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    Wyświetlanie 1-12 z 12
    Tytuł:
    Representable dually residuated lattice-ordered monoids
    Autorzy:
    Kühr, Jan
    Powiązania:
    https://bibliotekanauki.pl/articles/728960.pdf
    Data publikacji:
    2003
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    DRl-monoid
    ideal
    prime ideal
    polar
    normal ideal
    representable DRl-monoid
    Opis:
    Dually residuated lattice-ordered monoids (DRl-monoids) generalize lattice-ordered groups and include also some algebras related to fuzzy logic (e.g. GMV-algebras and pseudo BL-algebras). In the paper, we give some necessary and sufficient conditions for a DRl-monoid to be representable (i.e. a subdirect product of totally ordered DRl-monoids) and we prove that the class of representable DRl-monoids is a variety.
    Źródło:
    Discussiones Mathematicae - General Algebra and Applications; 2003, 23, 2; 115-123
    1509-9415
    Pojawia się w:
    Discussiones Mathematicae - General Algebra and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On a complete lattice of retracts of a free monoid generated by three elements
    Autorzy:
    Foryś, W.
    Powiązania:
    https://bibliotekanauki.pl/articles/255748.pdf
    Data publikacji:
    2008
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    free monoid
    retract
    lattice
    complete lattice
    Opis:
    We prove that the family of retracts of a free monoid generated by three elements, partially ordered with respect to the inclusion, is a complete lattice.
    Źródło:
    Opuscula Mathematica; 2008, 28, 2; 123-127
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Direct decompositions of dually residuated lattice-ordered monoids
    Autorzy:
    Rachůnek, Jiří
    Šalounová, Dana
    Powiązania:
    https://bibliotekanauki.pl/articles/728920.pdf
    Data publikacji:
    2004
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    DRl-monoid
    lattice-ordered monoid
    ideal
    normal ideal
    polar
    direct factor
    Opis:
    The class of dually residuated lattice ordered monoids (DRl-monoids) contains, in an appropriate signature, all l-groups, Brouwerian algebras, MV- and GMV-algebras, BL- and pseudo BL-algebras, etc. In the paper we study direct products and decompositions of DRl-monoids in general and we characterize ideals of DRl-monoids which are direct factors. The results are then applicable to all above mentioned special classes of DRl-monoids.
    Źródło:
    Discussiones Mathematicae - General Algebra and Applications; 2004, 24, 1; 63-74
    1509-9415
    Pojawia się w:
    Discussiones Mathematicae - General Algebra and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A semantic construction of two-ary integers
    Autorzy:
    Ricci, Gabriele
    Powiązania:
    https://bibliotekanauki.pl/articles/729095.pdf
    Data publikacji:
    2005
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    universal matrix
    analytic monoid
    LISP
    semantics
    jump
    Opis:
    To binary trees, two-ary integers are what usual integers are to natural numbers, seen as unary trees. We can represent two-ary integers as binary trees too, yet with leaves labelled by binary words and with a structural restriction. In a sense, they are simpler than the binary trees, they relativize. Hence, contrary to the extensions known from Arithmetic and Algebra, this integer extension does not make the starting objects more complex.
    We use a semantic construction to get this extension. This method differs from the algebraic ones, mainly because it is able to find equational features of the extended objects. Two-ary integers turn out to form the free algebra corresponding to the Jónsson-Tarski's "paradoxical" equations. This entails that they have a "sum" operation as well as other operations of higher dimensions.
    Two-ary integers can provide LISP memories with convenient direct access jumps and the above low complexity hints at feasible hardware implementations.
    Źródło:
    Discussiones Mathematicae - General Algebra and Applications; 2005, 25, 2; 165-219
    1509-9415
    Pojawia się w:
    Discussiones Mathematicae - General Algebra and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On lattice-ordered monoids
    Autorzy:
    Jasem, Milan
    Powiązania:
    https://bibliotekanauki.pl/articles/728966.pdf
    Data publikacji:
    2003
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    lattice-ordered monoid
    normal lattice-ordered monoid
    dually residuated lattice-ordered semigroup
    direct decomposition
    polar
    Opis:
    In the paper lattice-ordered monoids and specially normal lattice-ordered monoids which are a generalization of dually residuated lattice-ordered semigroups are investigated. Normal lattice-ordered monoids are metricless normal lattice-ordered autometrized algebras. It is proved that in any lattice-ordered monoid A, a ∈ A and na ≥ 0 for some positive integer n imply a ≥ 0. A necessary and sufficient condition is found for a lattice-ordered monoid A, such that the set I of all invertible elements of A is a convex subset of A and A¯ ⊆ I, to be the direct product of the lattice-ordered group I and a lattice-ordered semigroup P with the least element 0.
    Źródło:
    Discussiones Mathematicae - General Algebra and Applications; 2003, 23, 2; 101-114
    1509-9415
    Pojawia się w:
    Discussiones Mathematicae - General Algebra and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Minimal state automata for detecting a β globin gene mutation
    Autorzy:
    Ferdania, Devi Fitri
    Irawati, -
    Garminia, Hanni
    Akhmaloka, -
    Rachmansyah, Kemal Aziez
    Powiązania:
    https://bibliotekanauki.pl/articles/1838203.pdf
    Data publikacji:
    2021
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    minimal state automata
    syntactic monoid
    β-thalassemia
    biological sequences
    automat stanu minimalnego
    monoid syntaktyczny
    sekwencja biologiczna
    Opis:
    Beta-thalassemia is an autosomal recessive blood disorder characterized by abnormalities in the synthesis of β globin. Together with α globin, it is a subunit of globin protein, called hemoglobin, located inside our red blood cells to deliver oxygen from the lungs to all of the tissues throughout our body. Thereby, individuals with β-thalassemia will often feel limp due to a lack of oxygen dissolved in their blood. In this paper, a finite state automaton to detect and classify β globin gene mutations using its DNA sequence is constructed. Finite state automata have a close connection to an algebraic structure, that is, a monoid. Together with the theory of the syntactic monoid, we present a methodology to minimize the number of the internal states of an automaton to have minimal state automata. Therefore, a minimal state automaton can be constructed to detect β globin gene mutation causing the β-thalassemia disease. We have developed a MATLAB program to conduct the appropriate simulations.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2021, 31, 2; 337-351
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Boolean matrices ... neither Boolean nor matrices
    Autorzy:
    Ricci, Gabriele
    Powiązania:
    https://bibliotekanauki.pl/articles/728832.pdf
    Data publikacji:
    2000
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    universal matrix
    functional application
    generalized matrix
    analytic monoid
    Opis:
    Boolean matrices, the incidence matrices of a graph, are known not to be the (universal) matrices of a Boolean algebra. Here, we also show that their usual composition cannot make them the matrices of any algebra. Yet, later on, we "show" that it can. This seeming paradox comes from the hidden intrusion of a widespread set-theoretical (mis) definition and notation and denies its harmlessness. A minor modification of this standard definition might fix it.
    Źródło:
    Discussiones Mathematicae - General Algebra and Applications; 2000, 20, 1; 141-151
    1509-9415
    Pojawia się w:
    Discussiones Mathematicae - General Algebra and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The monoid of generalized hypersubstitutions of type τ = (n)
    Autorzy:
    Puninagool, Wattapong
    Leeratanavalee, Sorasak
    Powiązania:
    https://bibliotekanauki.pl/articles/729031.pdf
    Data publikacji:
    2010
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    monoid
    regular elements
    idempotent elements
    Green's relations
    generalized hypersubstitution
    Opis:
    A (usual) hypersubstitution of type τ is a function which takes each operation symbol of the type to a term of the type, of the same arity. The set of all hypersubstitutions of a fixed type τ forms a monoid under composition, and semigroup properties of this monoid have been studied by a number of authors. In particular, idempotent and regular elements, and the Green's relations, have been studied for type (n) by S.L. Wismath.
    A generalized hypersubstitution of type τ=(n) is a mapping σ which takes the n-ary operation symbol f to a term σ(f) which does not necessarily preserve the arity. Any such σ can be inductively extended to a map σ̂ on the set of all terms of type τ=(n), and any two such extensions can be composed in a natural way. Thus, the set $Hyp_{G}(n)$ of all generalized hypersubstitutions of type τ=(n) forms a monoid. In this paper we study the semigroup properties of $Hyp_{G}(n)$. In particular, we characterize the idempotent and regular generalized hypersubstitutions, and describe some classes under Green's relations of this monoid.
    Źródło:
    Discussiones Mathematicae - General Algebra and Applications; 2010, 30, 2; 173-191
    1509-9415
    Pojawia się w:
    Discussiones Mathematicae - General Algebra and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Equimorphy in varieties of double Heyting algebras
    Autorzy:
    Koubek, V.
    Sichler, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/966055.pdf
    Data publikacji:
    1998
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    categorical universality
    variety
    double Heyting algebra
    endomorphism monoid
    equimorphy
    Opis:
    We show that any finitely generated variety V of double Heyting algebras is finitely determined, meaning that for some finite cardinal n(V), any class $\Cal S$ ⊆ V consisting of algebras with pairwise isomorphic endomorphism monoids has fewer than n(V) pairwise non-isomorphic members. This result complements the earlier established fact of categorical universality of the variety of all double Heyting algebras, and contrasts with categorical results concerning finitely generated varieties of distributive double p-algebras.
    Źródło:
    Colloquium Mathematicum; 1998, 77, 1; 41-58
    0010-1354
    Pojawia się w:
    Colloquium Mathematicum
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Interior and closure operators on bounded commutative residuated l-monoids
    Autorzy:
    Rachůnek, Jiří
    Švrček, Filip
    Powiązania:
    https://bibliotekanauki.pl/articles/728848.pdf
    Data publikacji:
    2008
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    residuated l-monoid
    residuated lattice
    closure operator
    BL-algebra
    MV-algebra
    Opis:
    Topological Boolean algebras are generalizations of topological spaces defined by means of topological closure and interior operators, respectively. The authors in [14] generalized topological Boolean algebras to closure and interior operators of MV-algebras which are an algebraic counterpart of the Łukasiewicz infinite valued logic. In the paper, these kinds of operators are extended (and investigated) to the wide class of bounded commutative Rl-monoids that contains e.g. the classes of BL-algebras (i.e., algebras of the Hájek's basic fuzzy logic) and Heyting algebras as proper subclasses.
    Źródło:
    Discussiones Mathematicae - General Algebra and Applications; 2008, 28, 1; 11-27
    1509-9415
    Pojawia się w:
    Discussiones Mathematicae - General Algebra and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Pseudocomplements in sum-ordered partial semirings
    Autorzy:
    Cīrulis, Jānis
    Powiązania:
    https://bibliotekanauki.pl/articles/728872.pdf
    Data publikacji:
    2007
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    Glivenko theorem
    partial monoid
    partial semiring
    pseudocomplementation
    semigroup
    Stone semiring
    sum-ordering
    Opis:
    We study a particular way of introducing pseudocomplementation in ordered semigroups with zero, and characterise the class of those pseudocomplemented semigroups, termed g-semigroups here, that admit a Glivenko type theorem (the pseudocomplements form a Boolean algebra). Some further results are obtained for g-semirings - those sum-ordered partially additive semirings whose multiplicative part is a g-semigroup. In particular, we introduce the notion of a partial Stone semiring and show that several well-known elementary characteristics of Stone algebras have analogues for such semirings.
    Źródło:
    Discussiones Mathematicae - General Algebra and Applications; 2007, 27, 2; 169-186
    1509-9415
    Pojawia się w:
    Discussiones Mathematicae - General Algebra and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On monadic quantale algebras: basic properties and representation theorems
    Autorzy:
    Solovyov, Sergey
    Powiązania:
    https://bibliotekanauki.pl/articles/729061.pdf
    Data publikacji:
    2010
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    m-semilattice
    ⋁-lattice
    quantale
    quantale module
    topological system
    tropological system
    quantale algebra
    quantaloid
    quantale algebroid
    quantifier
    monadic quantale algebra
    Girard quantale
    Q-equivalence relation
    Ω-valued set
    GL-monoid
    commutative integral cl-monoid
    Opis:
    Motivated by the concept of quantifier (in the sense of P. Halmos) on different algebraic structures (Boolean algebras, Heyting algebras, MV-algebras, orthomodular lattices, bounded distributive lattices) and the resulting notion of monadic algebra, the paper introduces the concept of a monadic quantale algebra, considers its properties and provides several representation theorems for the new structures.
    Źródło:
    Discussiones Mathematicae - General Algebra and Applications; 2010, 30, 1; 91-118
    1509-9415
    Pojawia się w:
    Discussiones Mathematicae - General Algebra and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
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