Positive semigroups and perturbations of boundary conditions

We present a generation theorem for positive semigroups on an $L^1$ space. It provides sufficient conditions for the existence of positive and integrable solutions of initial-boundary value problems. An application to a two-phase cell cycle model is given

A model for random fire induced tree-grass coexistence in savannas

Tree-grass coexistence in savanna ecosystems depends strongly on environmental disturbances out of which crucial is fire. Most modeling attempts in the literature lack stochastic approach to fire occurrences which is essential to reflect their unpredictability. Existing models that actually include stochasticity of fire are usually analyzed only numerically. We introduce a new minimalistic model of treegrass coexistence where fires occur according to a stochastic process. We use the tools of the linear semigroup theory to provide a more careful mathematical analysis of the model. Essentially we show that there exists a unique stationary distribution of tree and grass biomasses

A model of seasonal savanna dynamics

We introduce a mathematical model of savanna vegetation dynamics. The usual approach of nonequilibrium ecology is extended by including the impact of wet and dry seasons. We present and rigorously analyze a model describing a mixed woodland-grassland ecosystem with stochastic environmental noise in the form of vegetation biomass losses manifesting fires. Both, the probability of ignition and the strength of these losses depend on the current season (as well as vegetation growth rates etc.). Formally it requires an introduction and analysis of a system that is a piecewise deterministic Markov process with parameters switching between given constant periods of time. We study the long time behavior of time averages for such processes.Comment: 22 pages, 3 figure

Dawne i współczesne metody konserwacji i restauracji witraży na przykładzie witrażu Św. Piotr ze zbiorów Muzeum Uniwersytetu Jagiellońskiego Collegium Maius w Krakowie

Old and modern methods of stained glass conservation and renovation, using as an example the stained glass depicting St Peter in the collection of the Collegium Maius of the Jagiellonian University in Kraków Stained glass is exposed to a number of harmful chemical and physical agents. Considering its combined protective and artistic functions, materials used for stained glass production must have very good physical and chemical properties. Despite that, individual elements of stained glass often suffer irreversible damage. The present paper is aimed to present the development of conservation concepts with respect to this art discipline. The causes and types of damage to elements of stained glass are discussed. Various methods of conservation and renovation of stained glass since the 19th century to the present are covered. The analysis of selected treatment and stages of conservation works in view of their safety, effectiveness and influence on the artwork’s aesthetic qualities has been carried out. In addition, the results of tests of adhesives used for repairing damaged glass have been presented. Theoretical discussion is supported by practical examples of the use of some methods of conservation applied to the 17th-century stained glass with the image of St Peter, in the collection of the Collegium Maius of the Jagiellonian University in Kraków

Multidirectional changes in parameters related to sulfur metabolism in frog tissues exposed to heavy metal-related stress

The investigations showed changes of the cystathionine $\gamma$ -lyase (CTH), 3-mercaptopyruvate sulfurtransferase (MPST) and rhodanese (TST) activity and gene expression in the brain, heart, liver, kidney, skeletal muscles and testes in frogs Pelophylax ridibundus, Xenopus laevis and Xenopus tropicalis in response to Pb$^{2+}$, Hg$^{2+}$ and Cd$^{2+}$ stress. The results were analyzed jointly w ith changes in the expression of selected antioxidant enzymes (cytoplasmic and mitochondrial superoxide dismutase, glutathione peroxidase, catalase and thioredoxin reducatase) and with the level of malondialdehyde (a product of lipid peroxidation). The obtained results allowed for confirming the role of sulfurtransferases in the antioxidant protection of tissues exposed to heavy metal ions. Our results revealed different transcriptional responses of the investigated tissues to each of the examined heavy metals. The CTH, MPST and TST genes might be regarded as heavy metal stress-responsive. The CTH gene expression up-regulation w as confirmed in the liver (Pb$^{2+}$, Hg$^{2+}$, Cd$^{2+}$) and skeletal muscle (Hg$^{2+}$), MPST in the brain (Pb$^{2+}$ , Hg$^{2+}$), kidney (Pb$^{2+}$, Cd$^{2+}$ ), skeletal muscle (Pb$^{2+}$, Hg$^{2+}$,Cd$^{2+}$) and TST in the brain (Pb$^{2+}$) and kidney (Pb$^{2+}$, Hg$^{2+}$, Cd$^{2+}$ ). Lead, mercury and cadmium toxicity was demonstrated to affect the glutathione (GSH) and cysteine levels, the concentration ratio of reduced to oxidized glutathione ([GSH]/[GSSG]) and the level of sulfane sulfur-containing compounds, which in case of enhanced reactive oxygen species generation can reveal their antioxidative properties. The present report is the first to widely describe the role of the sulfane sulfur/H$_{2}$S generating enzymes and the cysteine/glutathione system in Pb$^{2+}$, Hg$^{2+}$ and Cd$^{2+}$ stress in various frog tissues, and to explore the mechanisms mediating heavy metal-related stress

The Mathematical Legacy of Andrzej Lasota

Professor Andrzej Lasota (1932–2006) was a Polish mathematician with wide ranging interests in dynamical systems, probability theory and ergodic theory who saw the inter-relationships between all three and who successfully synthesized these apparently disparate fields. He used that synthesis to both further mathematical research as well as to investigate problems in biology. One of his over-riding interests was the way in which seemingly “random” or “probabilistic” processes (in a mathematical sense) could actually be thought of as equivalently coming from deterministic dynamics. How did we each come to know him and his work? Michael C. Mackey met Lasota in Cracow in 1977 through his collaborator Dr. MariaWazewska-Czyzewska, a hematologist and daughter of Professor Tadeusz Wazewski. That meeting blossomed into an almost 30-year-long friendship and collaboration in biomathematics. Marta Tyran-Kaminska met Lasota during her mathematical studies at the University of Silesia in Katowice in 1992 and did her Ph.D. under his supervision. Hans-Otto Walther met Lasota during a year at Michigan State University, 1979–1980, where Pavel Brunovský was also visiting, and they had all been brought together by Shui-Nee Chow