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.
Karst landforms can result from a single stage process in which chemical dissolution and mechanical erosion proceed simultaneously or from a two stage process in which chemical dissolution precedes mechanical erosion. During the second of these processes, chemical dissolution leads to the creation of karst features hosting a residual weathering product, here referred to as alterite. An example of one such feature is the enclosed mass of altered rock at Červený Quarry near Klukovice which represents one of the richest localities for exceptionally preserved echinoderm ossicles in the Prague Synform. In this study the processes responsible for the formation of this feature have been investigated. Nineteen samples were obtained from the bioclastic Slivenec Limestone and from these it has been possible to calculate the carbonate volume content, which defines the weathering intensity, and the carbonate rock weathering index, which defines the weathering state. The results demonstrate that carbonate dissolution has not been accompanied by gravitational compaction or the incorporation of mineral inputs. Thin sections analysed under polarised light and under cathodoluminescence emphasise heterogeneous dolomitisation of the limestone. As the weathering grade intensifies, empty rhomboidal pores become increasingly common until, ultimately, the rhomboidal forms are lost due to corrosion and enlargement. In contrast it is rare to find evidence of calcite dissolution and, therefore, the altered mass still hosts almost all of its post dolomitisation micrite, sparite, and bioclasts. Negligible calcite dissolution helps to explain the exceptional nature of the fossil preservation at the site while the dolomite dissolution accounts for the ease with which it is possible to extract the fossils. Further research should focus on better understanding the role of dolomite dissolution in the formation of other important palaeontological localities in the Prague Synform., Matt Rowberry, Caroline Dubois, Olivier Kaufmann, Jean-Marc Baele and Jan Blahůt., and Obsahuje bibliografii
Drawing on a wide range of sources, including informant testimonies, government and diplomatic archives and contemporary published account, the present article seeks to investigate the Ethiopian experience in international food exchange in the first half of the 20th century. Specifically, it sheds light on the primary causes of the internationalization of the country´s food market and the impact this has had on the important question of access to the valued agricultural resources at production sites. Its findings reveal how first the absence and then the slow growth of the food market within the country´s boundaries - most notably in the capital Addis Ababa - contributed to the globalization of the country´s food trade in the half century after its expansion in 1907. The paper demonstrates that the country´s experience in transnational food exchange was unprecedented and its growth and transformation was embedded in politics rather than the economics of supply and demand alone.