Showing papers in "Periodica Mathematica Hungarica in 1992"

Complete convergence for arrays

Abstract: Let {(X nk , 1≤k≤n),n≥1}, be an array of rowwise independent random variables. We extend and generalize some recent results due to Hu, Moricz and Taylor concerning complete convergence, in the sense of Hsu and Robbins, of the sequence of rowwise arithmetic means.

Integral solutions in arithmetic progression for y2=x3+k

Abstract: Integral solutions toy 2=x 3+k, where either thex's or they's, or both, are in arithmetic progression are studied. When both thex's and they's are in arithmetic progression, then this situation is completely solved. One set of solutions where they's formed an arithmetic progression of length 4 had already been constructed. In this paper, we construct infinitely many sets of solutions where there are 4x's in arithmetic progression and we disprove Mohanty's Conjecture [8] by constructing infinitely many sets of solutions where there are 4, 5 and 6y's in arithmetic progression.

A preconditioned domain decomposition algorithm for the solution of the elliptic Neumann problem

Abstract: A new preconditioned conjugate gradient (PCG)-based domain decomposition method is given for the solution of linear equations arising in the finite element method applied to the elliptic Neumann problem. The novelty of the proposed method is in the recommended preconditioner which is constructed by using cyclic matrix. The resulting preconditioned algorithms are well suited to parallel computation.

A generalization of Dirac’s theorem for K(1,3)-free graphs

Abstract: It is known that if a 2-connected graphG of sufficiently large ordern satisfies the property that the union of the neighborhoods of each pair of vertices has cardinality at leastn/2, thenG is hamiltonian. In this paper, we obtain a similar generalization of Dirac’s Theorem forK(1,3)-free graphs. In particular, we show that ifG is a 2-connectedK(1,3)-free graph of ordern with the cardinality of the union of the neighborhoods of each pair of vertices at least (n+1)/3, thenG is hamiltonian. We also investigate several other related properties inK(1,3)-free graphs such as traceability, hamiltonian-connectedness, and pancyclicity.

On the periodic solutions of certain class of seventh-order differential equations

Abstract: The aim of this paper is to investigate sufficient conditions (Theorem 1) for the nonexistence of nontrivial periodic solutions of equation (1.1) withp ≡ 0 and (Theorem 2) for the existence of periodic solutions of equation (1.1).

On some properties of Musielak-Orlicz spaces and their subspaces of order continuous elements

Abstract: Some criterions in order thatl1 embeds complementably inEΦ(μ) and inLΦ(μ) are given. It is also proved that every idealL inLΦ(μ) such thatIΦ(x/‖x‖Φ)=1 for anyxeL/{0} is contained inEΦ(μ).

Rings whose additive endomorphisms aren-multiplicative, II

Abstract: A ringR is called anAE n -ring,n≥2 a positive integer, if every endomorphism ϕ of additive group ofR satisfies ϕ(a 1 a 2a n )=ϕ(a 1)ϕ(a 2)ϕ(a n ) for alla 1,,a n eR Several results concerning the structure ofAE n -rings are obtained in this note, including an (incomplete) description ofAE n -ringsR satisfyingR t R n−1 ≠0, whereR t is the torsion ideal inR

Parallel axiom in convexity lattices

Abstract: The convexity lattices, introduced by Bennett and Birkhoff, generalize the lattices of convex sets. We present three forms of Parallel Axiom in such lattices and define Euclidean and two classes of non-Euclidean lattices via the number of parallel lines through a point. The paper deals with these three classes of lattices.

Subalgebras of closure algebras

Abstract: Closure algebras have been intensively studied in literature ([2], [3], [11], ) but, up to now, little interest has been devoted to subalgebras of closure algebras In this paper, the methods of [16] are adapted to characterize closure algebras with a distributive, or a Boolean, subalgebra lattice

Sequences of polynomials whose zeros lie on fixed lemniscates

Abstract: For fixed integersk≥2 we study sequences of polynomialsP n (z) with the following properties: (i) degP n → ∞; (ii) the zeros of all theP n (z) lie on a certain lemniscate withk 1≤k foci, one of which is the origin; (iii) theP n (z) can be cut in such a way that the zeros of the “lower part” all lie on the unit circle and those of the “upper part” lie on a lemniscate having the foci in (ii) excluding the origin. Several special cases and examples are considered.

Prime modules of a gamma ring

Abstract: We define a prime ΓM-module for a Γ-ringM. It is shown that a subsetP ofM is a prime ideal ofM if and only ifP is the annihilator of some prime ΓM-moduleG. s-prime ideals ofM were defined by the first author. We defines-modules ofM, analogous to a concept defined by De Wet for rings. It is shown that a subsetQ ofM is ans-prime ideal ofM if and only ifQ is the annihilator of somes-moduleG ofM. Relationships between prime ΓM-modules and primeR-modules are established, whereR is the right operator ring ofM. Similar results are obtained fors-modules.

Asymptotic independence of maximum waiting times for increasing alphabet

Abstract: For everyk≥1 consider the waiting time until each pattern of lengthk over a fixed alphabet of sizen appears at least once in an infinite sequence of independent, uniformly distributed random letters. Lettingn→∞ we determine the limiting finite dimensional joint distributions of these waiting times after suitable normalization and provide an estimate for the rate of convergence. It will turn out that these waiting times are getting independent.

On existence of sets of distinct representatives for families of subsets of a multiset

Abstract: IfX is a family ofl-subsets of a multiset, then there is a set of distinct representatives of the members ofX among the (l-k)-subsets of the members ofX provided the cardinality ofX does not exceed a certain bound. An algorithm for calculating this bound is given.

Distributive multiplication rings

Abstract: A ringR is said to be a left (right)n-distributive multiplication ring, n>1 a positive integer, if aa1a2...an=aa1aa2...aan (a1a2...ana=a1aa2a...ana) for all a, a1,...,an ∋R. It will be shown that the semi-primitive left (right)n-distributive rings are precisely the generalized boolean ringsA satisfying an=a for all a ∋A. An arbitrary left (right)n-distributive multiplication ring will be seen to be an extension of a nilpotent ringN satisfyingN n+1=0 by a generalized boolean ring described above. Under certain circumstances it will be shown that this extension splits.

Finite linear coverings of locally connected continua

Abstract: A concept of finite coverings of continua with a linear order of their members is given. A characterization is obtained of hereditarily locally connected continua which have a finite supremum of cardinalities of the considered coverings.

The associated geometric category of the category of Steiner triple systems

Abstract: In this paper it will be constructed an abstract geometry will be called a triple space, which is defined in general sense by the closure theoretic definition of geometry “see [4]”. And it is proved that the category of triple spaces is isomorphic to the category of Steiner triple systems. And hence it could be shown that the class of Steiner triple systems which satisfy the geometric axiomI 3, (I3) $$\forall x_1 ,x_2 ,x_{3,} y;ify \in \backslash \Rightarrow x_3 \in $$ is exactly the class of all Steiner triple systems in which every triangle generate a planar subsystem.

On*-primes and*-valuations

Abstract: We study the relation between*-primes and*-valuations to deduce a necessary and sufficient condition for extending*-valuations.

Periodic solutions of autonomous systems of difference and difference-differential equations with a small delay

Abstract: In the present paper the method of the equivalent differential-operator equation has been applied in the study of the existence and asymptotic representation of periodic solutions of autonomous systems of the form