Abstract:
Three sections (Rebro, Lyalintsi and Velinovo) of the Upper Jurassic-Lower Cretaceous carbonate sequences from the Lyubash unit (Srednogorie, Balkanides, SW Bulgaria) have been studied for elucidation of biostratigraphy and palaeoenvironmental evolution. Palaeontological studies of foraminifera, supplemented by studies of calcareous dinoflagellate cysts and corals, enabled the determination of the Oxfordian-Valanginian age of the analysed sequences. They were deposited on the Dragoman Block (western part of the Moesian Platform), and during Mid-Late Cretaceous included to the Srednogorie. A possible Middle to Late Callovian age of the lowermost part (overlying the Bajocian-Lower Bathonian Polaten Formation) of the studied sections assumed till now has not been confirmed by the present studies. Eleven facies have been distinguished and attributed to depositional environments. Marine sedimentation on a homoclinal ramp started in the Oxfordian and till the Early Kimmeridgian - in all three sections - was dominated by fine-grained peloidal-bioclastic wackestones to grainstones. Since the Late Kimmeridgian, when a rimmed platform established, facies pattern underwent differentiation into (i) the inner platform (lagoon and tidal flat facies) - only in Velinovo, (ii) reef and peri-reef facies/bioclastic shoals - mainly in Lyalintsi, and (iii) platform slope - mainly in Rebro. Sedimentation generally displays a shallowing-upward trend. Two stages in evolution of the rimmed platform are postulated. The mobile stage lasting till the Tithonian/Berriasian boundary was followed by a more stable stage in the Berriasian to Valanginian time. Reefs are developed mainly as coral-microbial biostromes, lower coral bioherms or coral thickets, in the environment of moderate energy and sedimentation. They contain highly diversified corals (72 species). Micro- bialites contributed to the reef framework, but they never dominated. Locally, microencrusters and cement crusts formed important part of reefal framework. During the mobile stage of the platform evolution a relative sea-level rise interrupted reef development, as evidenced by intercalations of limestones with Saccocoma. During the second stage high carbonate production and/or regressive eustatic events, not balanced by subsidence, decreased accommodation space, limiting reef growth and enhancing carbonate export to distal parts of the platform.

Abstract:
The topmost part of the Oxfordian limestones, building the Zakrzówek Horst in Kraków, is featured by a network of minute fissures, filled with Upper Cretaceous limestones. Fissures are dominantly subhorizontal, anastomosing and polygonal in plane. They are filled with white limestones representing mostly foraminiferal- calcisphere wackestones, with subordinate amount of quartz pebbles and fragments of stromatolite coming from the latest Turonian-?Early Coniacian conglomerate overlying Oxfordian basement. The fissures are seismically- induced injection dykes. In contrast to gravitationally-filled neptunian dykes the recognised injection dykes were filled by overpressured soft sediments. Foraminifera within some dykes are abundant, and dominated by plankto- nic forms, which indicate the Early/Late Campanian age (Globotruncana ventricosa and Globotruncanita calcarata zones) of the filling, and hence date also the synsedimentary tectonics. Abundant and diversified keeled globo- truncanids in the Campanian of the Kraków region are recognised for the first time. Other important findings at the studied section include karstic cavities featuring the surface of the Oxfordian bedrock filled with conglomerates of the latest Turonian-?Early Coniacian age based on foraminifera and nannoplankton, and lack of Santonian deposits, which elsewhere are common in the Upper Cretaceous sequences in the Kraków region. The discovered Campanian dykes provide new evidence for the Late Cretaceous tectonic activity on the Kraków Swell related to the Subhercynian tectonism, which resulted among others in stratigraphic hiatuses and unconformities characte- ristic of the Turonian-Santonian interval of this area.

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 .

Abstract:
W trakcie ostatnich lat jest obserwowany wyra ny post p w dziedzinie diagnostyki kardiologicznej oraz stratyfikacji ryzyka kr eniowego. Sta o si to mo liwe dzi ki zastosowaniu nowoczesnych metod biochemicznych i immunologicznych. Szczególn rol przypisuje si ostatnio markerom procesu zapalnego, a w ród nich – atwo dost pnemu oznaczeniu bia ka C-reaktywnego. Poni sza praca stanowi przegl d najnowszych doniesień na ten temat.

Abstract:
Kardiologiczny zespó X pozostaje niewyja nion jednostk nozologiczn . Wielu badaczy próbowa o rozwi za ten problem, w szczególno ci jego etiopatogenez . Poni szy artyku jest przegl dem najnowszego pi miennictwa dotycz cego tego zagadnienia. Niedokrwienie mi nia sercowego jest prawdopodobnie jednym z kilku patomechanizmów omawianego zespo u. Niedawne doniesienia wykazuj równie skuteczno metod leczenia innych ni zapobieganie niedokrwieniu miokardium w tej grupie pacjentów.

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].

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.