Acta Mathematica Hungarica最新文献

We investigate first Baire functionals on the dual ball of a separable Banach space (X) which are pointwise limit of a sequence of (X) whose closed span does not contain any copy of (ell_1) (or has separable dual). We propose an example of a (C(K)) space where not all such first Baire functionals exhibit this behavior. As an application, we study a quantitative version, in terms of descriptive set theory, of family a separable Banach spaces with this peculiarity.

We generalize two results about conjugacy class sizes of real elements to sub-class sizes of real elements.

An almost cover of a finite set in the affine space is a collectionof hyperplanes that together cover all points of the set except one. Using thepolynomial method, we determine the minimum size of an almost cover of thevertex set of the permutohedron and address a few related questions.

Using a modification of the adapted Riccati transformation, weprove an oscillation criterion for generalizations of linear and half-linear Euler differenceequations. Our main result complements a large number of previouslyknown oscillation criteria about several similar generalizations of Euler differenceequations. The major part of this paper is formed by the proof of the main theorem.To illustrate the fact that the presented criterion is new even for linearequations with periodic coefficients, we finish this paper with the correspondingcorollary together with concrete examples of simple equations whose oscillatoryproperties do not follow from previously known criteria.

This paper aims to study some important topological properties of the regular topology on C(X, Y), the set of all continuous functions from a Tychonoff space X to a metric space (Y, d). In particular, we study in detail the connectedness of the regular topology on C(X, Y). In the end, some important countability properties are studied.

For an infinite family of real biquadratic fields k we give the structure of the Iwasawa module (X=X(k_{infty})) of the (mathbb{Z}_{2})-extension of k. For these fields, we obtain that (lambda=mu=0 mbox{ and }nu=2). where (lambda), (mu) and (nu) are the Iwasawa invariants of the cyclotomic (mathbb{Z}_{2})-extension of k

We deal with the class of Hausdorff spaces having a (pi)-base whose elements have an H-closed closure. Carlson proved that (|X|leq 2^{wL(X)psi_c(X)t(X)}) for every quasiregular space (X) with a (pi)-base whose elements have an H-closed closure. We provide an example of a space (X) having a (pi)-base whose elements have an H-closed closure which is not quasiregular (neither Urysohn) such that (|X|> 2^{wL(X)chi(X)}) (then (|X|> 2^{wL(X)psi_c(X)t(X)})). Always in the class of spaces with a (pi)-base whose elements have an H-closed closure, we establish the bound (|X|leq2^{wL(X)k(X)}) for Urysohn spaces and we give an example of an Urysohn space (Z) such that (k(Z)<chi(Z)). Lastly, we present some equivalent conditions to the Martin's Axiom involving spaces with a (pi)-base whose elements have an H-closed closure and, additionally, we prove that if a quasiregular space has a (pi)-base whose elements have an H-closed closure then such a space is Baire.

Elsner, Luca and Tachiya proved in [4] that the values of the Jacobi-theta constants (theta_3(mtau)) and (theta_3(ntau)) are algebraically independent over (mathbb{Q}) for distinct integers (m), (n) under some conditions on (tau). On the other hand, in [3] Elsner and Tachiya also proved that three values (theta_3(mtau),theta_3(ntau)) and (theta_3(ell tau)) are algebraically dependent over (mathbb{Q}). In this article we prove the non-vanishing of linear forms in (theta_3(mtau)), (theta_3(ntau)) and (theta_3(ell tau)) under various conditions on (m), (n), (ell), and (tau). Among other things we prove that for odd and distinct positive integers (m,n>3) the three numbers (theta_3(tau)), (theta_3(mtau)) and (theta_3(n tau)) are linearly independent over (overline{mathbb{Q}}) when (tau) is an algebraic number of some degree greater or equal to 3. In some sense this fills the gap between the above-mentioned former results on theta constants. A theorem on the linear independence over (mathbb{C(tau)}) of the functions (theta_3(a_1 tau), dots, theta_3(a_m tau))for distinct positive rational numbers (a_{1}, {dots}, a_{m}) is also established.

Suppose that (R_{alpha}) is a rhombus with side length (1) and with acute angle (alpha). Let ({S_{n}}) be any collection of squares. In this note a tight upper bound of the sum of the areas of squares from ({S_{n}}) that can be parallel packed into (R_{alpha}) is given.

By using the structure and some properties of extraspecial and generalized/almost extraspecial (p)-groups, we explicitly determine the number of elements of specific orders in such groups. As a consequence, one may find the number of cyclic subgroups of any (generalized/almost) extraspecial group. For a finite group (G), the ratio of the number of cyclic subgroups to the number of subgroups is called the cyclicity degree of (G) and is denoted by cdeg ((G)). We show that the set containing the cyclicity degrees of all finite groups is dense in ([0, 1]). This is equivalent to giving an affirmative answer to the following question posed by Tóth and Tărnăuceanu: “For every (ain [0, 1]), does there exist a sequence ((G_n)_{ngeq 1}) of finite groups such that ( lim_{ntoinfty} text{cdeg} (G_n)=a)?”. We show that such sequences are formed of finite direct products of extraspecial groups of a specific type.