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Search Results: 1 - 10 of 22010 matches for " Bogus？aw Bo？ek "
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 Applied Mathematics (AM) , 2015, DOI: 10.4236/am.2015.66095 Abstract: In this paper, three types of three-parameters families of quadrature formulas for the Riemann’s integral on an interval of the real line are carefully studied. This research is a continuation of the results in the [1]-[3]. All these quadrature formulas are not based on the integration of an interpolant as so as the Gregory rule, a well-known example in numerical quadrature of a trapezoidal rule with endpoint corrections of a given order (see [4]). In some natural restrictions on the parameters we construct the only one quadrature formula of the eight order which belongs to the first, second and third family. For functions whose 8th derivative is either always positive or always negative, we use these quadrature formulas to get good two-sided bound on . Additionally, we apply these quadratures to obtain the approximate sum of slowly convergent series , where .
 Opuscula Mathematica , 2009, Abstract: How can one compute the sum of an infinite series \$s := a_1 + a_2 + \ldots\$? If the series converges fast, i.e., if the term an tends to 0 fast, then we can use the known bounds on this convergence to estimate the desired sum by a finite sum \$a_1 + a_2 + \ldots + a_n\$. However, the series often converges slowly. This is the case, e.g., for the series \$a_n = n^{-t}\$ that defines the Riemann zeta-function. In such cases, to compute \$s\$ with a reasonable accuracy, we need unrealistically large values \$n\$, and thus, a large amount of computation. Usually, the \$n\$-th term of the series can be obtained by applying a smooth function \$f(x)\$ to the value \$n: a_n = f(n)\$. In such situations, we can get more accurate estimates if instead of using the upper bounds on the remainder infinite sum \$R = f(n + 1) + f(n + 2) + \ldots\$, we approximate this remainder by the corresponding integral \$I\$ of \$f(x)\$ (from \$x = n + 1\$ to infinity), and find good bounds on the difference \$I - R\$. First, we derive sixth order quadrature formulas for functions whose 6th derivative is either always positive or always negative and then we use these quadrature formulas to get good bounds on \$I - R\$, and thus good approximations for the sum \$s\$ of the infinite series. Several examples (including the Riemann zeta-function) show the efficiency of this new method. This paper continues the results from [3] and [2].
 Opuscula Mathematica , 2005, Abstract: The present paper suplements and continues [2]. Galerkin method for the Fourier–Kirchhoff equation in the case when \$\Omega(t)\$–equation domain, dependending on time \$t\$, is constructed. For special case \$\Omega(t) \subset \mathbb{R}^2\$ the computer program for above method is written. Binaries and sources of this program are available on http://wms.mat.agh.edu.pl/~bozek.
 Opuscula Mathematica , 2008, Abstract: In this paper a construction of a one-parameter family of quadrature formulas is presented. This family contains the classical quadrature formulas: trapezoidal rule, midpoint rule and two-point Gauss rule. One can prove that for any continuous function there exists a parameter for which the value of quadrature formula is equal to the integral. Some applications of this family to the construction of cubature formulas, numerical solution of ordinary differential equations and integral equations are presented.
 Limnological Review , 2011, DOI: 10.2478/v10194-011-0032-2 Abstract: The aim of the research was to determine the successional changes proceeding in the phytoplankton of a lake. The basis of the study was the analysis of long-term seasonal changes in the taxonomic structure and the estimation of the intensity of algal community development in phytoplankton of Lake Kortowskie. Seasonal changes in the phytoplankton taxonomic structure manifested themselves as a decreasing share of Bacillariophyceae in spring and autumn and Chlorophyta in summer phytoplankton. The retreating chlorophytes and the diatoms were replaced by blue-green algae, the increasing share of which caused a reduction in the stability of the remaining phytoplankton taxonomic groups, and consequently, taxonomic shifts and progressive development of the overall phytoplankton community in all phenological seasons. Intensive algal growth was observed in spring and lasted until late autumn. The highest phytoplankton biomass was always recorded in summer. Summer phytoplankton development was related to increased bluegreen algae domination, the massive growth of which was observed from spring to autumn. The development of the Cyanoprokaryota community had a negative impact on the diatoms, since the latter earlier disappeared from the biocenosis in spring and re-developed to a lesser degree in autumn.
 Polish Journal of Cardiology , 2004, Abstract: Cel pracy: Analiza rodzaju i skuteczno ci leczenia arytmicznego migotania przedsionków (AF – atrial fibrillation) u pacjentów we wczesnym okresie po zabiegach pomostowania t tnic wieńcowych (CABG – coronary artery bypass grafting). Materia i metodyka: Badaniem obj to 1578 chorych (1283 m czyzn i 295 kobiet; w wieku 25-85 lat, rednia wieku 59,4±;8,7 lat), poddanych izolowanym zabiegom pomostowania t tnic wieńcowych z u yciem kr enia pozaustrojowego, w okresie 1.01.1998-31.12.1999 r. Pooperacyjne migotanie przedsionków wyst pi o u 193 osób (12,2% grupy po CABG). Chorzy z pooperacyjnym migotaniem przedsionków stanowili grup badan (193 pacjentów; rednia wieku 62,4±;7,1 lat). W grupie tej oceniano: czas wyst pienia migotania przedsionków i jego nawrotów w odniesieniu do zabiegu operacyjnego oraz rodzaj i skuteczno zastosowanego leczenia antyarytmicznego. Wyniki: Oko o 13% przypadków AF po CABG uleg o samoistnemu umiarowieniu. W leczeniu pooperacyjnego migotania przedsionków stosowano: kardiowersj elektryczn , glikozydy naparstnicy, blokery kana u wapniowego, amiodarone, sotalol, rzadko leki beta-adrenolityczne. Najni sz skuteczno w przerywaniu napadu AF wykazywa y glikozydy naparstnicy. Najwy sz skuteczno ci w konwersji do rytmu zatokowego charakteryzowa y si : propranolol, amiodarone, sotalol. Wnioski: 1. Rzadko dochodzi do samoistnej konwersji pooperacyjnego migotania przedsionków do rytmu zatokowego. 2. Najwy sz skuteczno w konwersji pooperacyjnego AF do rytmu zatokowego wykazywa y: amiodarone i leki beta-adrenolityczne; powinny by one stosowane jako leki pierwszego rzutu w przypadkach AF po CABG.
 Bogus？aw Ratkiewicz Advances in Difference Equations , 2006, Abstract: We discuss the discretizations of the second-order linear ordinary diffrential equations with constant coefficients. Special attention is given to the exact discretization because there exists a difference equation whose solutions exactly coincide with solutions of the corresponding differential equation evaluated at a discrete sequence of points. Such exact discretization can be found for an arbitrary lattice spacing.
 Bogus？aw ？y？ko Entretextos : Revista Electronica Semestral de Estudios Semióticos de la Cultura , 2005, Abstract:
 Bogus？aw ？y？ko Entretextos : Revista Electronica Semestral de Estudios Semióticos de la Cultura , 2006, Abstract:
 Bogus？aw ？y？ko Entretextos : Revista Electronica Semestral de Estudios Semióticos de la Cultura , 2007, Abstract:
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