Showing papers in "Acta Mathematica Hungarica in 1999"
TL;DR: In this paper, it was shown that any finite direct sum of ⌖-supplemented modules is a submodule of a right R-module, and that if every submodule has a supplement that is a direct summand of M, then it is a right-R-module.
Abstract: Let R be a ring and M a right R-module. M is called ⌖-supplemented if every submodule of M has a supplement that is a direct summand of M, and M is called completely ⌖-supplemented if every direct summand of M is ⌖-supplemented. In this paper various properties of these modules are developed. It is shown that (1) Any finite direct sum of ⌖-supplemented modules is ⌖-supplemented. (2) If M is ⌖-supplemented and (D3) then M is completely ⌖-supplemented.
68 citations
TL;DR: This work gives a complete characterization of that polynomial of degree n which has n + l extremal points on El and demonstrates how to generate in a very simple illustrative geometric way from a T-polynomial on l intervals a T -polynomials on l or more intervals.
Abstract: First, T-polynomials, which were investigated in Part I, are used for a complete description of minimal polynomials on two intervals, of Zolotarev polynomials, and of polynomials minimal under certain constraints as Schur polynomials or Richardson polynomials. Then, based on an approach of W. J. Kammerer, it is shown that there exists a T-polynomial on a set of l intervals El if l + 1 boundary points of El and the number of extremal points in each interval of El are given. Finally, a fast algorithm for the numerical computation is provided and for two intervals it is demonstrated how to get T-polynomials with the help of Grobner bases.
56 citations
TL;DR: In this paper, the authors studied the harmonic Bergman functions on the unit ball B in Rn and showed that the Bergman projection Pα is bounded for the range 1 0 and α > 0.
Abstract: We study harmonic Bergman functions on the unit ball B in Rn. Among our main results are: For the Bergman kernel Kα(x, y) of the orthogonal projection Pα of L2,α-1 onto the harmonic Bergman space l2,α-1 the following estimate holds:
$$\left| {K_\alpha (x,y)} \right| = O\left( {\left| {x - y} \right|^{ - n + 1 - \alpha } } \right),{\text{ }}x \in B,{\text{ }}y \in \partial B$$
. The Bergman projection Pα is bounded for the range 1 0 and α > 0.
50 citations
TL;DR: In this article, it was shown that a compact φ-conformally flat K-contact manifold with regular contact vector field is a principal S1-bundle over an almost Kaehler space of constant holomorphic sectional curvature.
Abstract: In this paper we study a class of K-contact manifolds, namely φ-conformally flat K-contact manifolds and we show that a compact φ-conformally flat K-contact manifold with regular contact vector field is a principal S1-bundle over an almost Kaehler space of constant holomorphic sectional curvature.
37 citations
TL;DR: In this paper, a Hahn-Banach type theorem in the frame of quasi-normed spaces (a class of linear spaces with a quasi-uniform structure that contains all linear lattices) is given.
Abstract: A Hahn-Banach type theorem in the frame of quasi-normed spaces (a class of linear spaces with a quasi-uniform structure that contains all linear lattices) is given. The classical result for positive functionals follows as a particular case.
35 citations
TL;DR: In this article, it was shown that every lattice with more than one element has a proper congruence-preserving extension, and that any lattice having more than two elements has one element is congruent.
Abstract: We prove that every lattice with more than one element has a proper congruence-preserving extension.
31 citations
TL;DR: In this paper, the Minty-Browder monotonicity notion was generalized for vector fields of a Riemannian manifold M. If M is a Hadamard manifold, complementary vector fields for maps f : M → M were introduced.
Abstract: The Minty-Browder monotonicity notion will be generalized for vector fields of a Riemannian manifold M. If M is a Hadamard manifold, complementary vector fields of maps f : M → M will be introduced. If f is nonexpansive it is proved that the complementary vector field of f is monotone. In particular, compositions of projection maps onto convex sets will be considered.
25 citations
TL;DR: In this paper, the authors introduced a new class of functions called almost αg-closed and used the functions to improve several preservation theorems of normality and regularity and also their generalizations.
Abstract: We introduce a new class of functions called almost αg-closed and use the functions to improve several preservation theorems of normality and regularity and also their generalizations. The main result of the paper is that normality and weak normality are preserved under almost αg-closed continuous surjections.
23 citations
TL;DR: In this paper, the authors continue the study of semi-compact spaces, i.e., the spaces whose α-topologies are hereditarily compact, and deal with semi-closed graphs and semi-convergence in extremally disconnected spaces.
Abstract: The aim of this paper is to continue the study of semi-compact spaces, i.e. the spaces whose α-topologies are hereditarily compact. The last section deals with semi-closed graphs and semi-convergence in extremally disconnected spaces.
22 citations
TL;DR: The mean convergence of Lagrange interpolation at the zeros of the orthonormal polynomials associated with the Freud weight WW2 has been studied by several authors.
Abstract: Let W := exp(-Q), where Q is of smooth polynomial growth at ∞, for example Q(x) = |x|β, β > 1. We call W2 a Freud weight. The mean convergence of Lagrange interpolation at the zeros of the orthonormal polynomials associated with the Freud weight WW2 has been studied by several authors, as has the Lebesgue function of Lagrange interpolation. J. Szabados had the idea to add two additional points of interpolation, thereby reducing the Lebesgue constant to grow no faster than log n. In this paper, we show that mean convergence of Lagrange interpolation at this extended set of nodes displays a similar advantage over merely using the zeros of the orthogonal polynomials.
20 citations
TL;DR: In this paper, it was shown that these functions are weaker than strongly θ-semi-continuous functions and stronger than θ -semi continuous functions, and that strongly semi continuous functions are stronger than almost strongly continuous functions.
Abstract: Beceren et al. [2] introduced and investigated a new class of functions called almost strongly θ-semi-continuous functions. The purpose of this paper is to investigate some more properties of these functions. It is shown that these functions are weaker than strongly θ-semi-continuous functions and stronger than θ-semi-continuous functions.
TL;DR: In this paper, the authors define a multifunction F : X → Y to be upper (lower) almost β-continuous if F+(V) (F- (V)) is β-open in X for every regular open set V of Y.
Abstract: In this paper, the authors define a multifunction F : X → Y to be upper (lower) almost β-continuous if F+(V) (F- (V)) is β-open in X for every regular open set V of Y. They obtain some characterizations and several properties concerning upper (lower) almost β-continuous multifunctions.
TL;DR: In this article, the boundedness of integral operators of the form √( √ √ n, √ q n ) was obtained for the regularity condition of the integral operators.
Abstract: In this paper we study integral operators of the form
$$T\,f\left( x \right) = \int {k_1 \left( {x - a_1 y} \right)k_2 \left( {x - a_2 y} \right)k_m \left( {x - a_m y} \right)f\left( y \right)dy} ,$$
$$k_i \left( y \right) = \sum\limits_{j \in Z} {2^{\frac{{jn}}{{q_i }}} } \varphi _{i,j} \left( {2^j y} \right),\,1 \leqq q_i < \infty ,\frac{1}{{q_1 }} + \frac{1}{{q_2 }} + + \frac{1}{{q_m }} = 1 - r,$$
$$0 \leqq r < 1$$
, and
$$\varphi _{i,j}$$
satisfying suitable regularity conditions We obtain the boundedness of
$$T:L^p \left( {R^n } \right) \to T:L^q \left( {R^n } \right)$$
for
$$1 < p < \frac{1}{r}$$
and
$$\frac{1}{q} = \frac{1}{p} - r$$
TL;DR: In this article, the authors show that the Hermite-Fejer interpolation process is not optimal, but the Grunwald operator is the ideal case for weighted interpolation on real line.
Abstract: In this paper we deal with weighted interpolation on the real line. We show that the Hermite-Fejer interpolation process is not optimal, but the Grunwald operator is the ideal case.
TL;DR: In this paper, the authors show that a bounded subset K of Lp(μ,X) is relatively norm compact if and only if K is p-uniformly integrable, scalarly relatively compact, and either tight or flatly concentrated.
Abstract: We show that a bounded subset K of Lp(μ,X) is relatively norm compact if and only if K is p-uniformly integrable, scalarly relatively compact, and either tight or flatly concentrated. The scalar relative compactness can be also replaced by several oscillation criteria.
TL;DR: In this paper, the notions of approach-Cauchy structure and ultra-approach-cauchy structures were defined and the categorical properties of ACHY and uACHY were studied.
Abstract: We define the notions of approach-Cauchy structure and ultra approach-Cauchy structure. We study the categorical properties of ACHY and uACHY and show that in these schemes Cauchy spaces and extended pseudo-(ultra)metric spaces are regarded as entities of the same kind. Furthermore, we investigate the relation with convergence-approach spaces and obtain a relationship similar to that of CONV and CHY.
TL;DR: In this paper, the authors deal with quasilinear elliptic hemivariational inequalities of higher order as generalizations of elliptic variational inequalities for nonconvex functionals.
Abstract: In this paper we deal with quasilinear elliptic hemivariational inequalities of higher order as generalizations of elliptic variational inequalities of higher order to nonconvex functionals. This extension is strongly motivated by various problems in mechanics. Using the notion of the generalized gradient of Clarke, existence results of solutions have been obtained.
TL;DR: In this article, the authors consider discrete versions of the de la Vallee-Poussin algebraic operator and give a simple sufficient condition in order that such discrete operators interpolate, and in particular the case of the Bernstein-Szegő weights.
Abstract: We consider discrete versions of the de la Vallee-Poussin algebraic operator. We give a simple sufficient condition in order that such discrete operators interpolate, and in particular we study the case of the Bernstein-Szegő weights. Furthermore we obtain good error estimates in the cases of the sup-norm and L1-norm, which are critical cases for the classical Lagrange interpolation.
TL;DR: Using Taylor's formula for functions of several variables, the author establishes inequalities for the integral of a function defined on an m-dimensional rectangle, if the partial derivatives remain between bounds.
Abstract: Using Taylor's formula for functions of several variables, the author establishes inequalities for the integral of a function defined on an m-dimensional rectangle, if the partial derivatives remain between bounds. Hence Iyengar's inequality and related resullts in the references could be deduced.
TL;DR: In this paper, it was shown that for all η ∈ (N, 2N\ A) with a sufficiently large real number, the inequality p_1 + p_2 + ε c + pα c - ε ε − 1 − ε l 1 − 1/5 √ L l c = O(n exp √ 1/3) √ l c + 1/4 √ n 1/1/5 l c ) for any ε ≥ c < 15/14 and n ≥ n √ c.
Abstract: Let 1 < c < 15/14 and N a sufficiently large real number. In this paper we prove that, for all η ∈ (N, 2N\ A with \(\left| A \right| = O\left( {N exp\left( { - \frac{1}{3}\left( {\frac{L}{c}} \right)^{1/5} } \right)} \right)\), the inequality \(\left| {p_1 ^c + p_2 ^c - \eta } \right| < \eta ^{1 - \frac{{15}}{{14c}}} L^8 \) has solutions in primes \(p_1 ,p_2 \underline{\underline < } N^{\frac{1}{c}} \).
TL;DR: In this paper, it was shown that the property of four elements introduced in [16] is satisfied by latticially closed subsets of any Orlicz-Musielak space Xρ f.
Abstract: We show that the "property of four elements" introduced in [16] is satisfied by latticially closed subsets of any Orlicz-Musielak space Xρ f. Also a problem of the isotonicity of the metric projection operator is considered. This generalizes the results from [22] obtained for the case of L p -spaces.
TL;DR: In this article, the authors give necessary and sufficient conditions for H(So) in order to be proximinal in Xϱ with the distances d, dL and do.
Abstract: Let (Ω, Σ, μ) be a complete measure space, L0 the vector lattice of Σ-measurable real functions on Ω, ϱ : L0 → [0, ∞)] a lattice semimodular, \(X_\rho = \left\{ {x \in L^0 :\lim _{\user1{\lambda } \to 0} \rho (\user1{\lambda }x) = 0} \right\}\) the corresponding modular space, S0 the ideal generated by \(\left\{ {1_A :{\text{ }}A \in \Sigma ,{\text{ }}\mu (A) 0,{\text{ }}\exists {\text{ }}s \in {\text{ }}S_{\text{0}} {\text{ such that }}\rho \left( {\frac{{x - s}}{\user1{\lambda }}} \right) 0:\rho \left( {\frac{{x - y}}{\user1{\lambda }}} \right) \leqq \user1{\lambda }} \right\}\) and, if ϱ is convex, the distances dL, do subordinated to the Luxemburg and Amemiya-Orlicz norms, respectively. We give necessary and sufficient conditions for H(So) in order to be proximinal in Xϱ with the distances d, dL and do.
TL;DR: In this article, it was shown that adding a random real does not add a perfect set of mutually nonconstructible reals to a model V of ZFC, and the existence of perfect free subsets for projective functions f : (ww)n → ww.
Abstract: We present two ways of adjoining a perfect set of mutually random reals to a model V of ZFC. We show that adding a random real does not add a perfect set of mutually non-constructible reals. We also investigate the existence of perfect free subsets for projective functions f : (ww)n → ww.
TL;DR: In this paper, it was shown that if En is a symmetric perfect set and the length of the basic intervals in En is denoted by ln, then the Hausdorff dimension of En is O(log 2 n log n log ln log l n ) − log n − log l ln n − n.
Abstract: We consider nowhere dense perfect subsets of [0, 1] that are symmetric but have no additional nice properties. We prove that if E = ∩En is a symmetric perfect set and the length of the basic intervals in En is denoted by ln then the Hausdorff dimension of E is
$$s = \mathop {\lim inf}\limits_{n \to \infty } \{ s_n : 2^n l_n^{9_n } = 1\} = \mathop {\lim inf}\limits_{n \to \infty } \frac{{\log 2^n }}{{ - \log l_n }}$$
. The argument we use also shows that using natural covers of E; i.e., covers consisting of the 2n closed, equal length intervals of the nth stage, yield an estimate for the s-dimensional Hausdorff measure within a factor of four.
TL;DR: In this article, the frequency of zero in the β-expansion of x varies with respect to β for almost all x, where β is a function of the size of the expansion.
Abstract: We study how the frequency of zero in the β-expansion of x varies with respect to β for almost all x.
TL;DR: In this paper, the classification of degenerate and non-degenerate submanifolds of an almost para-Hermitian manifold of dimension four is presented, and examples from each class are shown.
Abstract: The classification of degenerate and non-degenerate submanifolds, and CR-submanifolds of an almost para-Hermitian manifold of dimension four is obtained, and examples from each class are shown.
TL;DR: In this paper, the existence of a nontangential weighted limit of the infinitesimal Caratheodory metric in such a point of a smooth bounded pseudoconvex domain in Cn is studied.
Abstract: A boundary point of a domain in Cn is said to be h-extendible if its Catlin's multitype coincides with its D'Angelo's type. The main purpose of this paper is to study the existence of nontangential weighted limit of the infinitesimal Caratheodory metric in such a point of a smooth bounded pseudoconvex domain in Cn.
[...]
TL;DR: In this paper, the main results proved that if R is a boolean hopfian ring then the polynomial ring R[T] is hop-fian, and if R and S are hopfians then R × S is a hop fian ring.
Abstract: The main results proved in this paper are: (i) If R is a boolean hopfian ring then the polynomial ring R[T] is hopfian. (ii) Let R and S be hopfian rings. Suppose the only central idempotents in S are 0 and 1 and that S is not a homomorphic image of R. Then R × S is a hopfian ring.
TL;DR: For a ring A with local units, this paper investigated unital overrings T of A, and compared the automorphism groups Aut (A) and Aut (T) with respect to local units.
Abstract: For a ring A with local units we investigate unital overrings T of A, and compare the automorphism groups Aut (A) and Aut (T).