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1. Annihilator-preserving congruence relations in distributive nearlattices

Creator:
Calomino, Ismael and Celani, Sergio
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
distributive nearlattice, ideal, filter, congruence, and annihilator
Language:
English
Description:
In this note we give some new characterizations of distributivity of a nearlattice and we study annihilator-preserving congruence relations.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. Characterizations of the 0-distributive semilattice

Creator:
Balasubramani, P.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
semilattice, prime ideal, and filter
Language:
English
Description:
The 0-distributive semilattice is characterized in terms of semiideals, ideals and filters. Some sufficient conditions and some necessary conditions for 0-distributivity are obtained. Counterexamples are given to prove that certain conditions are not necessary and certain conditions are not sufficient.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

3. Classes of fuzzy filters of residuated lattice ordered monoids

Creator:
Rachůnek, Jiří and Šalounová, Dana
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
residuated l-monoid, non-classical logics, basic fuzzy logic, intuitionistic logic, filter, fuzzy filter, BL-algebra, MV-algebra, and Heyting algebra
Language:
English
Description:
The logical foundations of processes handling uncertainty in information use some classes of algebras as algebraic semantics. Bounded residuated lattice ordered monoids (Rl-monoids) are common generalizations of BL-algebras, i.e., algebras of the propositional basic fuzzy logic, and Heyting algebras, i.e., algebras of the propositional intuitionistic logic. From the point of view of uncertain information, sets of provable formulas in inference systems could be described by fuzzy filters of the corresponding algebras. In the paper we investigate implicative, positive implicative, Boolean and fantastic fuzzy filters of bounded Rl-monoids.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

4. Interior and closure operators on bounded residuated lattice ordered monoids

Creator:
Švrček, Filip
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
$GMV$-algebra, $DRl$-monoid, and filter
Language:
English
Description:
$GMV$-algebras endowed with additive closure operators or with its duals-multiplicative interior operators (closure or interior $GMV$-algebras) were introduced as a non-commutative generalization of topological Boolean algebras. In the paper, the multiplicative interior and additive closure operators on $DRl$-monoids are introduced as natural generalizations of the multiplicative interior and additive closure operators on $GMV$-algebras.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

5. Local bounded commutative residuated $\ell$-monoids

Creator:
Rachůnek, Jiří and Šalounová, Dana
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
residuated $\ell $-monoid, residuated lattice, $BL$-algebra, $MV$-algebra, local $R\ell $-monoid, and filter
Language:
English
Description:
Bounded commutative residuated lattice ordered monoids ($R\ell $-monoids) are a common generalization of, e.g., $BL$-algebras and Heyting algebras. In the paper, the properties of local and perfect bounded commutative $R\ell $-monoids are investigated.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

6. On ideals in De Morgen residuated lattices

Creator:
Holdon, Liviu-Constantin
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
residuated lattice, De Morgan laws, filter, deductive system, ideal, ∩-prime, ∩-irreducible, and annihilator
Language:
English
Description:
In this paper, we introduce a new class of residuated lattices called De Morgan residuated lattices, we show that the variety of De Morgan residuated lattices includes important subvarieties of residuated lattices such as Boolean algebras, MV-algebras, BL-algebras, Stonean residuated lattices, MTL-algebras and involution residuated lattices. We investigate specific properties of ideals in De Morgan residuated lattices, we state the prime ideal theorem and the pseudo-complementedness of the ideal lattice, we pay attention to prime, maximal, ⊙-prime ideals and to ideals that are meet-irreducible or meet-prime in the lattice of all ideals. We introduce the concept of an annihilator of a given subset of a De Morgan residuated lattice and we prove that annihilators are a particular kind of ideals. Also, regular annihilator and relative annihilator ideals are considered.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

7. Pseudo BL-algebras and DRl-monoids

Creator:
Kühr, Jan
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
pseudo BL-algebra, DRl-monoid, filter, polar, and representable pseudo BL-algebr
Language:
English
Description:
It is shown that pseudo BL-algebras are categorically equivalent to certain bounded DRl-monoids. Using this result, we obtain some properties of pseudo BL-algebras, in particular, we can characterize congruence kernels by means of normal filters. Further, we deal with representable pseudo BL-algebras and, in conclusion, we prove that they form a variety.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

8. Starnutie pozorovacích objektov na sledovanie podzemných vôd

Creator:
Hulla, Jozef, Súľovská, Monika, Aldorf, Josef, and Rapantová, Naďa
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
perforated tube, filter, water level, filtration and critical velocity, piping, colmatation, perforovaná rúrka, hladina vody, filtračná a kritická rýchlosť, sufózia, and kolmatácia
Language:
Slovak
Description:
Observation objects, appropriately equiped boreholes, are widely used for analysis of water level, velocity and transport regimes, related to groundwater flows by solution of many practical problems. It concerns mainly hydrogeological investigation, optimal usage and protection of water resources against contamination, seepage through bodies and subsoils of dams as well as flood embankments, territory and excavation dewatering and many others problems. Aging processes of observations objects are related directly creation of objects, to medium stability problems in their vicinity, they used to be manifested fine particles deposition into the observation objects and, influencing of water level and flow velocities developments. The paper presents concrete information and knowledge from 32 years monitoring of aging processes of observation boreholes in subsoils of some Slovak dams. and Pozorovacie objekty, vhodne vystrojené vrty, sa široko využívajú na analýzy hladinových, rýchlostných i prenosových režimov súvisiacich s prúdením podzemných vôd pri riešení mnohých praktických problémov. Ide najmä o hydrogeologický prieskum, optimálne využívanie a ochranu vodných zdrojov pred znečistením, priesaky cez telesá a podložia priehrad i protipovodňových hrádzí, odvodňovanie území, stavebných jám a mnohé ďalšie problémy. Procesy starnutia bezprostredne súvisia s vytváraním pozorovacích objektov, s problémami stability prostredia v ich okolí, prejavujú sa zanášaním pevnými časticami i ovplyvnením vývoja hladín a rýchlostí prúdenia. V príspevku sú uvedené konkrétne poznatky z 32- ročného sledovania procesov starnutia pozorovacích objektov v podloží niektorých slovenských priehrad.
Rights:
http://creativecommons.org/licenses/by-nc-sa/4.0/ and policy:public

9. Unifying approach to observer-filter design

Creator:
Černý, Václav
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
observer, invariance, convergence, filter, signal power, and system energy
Language:
English
Description:
The paper examines similarities between observer design as introduced in Automatic Control Theory and filter design as established in Signal Processing. It is shown in the paper that there are obvious connections between them in spite of different aims for their design. Therefore, it is prospective to make them be compatible from the structural point of view. Introduced error invariance and error convergence properties of both of them are unifying tools for their design. Lyapunov's stability theory, signal power, system energy and a power balance relation are other basic terms used in the paper.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public