Taylor is prime

We study the Taylor varieties and obtain new characterizations of them via compatible reflexive digraphs. Based on our findings, we prove that in the lattice of interpretability types of varieties, the filter of the types of all Taylor varieties is prime

The number of slim rectangular lattices

Slim rectangular lattices are special planar semimodular lattices introduced by G. Grätzer and E. Knapp in 2009. They are finite semimodular lattices L such that the ordered set Ji L of join-irreducible elements of L is the cardinal sum of two nontrivial chains. After describing these lattices of a given length n by permutations, we determine their number, |SRectL(n)|. Besides giving recursive formulas, which are effective up to about n = 1000, we also prove that |SRectL(n)| is asymptotically (n - 2)! · (Formula presented.). Similar results for patch lattices, which are special rectangular lattices introduced by G. Czédli and E. T. Schmidt in 2013, and for slim rectangular lattice diagrams are also given. © 2015 Springer International Publishin

Quasiorder lattices in congruence modular varieties

Some elements of tame congruence theory can be applied to quasiorder lattices instead of congruence lattices. In particular, it is possible to consider minimal sets of an algebra with respect to one of its prime quasiorder quotients. It turns out that if a finite algebra is in a congruence modular variety, then it is minimal with respect to a quasiorder quotient iff it is minimal with respect to a congruence quotient — in which case it is either a two-element algebra, or has a Mal’tsev-polynomial. As an application of this fact, we prove that if an algebra is in a congruence modular variety, its congruence and quasiorder lattices satisfy the same identities

Long-Term Land Use and Landscape Pattern Changes in a Marshland of Hungary

This paper presents the trends of landscape change in the marshes on the southern shore of Lake Balaton, a wetland profoundly transformed by human activities. The study does not only deal with alterations in the areal proportions of land use classes but also quantitatively analyses landscape pattern, comparing landscape metrics on different dates. Based on the findings, proposals for rehabilitation are made. Through the restoration of wetland habitats, the provision level of ecosystem services can be raised. Landscape change was investigated from 1783 to 2020. For this purpose, archive maps were digitized, CORINE land cover datasets corrected by Sentinel-2 imagery were employed and from the vector data, the proportions of land use classes were calculated. For landscape pattern perimeter, area, neighbourhood and diversity metrics were used, calculated by ArcGIS vLATE plugin. It was pointed out that in land cover, the share of wetlands considerably declined over the centuries but in recent decades somewhat expanded. In the 20th century, grasslands were the predominant land use class, but with the spread of other categories, land use has become more complex. Landscape metrics show an increased fragmentation of natural habitats, a higher number of patches and edge density, leading to higher landscape diversity. Rehabilitation proposals include the establishment of rainwater retention reservoirs, the conversion of arable land which cannot be cultivated profitably to close-to-natural classes (first of all, grasslands) and the plantation of gallery forests of native tree species along canals. In comparison with other regions, similar temporal trends and spatial distributions are observed. For instance, the internationally well-known transformation of the Doñana wetland started later but was more intensive than in Hungary

Long-Term Land Use and Landscape Pattern Changes in a Marshland of Hungary

This paper presents the trends of landscape change in the marshes on the southern shore of Lake Balaton, a wetland profoundly transformed by human activities. The study does not only deal with alterations in the areal proportions of land use classes but also quantitatively analyses landscape pattern, comparing landscape metrics on different dates. Based on the findings, proposals for rehabilitation are made. Through the restoration of wetland habitats, the provision level of ecosystem services can be raised. Landscape change was investigated from 1783 to 2020. For this purpose, archive maps were digitized, CORINE land cover datasets corrected by Sentinel-2 imagery were employed and from the vector data, the proportions of land use classes were calculated. For landscape pattern perimeter, area, neighbourhood and diversity metrics were used, calculated by ArcGIS vLATE plugin. It was pointed out that in land cover, the share of wetlands considerably declined over the centuries but in recent decades somewhat expanded. In the 20th century, grasslands were the predominant land use class, but with the spread of other categories, land use has become more complex. Landscape metrics show an increased fragmentation of natural habitats, a higher number of patches and edge density, leading to higher landscape diversity. Rehabilitation proposals include the establishment of rainwater retention reservoirs, the conversion of arable land which cannot be cultivated profitably to close-to-natural classes (first of all, grasslands) and the plantation of gallery forests of native tree species along canals. In comparison with other regions, similar temporal trends and spatial distributions are observed. For instance, the internationally well-known transformation of the Doñana wetland started later but was more intensive than in Hungary