Fourier coefficients for Laguerre–Sobolev type orthogonal polynomials

Purpose In this paper, the authors take the first step in the study of constructive methods by using Sobolev polynomials.Design/methodology/approach To do that, the authors use the connection formulas between Sobolev polynomials and classical Laguerre polynomials, as well as the well-known Fourier coefficients for these latter.Findings Then, the authors compute explicit formulas for the Fourier coefficients of some families of Laguerre–Sobolev type orthogonal polynomials over a finite interval. The authors also describe an oscillatory region in each case as a reasonable choice for approximation purposes.Originality/value In order to take the first step in the study of constructive methods by using Sobolev polynomials, this paper deals with Fourier coefficients for certain families of polynomials orthogonal with respect to the Sobolev type inner product. As far as the authors know, this particular problem has not been addressed in the existing literature.

Comparison of Anti-factor Xa Levels in Female and Male Patients with Obesity After Enoxaparin Application for Thromboprophylaxis

Purpose Venous thromboembolic events (VTEs) are common complications after bariatric surgery, and enoxaparin is commonly used to prevent VTEs. The risk for VTEs is sex-specific. Whether enoxaparin application results in similar anti-factor Xa activities (aFXa) in males and females with obesity remains to be determined. We investigated whether our dosage regimen of enoxaparin resulted in similar serum aFXa levels in female and male patients undergoing bariatric surgery. Materials and Methods We administered enoxaparin twice daily in patients undergoing bariatric surgery. Patients with a body mass index (BMI) > 60 kg/m2 (n = 11) received 60 mg enoxaparin (group 2), and patients with lower BMI (n = 86) received 40 mg per dose (group 1). Peak aFXa levels were measured 3 days after surgery. The primary outcome was the aFXa level. As a secondary outcome, we detected VTEs and major bleeding events and explored the possible influencing factors of aFXa. Results Women had higher aFXa than men, but after matching for anthropometric values, the two groups were similar (females: 0.17 ± 0.08 U/ml; males: 0.18 ± 0.08 U/ml). Linear regression revealed a moderate relationship between weight and aFXa levels. The 3-month follow-up was attended by 94.9%, at which one patient had pulmonary embolism. Conclusion Individual enoxaparin dosage regimens for men and women do not seem to be required. Weight-based dosing regimen seems to be a more reasonable choice. Graphical abstract

Analysis of application and improvement of methods to solve discrete models of Boltzmann equation

To describe technological systems using models of Markov chains and discrete models of the Boltzmann equation it is necessary to determine the probabilities of transition of a system from one state to another. An urgent topic of a scientific research is to improve the accuracy of solving the Boltzmann equation by making a reasonable choice of probabilities of transition and admissible areas of their application. The strategy to model and determine the probabilities of transitions is based on the finite volume method, the ratios of the theory of probability and the joint analysis of material and energy balances. Considering the ratios of the theory of probability, the authors have obtained the refined formula for the probabilities of transitions over the cells of the computational space of discrete models of the Boltzmann equations in case of the description of technological systems. Recommendations to choose the area of application of the model are presented. The computational analysis has showed a significant improvement of the quality of forecasting when we implement the proposed dependencies and recommendations. The relative error of calculating the energy of the system is reduced from 8,4 to 2,8 %. The presented calculated dependencies to determine the probabilities of transition and recommendations for their application can be used to simulate various technological processes and improve the quality of their description.

Comparative phytochemical analysis of the aerial parts of Empetrum nigrum L. samples, collected in various regions of the Russian Federation

Introduction. A number of studies have shown that various genetic and environmental factors can affect the biosynthesis and accumulation of secondary metabolites. In particular, it is known that the local geoclimate, seasonal changes, external conditions such as light, temperature, moisture and soil fertility can affect the chemical composition and, as a result, the therapeutic properties of plants used in the pharmaceutical and food industries. Empetrum nigrum L. is a rich source of various pharmacologically active secondary metabolites – chalcones, dihydrochalcones, bibenzyls, 9,10-dihydrophenanthrenes, flavonoids, and proanthocyanidins. In the scientific literature, there is no data on the variation in the chemical composition of E. nigrum depending on the growing area. The obtained data are necessary for a reasonable choice of the collecting location for the plant, with the aim of its further chemical and pharmacological research for the development of promising drug candidates.Aim. To carry out a comparative analysis of secondary metabolites composition in the aerial parts of Empetrum nigrum growing in different regions of the Russian Federation.Materials and methods. Samples collected in three different areas were used to compare HPLC profiles: sample 1 was collected next to SPCPU nursery garden of medicinal plants (Leningrad region, Vsevolozhsky district, Priozerskoe highway, 38 km) in July 2020, sample 2 was collected on the Kola Peninsula, around the Khibiny mountains in July 2020, sample 3 was collected on the Kamchatka Peninsula, next to Khalaktyrsky beach (Pacific Ocean coast) in July 2020. Extracts were analyzed by analytical high performance liquid chromatography (HPLC) using a Prominence LC-20 device (Shimadzu, Japan) equipped with a diode array detector.Results and discussion. As a result of the research, for the first time, a significant variation in the qualitative chemical composition in the aerial parts of Empetrum nigrum growing in different regions of Russian Federation was established. Sample 3, collected on the Kamchatka Peninsula, in comparison with samples 1 and 2, contain the greatest variety of polar secondary metabolites belonging to the classes of flavonoids, tannins, and phenol carboxylic acids, while in the shoots collected in the Leningrad region, the major metabolites were weakly polar compounds belonging to the classes of chalcones, dihydrochalcones, bibenzyls, and 9,10-dihydrophenanthrenes, and in sample 2, collected in the Khibiny mountains, the lowest qualitative content of secondary metabolites was found. This variation may be caused by various environmental factors (biotic and abiotic).Conclusion. For the first time, the comparison of HPLC profiles of aerial part samples of E. nigrum, collected in different regions of the Russia Federation has been carried out. As a result, significant variations in the secondary metabolites composition of the studied samples were established, depending on the regions and growing conditions of the plants. The data obtained can be used for a reasonable choice of the collection location for the plant, with the aim of its further chemical and pharmacological research for the development of promising drug candidates.

Idiopathic and radiation-induced myxofibrosarcoma in the head and neck—case report and literature review

Background Myxofibrosarcoma (MFS), especially radiation-Induced MFS (RIMFS) in the head and neck, is an extremely rare malignant fibroblastic tumor. The diagnosis and treatment of MFS remain great challenges. In the present study, we presented one case of RIMFS. Combined with previous literature, the clinical features, essentials of diagnosis, and treatment modalities of MFS in the head and neck were reviewed to better understand this rare entity. Case presentation We reported a case of RIMFS under the left occipital scalp in a 20-year-old girl with a history of medulloblastoma surgery and radiotherapy in 2006. A total tumor resection was performed with preservation of the overlying scalp the underlying bone, and no adjuvant therapy was administered after the first operation. The postoperative pathological diagnosis was high-grade MFS. The tumor relapsed 6 months later, and then, a planned extensive resection with negative surgical margins was carried out, followed by radiotherapy. No relapse occurred in a 12-month postoperative follow-up. Conclusions Planned gross total resection (GTR) with negative margins is the reasonable choice and footstone of other treatments for MFS. Ill-defined infiltrated borders and the complicated structures make it a great trouble to achieve total resection of MFS in the head and neck, so adjuvant radiotherapy and chemotherapy seem more necessary for these lesions.

Optically Transparent and Highly Conductive Electrodes for Acousto-Optical Devices

The study was devoted to the creation of transparent electrodes based on highly conductive mesh structures. The analysis and reasonable choice of technological approaches to the production of such materials with a high Q factor (the ratio of transparency and electrical conductivity) were carried out. The developed manufacturing technology consists of the formation of grooves in a transparent substrate by photolithography methods, followed by reactive ion plasma etching and their metallization by chemical deposition using the silver mirror reaction. Experimental samples of a transparent electrode fabricated using this technology have a sheet resistance of about 0.1 Ω/sq with a light transmittance in the visible wavelength range of more than 60%.

Endovascular treatment of anterior inferior cerebellar artery trunk aneurysms

Background The anterior inferior cerebellar artery (AICA) is a very slender and anatomically variable artery that gives off many important perforating arteries that feed the brainstem and nerve-related arteries that feed the inner ear and labyrinth. AICA trunk aneurysms are rare entities that are also difficult to manage. At present, endovascular treatment (EVT) is the preferred choice; however, the understanding of EVT for AICA trunk aneurysms is limited. Methods In this article, we present a literature review on EVT for AICA trunk aneurysms. To promote understanding, we would also provide some illustrative educational cases of our institute. Results Aneurysms along the AICA trunk can occur alone (isolated AICA aneurysm) or secondary to cerebrovascular shunts (flow-related AICA aneurysm). According to their anatomical location, they can also be divided into proximal and distal types. At present, EVT is the mainstream treatment, mainly including selective coiling with parent artery preservation and parent artery occlusion. Both coils and liquid embolization materials can be used. Conclusions For AICA trunk aneurysms, EVT is a reasonable choice and should be based on the specific anatomical location, pathology, and collateral circulation. However, there is still controversy as to the specific type of treatment that should be chosen.

COMPONENT ALLERGY DIAGNOSTICS AS A TOOL FOR THEMANAGEMENT OF PATIENTS WITH ALLERGIC DISEASES

Molecular diagnostics makes it possible to determine true and cross reactivity differentially, which is of great clinical importance not only for the diagnosis of the true spectrum of sensitization, but also for the reasonable choice of pathogenetic therapy, prediction of the effectiveness and risks associated with allergenspecific immunotherapy. A number of clinical cases are presented as examples demonstrating the clarifying nature of molecular allergodiagnostics.