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If (T-t) is a semigroup of Markov operators on an L-1-space that admits a nontrivial lower bound, then a well-known theorem of Lasota and Yorke asserts that the semigroup is strongly convergent as t -> infinity. In this article we generalize and improve this result in several respects. First, we give a new and very simple proof for the fact that the same conclusion also holds if the semigroup is merely assumed to be bounded instead of Markov. As a main result, we then prove a version of this theorem for semigroups which only admit certain individual lower bounds. Moreover, we generalize a theorem of Ding on semigroups of Frobenius-Perron operators. We also demonstrate how our results can be adapted to the setting of general Banach lattices and we give some counterexamples to show optimality of our results. Our methods combine some rather concrete estimates and approximation arguments with abstract functional analytical tools. One of these tools is a theorem which relates the convergence of a time-continuous operator semigroup to the convergence of embedded discrete semigroups.
Since the beginning of the 21st century, spotted fever rickettsioses are known as emerging diseases worldwide. Rickettsiae are obligately intracellular bacteria transmitted by arthropod vectors. The ecology of Rickettsia species has not been investigated in detail, but small mammals are considered to play a role as reservoirs. Aim of this study was to monitor rickettsiae in wild small mammals over a period of five years in four federal states of Germany. Initial screening of ear pinna tissues of 3939 animals by Pan-Rick real-time PCR targeting the citrate synthase (gltA) gene revealed 296 rodents of seven species and 19 shrews of two species positive for rickettsial DNA. Outer membrane protein gene (ompB, ompAIV) PCRs based typing resulted in the identification of three species: Rickettsia helvetica (90.9%) was found as the dominantly occurring species in the four investigated federal states, but Rickettsia felis (7.8%) and Rickettsia raoultii (1.3%) were also detected. The prevalence of Rickettsia spp. in rodents of the genus Apodemus was found to be higher (approximately 14%) than in all other rodent and shrew species at all investigated sites. General linear mixed model analyses indicated that heavier (older) individuals of yellow-necked mice and male common voles seem to contain more often rickettsial DNA than younger ones. Furthermore, rodents generally collected in forests in summer and autumn more often carried rickettsial DNA. In conclusion, this study indicated a high prevalence of R. helvetica in small mammal populations and suggests an age-dependent increase of the DNA prevalence in some of the species and in animals originating from forest habitats. The finding of R. helvetica and R. felis DNA in multiple small mammal species may indicate frequent trans-species transmission by feeding of vectors on different species. Further investigations should target the reason for the discrepancy between the high rickettsial DNA prevalence in rodents and the so far almost absence of clinical apparent human infections.
Nowadays, the role of trace elements (TE) is of growing interest because dyshomeostasis of selenium (Se), manganese (Mn), zinc (Zn), and copper (Cu) is supposed to be a risk factor for several diseases. Thereby, research focuses on identifying new biomarkers for the TE status to allow for a more reliable description of the individual TE and health status. This review mirrors a lack of well-defined, sensitive, and selective biomarkers and summarizes technical limitations to measure them. Thus, the capacity to assess the relationship between dietary TE intake, homeostasis, and health is restricted, which would otherwise provide the basis to define adequate intake levels of single TE in both healthy and diseased humans. Besides that, our knowledge is even more limited with respect to the real life situation of combined TE intake and putative interactions between single TE.