Asymptotic properties of a general model of immune status

We consider a model of dynamics of the immune system. The model is based on three factors: occasional boosting and continuous waning of immunity and a general description of the period between subsequent boosting events. The antibody concentration changes according to a non-Markovian process. The density of the distribution of this concentration satisfies some partial differential equation with an integral boundary condition. We check that this system generates a stochastic semigroup and we study the long-time behaviour of this semigroup. In particular we prove a theorem on its asymptotic stability.Comment: 25 pages, 2 figure

Stability of Markov Semigroups and Applications to Parabolic Systems

AbstractA new theorem for asymptotic stability of Markov semigroups is proved. This result is applied to semigroups generated by parabolic systems describing the evolution of densities of two-state diffusion processes

Suchość jamy ustnej - niedoceniany problem kliniczny

Suchość jamy ustnej lub kserostomia definiowana jako zmniejszenie ilości wydzielanej śliny z towarzyszącym uczuciem suchości w jamie ustnej to częsty problem osób przewlekle chorych, zwłaszcza w wieku podeszłym. Zaburzenie prawidłowej pracy gruczołów ślinowych może wynikać ze stanu ogólnego organizmu, może też być objawem chorób ogólnoustrojowych, ale często jest efektem ubocznym stosowanego leczenia. Objawy kserostomii powodują pogorszenie jakości życia chorego, zwiększenie podatności na infekcje jamy ustnej oraz utrudnienie mówienia i połykania. Zaawansowanie kserostomii można oceniać, stosując testy sialometryczne lub za pomocą Inwentarza Kserostomii. Ma to szczególne znaczenie w monitorowaniu skuteczności terapii. W leczeniu suchości w jamie ustnej istotne znaczenie mają higiena i pielęgnacja błon śluzowych oraz środki i preparaty pobudzające wydzielanie gruczołów ślinowych. W przypadku braku odpowiedzi komórek gruczołowych na stymulację zaleca się substytuty śliny

Effect of basalt powder addition on properties of mortar

The study evaluates the use of waste basalt powder as a replacement of cement to enhance hydration of cement and mortar properties. The basalt powder is a waste resulting from preparation of aggregate used in asphalt mixture production. Previous studies have shown that analysed waste used as a fine aggregate replacement has a beneficial effect on some properties of mortar and concrete, i.e. compressive strength, flexural strength and freeze resistance. The present study shows the results of the research concerning the modification of cement paste and mortar with basalt powder. The modification consists in adding the powder waste as a partial replacement of cement. The percentages of basalt powder in this research are 0-40% and 0-20% by mass of cement in the pastes and mortars respectively. The experiments were carried out to determine the influence of basalt powder on cement hydration, as well as compressive and flexural strength. Results indicate that addition of basalt powder as a replacement of cement leads to deterioration of compressive strength. The flexural strength of mortar is improved in some cases. Waste basalt powder only slightly influences the cement hydration

Stochastic semigroups and their applications to biological models

Some recent results concerning generation and asymptotic properties of stochastic semigroups are presented. The general results are applied to biological models described by piecewise deterministic Markov processes: birth-death processes, the evolution of the genome, genes expression and physiologically structured models

Effects of Noise on Entropy Evolution

We study the convergence properties of the conditional (Kullback-Leibler) entropy in stochastic systems. We have proved very general results showing that asymptotic stability is a necessary and sufficient condition for the monotone convergence of the conditional entropy to its maximal value of zero. Additionally we have made specific calculations of the rate of convergence of this entropy to zero in a one-dimensional situations, illustrated by Ornstein-Uhlenbeck and Rayleigh processes, higher dimensional situations, and a two dimensional Ornstein-Uhlenbeck process with a stochastically perturbed harmonic oscillator and colored noise as examples. We also apply our general results to the problem of conditional entropy convergence in the presence of dichotomous noise. In both the single dimensional and multidimensional cases we are to show that the convergence of the conditional entropy to zero is monotone and at least exponential. In the specific cases of the Ornstein-Uhlenbeck and Rayleigh processes as well as the stochastically perturbed harmonic oscillator and colored noise examples, we have the rather surprising result that the rate of convergence of the entropy to zero is independent of the noise amplitude.Comment: 23 page

The discrete fragmentation equations : semigroups, compactness and asynchronous exponential growth

In this paper we present a class of fragmentation semigroups which are compact in a scale of spaces defined in terms of finite higher moments. We use this compactness result to analyse the long time behaviour of such semigroups and, in particular, to prove that they have the asynchronous growth property. We note that, despite compactness, this growth property is not automatic as the fragmentation semigroups are not irreducible