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1. Coexistence of small and large amplitude limit cycles of polynomial differential systems of degree four

Creator:
Sáez, Eduardo, Stange, Eduardo, and Szántó, Iván
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
stability, limit cycle, center, and bifurcation
Language:
English
Description:
A class of degree four differential systems that have an invariant conic $ x^2+Cy^2=1$, $C\in {\mathbb{R}}$, is examined. We show the coexistence of small amplitude limit cycles, large amplitude limit cycles, and invariant algebraic curves under perturbations of the coefficients of the systems.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. Graphs with the same peripheral and center eccentric vertices

Creator:
Kyš, Peter
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
graph, radius, diameter, center, eccentricity, and distance
Language:
English
Description:
The eccentricity e(v) of a vertex v is the distance from v to a vertex farthest from v, and u is an eccentric vertex for v if its distance from v is d(u, v) = e(v). A vertex of maximum eccentricity in a graph G is called peripheral, and the set of all such vertices is the peripherian, denoted PeriG). We use Cep(G) to denote the set of eccentric vertices of vertices in C(G). A graph G is called an S-graph if Cep(G) = Peri(G). In this paper we characterize S-graphs with diameters less or equal to four, give some constructions of • S-graphs and investigate S-graphs with one central vertex. We also correct and generalize some results of F. Gliviak.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

3. Mac Neille completion of centers and centers of Mac Neille completions of lattice effect algebras

Creator:
Kalina, Martin
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
lattice effect algebra, center, atom, and Mac Neille completion
Language:
English
Description:
If element z of a lattice effect algebra (E,⊕,0,1) is central, then the interval [0,z] is a lattice effect algebra with the new top element z and with inherited partial binary operation ⊕. It is a known fact that if the set C(E) of central elements of E is an atomic Boolean algebra and the supremum of all atoms of C(E) in E equals to the top element of E, then E is isomorphic to a subdirect product of irreducible effect algebras (\cite{R2}). This means that if there exists a MacNeille completion E^ of E which is its extension (i.e. E is densely embeddable into E^) then it is possible to embed E into a direct product of irreducible effect algebras. Thus E inherits some of the properties of E^. For example, the existence of a state in E^ implies the existence of a state in E. In this context, a natural question arises if the MacNeille completion of the center of E (denoted as MC(C(E))) is necessarily the same as the center of E^, i.e., if MC(C(E))=C(E^) is necessarily true. We show that the equality is not necessarily fulfilled. We find a necessary condition under which the equality may hold. Moreover, we show also that even the completeness of C(E) and its bifullness in E is not sufficient to guarantee the mentioned equality.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

4. On a theorem of Cantor-Bernstein type for algebras

Creator:
Jakubík, Ján
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
lattice, $\mathcal L^*$-variety, center, and internal direct factor
Language:
English
Description:
Freytes proved a theorem of Cantor-Bernstein type for algbras; he applied certain sequences of central elements of bounded lattices. The aim of the present paper is to extend the mentioned result to the case when the lattices under consideration need not be bounded; instead of sequences of central elements we deal with sequences of internal direct factors of lattices.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

5. On central atoms of Archimedean atomic lattice effec algebras

Creator:
Kalina, Martin
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
lattice effect algebra, center, atom, and bitfullness
Language:
English
Description:
If element z of a lattice effect algebra (E,⊕,0,1) is central, then the interval [0,z] is a lattice effect algebra with the new top element z and with inherited partial binary operation ⊕. It is a known fact that if the set C(E) of central elements of E is an atomic Boolean algebra and the supremum of all atoms of C(E) in E equals to the top element of E, then E is isomorphic to a direct product of irreducible effect algebras (\cite{R2}). In \cite{PR} Paseka and Riečanová published as open problem whether C(E) is a bifull sublattice of an Archimedean atomic lattice effect algebra E. We show that there exists a lattice effect algebra (E,⊕,0,1) with atomic C(E) which is not a bifull sublattice of E. Moreover, we show that also B(E), the center of compatibility, may not be a bifull sublattice of E.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public