In the paper, we discuss convergence properties and Voronovskaja type theorem for bivariate $q$-Bernstein polynomials for a function analytic in the polydisc $D_{R_{1}}\times D_{R_{2}}=\{z\in C\colon \vert z\vert <R_{1}\} \times \{ z\in C\colon \vert z\vert <R_{1}\}$ for arbitrary fixed $q>1$. We give quantitative Voronovskaja type estimates for the bivariate $q$-Bernstein polynomials for $q>1$. In the univariate case the similar results were obtained by S. Ostrovska: $q$-Bernstein polynomials and their iterates. J. Approximation Theory 123 (2003), 232–255. and S. G. Gal: Approximation by Complex Bernstein and Convolution Type Operators. Series on Concrete and Applicable Mathematics 8. World Scientific, New York, 2009.
The paper deals with a class of discrete-time stochastic control processes under a discounted optimality criterion with random discount rate, and possibly unbounded costs. The state process { x_{t} } and the discount process { \alpha_{t} } evolve according to the coupled difference equations x_{t+1}=F(x_{t},\alpha _{t},a_{t},\xi _{t}), \alpha_{t+1}=G(\alpha _{t},\eta _{t}) where the state and discount disturbance processes { \xi _{t} } and { \eta _{t} } are sequences of i.i.d. random variables with densities \rho^{\xi } and \rho^{\eta } respectively. The main objective is to introduce approximation algorithms of the optimal cost function that lead up to construction of optimal or nearly optimal policies in the cases when the densities \rho ^{\xi } and \rho ^{\eta } are either known or unknown. In the latter case, we combine suitable estimation methods with control procedures to construct an asymptotically discounted optimal policy.
In this paper, we show two applications of the Banach's Fixed-Point Theorem: first, to approximate the ultimate ruin probability in the classical risk model or Cramér-Lundberg model when claim sizes have some arbitrary continuous distribution and second, we propose an algorithm based in this theorem and some conditions to guarantee the continuity of the ruin probability with respect to the weak metric (Kantorovich). In risk theory literature, there is no methodology based in the Banach's Fixed-Point Theorem to calculate the ruin probability. Numerical results in this paper, guarantee a good approximation to the analytic solution of the ruin probability problem. Finally, we present numerical examples when claim sizes have distribution light and heavy-tailed.
In the present paper, using a Picard type method of approximation, we investigate the global existence of mild solutions for a class of Ito type stochastic differential equations whose coefficients satisfy conditions more general than the Lipschitz and linear growth ones.
The aim of this paper is to present some ideas how to relax the notion of the optimal solution of the stochastic optimization problem. In the deterministic case, ε-minimal solutions and level-minimal solutions are considered as desired relaxations. We call them approximative solutions and we introduce some possibilities how to combine them with randomness. Relations among random versions of approximative solutions and their consistency are presented in this paper. No measurability is assumed, therefore, treatment convenient for nonmeasurable objects is employed.
An invasive sawfly Aproceros leucopoda Takeuchi, 1939, which originates from East Asia, has colonized elms (Ulmus spp.) in Austria, Hungary, Poland, Romania, Slovakia and the Ukraine, at least since 2003. In Europe, the larvae can completely defoliate native and non-native elm trees and may cause at least partial dieback. Field observations indicate that elms are infested independent of their age and site characteristics. The life cycle of A. leucopoda is described based on material reared in Hokkaido, Japan. Parthenogenetic reproduction, short life cycle of summer generations and the ability to produce four generations per year result in the production of numerous progeny. The evolution of a seasonal dimorphism in head morphology, a simple cocoon that is attached directly to the host plant and a short period spent in the cocoon stage during summer, are putative apomorphies shared by Aproceros Takeuchi, 1939 and Aprosthema Konow, 1899. These traits reduce developmental costs and contribute to the proliferation of A. leucopoda. No specialized parasitoid, that can effectively reduce outbreaks of this species, is known. It is likely that this pest will spread into central and south-western Europe. Further monitoring of A. leucopoda is required to assess future range extensions in Europe, its exacerbating effect on Dutch elm disease and to find a suitable biocontrol agent. Concise keys to imaginal and larval stages are presented that will facilitate the identification of A. leucopoda.
Aprotinin, a nonspecific serine protease inhibitor, has been primarily used as a haemostatic drug in cardiac surgery with cardio-pulmonary bypass (CPB). This study investigated the effect of Aprotinin on the post-operative levels of procalcitonin (PCT) and a set of cytokines in patients undergoing pulmonary artery endarterectomy (PEA). We analyzed 60 patients with chronic thromboembolic pulmonary hypertension undergoing PEA. 30 patients (Group A) were treated with Aprotinin (2000000 IU prior anesthesia, then 2000000 IU in CPB prime and 50000 IU per hour continuously); a further 30 patients (Group B) received Tranexamic Acid (1 g before anesthesia, 1 g after full heparin dose and 2 g in CPB prime). PCT, TNFα, IL-1β, IL-6, and IL-8 arterial concentrations were measured from before until 72 hours after surgery. Aprotinin significantly affected early post-PEA plasma PCT. Patients treated with Aprotinin (Group A) had lower peak PCT levels compared to patients in Group B (1.52 ng/ml versus 2.18, p=0.024). Postoperative peak values of PCT and IL- 6 correlated closely in both groups (r=0.78, r=0.83 respectively). Aprotinin attenuates the post-PEA increase of PCT in the same manner as other pro-inflammatory cytokines. Significant correlation between PCT and IL-6 post-surgery may be indicative of an indirect IL-6-mediated pathway of PCT alteration., P. Maruna, ... [et al.]., and Obsahuje seznam literatury
The expression of aquaporins (AQPs ) in the fetal porcine urinary tract and its relation to gestational age has not been established. Tissue samples from the renal pelvis, ureter, bladder and urethra were obtained from porcine fetuses. Samples were examined by RT-PCR (AQPs 1-11 ), QPCR (AQPs positive on RT-PCR), and immunohistochemistry. Bladder samples were additionally examined by Western blotting. RNA was extracted from 76 tissue samples obtained from 19 fetuses. Gestational age was 60 (n=11) or 100 days (n=8). PCR showed that AQP1, 3, 9 and 11 mRNA was expressed in all locations. The expression of AQP3 increased significantly at all four locations with gestational age, whereas AQP11 significantly decreased. AQP1 expression increased in the ureter, bladder and urethra. AQP9 mRNA expression increased in the urethra and bladder, but decreased in the ureter. AQP5 was expressed only in the urethra. Immunohistochemistry showed AQP1 staining in sub-urothelial vessels at all locations. Western blotting analysis confirmed increased AQP1 protein levels in bladder samples during gestation. Expression levels of AQP1, 3, 5, 9 and 11 in the urinary tract change during gestation, and further studies are needed to provide insights into normal and pathophysiological water handling mechanisms in the fetus., L. K. Jakobsen, K. F. Trelborg, P. S. Kingo, S. Høyer, K.-E. Andersson, J. C. Djurhuus, R. Nørregaard, L. H. Olsen., and Seznam literatury
1_Chestnut (Castanea sativa Mill.) is one of the economically more important trees in the north of Portugal. Spiders, as generalist predators, are potential controlling agents of pests, yet the composition of the community of spiders associated with this crop is only poorly known. The objective of this study was to determine the spider communities in the canopies of chestnut trees subject to three different soil management practices in northeastern Portugal. Three chestnut groves each subject to a different agricultural practice (grazed, tilled or untilled) were studied in 2008 and 2009. The Araneae communities were sampled by beating the branches and the individuals collected were identified to family and species when possible. To investigate the structure of the spider community in each grove the abundance and family richness of spiders were calculated and compared between managements. In total, 4172 spiders were collected and, in both years, the three most abundant families were Araneidae, Philodromidae and Linyphiidae. In 2008, there was a greater abundance of spiders in the grazed, followed by the tilled and untilled groves, but no significant differences among groves. However, in 2009 there was a greater abundance of spiders in the tilled grove, followed by grazed and untilled groves and the differences between the untilled and the other two groves were significant. Araniella, Oxyopes and Anyphaena were the most abundant genera in the three groves. This study showed that soil management may influence the diversity of spiders, but the effects were weak and not consistent between years., 2_The reduction or absence of a suitable habitat for spiders under the trees in the tilled treatment might have resulted in the spiders migrating up into the canopy. However, based on the weak effects on spider abundance recorded and its potentially adverse effects on soils, tillage is not recommended for managing the incidence of pests in chestnut groves., Jacinto Benhadi-Marin ... [et al.]., and Obsahuje seznam literatury