Acta Mathematica Hungarica最新文献

This work aims to investigate various properties of some special Z-symmetric manifolds and their applications on space-times. Having an important place of the study, classifications of second-order symmetric tensor fields on space-times and holonomy theory are considered. Z-symmetric manifolds in the holonomy structure are investigated and some results are obtained. Various special vector fields are examined on Z-recurrent and weakly Z-symmetric manifolds and some relations associated with the eigenvector structure of the Z-tensor are found. In addition, several examples related to the outcomes of the study are given. Finally, some links between the Z-tensor and Ricci solitons on space-times are determined.

We show that pseudocharacter turns out to be discretely reflexivein Lindelöf (Sigma)-groups but countable tightness is notdiscretely reflexive in hereditarily Lindelöf spaces. We alsoestablish that it is independent of ZFC whether countablecharacter, countable weight or countable network weight isdiscretely reflexive in spaces (C_p(X)). Furthermore, we provethat any hereditary topological property is discretely reflexivein spaces (C_p(X)) with the Lindelöf (Sigma)-property. If(C_p(X)) is a Lindelöf (Sigma)-space and (L D) is a(k)-space for any discrete subspace ( { D C_p(X) } ), then it isconsistent with ZFC that (C_p(X)) has the Fréchet–Urysohnproperty. Our results solve two published open questions.

Let (mathbb{H}^{n}) be the Heisenberg group. For (0 leq alpha < Q=2n+2) and (N in mathbb{N}) we consider exponent functions (p (cdot) colon mathbb{H}^{n} to (0, +infty)), which satisfy log-Hölder conditions, such that (frac{Q}{Q+N} < p_{-} leq p (cdot) leq p_{+} < frac{Q}{alpha}). In this article we prove the (H^{p (cdot)}(mathbb{H}^{n}) to L^{q (cdot)}(mathbb{H}^{n})) and (H^{p (cdot)}(mathbb{H}^{n}) to H^{q (cdot)}(mathbb{H}^{n})) boundedness of convolution operators with kernels of type ((alpha, N)) on (mathbb{H}^{n}), where (frac{1}{q (cdot)} = frac{1}{p (cdot)} - frac{alpha}{Q}). In particular, the Riesz potential on (mathbb{H}^{n}) satisfies such estimates.

We introduce the martingale local Morrey spaces. We establish the Doob's inequality, the Burkholder–Gundy inequality and the boundedness of the martingale transforms to martingale local Morrey spaces defined on complete probability spaces.

Let G be an additive finite abelian group. Denote by disc(G) the smallest positive integer t such that every sequence S over G of length (|S|geq t) has two nonempty zero-sum subsequences of distinct lengths. In this paper, we focus on the direct and inverse problems associated with disc(G) for certain groups of rank three. Explicitly, we first determine the exact value of disc(G) for (Gcong C_2oplus C_{n_1}oplus C_{n_2}) with (2mid n_1mid n_2) and (Gcong C_3oplus C_{6n_3}oplus C_{6n_3}) with (n_3geq 1). Then we investigate the inverse problem. Let (mathcal {L}_1(G)) denote the set of all positive integers t satisfying that there is a sequence S over G of length (|S|=operatorname{disc}(G)-1) such that every nonempty zero-sum subsequence of S has the same length t. We determine (mathcal {L}_1(G)) completely for certain groups of rank three.

Given a real interval (I), a group of homeomorphisms (mathcal{G} left(M,Iright)) is associated to every continuous mean defined (i)n (I). Twomeans (M), (N) defined in (I) will belong to the same class when (mathcal{G} (M, I) = mathcal{G} (N,I)). The equivalence relationdefined in this way in (mathcal{CM}(I)), the family ofcontinuous means defined in (I), gives a principle of classification basedon the algebrai object (mathcal{G}(M, I)). Two major questionsare raised by this classification: 1) the problem of computing (mathcal{G} (M, I)) for a given mean (M in mathcal{CM} (I)), and 2) the determination of general properties of the means belonging to asame class. Some instances of these questions will find suitable responsesin the present paper.

We provide a construction of binary pseudorandom sequencesbased on Hardy fields (mathcal{H}) as considered by Boshernitzan. In particular we give upperbounds for the well distribution measure and the correlation measure definedby Mauduit and Sárközy. Finally we show that the correlation measure of order sis small only if s is small compared to the “growth exponent” of (mathcal{H}).

Answering a question posed by Vladimir Tkachuk, we prove thatevery connected first countable T₁-space is a continuous open image of a connectedmetrizable space.

In this work we shall concentrate on fractal-harmonic analysis of a class of Moran measures. Let ({M_n}_{n=1}^{infty}) be a sequence of expanding matrix in (M_2(mathbb{Z})) and({D_n}_{n=1}^{infty}) be a sequence of non-collinear integer digit sets satisfying

The associated Moran-type measure (mu_{{M_n},{D_n}}) is generated by the infinite convolution

in the weak(^*)-topology. Our result shows that if ({alpha_{n1}alpha_{n2}beta_{n1}beta_{n2}}_{n=1}^{infty}) is bounded, then (L^{2}(mu_{{M_n},{D_n}})) admits an infinite orthogonal set of exponential functions if and only if there exists a subsequence ({n_{k}}_{k=1}^{infty}) of ({n_{k}}_{k=1}^{infty}) such that (det(M_{n_{k}})in 2mathbb{Z}).

The enhanced power graph of a group G is a graph with vertex set G, where two distinct vertices (mathbb{x}) and (mathbb{y}) are adjacent if and only if there exists an element (mathbb{w}) in G such that both (mathbb{x}) and (mathbb{y}) are powers of (mathbb{w}). To obtain the proper enhanced power graph, we consider the induced subgraph on the set (G setminus D), where D represents the set of dominating vertices in the enhanced power graph. In this paper, we aim to determine the strong domination number of the proper enhanced power graphs of finite nilpotent groups.