The Structure of Disjoint Iteration Groups on the Circle

The aim of the paper is to investigate the structure of disjoint iteration groups on the unit circle that is, families of homeomorphisms such that and each F ^veither is the identity mapping or has no fixed point ((V, +) is an arbitrary 2-divisible nontrivial (i.e., card V> 1) abelian group).     

A Completion of \mathbb{Z} is a Field

We define various ring sequential convergences on and . We describe their properties and properties of their convergence completions. In particular, we define a convergence on by means of a nonprincipal ultrafilter on the positive prime numbers such that the underlying set of the completion is the ultraproduct of the prime finite fields Further, we show that is sequentially precompact but fails to be strongly sequentially precompact; this solves a problem posed by D. Dikranjan.     

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].     

Isometries and direct decompositions of pseudo MV-algebras

In the paper isometries in pseudo MV-algebras are investigated. It is shown that for every isometry f in a pseudo MV-algebra = (A, ⊕, ⁻, ^∼, 0, 1) there exists an internal direct decomposition of with commutative such that and for each x ∈ A. On the other hand, if is an internal direct decomposition of a pseudo MV-algebra = (A, ⊕, ⁻, ^∼, 0, 1) with commutative, then the mapping g: A → A defined by is an isometry in and .      

Hypersurfaces in ℝn and critical points in their external region

In this paper we study the hypersurfaces given as connected compact regular fibers of a differentiable map , in the cases in which has finitely many nondegenerate critical points in the unbounded component of .     

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

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.     

Boundedness of Riesz Potential Generated by Generalized Shift Operator on B<Emphasis Type="Italic">a</Emphasis> Spaces

In this paper, the boundedness of the Riesz potential generated by generalized shift operator from the spaces to the spaces is examined.     

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.     

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.     

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

Pointwise convergence fails to be strict

It is known that the ring of all Baire functions carrying the pointwise convergence yields a sequential completion of the ring of all continuous functions. We investigate various sequential convergences related to the pointwise convergence and the process of completion of . In particular, we prove that the pointwise convergence fails to be strict and prove the existence of the categorical ring completion of which differs from .     

Rings of maps: sequential convergence and completion

The ring B(R) of all real-valued measurable functions, carrying the pointwise convergence, is a sequential ring completion of the subring C(R) of all continuous functions and, similarly, the ring of all Borel measurable subsets of R is a sequential ring completion of the subring of all finite unions of half-open intervals; the two completions are not categorical. We study -rings of maps and develop a completion theory covering the two examples. In particular, the -fields of sets form an epireflective subcategory of the category of fields of sets and, for each field of sets , the generated -field yields its epireflection. Via zero-rings the theory can be applied to completions of special commutative -groups.     

Remarks on ample vector bundles of curve genus two

Let be an ample vector bundle of rank n – 1 on a smooth complex projective variety X of dimension n≥ 3 such that X is a -bundle over and that for any fiber F of the bundle projection . The pairs with = 2 are classified, where is the curve genus of . This allows us to improve some previous results. Received: 13 June 2006     

On transformations z(t) = y(ϕ(t)) of ordinary differential equations

The paper describes the general form of an ordinary differential equation of the order n + 1 (n 1) which allows a nontrivial global transformation consisting of the change of the independent variable. A result given by J. Aczél is generalized. A functional equation of the form where are given functions, is solved on .     

The maximal Fejér operator on real Hardy spaces

We prove that the maximal Fej'er operator is not bounded on the real Hardy spaces H ¹, which may be considered over and . We also draw corollaries for the corresponding Hardy spaces over ² and ². This revised version was published online in August 2006 with corrections to the Cover Date.     

Extending n times differentiable functions of several variables

It is shown that n times Peano differentiable functions defined on a closed subset of and satisfying a certain condition on that set can be extended to n times Peano differentiable functions defined on if and only if the nth order Peano derivatives are Baire class one functions.     

Abundant and ample straight left orders

A subsemigroup S of a semigroup Q is a straight left order in Q and Q is a semigroup of straight left quotients of S if every q ∈ Q can be written as for some with a b in Q and if, in addition, every element of S that is square cancellable lies in a subgroup of Q. Here a ^♯ denotes the group inverse of a in some (hence any) subgroup of Q. If S is a straight left order in Q, then Q is necessarily regular; the idea is that Q has a better understood structure than that of S. Necessary and sufficient conditions exist on a semigroup S for S to be a straight left order. The technique is to consider a pair of preorders on S. If such a pair satisfies conditions mimicking those satisfied by on a regular semigroup, and if certain subsemigroups of S are right reversible, then S is a straight left order. The conditions required for to satisfy are somewhat lengthy. In this paper we aim to circumvent some of these by specialising in two ways. First we consider only fully stratified left orders, that is, the case where (certainly the most natural choice for ) and the other is to insist that S be abundant, that is, every -class and every -class of S contains an idempotent. Our results may be used to show that the monoid of endomorphisms of a hereditary basis algebra of finite rank is a fully stratified straight left order. This revised version was published online in August 2006 with corrections to the Cover Date.     

Graph homology of the moduli space of pointed real curves of genus zero

The moduli space parameterizes the isomorphism classes of S-pointed stable real curves of genus zero which are invariant under relabeling by the involution σ. This moduli space is stratified according to the degeneration types of σ-invariant curves. The degeneration types of σ-invariant curves are encoded by their dual trees with additional decorations. We construct a combinatorial graph complex generated by the fundamental classes of strata of . We show that the homology of is isomorphic to the homology of our graph complex. We also give a presentation of the fundamental group of .      

The type set for some measures on \mathbb{R}^{2n} with n-dimensional support

Let be realhomogeneous functions in ofdegree and let bethe Borel measure on given by