Equivalence Between K-functionals Based on Continuous Linear Transforms

2000 Mathematics Subject Classification: 46B70, 41A10, 41A25, 41A27, 41A35, 41A36, 42A10.The paper presents a method of relating two K-functionals by means of a continuous linear transform of the function. In particular, a characterization of various weighted K-functionals by unweighted fixed-step moduli of smoothness is derived. This is applied in estimating the rate of convergence of several approximation processes.Partially supported by grant No. 103/2007 of the National Science Fund of the Sofia University

A New Characterization of Weighted Peetre K-Functionals (II)

2000 Mathematics Subject Classification: 46B70, 41A25, 41A17, 26D10. ∗Part of the results were reported at the Conference “Pioneers of Bulgarian Mathematics”, Sofia, 2006.Certain types of weighted Peetre K-functionals are characterized by means of the classical moduli of smoothness taken on a proper linear transforms of the function. The weights with power-type asymptotic at the ends of the interval with arbitrary real exponents are considered. This paper extends the method and results presented in [3].Partially supported by grant No. 22/2006 of the Sofia University with the National Science Fund of the Bulgarian Ministry of Education and Science

On Convex Approximation by Quadratic Splines

AbstractIn a recent paper by Hu it is proved that for any convex functionfthere is aC1convex quadratic splineswithnknots that approximatesfat the rate ofω3(f, n−1). The knots of the spline are basically equally spaced. In this paper we give a simple construction of such a spline with equally spaced knots

A characterization of weighted approximations by the Post–Widder and the Gamma operators, II

AbstractWe present a characterization of the approximation errors of the Post–Widder and the Gamma operators in Lp(0,∞),1≤p≤∞, with a weight xγ0(1+x)γ∞−γ0 with arbitrary real γ0,γ∞. Characteristics of two types are used — weighted K-functionals of the approximated function itself and the classical fixed-step moduli of smoothness taken on simple modifications of it

The role of postoperative trimetazidine therapy in on-pump coronary artery bypass surgery

Introduction: Coronary artery bypass surgery remains the gold standard in the treatment of patients with ischemic heart disease. However, the increased oxidative stress caused by the release of free radicals during the ischemia-reperfusion time is a well-known pathophysiological process during and after coronary revascularization procedures. It may lead to reversible and irreversible myocardial injury. The focus of this prospective single-blinded randomized controlled trial is to investigate and analyze the effectiveness of the drug trimetazidine on reducing postoperative myocardial ischemia-reperfusion injury. Aim: We evaluated the effects of trimetazidine on reactive oxygen species that may arise from myocardial ischemia-reperfusion period or systemic inflammation after coronary artery bypass grafting (CABG) surgery. Materials and methods: The study included 90 patients divided into two groups who underwent elective coronary artery bypass surgery between March 2018 and October 2018. The patients in one of the groups received 35 mg trimetazidine twice daily as soon as they were extubated. The remainder of the pharmaceutical therapy was the same for all participants. Preoperative and postoperative levels of several blood-based biochemical markers including malondialdehyde (MDA), creatinine kinase-MB fraction (CK-MB) and high-sensitivity troponin T (hs-TnT) were measured. The data was classified and analyzed by the timing of sample collection. Results: The results indicate that postoperative trimetazidine medication reduces MDA production, resulting in reduced oxidative stress and improved cardiac cell protection via antioxidant status augmentation. The follow-up was 6 months after the surgery. The Minnesota Living with Heart Failure Questionnaire was used to assess the quality of life of patients, and the results were excellent. Conclusions: Postoperative trimetazidine therapy leads to improvement of the myocardial cell metabolism and thus reduction in post CABG ischemia-reperfusion injury