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1
Content available remote Semigroup of k-bi-ideals of a semiring with semilattice additive reduct
Bhuniya A. K., Jana K.
Demonstratio Mathematica
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2016
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Vol. 49, nr 2
119--128
EN
We associate a semigroup B(S) to every semiring S with semilattice additive reduct, namely the semigroup of all k-bi-ideals of S; and such semirings S have been characterized by this associated semigroup B(S). A semiring S is k-regular if and only if B(S) is a regular semigroup. For the left k-Clifford semirings S, B(S) is a left normal band; and consequently, B(S) is a semilattice if S is a k-Clifford semiring. Also we show that the set Bm(S) of all minimal k-bi-ideals of S forms a rectangular band and Bm(S) is a bi-ideal of the semigroup B(S).
2
Content available remote Asymtotic stability of solutions to the equations of linear elasticity and thermoelasticity in viscoporus media
Głowiński P., Łada A.
Demonstratio Mathematica
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2009
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Vol. 42, nr 4
757-779
EN
The systems of evolution equations modelling elasticity and thermoelas-ticity of viscoporous bounded media are considered. The existence of co-semigroups of contractions defining solutions to the systems is proved. The asymptotic vanishing of energies of solutions when t -> (infinity) is explained.
3
Content available Dynamical model of propagation of pollutants in a river
Żołopa E., Grabowski P.
Automatyka / Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie
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2008
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T. 12, z. 2
169-182
EN
In this paper a dynamical model of propagation of pollutants in a river with M point controls in the form of aerators and K point measurements is being transformed to an abstract model on a suitably chosen Hilbert space. Our model belongs to the class of abstract models of the factor-type. It is shown that the semigroup generated by the state operator A has a property of decaying in a finite-time, the observation operator is admissible, and the system transfer function is in the space H∞ (C+, L(CM, CK)). In the final part we also formulate the LQ problem with infinite-time horizon.
PL
W artykule przekształcany jest model dynamiczny rozprzestrzeniania się zanieczyszczeń w rzece, z punktowymi sterowaniami w postaci M aeratorów i K punktami pomiarowymi, do modelu abstrakcyjnego na odpowiednio dobranej przestrzeni Hilberta. Model abstrakcyjny jest typu sfaktoryzowanego. Pokazano, że półgrupa generowana przez operator stanu A ma własność zanikania w skończonym czasie, operator obserwacji jest dopuszczalny i transmitancja systemu należy do przestrzeni H∞ (C+, L(CM, CK)). W końcowej części pracy formułuje się problem liniowo-kwadratowy z nieskończonym horyzontem czasowym.
4
Content available remote On subsemigroups of the L1/s
Jabłoński W.
Demonstratio Mathematica
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2006
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Vol. 39, nr 4
815-823
EN
In this paper we consider subsemigroups of the group L1/s such that the r–th parameter of xs is the function of the remaining ones. Moreover we generalize some results concerning the existence of certain form subsemigroups of the group L1/s.
5
Content available remote On residualities in the set of Markov continuous semigroups on C1
Kuna B.
Demonstratio Mathematica
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2006
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Vol. 39, nr 2
439-453
EN
We show that the set of all stochastic strongly continuous semigroups on C1 such that limt-oo |||T(t) - Qx*||| = 0, where Qx* is one-dimensional projection for some state X*, is norm open and dense. Moreover this set forms a norm dense Gb if a state X* is strictly positive.
6
Content available remote Cocycles of disjoint continuous iteration semigroups on the circle
Ciepliński K.
Demonstratio Mathematica
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2006
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Vol. 39, nr 3
519-522
EN
In this note we give the form ofcocycles of disjoint and continuous iteration semigroups on the unit circle.
7
On an interpretation of globularity of higher graphs
Bartosik J.
Zeszyty Naukowe Politechniki Świętokrzyskiej. Elektryka
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2005
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Z. 42
39-46
EN
In [7] a common structure of various "stepwise" decomposition has been described. Such decompositions are represented by the so called n-hypergraphs being generalizations of the well known globular sets (see [2] or [3]). In this paper an example of such n-hypergraphs is presented. The example is well known from the theory of (object oriented) programming, data bases and linear algebra.
PL
W pracy [7] została opisana pewna wspólna struktura rozmaitych "krok po kroku". Rozkłady takie są reprezentowane przez tzw. n-hipergrafy będące uogólnieniami zbiorów globularnych (patrz [2] lub [3]). W pracy pokazano przykład takiego n-hipergrafu znanego z teorii (obiektowego) projektowania baz danych i algebry liniowej.
8
Content available remote Von inversen Operatoren erzeugte Einparameter-Halbgruppen
Scheffold E.
Demonstratio Mathematica
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2004
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Vol. 37, nr 4
893--904
9
Content available remote The null-exact controllability of the generalized wave problem governed by once integrated semigroups
Kowalski T., Sadkowski W.
Demonstratio Mathematica
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2004
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Vol. 37, nr 3
745--760
EN
The existence and the uniqueness of an integrated solution of the generalized wave problem were proved by using once integrated semigroups. Also a null-exact controllability of the generalized wave system was obtained.
10
Content available remote Note on logics of idempontents
Katrnoška F.
Demonstratio Mathematica
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2004
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Vol. 37, nr 2
267--274
EN
The main result of this paper is the characterization of certain logics of idempotents by Boolean semirings. Moreover some interesting examples are likewise added.
11
Content available remote Groupoids, their representations and imprimitivity systems
Pysiak L.
Demonstratio Mathematica
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2004
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Vol. 37, nr 3
661--670
12
Content available remote Semigroups, groups and grammar inference problem
Skolicki Z.
Computer Science
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2002
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Vol. 4
39-54
EN
In the paper we analyse a problem of inferring a grammar from a given sample of a language. We try to present an algebraic formalism capable of describing the issue. We consider two cases: a case of inferring canonical finite-state grammars, and a case of inferring general grammars. In both cases we define a semigroup structure. Finally we look at the possibility of getting a structure of a group.
PL
Praca omawia problem wnioskowania gramatycznego na podstawie próbki języka. Problem przedstawiony jest w kontekście algebraicznym, poprzez próbę stworzenia adekwatnego formalizmu opisującego to zagadnienie. W pracy rozważone są dwa przypadki - kanonicznej gramatyki regularnej oraz ogólnej gramatyki. Dla obu podproblemów stworzony został opis używający półgrup. W końcowej części pracy rozważamy możliwość opisania wnioskowania gramatycznego przy użyciu grup.
13
Content available remote On subclasses of groups without free subsemigroups
Bajorska B., Macedońska O.
Demonstratio Mathematica
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2000
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Vol. 33, nr 1
35-42
EN
The paper is inspired by the question of A. Shalev about possible coincidence of the class of collapsing groups and groups satisfying positive laws. We split the class of collapsing groups for subclasses, corresponding to different functions on natural numbers and give a positive answer for some of them.
14
Content available remote Co-semigroups with weak singularity and its applications
Bochenek J., Winiarska T.
Demonstratio Mathematica
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2000
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Vol. 33, nr 4
851-864
EN
In this paper we define the Co - semigroup with weak singularity and we give a characterization of its generator. We prove an analogue of the Hille-Yosida theorem.
15
Content available remote Semigroups in Banach C(K)-modules and their adjoints
Gok O.
Demonstratio Mathematica
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1998
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Vol. 3, nr 3
547-552
16
Content available remote Varieties of Ordered Semigroups
Kuřil M.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2000/2001
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Vol. 8
45--49
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