In this note we consider the third order linear difference equations of neutral type (E) ∆ 3 [x(n) − p(n)x(σ(n))] + δq(n)x(τ (n)) = 0, n ∈ N(n0), where δ = ±1, p, q : N(n0) → ℝ+; σ, τ : N(n0) → ℕ, lim n→∞ σ(n) = lim n→∞ τ (n) = ∞. We examine the following two cases: {0 < p(n) ≤ 1, σ(n) = n + k, τ (n) = n + l}, {p(n) > 1, σ(n) = n − k, τ (n) = n − l}, where k, l are positive integers and we obtain sufficient conditions under which all solutions of the above equations are oscillatory.
The asymptotic and oscillatory behavior of solutions of Volterra summation equations yn = pn ± n−1 ∑ s=0 K(n, s)f(s, ys), n ∈ where = {0, 1, 2,...}, are studied. Examples are included to illustrate the results.
The effect of three therapeutically used drugs and five polyphenolic compounds on the mechanism of oxidative burst was compared in whole blood and isolated neutrophils at cellular and molecular level. In 10 μM concentration, the compounds investigated decreased the oxidative burst of whole blood in the rank order of potency: N-feruloylserotonin (N-f-5HT) > curcumin (CUR) > quercetin (QUER) > arbutin (ARB) > resveratrol (RES) > dithiaden (DIT) > carvedilol (CARV) > brompheniramine (BPA). The ratio between the percentage inhibition of extracellular versus intracellular chemiluminescence (CL) followed the rank order QUER > N-f-5HT > RES > CUR > DIT and is indicative of the positive effect of the compounds tested against oxidative burst of neutrophils, demonstrating suppression of reactive oxygen species extracellularly with minimal alteration of intracellular reactive oxygen species (ROS). Activation of protein kinase C was significantly decreased by DIT, CUR, QUER and N-f-5HT. CARV, DIT, QUER and ARB reduced activated neutrophil myeloperoxidase release more significantly compared with the effect on superoxide anion generation. All compounds tested increased the activity of caspase-3 in cell-free system. It is suggested that other regulatory mechanisms than protein kinase C might participate in the inhibition of neutrophil activation with the compounds tested. Different mechanisms are concerned in controlling the assembly of NADPH oxidase and the regulatory role of calcium ions is suggested. Compounds decreasing the amount of extracellular ROS generation, yet affecting but minimally intracellular ROS generation, are promising for further investigation in vivo., R. Nosáľ, K. Drábiková, V. Jančinová, T. Mačičková, J. Pečivová, T. Perečko, J. Harmatha, J. Šmidrkal., and Obsahuje bibliografii
During the years 1996–2001 phytosociological relevés were made of stands containing Senecio inaequidens in the city of Berlin and its surrounding. Data on the structure of the stands were recorded, life form spectra and ecological indicator values were calculated. This species, previously not known in the region before 1993, was found in 9 different phytosociological units (allliances). Growth parameters of S. inaequidens differed widely between these units and were positively correlated with cover and height of the surrounding vegetation. The conclusion drawn was that this species is one of the driving forces in the development from annual to perennial vegetation and has a role similar to that of other dominant species. From the indicator values of the stands surrounding S. inaequidens the following Ellenberg indicator values for the species were derived: Light L 8, temperature T 6, continentality K 4, moisture F 4, soil reaction R 7, nitrogen N 0 (= vague), and hemeroby values H α- and β- euhemerobic. Comparisons with data in literature from W and NW Germany show a broader sociological and ecological amplitude of S. inaequidens in this area, which was colonized by this species in the 1970s. The geographical expansion of this species is not yet finished, and further colonization within its area of distribution is likely to occur in plant communities with low degrees of hemeroby and growing in moister habitats.
We consider the question of preservation of Baire and weakly Baire category under images and preimages of certain kind of functions. It is known that Baire category is preserved under image of quasi-continuous feebly open surjections. In order to extend this result, we introduce a strictly larger class of quasi-continuous functions, i.e. the class of quasi-interior continuous functions. We show that Baire and weakly Baire categories are preserved under image of feebly open quasi-interior continuous surjections. We also give a new definition for countably fiber-completeness of a function. We prove that Baire category is preserved under inverse image of a countably fiber-complete function provided that it is feebly open and feebly continuous.
We consider the two-sided eigenproblem <span class="tex">A * x = λ * B * x</span> over max algebra. It is shown that any finite system of real intervals and points can be represented as spectrum of this eigenproblem