Acta Mathematica Hungarica最新文献

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.

Abstract

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

Recently, Devaiya and Srivastava [3] studied the (T^r)-strong convergence of numerical sequences and Fourier series using a lower triangular matrix (T=(b_{m,n})), and generalized the results of Kórus [8]. The main objective of this paper is to introduce ([T^r,G,u,q])-strongly convergent sequence spaces for (rinmathbb{N}), and defined by a sequence of modulus functions. We also provide a relationship between ([T,G,u,q]) and ([T^r,G,u,q])-strongly convergent sequence spaces. Further, we investigate some geometrical and topological characteristics and establish some inclusion relationships between these sequence spaces. In the last, we derive some results on characterizations for ({T}^{r})-strong convergent sequences, statistical convergence and Fourier series using the idea of ([T^r,G,u,q])-strongly convergent sequence spaces.

We give characterizations of the Dunkl polyharmonic functions,i.e., solutions to the iteration of the Dunkl-Laplace operator (Delta_kappa) whichis a differential-reflection operator associated with a Coxeter–Weil group (W) generatedby a finite set of reflections and an invariant multiplicity function (kappa), interms of integral means over Euclidean balls and spheres.