Acta Mathematica Hungarica最新文献

The present article deals with properties of one class of functions with complicated local structure. These functions can be modeled by certain operators of digits. Such operators were considered by the author earlier (for example, see [27,39] and references therein). This research is a generalization of investigations presented in the last-mentioned papers.

We study the arrangements of the roots in the complex planefor the lacunary harmonic polynomials called harmonic trinomials. We providenecessary and sufficient conditions so that two general harmonic trinomials havethe same set of roots up to a rotation around the origin in the complex plane, areflection over the real axis, or a composition of the previous both transformations.This extends the results of Jenő Egerváry given in [19] for the setting oftrinomials to the setting of harmonic trinomials.

Let R be a commutative Noetherian ring and I a proper ideal of R. In this paper, we study finitely generated R-modules M with only one non-vanishing local cohomology module ({H}_I^c(M)) where (c=cd(I,M)). Let C be a semidualizing R-module. We investigate the conditions under which ({H}_I^c(M)) belongs to either the Auslander class (mathscr{A}_C(R)) or the Bass class (mathscr{B}_C(R)).

Suppose that (R(h, alpha)) is a parallelogram with the longer side 1, with acute angle (alpha) and with height h. Let S be a square with a side parallel to the longer side of (R(h, alpha)) and let ({S_{n}}) be acollection of the homothetic copies of S. In this note a tight lower boundof the sum of the areas of squares from ({S_{n}}) that can parallel cover(R(h, alpha)) is given.

We prove that the existence of a non-special tree of size (lambda) is equivalent to the existence of an uncountably chromatic graph with no (K_{omega1}) minor of size (lambda), establishing a connection between the special tree number and the uncountable Hadwiger conjecture. Also characterizations of Aronszajn, Kurepa and Suslin trees using graphs are deduced. A new generalized notion of connectedness for graphs is introduced using which we are able to characterize weakly compact cardinals.

We provide a geometric condition which characterises when thePrinciple of Dependent Choice holds in a Fraenkel-Mostowski-Specker permutationmodel. This condition is a slight weakening of requiring the filter of groups tobe closed under countable intersections. We show that this condition holds nontriviallyin a new permutation model we call "the nowhere dense model" and westudy its extensions to uncountable cardinals as well.

We say a group G = AB is the totally semipermutable product of subgroups A and B if every Sylow subgroup P of A is totally permutable with every Sylow subgroup Q of B whenever ( gcd(|P|,|Q|)=1 ). Products of pairwise totally semipermutable subgroups are studied in this article. Let ( mathfrak{U} ) denote the class of supersoluble groups and ( mathfrak{D} ) denote the formation of all groups which have an ordered Sylow tower of supersoluble type. We obtain the ( mathfrak{F} )-residual of the product from the ( mathfrak{F} )-residuals of the pairwise totally semipermutable subgroups when ( mathfrak{F} ) is a subgroup-closed saturated formation such that ( mathfrak{U}subseteq mathfrak{F}subseteq mathfrak{D} ).

Let (beta>1). For (x in [0,infty)), we have so-called a beta-expansion of (x) in base (beta) as follows:

where (k in mathbb{Z}), (beta^{k} leq x < beta^{k+1}), (x_{j} in mathbb{Z} cap [0,beta)) for all (j leq k) and (sum_{j leq n}x_{j}beta^{j}<beta^{n+1}) for all (n leq k). In this paper, we give a sufficient condition (for (beta)) such that each element of (mathbb{N}) has a finite beta-expansion in base (beta). Moreover we also find a (beta) with this finiteness property which does not have positive finiteness property.

We obtain explicit upper bounds for the Touchard polynomials(T_n(x)), for (x>0). When applied to the Bell numbers (B_n=T_n(1)), such boundsare asymptotically sharp. A simple probabilistic approach based on estimatesof moments of nonnegative random variables is used. Applications giving upperbounds for the moments of a certain subset of Jakimovski-Leviatan operators arealso provided.

The contraction condition in the Banach contraction principleforces a function to be continuous. Many authors overcome this obligation andweaken the hypotheses via metric spaces endowed with a partial order. In this paper,we present some coupled fixed point theorems for the functions having mixedmonotone properties on ordered vector metric spaces, which are more generalspaces than partially ordered metric spaces. We also define the double monotoneproperty and investigate the previous results with this property. In the lastsection, we prove the uniqueness of a coupled fixed point for non-monotone functions.In addition, we present some illustrative examples to emphasize that ourresults are more general than the ones in the literature.