Acta Mathematica Hungarica最新文献

We introduce a new type of mappings in metric spaces which arethree-point analogue of the well-known Chatterjea type mappings, and call themgeneralized Chatterjea type mappings. It is shown that such mappings can be discontinuous as is the case of Chatterjea type mappings and this new class includesthe class of Chatterjea type mappings. The fixed point theorem for generalizedChatterjea type mappings is proven.

Ellipsephic or Kempner-like harmonic series are series of inverses of integers whose expansion in base B, for some (B geq 2), contains no occurrence of some fixed digit or some fixed block of digits. A prototypical example was proposed by Kempner in 1914, namely the sum inverses of integers whose expansion in base 10 contains no occurrence of a nonzero given digit. Results about such series address their convergence as well as closed expressions for their sums (or approximations thereof). Another direction of research is the study of sums of inverses of integers that contain only a given finite number, say k, of some digit or some block of digits, and the limits of such sums when k goes to infinity. Generalizing partial results in the literature, we give a complete result for any digit or block of digits in any base.

Related to a stochastic investment problem which aims to deter-mine when is it better to first invest a larger amount of money and afterwards asmaller one, in this paper we introduce a new preference relation between randomvariables. We investigate the link between this new relation and some well-knownstochastic order relations and present some characterization properties illustratedwith numerical examples.

We answer some questions about two cardinal invariants associated with separating and almost disjoint families and a partition relation involving indecomposable countable linear orderings.

Recently, Mangerel extended the Matomäki–Radziwiłł theorem to a large collection of unbounded multiplicative functions in typical short intervals. In this paper, we combine Mangerel's result with Halász-type result recently established by Granville, Harper and Soundararajan to consider the distribution of a class of multiplicative functions in short intervals. First, we prove cancellation in the sum of the coefficients of the standard L-function of an automorphic irreducible cuspidal representation of (mathrm{GL}_m) over (mathbb{Q}) with unitary central character in typical intervals of length (h(log X)^c) with (h = h(X) rightarrow infty) and some constant (c > 0) (under Vinogradov–Korobov zero-free region and GRC). Then we also establish a non-trivial bound for the product of divisor-bounded multiplicative functions with the Liouville function in arithmetic progressions over typical short intervals.

The present note is an addition to the author’s recent paper[44], concerning general multiplicative systems of random variables. Using somelemmas and the methodology of [13], we obtain a general extremal inequality,with corollaries involving Rademacher chaos sums and those analogues for multiplicativesystems. In particular we prove that a system of functions generated bybounded products of a multiplicative system is a convergence system.

For the Borromean link, we determine its irreducible ({rm SL}(2,mathbb{C}))-character variety, and find a formula for the twisted Alexander polynomial as a function on the character variety.

We characterize the approximate Cohen–Macaulayness of amodule in terms of the length function and the Hilbert coefficient of the modulewith respect to an almost p-standard system of parameters (a strict subclass ofd-sequences). As applications, we characterize the approximate Cohen–Macaulayproperty of Stanley–Reisner rings, localizations, idealizations, and power seriesrings. Furthermore, for power series rings, we construct almost p-standard systemsof parameters of them. From this result, we give a class of Cohen–MacaulayRees algebras and give precise formulas computing all Hilbert coefficients of theformal power series ring with respect to an almost p-standard system of parameters.

This paper explores the concept of approximate Birkhoff–James orthogonality in the context of operators on semi-Hilbert spaces. These spaces are generated by positive semi-definite sesquilinear forms. We delve into the fundamental properties of this concept and provide several characterizations of it. Using innovative arguments, we extend a widely known result initially proposed by Magajna [17]. Additionally, we improve a recent result by Sen and Paul [24] regarding a characterization of approximate numerical radius orthogonality of two semi-Hilbert space operators, such that one of them is (A)-positive. Here, (A) is assumed to be a positive semi-definite operator.

Let (S) be a set of four points chosen independently, uniformly at random from a square. Join every pair of points of (S) with a straight line segment. Color these edges red if they have positive slope and blue, otherwise. We show that the probability that (S) defines a pair of crossing edges of the same color is equal to (1/4). This is connected to a recent result of Aichholzer et al. [1] who showed that by 2-colouring the edges of a geometric graph and counting monochromatic crossings instead of crossings, the number of crossings can be more than halved. Our result shows that for the described random drawings, there is a coloring of the edges such that the number of monochromatic crossings is in expectation (frac{1}{2}-frac{7}{50}) of the total number of crossings.