Acta Mathematica Hungarica最新文献

The aim of this paper is to establish the Olsen's inequality for discrete Morrey spaces. Specifically, it focuses on a bilinear operator associated with the discrete fractional integral operator of order (alpha) within these spaces. To achieve this, the decomposition method for discrete Morrey spaces is thoroughly examined.

Continuing recent studies of both the hereditary and super properties of certain classes of Abelian groups, we explore in-depth what is the situation in the quite large class consisting of directly finite Abelian groups.

Trying to connect some of these classes, we specifically succeeded to prove the surprising criteria that a relatively Hopfian group is hereditarily Hopfian only when it is extended Bassian, as well as that, a relatively Hopfian group is super Hopfian only when it is extended Bassian. In this aspect, additional relevant necessary and sufficient conditions in a slightly more general context are also proved.

Let (Omega) be a perfectly normal topological space, let (A) be a non-empty (G_delta)-subset of (Omega) and let (mathscr{B}_1(A)) denote the space of all functions (Atomathbb {R}) of Baire-one class on (A).Let also (|cdot|_infty) be the supremum norm. The symbol (chi_A) stands for the characteristic function of (A). We prove that for every bounded function (finmathscr {B}_1(A)) there is a sequence ((H_n))of both (F_sigma)- and (G_delta)-subset of (Omega) such that the function (overline{f}colonOmegatomathbb {R}) given by the uniformly convergent series on (Omega) with the formula:( overline{f}:=csum_{n=0}^infty (frac{2}{3})^{n+1}(frac{1}{2}-chi_{H_n}) )extends (f) with (overline{f}in{mathscr{B}}_1(Omega)), (c=sup_{xinOmega}lvert{overline{f}(x)}rvert) and the condition ((triangle)) of the form:(|f|_infty=|overline{f}|_infty).We apply the above series to obtain an extension of (f) positive to (overline{f}) positive with the condition ((triangle)). A similar technique allows us to obtain an extension of Baire-alpha functionon (A) to Baire-alpha function on (Omega).

Let (alpha(G)) and (mu(G)) denote the cardinality of a maximum independentset and the size of a maximum matching, respectively, in the graph (G= (V,E) ). If (alpha(G)+mu(G)= lvert V rvert ), then G is aKőnig–Egerváry graph.

The number (d (G) =max{ lvert A rvert - lvert N (A) rvert :Asubseteq V}) is the criticaldifference of the graph G, where (N (A) =left{ v:vin V,N (v) cap Aneqemptysetright} ). Every set (Bsubseteq V)satisfying (d (G) = lvert B rvert - lvert N (B) rvert ) is critical. Let (varepsilon (G) = lvert mathrm{ker}(G) rvert ) and (xi (G) = lvert mathrm{core} (G) rvert ), where (mathrm{ker}(G)) is the intersection of all critical independent sets, and ( mathrm{core} (G) ) is the intersection of all maximum independent sets. Itis known that (mathrm{ker}(G)subseteq) ( mathrm{core} (G) )holds for every graph.

Let us define

• (varrho_{v} (G) = lvert { vin V:G-v ) is a Kőnig–Egerváry graph (} rvert );

• (varrho_{e} (G) = lvert { ein E:G-e ) is a Kőnig–Egerváry graph ( } rvert ).

Clearly, (varrho_{v} (G) = lvert V rvert ) and(varrho_{e} (G) = lvert E rvert ) for bipartite graphs.Unlike the bipartiteness, the property of being a Kőnig–Egerváry graphis not hereditary.

In this paper, we show that

for every Kőnig–Egerváry graph G.

Let q be a Pisot or Salem number. Let (f_j(x) quad (j=1,2,dots)) be integer-valued polynomials of degree (ge2) with positive leading coefficients, and let ({a_j (n)}_{nge1} quad (j=1,2,dots)) be sequences of algebraic integers in the field (Q(q)) with suitable growth conditions. In this paper, we investigate linear independence over (Q(q)) of the numbers

In particular, when (a_j(n) quad (j=1,2,dots)) are polynomials of n, we give a linear independence criterion for the above numbers.

This paper concerns with implementations of constructions inthe Poincaré model of hyperbolic geometry and their applications to proofs ofselected theorems. The main motivation is how some hyperbolic geometric statements can be proven using elementary methods within the model. By embeddinghyperbolic geometry into the Euclidean plane, certain proofs can become moreaccessible and comprehensible.

In this paper, we present two elementary constructions developed by usingthe Poincaré model, followed by novel-approached answers to the following questions. Does a common perpendicular always exist for two ultraparallel lines? Cana given line segment be divided into (n) equal parts? Is it possible to construct atriangle from three given angles, provided their sum is less than 180 degrees?

Although there exist known answers to these questions, the usual proofs involve strong theorems or trigonometric functions requiring extensive calculations(e.g. [6] and [2]). Instead, hereby we present proofs using elementary tools witheasily understandable steps.

In the investigations of the boundedness of some sublinear operators, which do not hold the strong estimates, the researchers treat the weak estimates. In this occasion for the Herz spaces (dot{K}_q^{alpha,p}({mathbb{R}}^n)), in order to obtain more precise estimates than the weak estimates, the author [40] introduced the new “weak” Herz spaces (widetilde{W}dot{K}_q^{alpha,p}({mathbb{R}}^n)) and showed the new “weak” boundedness on (dot{K}_q^{alpha,p}({mathbb{R}}^n)). In this paper, we will extend the above new “weak” estimates to the sublinear operators satisfying another size condition. Further, we will extend these results on the Herz spaces with constant exponents (dot{K }_q^{alpha,p}({mathbb{R}}^n)) to one’s on the Herz spaces with variable exponent (dot{K}_{q(cdot)}^{alpha,p}({mathbb{R}}^n)).

We characterize the nontriviality of the module of relations of an irreducible quartic polynomial in terms of a quotient between its roots. In the case where the base field is (mathbb{Q}), we also give a characterization in terms of the roots of the cubic resolvent of the polynomial.

Let (r) be a positive integer, (N) a nonnegative integer and (Omega subset mathbb{R}^{r}) be a domain. Further, for all multi-indices (alpha in mathbb{N}^{r}), (|alpha|leq N), let us consider the partial differential operator (D^{alpha}) defined by (D^{alpha}= frac{partial^{|alpha|}}{partial x_{1}^{alpha_{1}}cdots partial x_{r}^{alpha_{r}}},)where (alpha= (alpha_{1}, ldots, alpha_{r})). Here, by definition, we mean (D^{0}equiv mathrm{id}). A straightforward computation shows that if (f, gin mathscr{C}^{N}(Omega)) and (alpha in mathbb{N}^{r}) with (|alpha|leq N), then we have

This paper is devoted to the study of the identity ((ast)) in the space (mathscr{C}(Omega)). More precisely, if (r) is a positive integer, (N) is a nonnegative integer and (Omega subset mathbb{R}^{r}) is a domain, then we describe all mappings (not necessarily linear) that satisfy the identity ((ast)) for all possible multi-indices (alphain mathbb{N}^{r}), (|alpha|leq N). Our main result states that if the domain is (mathscr{C}(Omega)),then the mappings in question take a particularly specific form. Related results for the space (mathscr{C}^{N}(Omega)) are also presented.

This paper investigates the perimetric contraction principle for quadrilaterals, a four-point extension of the Banach contraction principle, within the framework of semimetric spaces using triangle functions introduced by M. Bessenyei and Zs. Páles. We provide new insights into the fixed point theorem for perimetric contractions on quadrilaterals, demonstrating its applicability beyond metric spaces to include ultrametric spaces and distance spaces with power triangle functions.