The classical Hardy-Littlewood maximal operator is bounded not only on the classical Lebesgue spaces Lp(Rd) (in the case p > 1), but (in the case when 1/p(·) is log-Hölder continuous and p- = inf{p(x): x\in Rd > 1) on the variable Lebesgue spaces Lp(·)(Rd), too. Furthermore, the classical Hardy-Littlewood maximal operator is of weak-type (1, 1). In the present note we generalize Besicovitch’s covering theorem for the so-called γ-rectangles. We introduce a general maximal operator Msγδ, and with the help of generalized Φ-functions, the strong- and weak-type inequalities will be proved for this maximal operator. Namely, if the exponent function 1/p(·) is log-Hölder continuous and p- ≥ s, where 1 ≤ s ≤ ∞ is arbitrary (or
p- ≥ s), then the maximal operator Msγδ is bounded on the space Lp(·)(Rd) (or the maximal operator is of weak-type (p(·), p(·)))., Kristóf Szarvas, Ferenc Weisz., and Obsahuje seznam literatury
The main results of this paper are that (1) a space $X$ is $g$-developable if and only if it is a weak-open $\pi $ image of a metric space, one consequence of the result being the correction of an error in the paper of Z. Li and S. Lin; (2) characterizations of weak-open compact images of metric spaces, which is another answer to a question in in the paper of Y. Ikeda, C. liu and Y. Tanaka.
Some sufficient conditions are provided that guarantee that the difference of a compact mapping and a proper mapping defined between any two Banach spaces over $\mathbb {K}$ has at least one zero. When conditions are strengthened, this difference has at most a finite number of zeros throughout the entire space. The proof of the result is constructive and is based upon a continuation method.
A dominating set $D\subseteq V(G)$ is a {\it weakly connected dominating set} in $G$ if the subgraph $G[D]_w=(N_G[D],E_w)$ weakly induced by $D$ is connected, where $E_w$ is the set of all edges having at least one vertex in $D$. {\it Weakly connected domination number} $\gamma _w(G)$ of a graph $G$ is the minimum cardinality among all weakly connected dominating sets in $G$. A graph $G$ is said to be {\it weakly connected domination stable} or just $\gamma _w$-{\it stable} if $\gamma _w(G)=\gamma _w(G+e)$ for every edge $e$ belonging to the complement $\overline G$ of $G.$ We provide a constructive characterization of weakly connected domination stable trees.
We deal with real weakly stationary processes \procX with non-positive autocorrelations {rk}, i. e. it is assumed that rk≤0 for all k=1,2,…. We show that such processes have some special interesting properties. In particular, it is shown that each such a process can be represented as a linear process. Sufficient conditions under which the resulting process satisfies rk≤0 for all k=1,2,… are provided as well.
The timing of egg laying by songbirds is known to be strongly affected by local climate, with temperature and precipitation being the most influential factors. However, most research to date relates only to the start of the breeding season: later records and the duration of the whole have not been taken into consideration. In the case of multibrooded species, productivity usually depends on the length of the breeding season. In this work we analysed climatic factors affecting breeding season length of an urban blackbird (Turdus merula) population. The study was conducted in two parks in the city of Szczecin, north-western Poland, spanning 14 breeding seasons since 1997. We found that over the study period, the breeding season became shorter as a result of colder springs and possibly because
of warmer June-July temperatures. Our study revealed a positive relationship between breeding season length and the mean and mean
minimum temperatures in April. Total precipitation in April-July also positively influenced breeding season length. The present survey confirms the influence of temperature and precipitation on the breeding season length of blackbird.
Males of the small copper butterfly, Lycaena phlaeas daimio, exhibit two mate-locating tactics: patrolling and perching. Field investigations were conducted to determine the biotic and abiotic factors affecting the mate-locating behaviour of male L. phlaeas. Patrolling was often observed when light intensity was high. Perching was performed throughout the day regardless of environmental conditions, but the chasing of passing insects increased at high light intensities. The activity patterns of the males were not affected by those of the females. The thoracic temperatures of patrolling males were lower than those of perching males under cool conditions, suggesting that patrolling males lose heat more easily. In contrast, perching males may more easily regulate their body temperature to a suitable level as they fly for shorter periods and can bask while waiting for mates. These results highlight several reasons (i.e., heat loss, energetic costs) why males patrol when weather conditions are favourable.
Population fluctuations of the well-known oak defoliator, the oak processionary moth (Thaumetopoea processionea L.), were studied using light trap data and basic meteorological parameters (monthly average temperatures, and precipitation) at three locations in Western Hungary over a period of 15 years (1988-2012). The fluctuations in the numbers caught by the three traps were strongly synchronized. One possible explanation for this synchrony may be similar weather at the three trapping locations. Cyclic Reverse Moving Interval Techniques (CReMIT) were used to define the period of time in a year that most strongly influences the catches. For this period, we defined a species specific aridity index for Thaumetopoea processionea (THAU-index). This index explains 54.8-68.9% of the variation in the yearly catches, which indicates that aridity, particularly in the May-July period was the major determinant of population fluctuations. Our results predict an increasing future risk of Oak Processionary Moth (OPM) outbreaks and further spread if the frequency of severe spring/summer droughts increases with global warming., György Csóka, Anikó Hirka, Levente Szöcs, Norbert Móricz, Ervin Rasztovits, Zoltán Pödör., and Obsahuje bibliografii