Showing papers in "Periodica Mathematica Hungarica in 1996"
35 citations
TL;DR: In this paper, it was shown that if a commutative Frechet-Lie group G has an exponential map, which is a local diffeomorphism, then G is the limit of a projective system of Banach-Lie groups.
Abstract: In this paper we characterize commutative Frechet-Lie groups using the exponential map. In particular we prove that if a commutative Frechet-Lie groupG has an exponential map, which is a local diffeomorphism, thenG is the limit of a projective system of Banach-Lie groups.
29 citations
TL;DR: In this article, the authors considered finite and undirected graphs G with the vertex set V(G) and the edge set E(G), and they considered the cyclomatic number of cycles.
Abstract: In this note, we consider finite and undirected graphs G with the vertex set V(G) and the edge set E(G). By n = n(G) = IV(G)1 and 1~). = m(G) = [E(G)1 we denote the order and the size of the graph, respectively. If z is a vertex of G, then we write d(z) = d(z, G) for the degree of z, d = 6(G) for the minimum degree and A = A(G) for the maximum degree of G. Let N(X) = N(:c,G), z E V(G), be the set of all vertices adjacent to 2 in G and N(S) = N(S, G) = UzES N(:c, G) for S C V(G). If K = K(G) is the number of components of G, then /.L = p(G) = m(G) - n(G) + n(G) is the well-known cyclomatic number of G. The oldest estimations for the number of cycles u = v(G) in a graph G are the following two inequalities: p(G) 5 u(G) 5 2j‘(“) - 1.
25 citations
TL;DR: In this paper, a 3-dimensional quasi-Sasakian manifold is defined and the structure function β is defined on such a manifold, and necessary and sufficient conditions for M to be conformally flat are given.
Abstract: LetM be a 3-dimensional quasi-Sasakian manifold. On such a manifold, the so-called structure function β is defined. With the help of this function, we find necessary and sufficient conditions forM to be conformally flat. Next it is proved that ifM is additionally conformally flat with β = const., then (a)M is locally a product ofR and a 2-dimensional Kahlerian space of constant Gauss curvature (the cosymplectic case), or (b)M is of constant positive curvature (the non cosymplectic case; here the quasi-Sasakian structure is homothetic to a Sasakian structure). An example of a 3-dimensional quasi-Sasakian structure being conformally flat with nonconstant structure function is also described. For conformally flat quasi-Sasakian manifolds of higher dimensions see [O1]
23 citations
TL;DR: In this article, the general theory of ultrametric spaces is presented, and detailed proofs can be found in [Pr-Cr, Ri1], [PrCr, this article.
Abstract: Hopefully, this presentation of the general theory of ultrametric spaces may already hint of the interest of this study. Detailed proofs may be found in [Pr-Cr, Ri1], [Pr-Cr, Ri2].
23 citations
19 citations
19 citations
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TL;DR: In this article, an expository account of R. McKenzie's recent refutation of the RS conjecture is given, based on an expositional account of the original RS conjecture.
Abstract: This is an expository account of R. McKenzie's recent refutation of the RS conjecture.
18 citations
TL;DR: In this paper, the group algebras of finite groups over a field of characteristic 2 with metabelian groups of units are characterized, and the same authors characterize the groups of groups over the same field with different types of units.
Abstract: We characterize the group algebras of finite groups over a field of characteristic 2 with metabelian groups of units.
11 citations
TL;DR: The principal application of a general theorem proved in this paper is to show that for any choice 1≤m≤n≤p of integers there exist metric spaces X and Y such that the initial k-segments of their clones of continuous maps coincide exactly whenk ≥ m, are isomorphic whenk≤ n, and are elementarily equivalent whenk ≤ p.
Abstract: The principal application of a general theorem proved here shows that for any choice 1≤m≤n≤p of integers there exist metric spacesX andY such that the initialk-segments of their clones of continuous maps coincide exactly whenk≤m, are isomorphic exactly whenk≤n, and are elementarily equivalent exactly whenk≤p.
10 citations
TL;DR: In this article, the authors present an alternative proof of the known result that no recursively enumerable number theory has the joint embedding property, and prove that it does not.
Abstract: The paper presents an alternative proof of the known result that no recursively enumerable number theory has the joint embedding property.
TL;DR: In this article, the relationship between absolute retracts, injectives and equationally compact algebras in finite generated congruence distributive varieties with 1-element subalgesas is considered and several characterization theorems are proven.
Abstract: The relationship between absolute retracts, injectives and equationally compact algebras in finitely generated congruence distributive varieties with 1- element subalgebras is considered and several characterization theorems are proven. Amongst others, we prove that the absolute retracts in such a variety are precisely the injectives in the amalgamation class and that every equationally compact reduced power of a finite absolute retract is an absolute retract. We also show that any elementary amalgamation class is Horn if and only if it is closed under finite direct products.
Abstract: An asserted program is presented whose correctness is provable by the Floyd-Hoare-Naur method in each finite field separately, which, however, admits no universal derivation, i.e. one which would work on all but finitely many finite fields of a given characteristic. Also, it is proved in general that if “executing a program twice with the same input, the outputs agree” is a provable property, then the output of the program is first order definable from the input.
TL;DR: In this article, it was shown that every nilpotent group of class 2 and exponent 4 is the circle group of a nil-potent ring of index 3 and characteristic 2.
Abstract: We prove that every nilpotent group of class 2 and exponent 4 is the circle group of a nilpotent ring of index 3 and characteristic 2.
TL;DR: In this paper, self-similarity of Bernstein polynomials, embodied in their subdivision property, is used for construction of an Iterative (hyperbolic) Function System (IFS) whose attractor is the graph of a given algebraic polynomial of arbitrary degree.
Abstract: Self-similarity of Bernstein polynomials, embodied in their subdivision property is used for construction of an Iterative (hyperbolic) Function System (IFS) whose attractor is the graph of a given algebraic polynomial of arbitrary degree. It is shown that such IFS is of just-touching type, and that it is peculiar to algebraic polynomials. Such IFS is then applied to faster evaluation of Bezier curves and to introduce interactive free-form modeling component into fractal sets.
TL;DR: In this paper, a more general type of Ekeland's variational principle and Caristi's coincidence theorem for set-valued mappings in probabilistic metric spaces are given.
Abstract: By using the partial ordering method, a more general type of Ekeland's variational principle and Caristi's coincidence theorem for set-valued mappings in probabilistic metric spaces are given in this paper. In addition, we give also a directly simple proof of the equivalence between theses theorems in probabilistic metric spaces.
TL;DR: In this paper, the authors generalize the well-known fact that for a pair of Morita equivalent rings R and S their maximal rings of quotients are again Morita-equivalent.
Abstract: We generalize the well-known fact that for a pair of Morita equivalent ringsR andS their maximal rings of quotients are again Morita equivalent: If τn (M) denotes the torsion theory cogenerated by the direct sum of the firstn+1 injective modules forming part of the minimal injective resolution ofM then ατn (R)=τn (S) where α is the category equivalenceR-Mod→S-Mod. Consequently the localized ringsRτn(R) andSτn(S) are Morita equivalent.
TL;DR: Riemann's function satisfies the following infinite system of functional equations as discussed by the authors : ǫ = Σv = 1∞v−2 sin(2πv2x).
Abstract: Riemann's functionR=Σv=1∞v−2 sin(2πv2x) satisfies the following infinite system of functional equations:
$$\sum\limits_{k = 0}^{n - 1} {R\left( {\frac{{x + k}}{n}} \right) = \frac{1}{q}R(qx)} $$
(*)
TL;DR: In this paper, the generalized Hardy inequality was used to obtain the weighted-norm estimates for first and higher derivatives by a function defined on [−1, 1] using a 2π-periodic function F(θ).
Abstract: Using the correspondence x↔ cos θ, where −1≤x ≤ 1 and 0 ≤ θ ≤ π, a function f(x) defined on [−1, 1] can be represented as a 2π-periodic function F(θ), and then the derivative f′(x) corresponds to \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\frac{{F^1 (\theta )}}{{ - \sin \theta }}$$ \end{document} . From these observations, weighted-norm estimates for first and higher derivatives by x will be obtained, using a generalized Hardy inequality. The results in turn imply the generalized Hardy inequality upon which they depend and will hold true in any weighted norm for which the generalized Hardy is true.
TL;DR: In this paper, the authors generalize the concept of rigid algebra by enlarging the set of functions to be considered as trivial, and give a criterion for H-rigidity in terms of so-minimal clones.
Abstract: An algebra or relational system usually is called rigid if its automorphism group or endomorphism monoid is trivial, i.e. consists of the indentity only. Sometimes constants are also considered as trivial what gives rise to the notion of a C-rigid system (cf. [Lan-P 841). In this paper, which is an extended version of a talk given in Budapest at the Conference on Ordered Structures and Universal Algebra in honour of L. Fuchs on the occasion of his 70 ” birthday, we shall generalize the concept of rigidity simply by enlarging the set of functions to be considered as trivial. Thus, for a set H of functions, H-rigid means that the automorphisms, endomorphisms or in general the polymorphisms belong to H. Our aim is to give a criterion for H-rigidity. This will be done in terms of so-called H-minimal clones (see Theorem 2.1). Of course, for applications it remains the problem to determine these H-minimal clones. As an example, they are determined for some few special cases on a twoor three-element base set.
TL;DR: In this article, a parametrization of all positive extensions of a suboperator of smallest possible norm with a "unit interval" of operators on an appropriate Hilbert space is given.
Abstract: Operator extensions on Hilbert spaces with recent applications to dilation and interpolation problems appeared in [3] while existence theorems are proved in [l-6]. Extremal extensions are described in [4] (in that paper extremal extension means smallest or largest element in a given set of extensions). Here a suboperator means a restriction of a continuous linear operator to a linear (not necessarily closed) subspace of the given Hilbert space. The results in this paper are mainly supplements of the previously known theorems from [l-6]. Nevertheless, as far as the author is aware, they have been remained unnoticed so far. First we give a parametrization of all positive extensions of a suboperator of smallest possible norm with a “unit interval” of operators on an appropriate Hilbert space. This is not really new since it was first proved by Krein [l], that those selfadjoint extensions of a symmetric suboperator, the norm of which does not exceed one, make up an operator interval. Parametrizations of operator intervals similar to ours have appeared in literature before. Then we characterize projection and compact extensions. We are going to use the following construction of Sebestydn [2,3].
TL;DR: In particular, if the maximal ideal space Δ(A) of a semisimple commutative complete metrizable locally convex algebra contains no isolated points, then every compact multipliers is trivial as discussed by the authors.
Abstract: It is shown that if the maximal ideal space Δ(A) of a semisimple commutative complete metrizable locally convex algebra contains no isolated points, then every compact multiplies is trivial. In particular, compact multipliers on semisimple commutative Frechet algebras whose maximal ideal space has no isolated points are identically zero.
TL;DR: In this article, the problem of common extension of charges (finitely additive measures) is generalised to include group-valued functions defined on a system of sets (u-systems).
Abstract: The problem of common extension ofcharges (finitely additive measures) is generalised to include group-valued functions defined on a system of sets (u-systems). To eachu-systemU an Abelian groupH(U) is attached. Every Abelian group is isomorphic to one of the formH(U). The groupH(U) is an indicator for extendability of charges fromU to the Boolean algebra generated byU. AllG-valued measures extend if and only if Ext(H(U),G)=0, for instance.
TL;DR: A survey of lattices as lattices of congruences and as lattice of equational theories can be found in this paper, where recent results and open problems are discussed.
Abstract: We survey results concerning the representations of lattices as lattices of congruences and as lattices of equational theories. Recent results and open problems will be mentioned.
TL;DR: In this paper it is shown that the class of primitive spaces is closed under the formation of finite topological sums and finite Cartesian products (see Fig. 1 ). But this is not the case for finitary Boolean spaces.
Abstract: A Boolean space is a compact Hausdorff zero-dimensional space. Boolean spaces arise as Stone duals of Boolean algebras and the duals of the countable Boolean algebras are the countably baaed (or equivalently metrizable) Boolean spaces. Among the latter spaces, primitive spaces and more particularly finitary spaces form two very peculiar subclasses. A countably baaed Boolean space is primitive if it admits a basis of pi clopen sets, where X is pi if for each clopen U C X, either X z U or X Z X \ U. It is finitary if the set of homeomorphism types of its pi clopen subsets is finite. These spaces have been introduced through utterly different means by Hanf [2], Pierce [21] and also by Paljutin 1201. They were also studied by Dobbertin [I], Heindorf [12], Myers [18], the author [6] and others ([17], [23] . . . ). Primitive spaces can be handled by easy-to-use combinatorial tools : their diagrams ([2] or [7]) and the structure of their homeomorphism types is at present fairly well understood ([22], [12], [7]). Their pl ace in Ketonen’s hierarchy ([13]) is well-known, at least in the finitary case ([12]). In the class of primitive spaces, Tarski’s cube problem (X+X+X E X implies X+X E X, see [2l] or [S]) has a positive answer, but otherwise the diagram technique enables to produce easy examples of pathological behaviour of product of spaces ([22], [S]). It should be noted that the primitive spaces bear some surprising relationships with the variable-free fragment of the modal system K4 ([9]) and that Paljutin has used finitary spaces to obtain some decidability results ([20]). Finally, it turns out that many Lindenbaum-Tarski algebras of important first-order theories (such as abelian groups, well-orders and linear orders, Boolean algebras, . . ) are primitive ([lS]). It is well-known that the class of primitive spaces is closed under the formation of finite topological sums and finite Cartesian products ([22], [24]). In this paper, we introduce other operations on Boolean spaces under which the class of primitive
TL;DR: In this article, the authors apply the structure theory of locally compact groups to reduce the general case to certain subcases, which were studied in this paper, and show that it is possible to generalize the method of the previous section to all commutative locally compact group.
Abstract: It would be interesting to know whether it is possible to generalize the method of the previous section to all commutative locally compact groups. For a long time I tried in vain to do this. Mauclaire uses a different approach. He applies the structure theory of locally compact groups to reduce the general case to certain subcases, which were studied in this paper.