Acta Mathematica Hungarica最新文献

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.

Let G be a finite group and G be a split extension of A by B, that is, G is a semidirect product: (G=Artimes B), where A and B are subgroups of G. Under the condition that B permutes with every maximal subgroup of Sylow subgroups of A, every maximal subgroup of A or every nontrivial normal subgroup of A, we prove that the supersolvable residual of G is the product of the supersolvable residuals of A and B.

We obtain recovery formulas for coefficients of orthonormal spline series by means of its sum, if the partial sums of an orthonormal spline series converge in measure to a function and the majorant of partial sums satisfies some necessary condition, provided that the spline system corresponds to a “regular” sequence. Additionally, it is proved that the regularity of the sequence is essential.

The problems of continuation of a partially defined metric and apartially defined ultrametric were considered in [12] and [13], respectively. Usingthe language of graph theory we generalize the criteria of existence of continuationobtained in these papers. For these purposes we use the concept of a trianglefunction introduced by M. Bessenyei and Z. Páles in [6], which gives a generalizationof the triangle inequality in metric spaces. The obtained result allowsus to get criteria of the existence of continuation for a wide class of semimetricsincluding not only metrics and ultrametrics, but also multiplicative metrics andsemimetrics with power triangle inequality. Moreover, the explicit formula for themaximal continuations is also obtained.

We confirmed the following special case of Füredi’s conjecture:Let (t) be a non-negative integer. Let ( mathcal{ P}={(A_i,B_i)}_{1leq ileq m}) be a set-pair family satisfying (|A_i cap B_i|leq t) for (1leq i leq m) and (|A_icap B_j|>t) for all (1leq ineq j leq m). Define (a_i:=|A_i|) and (b_i:=|B_i|) for each (i). Assume that there exists a positive integer (N) such that (a_i+b_i=N) for each (i). Then

Lutwak established the Brunn–Minkowski inequality for projectionbodies. Schuster [13] obtained the Brunn–Minkowski inequality for polarprojection bodies. Associated with the (L_p)-Minkowski combinations of convexbodies, we extend Lutwak's result and Schuster's result to (L_p) forms, respectively.

We investigate optimal expansions of Kakeya sequences for the representation of real numbers. Expansions of Kakeya sequences generalize the expansions in non-integer bases and they display analogous redundancy phenomena. In this paper, we characterize optimal expansions of Kakeya sequences, and we provide conditions for the existence of unique expansions with respect to Kakeya sequences.