General Construction of Non-Dense Disjoint Iteration Groups on the Circle

Let be a disjoint iteration group on the unit circle , that is a family of homeomorphisms such that F ^v1 ○ F ^v2 = F ^v1+v2 for v ₁, v ₂ ∈ V and each F ^v either is the identity mapping or has no fixed point ((V, +) is a 2-divisible nontrivial Abelian group). Denote by the set of all cluster points of {F ^v (z), v ∈ V} for . In this paper we give a general construction of disjoint iteration groups for which .     

On sandwich sets and congruences on regular semigroups

Let S be a regular semigroup and E(S) be the set of its idempotents. We call the sets S(e, f)f and eS(e, f) one-sided sandwich sets and characterize them abstractly where e, f ∈ E(S). For a, a′ ∈ S such that a = aa′a, a′ = a′aa′, we call S(a) = S(a′a, aa′) the sandwich set of a. We characterize regular semigroups S in which all S(e; f) (or all S(a)) are right zero semigroups (respectively are trivial) in several ways including weak versions of compatibility of the natural order. For every a ∈ S, we also define E(a) as the set of all idempotets e such that, for any congruence ϱ on S, aϱa ² implies that aϱe. We study the restrictions on S in order that S(a) or be trivial. For , we define on S by a b if . We establish for which S are or congruences.     

On monotone permutations of`ℓ-cyclically ordered sets

For an ℓ-cyclically ordered set M with the ℓ-cyclic order C let P(M) be the set of all monotone permutations on M. We define a ternary relation on the set P(M). Further, we define in a natural way a group operation (denoted by ·) on P(M). We prove that if the ℓ-cyclic order C is complete and ≠ 0, then (P(M),·, ) is a half cyclically ordered group.     

Asymptotic behavior of solutions of A 2nth order nonlinear differential equation

In this paper we prove two results. The first is an extension of the result of G. D. Jones [4[:Every nontrivial solution for

Annihilators in Normal Autometrized Algebras

The concepts of an annihilator and a relative annihilator in an autometrized l-algebra are introduced. It is shown that every relative annihilator in a normal autometrized l-algebra is an ideal of and every principal ideal of is an annihilator of . The set of all annihilators of forms a complete lattice. The concept of an I-polar is introduced for every ideal I of . The set of all I-polars is a complete lattice which becomes a two-element chain provided I is prime. The I-polars are characterized as pseudocomplements in the lattice of all ideals of containing I.     

Almost periodic compactifications of group extensions

Let and be groups and let be an extension of by . Given a property of group compactifications, one can ask whether there exist compactifications and of N and K such that the universal -compactification of G is canonically isomorphic to an extension of by . We prove a theorem which gives necessary and sufficient conditions for this to occur for general properties and then apply this result to the almost periodic and weakly almost periodic compactifications of G.     

The All-Paths Transit Function of a Graph

A transit function R on a set V is a function satisfying the axioms and , for all . The all-paths transit function of a connected graph is characterized by transit axioms.     

Finite rank operators in Jacobson radical \mathcal{R}_{\mathcal{N} \otimes \mathcal{M}}

In this paper we investigate finite rank operators in the Jacobson radical of Alg( ), where are nests. Based on the concrete characterizations of rank one operators in Alg( ) and , we obtain that each finite rank operator in can be written as a finite sum of rank one operators in and the weak closure of equals Alg( ) if and only if at least one of is continuous.     

On Topological Classification of Non-Archimedean Fréchet Spaces

We prove that any infinite-dimensional non-archimedean Fréchet space E is homeomorphic to where D is a discrete space with card(D) = dens(E). It follows that infinite-dimensional non-archimedean Fréchet spaces E and F are homeomorphic if and only if dens(E) = dens(F). In particular, any infinite-dimensional non-archimedean Fréchet space of countable type over a field is homeomorphic to the non-archimedean Fréchet space .     

Another Perron type integration in n dimensions as an extension of integration of stepfunctions

For a new Perron-type integral a concept of convergence is introduced such that the limit f of a sequence of integrable functions is integrable and any integrable f is the limit of a sequence of stepfunctions .     

On vectorial inner product spaces

Let E be a real linear space. A vectorial inner product is a mapping from E×E into a real ordered vector space Y with the properties of a usual inner product. Here we consider Y to be a -regular Yosida space, that is a Dedekind complete Yosida space such that , where is the set of all hypermaximal bands in Y. In Theorem 2.1.1 we assert that any -regular Yosida space is Riesz isomorphic to the space B(A) of all bounded real-valued mappings on a certain set A. Next we prove Bessel Inequality and Parseval Identity for a vectorial inner product with range in the -regular and norm complete Yosida algebra .     

Properties of the Conformal Radius of a Domain

We consider the function , where is the conformal radius of a simply connected domain D at a point . We study relations between the values of the function at various points of the domain D. In Sec. 1, we establish exact inequalities relating the values of the function in an arbitrary simply connected domain with the position of the conformal center and with the maximal conformal radius of the domain D. The same values are related to the values of at another two points of the domain D. In Sec. 2, similar results are established for convex domains. This work supplements some recent results of Emel'yanov and Kovalev. Bibliography: 9 titles.     

On posets with isomorphic interval posets

Let be a partially ordered set, Int the system of all (nonempty) intervals of partially ordered by the set-theoretical inclusion . We are interested in partially ordered sets with Int isomorphic to Int . We are going to show that they correspond to couples of binary relations on A satisfying some conditions. If is a directed partially ordered set, the only with Int isomorphic to Int are corresponding to direct decompositions of ( denotes the dual of . The present results include those presented in the paper [11] by V. Slavík. Systems of intervals, particularly of lattices, have been investigated by many authors, cf. [1]–[11].     

Boundary functions in L2 H $$(\mathbb{B}^n )$$

We solve the Dirichlet problem for line integrals of holomorphic functions in the unit ball For a function u which is lower semi-continuous on we give necessary and sufficient conditions in order that there exists a holomorphic function f ∈ such that

Propriétés spectrales des restrictions d'opérateurs de la classe \mathbb{A}

We discuss here the question whether there exists an invariant subspace for a contraction T in the class such that the spectrum of the restriction of T on is the whole closed unit disc.     

On intervals and isometries of MV-algebras

Let Int be the lattice of all intervals of an MV-algebra . In the present paper we investigate the relations between direct product decompositions of and (i) the lattice Int , or (ii) 2-periodic isometries on , respectively.     

Representation of Connected Monounary Algebras by Means of Irreducibles

The aim of the present paper is to describe all connected monounary algebras for which there exists a representation by means of connected monounary algebras which are retract irreducible in the class _c (or in ). This work was supported by the Slovak Grant VEGA 1/0423/03.     

Problems Concerning <Emphasis Type="Italic">n</Emphasis>-Weak Amenability of a Banach Algebra

In this paper we extend the notion of n-weak amenability of a Banach algebra when n ∈ ℕ. Technical calculations show that when is Arens regular or an ideal in **, then * is an ⁽²ⁿ⁾-module and this idea leads to a number of interesting results on Banach algebras. We then extend the concept of n-weak amenability to n ∈ ∕.     

Division by a holomorphic matrix in strictly pseudoconvex Domains

LetF andG be respectively a vector- and a matrix-function in a bounded strictly pseudoconvex domainD, with entries holomorphic inD and continuous in . We prove that ifF can be divided locally byG with holomorphic factors in a neighborhood of a given pointw inD, and the rank ofG is maximal at all points of , then the division ofF byG holds globally, with some factors which are holomorphic inD and continuous in . This method applies also to other function algebras in pseudoconvex domains.     

Invariant subspaces of X** under the action of biconjugates

We study conditions on an infinite dimensional separable Banach space X implying that X is the only non-trivial invariant subspace of X** under the action of the algebra of biconjugates of bounded operators on . Such a space is called simple. We characterize simple spaces among spaces which contain an isomorphic copy of c ₀, and show in particular that any space which does not contain ℓ₁ and has property (u) of Pelczynski is simple.