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PL
W artykule W artykule przedstawiono, że półgrupa charakterystyczna sumy prostej i iloczynu prostego automatów "G" i "AG" asynchronicznych silnie spójnych i ustalone analogi ich rozszerzeń są izomorficzne. Wziąwszy pod uwagę iż półgrupa charakterystyczna określa zdolność do przetwarzania informacji, to sumę prosta iloczyn prosty można uważać za realizację – odpowiednio sekwencyjnych i równoległych obliczeń. Uzyskane rezultaty oznaczają iż owa zdolność nie zależy od realizacji sekwencyjnej lub równoległej (taka sama liczba klas abstrakcji odpowiednich półgrup charakterystycznych).
EN
In this article it is presented that the characteristic semi-group of the direct sum and direct product "G" and "AG" of the asynchronous automatons of the strongly connected and determined analogs of their extensions are isomorphism. Taking into account that the characteristic semi-group determines the ability to process the information then the direct sum and direct product can be consider as realization – the sequence and parallel calculation accordingly. The obtained results mean that this ability doesn’t depend on the sequence and parallel realization (the same number of abstract class of the suitable characteristic semi-groups).
EN
This paper is concerned with the H∞ control problem of a coupled transport-diffusion system with Neumann boundary condition, related to parallel-flow heat exchange process. It is shown that, by using the previous approach for a single diffusion system, the H∞ control problem can be solved by constructing a residual mode filter (RMF)-based controller which is of finite-dimension. A numerical simulation result is given to demonstrate the validity of the proposed method.
3
Content available remote Geometric stable and semistable distributions on Z+d
EN
The aim of this article is to study geometric F-semistable and geometric F-stable distributions on the d-dimensional lattice Zd+. We obtain several properties for these distributions, including characterizations in terms of their probability generating functions.We describe a relation between geometric F-semistability and geometric F-stability and their counterparts on Rd+ and, as a consequence, we derive some mixture representations and construct some examples.We establish limit theorems and discuss the related concepts of complete and partial geometric attraction for distributions on Zd+. As an application, we derive the marginal distribution of the innovation sequence of a Zd+-valued stationary autoregressive proces of order p with a geometric F-stable marginal distribution.
EN
This paper is devoted to the investigation of the existence and uniqueness of a suitably defined weak solution of the abstract semilinear value problem u'(t) = Au(t) + f(t, u(t)), u(0) = x with x ϵ X, where X is a Banach space. We are concerned with two types of solutions: weak and mild. Under the assumption that A is the generator of a strongly continuous semigroup of linear, bounded operators, we also establish sufficient conditions such that if u is a weak (mild) solution of the initial value problem, then u is a mild (weak) solution of that problem.
PL
Celem pracy jest przedstawienie twierdzenia o jednoznaczności i istnieniu słabego rozwiązania abstrakcyjnego semiliniowego równania różniczkowego u'(t) = Au(t) + f(t, u(t)), u(0) = x, gdzie x ϵ X, w przestrzeni Banacha X. W pracy rozważane są dwa typy rozwiązań: weak oraz mild. Przy założeniu, ze operator A jest generatorem silnie ciągłej półgrupy operatorów liniowych i ograniczonych, podane zostały również warunki wystarczające na to, aby rozwiązanie weak (mild) było rozwiązaniem mild (weak) tego zagadnienia.
5
Content available remote Idempotent tree languages
EN
A tree language of a fixed type τ is any set of terms of type τ. We consider here a binary operation +n on the set Wτ(Xn) of all n-ary terms of type τ, which results in semigroup (Wτ(Xn),+n). We characterize languages which are idempotent with respect to this binary operation, and look at varieties of tree languages containing idempotent languages. We also compare properties of semigroup homomorphisms from (P(Wτ(Xn));+n) to (P(Wτ(Xm));+m) with properties of homomorphisms between the corresponding absolutely free algebras Fτ(Xn) and Fτ(Xm).
6
Content available remote Some semilattice decompositions of dimonoids
EN
We show that the system of axioms of a dimonoid is independent and prove that every dimonoid with a commutative operation is a semilattice of Archimedean subdimonoids,every dimonoid with a commutative periodic semigroup is a semilattice of unipotent subdimonoids,every dimonoid with a commutative operation is a semilattice of a connected subdimonoids and every idempotent dimonoid is a semilattice of rectangular subdimonoids.
7
Content available remote On cartesian product of fuzzy prime and fuzzy semiprime ideals of semigroups
EN
The purpose of this paper is to study some properties of cartesian product of fuzzy prime and fuzzy semiprime ideals of semigroups.
8
Content available remote A note on stability of the popoviciu functional equation on restricted domain
EN
We prove the Hyers-Ulam stability, on restricted domain, of a functional equation of Jensen type, introduced by T. Popoviciu (1965).
9
Content available remote Characterizations of posets via weak states
EN
Weak states on posets are defined which are in some analogy to states on orthomodular posets used in axiomatic quantum mechanics. It is shown how certain properties of the set of weak states characterize certain properties of the underlying poset.
EN
In a previous paper we formulated and analyzed the structure of neighborhoods of cellular automata in an algebraic setting such that the cellular space S is represented by the Cayley graph of a finitely generated group and the neighbors are defined as a semigroup generated by the neighborhood N as a subset of S, Nishio and Margenstern 2004 [14,15]. Particularly we discussed the horse power problem whether the motion of a horse (knight) fills the infinite chess board or Z^2- that is, an algebraic problem whether a subset of a group generates it or not. Among others we proved that a horse fills Z^2 even when its move is restricted to properly chosen 3 directions and gave a necessary and sufficient condition for a generalized 3-horse to fill Z^2. This paper gives further developments of the horse power problem, say, on the higher dimensional Euclidean grid, the hexagonal grid and the hyperbolic plane.
11
Content available remote Minkowski difference and Sallee elements in an ordered semigroup
EN
In the manner of Pallaschke and Urbański ([5], chapter 3) we generalize the notions of the Minkowski difference and Sallee sets to a semigroup. Sallee set (see [7], definition of the family S on p. 2) is a compact convex subset A of a topological vector space X such that for all subsets B the Minkowski difference A-B of the sets A and B is a summand of A. The family of Sallee sets characterizes the Minkowski subtraction, which is important to the arithmetic of compact convex sets (see [5]). Sallee polytopes are related to monotypie poly topes (see [4]). We generalize properties of Minkowski difference and Sallee sets to semigroup and investigate the families of Sallee elements in several specific semigroups.
EN
In recent years, a number of classical results connecting rational languages with finite semigroups have been extended to infinite-word languages using the notion of an w-semigroup : a semigroup augmented with an associative infinite product. This paper takes a closer look at the associative infinite product itself. It suggests some improvements and presents a couple of new facts.
13
Content available remote Note on logics of idempontents
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.
14
Content available remote On reduced fractions
EN
In this paper introduce the notion of the reduced fraction and we give some of its properties.
15
Content available remote Semigroups, groups and grammar inference problem
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.
17
Content available remote On univalence of holomorphic mappings in Cn
EN
The method of subordination chains is used to obtain an univalence condition for holomorphic mappings in the unit ball of Cn.
18
Content available remote Co-semigroups with weak singularity and its applications
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.
19
Content available remote Six-dimensional Landau inequalities
20
Content available remote On minimal fractions
EN
In this paper we introduce the notion of the minimal fraction and we give some its properties.
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