0.502 (p<0.001)

On One Mathematical Model of the Extraction Process of Polydisperse Porous Material

We consider a mathematical model which represents the extraction process of a target component from the polydispersed porous material. The suggested model is demonstrated by the example of a flat solid material with bidispersed pores of different size in the form of a system of channels of macropores with micropores facing their walls. The macropores and the micropores in the material have homogeneous size. We model a case when micropores of the solid material (dispersed medium) are initially filled with an oil (dispersion phase), which is our target component. The macropores are filled in with a pure solvent. In the process of extraction the oil diffuses from the micropore to the macropore, and then from the micropores to the external solvent volume, wherein the ratio of concentrations in the macropore and the micropore is taken in accordance with the linear law of adsorption. The well-posedness of the formulated mathematical model has been justified.Рассматривается математическая модель, моделирующая процесс экстракции целевого компонента из пористого полидисперсного материала. Предлагаемая модель демонстрируется на примере плоского твердого материала с бидисперсными порами разного размера, в виде системы каналов макропор, на стенки которых выходят микропоры. Макропоры и микропоры в материале имеют однородный размер. Моделируется случай, когда микропоры твердого материала (дисперсионной среды) первоначально заполнены маслом (дисперсная фаза), являющимся нашей целевой компонентой. А макропоры заполнены чистым растворителем. В процессе экстракции масло диффундирует из микропоры в макропору, а затем из макропоры - во внешний объем растворителя, при этом соотношение концентраций в макропоре и микропоре принимается подчиненным линейному закону адсорбции. Обоснована корректность сформулированной математической модели

About the Nature of the Spectrum of the Periodic Problem for the Heat Equation with a Deviating Argument

We study the nature of the spectrum of the periodic problem for the heat equation with a lower-order term and with a deviating argument. A significant influence of the lower-order term on the correct solvability of this problem is found. We obtain a criterion for the strong solvability of the above-mentioned problem

Oxytocinergic regulation in pathogenesis of pelvic pain caused by adenomyosis

Objective: The aim of the study was to expand the understanding of pathogenesis of adenomyosis-associated pelvic pain. Material and Methods: We studied 30 (n = 30) biopsy samples obtained after hysterectomy in women with diffuse adenomyosis of grade II-III, accompanied by severe pain syndrome, who did not receive hormonal therapy. The morphologic comparison group comprised 30 (n = 30) biopsy samples obtained from women with adenomyosis, without pain syndrome, operated on for abnormal uterine bleeding, who also did not receive hormone therapy. Results: The total density of immunological OTR labeling in the adenomyotic lesion foci was 73.7 ± 1.8%, and in the morphological control group it was 35.2 ± 1.4% (p <0.05), which indicates a significant effect of oxytocin as a ureterotonic peptide. Processes of local neurogenesis and growth of nerve fibers was established due to an increase in the expression of the nervous system growth factor NGF in the myometrium stroma, in comparison with biopsy samples of morphological control. Conclusion: Pelvic pain pathogenesis in women with diffuse adenomyosis compared with the painless form of the disease is an increase in the activity of ureterotonic factors of OTR oxytocin. Compared to the painless form of adenomyosis, the myometrial innervation apparatus of patients with pelvic pain is characterized by a significantly higher expression of nerve growth factor. © 2020 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group on behalf of the UR MED GRUPP (LLC)

The modern concept of the pathogenesis of chronic pelvic pain syndrome induced denomyosis

Chronic pelvic pain (CPP) is a significant public health problem affected women in the world. Although many pathologies are associated with CPP, the pain experienced is often disproportionate to the extent of disease identified and frequently no pathology is found (chronic pelvic pain syndrome). Adenomyosis - a pathological condition characterized by the presence of ectopic endometrial glands and stroma in the myometrium thickness combined with hyperplasia of muscle fibers [6]. The syndrome of chronic pelvic pain of endometriosis is one of the most urgent problems of modern gynecology [8]. The evidence reviewed in this paper demonstrates that CPP is associated with significant central changes women. Moreover, the presence of these changes has the potential to both exacerbate symptoms and to predispose these women to the development of additional chronic conditions

Obstetric perineal trauma: a modern view of the problem. A prospective study

Trauma to the perineum during childbirth is still a common obstetric problem. The question of etiology and risk factors is still extremely debatable. The high risk of long-term consequences of perineal injuries creates the need for timely prediction and effective prevention of this complication of childbirth, which seems to be the main reserve for reducing future pelvic floor insufficiency and associated pathological conditions.&#x0D; Background. Perineal trauma during childbirth is still a common problem in obstetrics. Also, a high percentage of long-term consequences of perineal injuries creates the need for timely prediction and effective prevention of perineal trauma during childbirth, which is relevant today.&#x0D; Aim. To identify the main predictors of the risk of developing obstetric perineal injury.&#x0D; Materials and methods. We conducted a prospective randomized study between September 2020 and January 2022, which included 110 pregnant women. The observation of the patients began from the day of the first visit to the antenatal clinic and throughout pregnancy and the postpartum period, much attention was paid to a comprehensive perineological examination.&#x0D; Results. In group 1, a large number of grade I and II tears (n=37, 33% and n=24, 29%) were noted, and grade III tears were completely absent. In group 2, there were grade III perineal tears, the frequency was (n=5, 2.1%), but still their number was inferior to grade I and II tears (n=10, 26% and n=15, 14%). In group 3, the analysis showed a low frequency of perineal tears of I and II degrees (n=8, 11% and n=17, 18%) and a number of tears of degree III comparable to group 2 (n=8, 2.6%). Episiotomy in all groups was carried out in the range from 7 to 9%, strictly according to obstetric indications.&#x0D; Conclusion. According to the data obtained, the most significant clinical and anamnestic predictors of obstetric perineal trauma were: frequent abortions in anamnesis, chronic diseases of the ENT organs and the urinary system, vaginal dysbiosis (nonspecific vaginitis, bacterial vaginosis), changes in the pH of the vaginal environment, low tone of the perineum, the presence of scar on the perineum

Тренировка мышц тазового дна как метод профилактики и лечения несостоятельности тазового дна и генитального пролапса

Relevance. Pelvic floor dysfunction and pelvic organ prolapse are a significant problem today - even the initial manifestations of pelvic floor dysfunction can lead to reduced quality of sexual life, decreased activity, and then to social isolation and decreased self-esteem of women. Due to the growth of general life expectancy, the incidence rate is also increasing. One of the most popular conservative treatments for pelvic floor dysfunction is pelvic floor muscle training. The aim of this literature review is to consolidate the scattered information about the effectiveness of pelvic floor muscle training as a prevention and treatment of pelvic floor dysfunction. Materials and Methods. In writing the review, publications from the PubMed and Google Scholar databases from January 2019 were analyzed and systematized. Results and Discussion. Pelvic floor muscle training is one of the most prospective methods of non-invasive treatment for pelvic organ prolapse. It can take many forms and is represented by a range of different techniques: from the simple short-term muscle contraction and Kegel exercises to more complex and high-tech methods using electromyostimulation and biofeedback. However, timing of introduction and method for pelvic floor muscle training must be carefully considered in order to gain the maximum result. Conclusion. Based on the study, it can be concluded that the introduction of pelvic floor muscle training as part of prenatal care and in the antenatal period is the most appropriate way to prevent pelvic floor failure and genital prolapse. Further research is required to confirm the hypothesis.Актуальность. Несостоятельность тазового дна и пролапс тазовых органов на сегодняшний день являются существенной проблемой - даже начальные проявления несостоятельности тазового дна могут привести к снижению качества сексуальной жизни, снижению активности, а затем к социальной изоляции и снижению самооценки женщины. В связи с ростом общей продолжительности жизни, растет и заболеваемость. Одним из наиболее популярных методов консервативного лечения несостоятельности тазового дна является тренировка мышц тазового дна. Целью данного обзора является консолидация разрозненных сведений об эффективности тренировки мышц тазового дна в качестве профилактики и лечения дисфункции тазового дна. Материалы и методы . При написании обзора были проанализированы и систематизированы публикации из баз данных PubMed и Google Scholar с января 2019 года. Результаты и обсуждение . Тренировка мышц тазового дна является одним из наиболее перспективных методов неинвазивного лечения пролапса тазовых органов. Она может принимать различные формы и представлена целым рядом различных техник: от простых кратковременных сокращений мышц и упражнений Кегеля до более сложных и высокотехнологичных методов с использованием электромиостимуляции и биологической обратной связи. Тем не менее, время введения и метод тренировки мышц тазового дна должны быть тщательно продуманы, чтобы получить максимальный результат. Выводы . На основании проведенного исследования можно сделать вывод, что введение тренировки мышц тазового дна в рамках дородовой помощи и в антенатальном периоде является наиболее целесообразным способом профилактики несостоятельности тазового дна и генитального пролапса. Для подтверждения гипотезы необходимы дальнейшие исследования

Витамин D3 (холекальциферол) и тазовая боль, индуцированная эндометриозом яичников

The article studies the relation between vitamin D concentration and the presence and intensity of pelvic pain in women suffering from ovarian endometriosis. The aim of the study is to examine the relation between vitamin D levels and intensity of pelvic pain in women with ovarian endometriosis. Study design: cohort, prospective, non-comparative study. Materials and Methods : The study included 190 women of reproductive age suffering from ovarian endometriosis (OE), aged 20 to 41 years (mean age 29.1±3.3 years). Visual analogue scale (VAS) was used to determine the intensity of pelvic pain.The evaluation of vitamin D level in all patients (n=190) was initially performed by determining the level of total 25 (OH) D in blood serum by the method of mass spectrometry. Study Results: The average vitamin D level in the study was 23.98±6.82 ng/ml. The average concentration of vitamin D in the blood of the patients with low-intensity pelvic pain was 26.7±5.92 ng/ml, with moderate-intensity - 23.06±of5.55 ng/ml, with high pain intensity - 19.26±6,01 ng/ml. The content of vitamin D in the blood of the patients in the control group was 28.83±6.15 ng/ml, which met the criteria of insufficiency. An inverse correlation between the severity of pain based on VAS and vitamin D in women with endometriosis of the main group was established in the study, it amounted to 0.502 ( p <0.001). Conclusion: Women with endometriosis of the ovaries are characterized by a decrease in the level of vitamin D to lower values than those in the control group, which meets the criteria of insufficiency of 23.98±6.82 ng/ml, including severe pelvic pain up to 19.26±6,01 ng/ml, corresponding to the state of deficiency. A moderate inverse correlation was found between the intensity of pelvic pain caused by endometriosis of the ovaries and the level of vitamin D in the blood (-0,502).Статья посвящена изучению взаимосвязи концентрации витамина D с наличием и интенсивностью тазовой боли у женщин, страдающих эндометриозом яичников. Цель исследования: установить взаимосвязь уровня витамина D и интенсивности тазовой боли у женщин, страдающих эндометриозом яичников. Дизайн: когортное, проспективное, несравнительное исследование. Материалы и методы : В исследование были включены 190 женщин репродуктивного возраста с верифицированным диагнозом эндометриоз яичников, в возрасте от 20 до 41 года (средний возраст - 29,1±3,3 года). Для определения интенсивности тазовой боли использовали визуальную аналоговую шкалу (ВАШ). Всем пациенткам (n=190) исходно оценку уровня витамина D проводили путем определения уровня общего 25(ОН)D в сыворотке крови методом масс-спектрометрии, адаптированным к клинической практике, согласно международным стандартам, на тандемном масс-спектрометре AB SCIEX QTRAP 5500. Результаты: Средний уровень витамина D в исследуемой когорте женщин в целом составил 23,98±6,82 нг/мл. Средняя концентрация витамина D в крови у пациенток с тазовой болью слабой интенсивности составила 26,7±5,92 нг/мл, умеренной - 23,06±5,55 нг/мл, при выраженной - 19,26±6,01 нг/мл. В контрольной группе среднее содержание витамина D в крови составило 28,83±6,15 нг/мл, что соответствовало критериям недостаточности. В ходе исследования установлена обратная корреляционная связь между выраженностью болевых ощущений по ВАШ и содержанием витамина D у женщин основной группы с эндометриозом яичников (-0,502; p <0,001). Заключение: Для женщин с эндометриозом яичников характерно снижение уровня витамина D до более низких значений, чем в группе контроля. Обнаружена умеренная обратная корреляционная связь между интенсивностью тазовой боли, обусловленной ЭЯ, и уровнем витамина D в крови (-0,502)