On approximate solutions of a non-linear functional equation

O przybliżonych rozwiązaniach nieliniowego równania funkcyjneg

On approximate solutions of linear functional equations

W pracy są rozważane przybliżenia ciągłych rozwiązań liniowych jednorodnych równań funkcyjnych postaci (p [/(* )] = g(x) [/(* )] = g(x)<p(.x)+F(x), gdzie <p jest funkcją niewiadomą. Dokładne rozwiązania ciągłe równań liniowych, w przypadkach jednoznaczności, są granicami pewnych ciągów funkcyjnych {(p„(x)} utworzonych za pomocą funkcji danych. Jako rozwiązanie przybliżone przyjmuje się n-ty wyraz tego ciągu. Celem pracy jest dobór liczby rzeczywistej a w ten sposób, aby n-ty wyraz ciągu, a. Praca zawiera 4 twierdzenia podające sposób doboru liczby a w różnych przypadkach równań liniowych. W każdym przypadku sposób doboru jest zilustrowany na odpowiednim przykładzie

A novel in-vitro model of human aortic valve mineralization

Background and aim of the study: The study aim was to develop an in-vitro model of human aortic valve homograft (AVH) mineralization, as a basis for further research on the subject of calcific aortic valve disease (CAVD). Methods: Human aortic valves were excised during autopsy (12-24 h post-mortem) from donors who had died due to accident or suicide. The mean \left ( \pm SD \right ) donor age was \left ( 32.5\pm 11.4 \right ) years. Under sterile conditions each aortic cusp (three cusps per valve) was cut in half to provide a total of 240 tissue samples. AVH mineralization was assessed in solutions with different Ca and P concentrations and Ca x PO_{4} ionic product values. The impact of time on aortic valve mineralization rate was assessed using energy-dispersive X-ray fluorescence (ED-XRF). Results: The model showed that human AVH mineralization can be best observed in a solution with a Ca x PO_{4} ionic product of 2.2 mmol^{2}/l^{2}. The optimum incubation time for observing AVH mineralization was 21 days. Conclusion: A novel in-vitro AVH mineralization model was developed for use in future studies

Effects of a 15-month anti-TNF-α treatment on plasma levels of glycosaminoglycans in women with rheumatoid arthritis

Abstract Background In this study, the effect of 15-month anti-tumor necrosis factor alpha (TNF-α) treatment on circulating levels of plasma sulfated glycosaminoglycans (GAGs) and the nonsulfated GAG hyaluronic acid (HA) in female rheumatoid arthritis (RA) patients was assessed. Methods Plasma was obtained from healthy subjects and RA women treated with TNF-α antagonists (etanercept or adalimumab or certolizumab pegol) in combination with methotrexate. GAGs were isolated from plasma samples using ion exchange low-pressure liquid chromatography. Total sulfated GAGs were quantified using a hexuronic acid assay. Plasma levels of keratan sulfate (KS) and HA were measured using immunoassay kits. Results Total sulfated GAGs and HA levels were higher in female RA patients before treatment in comparison to healthy subjects. KS levels did not differ between RA women and controls. Anti-TNF-α treatment resulted in normalization of plasma total GAG and HA levels in RA patients, without any effect on KS levels. Conclusions Our results suggest that anti-TNF-α therapy has a beneficial effect on extracellular matrix remodeling in the course of RA