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1
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Distribution of lattice points on hyperbolic surfaces

100%
Lev V.
Acta Arithmetica
|
1996
|
tom 75
|
nr 1
85-95
EN
Let two lattices $Λ', Λ'' ⊂ ℝ^s$ have the same number of points on each hyperbolic surface $|x₁...x_s| = C$. We investigate the case when Λ', Λ'' are sublattices of $ℤ^s$ of the same prime index and show that then Λ' and Λ'' must coincide up to renumbering the coordinate axes and changing their directions.
2
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On varieties of orgraphs

80%
Haviar A., Monoszová G.
Discussiones Mathematicae Graph Theory
|
2001
|
tom 21
|
nr 2
207-221
EN
In this paper we investigate varieties of orgraphs (that is, oriented graphs) as classes of orgraphs closed under isomorphic images, suborgraph identifications and induced suborgraphs, and we study the lattice of varieties of tournament-free orgraphs.
3
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Two Infinite Sequences of Pre-Maximal Extensions of the Relevant Logic E

80%
Typańska-Czajka L.
Bulletin of the Section of Logic
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2019
|
tom 48
|
nr 1
EN
The only maximal extension of the logic of relevant entailment E is the classical logic CL. A logic L ⊆ [E,CL] called pre-maximal if and only if L is a coatom in the interval [E,CL]. We present two denumerable infinite sequences of premaximal extensions of the logic E. Note that for the relevant logic R there exist exactly three pre-maximal logics, i.e. coatoms in the interval [R,CL].
4
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Many Faces of Lattice Tolerances

70%
Grygiel J.
Bulletin of the Section of Logic
|
2019
|
tom 48
|
nr 4
EN
Our aim is to overview and discuss some of the most popular approaches to the notion of a tolerance relation in algebraic structures with the special emphasis on lattices.
5
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Flat semilattices

70%
Grätzer G., Wehrung F.
Colloquium Mathematicum
|
1999
|
tom 79
|
nr 2
185-191
6
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Linear model genealogical tree application to an odontology experiment

70%
Covas R.
Discussiones Mathematicae Probability and Statistics
|
2007
|
tom 27
|
nr 1-2
47-77
EN
Commutative Jordan algebras play a central part in orthogonal models. We apply the concepts of genealogical tree of an Jordan algebra associated to a linear mixed model in an experiment conducted to study optimal choosing of dentist materials. Apart from the conclusions of the experiment itself, we show how to proceed in order to take advantage of the great possibilities that Jordan algebras and mixed linear models give to practitioners.
7
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Subdirect decompositions of algebras from 2-clone extensions of varieties

61%
Płonka J.
Colloquium Mathematicum
|
1998
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tom 77
|
nr 2
189-199
EN
Let τ:F → ℕ be a type of algebras, where F is a set of fundamental operation symbols and ℕ is the set of nonnegative integers. We assume that |F|≥2 and 0 ∉ (F). For a term φ of type τ we denote by F(φ) the set of fundamental operation symbols from F occurring in φ. An identity φ ≉ ψ of type τ is called clone compatible if φ and ψ are the same variable or F(φ)=F(ψ)≠$\emptyset$. For a variety V of type τ we denote by $V^{c,2}$ the variety of type τ defined by all identities φ ≉ ψ from Id(V) which are either clone compatible or |F(φ)|, |F(ψ)|≥2. Under some assumption on terms (condition (0.iii)) we show that an algebra ${\gt A}$ belongs to $V^{c,2}$ iff it is isomorphic to a subdirect product of an algebra from V and of some other algebras of very simple structure. This result is applied to finding subdirectly irreducible algebras in $V^{c,2}$ where V is the variety of distributive lattices or the variety of Boolean algebras.
8
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Decomposition of topologies on lattices and hyperspaces

38%
Costantini C., Vitolo P.
Instytut Matematyczny Polskiej Akademii Nauk
EN
CONTENTS Introduction.................................................................................5 1. Decomposable topologies.......................................................6 2. Locally convex topologies......................................................10 3. Semilattices. Strong decomposability.....................................13 4. Convex topologies.................................................................15 5. Topologies on linearly ordered sets.......................................18 6. Topologies on lattices............................................................20 7. The Scott topology.................................................................26 8. Uniqueness of decomposition................................................28 9. Hyperspace topologies..........................................................32 10. The Vietoris topology...........................................................35 11. The Hausdorff metric topology.............................................37 12. The proximal topology..........................................................39 13. The Kuratowski convergence..............................................40 14. Uniqueness of decomposition for hypertopologies..............44 References................................................................................47
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