Abstract

We give an answer to a hypothesis formulated in one of our earlier papers, concerning boundaries and estimates of some segments of harmonic series.

Keywords: Harmonic series.

MSC: 26D15

Abstract

In this paper we study the invariance and the inverse invariance under fuzzy closed, fuzzy open, and various kinds of fuzzy perfect maps, of different properties of fuzzy topological spaces.

Keywords: Topology; categories; good extensions; fuzzy closed, fuzzy open and fuzzy perfect maps; invariance.

MSC: 54A40, 04A72

Abstract

In this paper the problem of the compatibility of the tangency relations $T_{l_i}(a_i,b_i,k,p)$ ($i=1,2$) of sets of the classes $\tilde M_{p,k}$ and $A^*_{p,k}$ in a generalized metric space is considered. Some sufficient conditions for the compatibility of these relations of sets of the above classes are given here.

Keywords: Generalized metric space, compatibility of the tangency of sets.

MSC: 53A99

Abstract

The concept of near paracompactness is a well known weaker form of paracompactness, first introduced by Singal and Arya [6], followed by its further pursuit by many others. In the present paper, the same concept has been investigated in terms of a certain type of cover, called regular even cover. A number of characterizations of almost regular nearly paracompact spaces, including those analogous to the famous Michael's results on a regular paracompact space, have been achieved.

Keywords: Nearly paracompact spaces, almost regular spaces, regular even cover, strongly locally finite cover, strongly discrete cover.

MSC: 54D20

Abstract

Linear delay difference equations as well as generalized characteristic equations and their importance at oscillation of all solutions of considered difference equations are studied in this paper. Some results of comparison of solutions of difference equations and inequalities as well as conditions for the existence of positive solutions are presented as the application of the generalized characteristic equation.

Keywords: Delay difference equation, generalized characteristic equation, oscillation of soultions.

MSC: 39A10

Abstract

The concepts of a filter-base and s-convergence and $\theta$-convergence of a filter-base in a fuzzy setting are defined and investigated. Fuzzy filter-base is used to characterize fuzzy S-closed and extremally disconnected spaces. Several other properties of these two types of spaces and comparison between different forms of compactness in fuzzy topology are established.

Keywords: s-converegence and $\theta$-convergence of a filter-base in a fuzzy setting; semi-open set; S-closed, extremally disconnected fuzzy topological spaces.

MSC: 54A40, 54D20

Abstract

The object of the present paper is to study some properties of generalized Ricci 2-recurrent spaces. At first it is proved that every 3-% dimensional generalized Ricci 2-recurrent space is a generalized 2-recurrent space. In section 3, it is shown that for such a space Ricci-principal invariant is $1/2R$. In section 4 we find a necessary condition for such a space to be a Ricci-recurrent space. Next it is proved that a conformally symmetric Ricci 2-recurrent space is a generalized 2-recurrent space and a conformally symmetric generalized Ricci 2-recurrent space with definite metric and zero scalar curvature can not exist. Lastly an example of a generalized Ricci 2-recurrent space is also constructed.

Keywords: Generalized Ricci spaces, Ricci principal-invariant, conformally symmetric spaces, zero scalar curvature.

MSC: 53C20

Abstract

This paper presents some recent time series models (the so-% called NAREX(1) models) for Laplace variables with first order autoregressive structures. They are analogs of standard AR(1) model and of the LAR(1), NLAR(1) and AREX(1) models, introduced by Andel, Lawrance, Lewis, Jevremovi{\cj} and others. Some of their models can be obtained from NAREX models as special cases. The distribution of the innovation sequence (a probability mixture) and the autoregressive structure of NAREX processes are discussed as well.

Keywords: Autoregressive model, stationary, Laplace marginal distribution, NAREX model, probability mixture.

MSC: 62M10

Abstract

We find a tensor of Kähler type for an almost Hermitian and almost para-Hermitian manifold. We show that this tenosr is closely related with the problem of almost Hermitian and almost para-Hermitian manifold with pointwise constant holomorphic sectional curvature.

Keywords: Almost Hermitian manifold, almost para-Hermitian manifold, curvature tensor.

MSC: 53C25, 53C55

Abstract

The paper {\bf A Note on Wavelets and S--asymptotics}, by A. Takači and N. Teofanov, appeared in Matematički Vesnik, Vol.\ {\bf49}, 3--4 (1997), 215--220. Unfortunately, due to an editorial error, an old version of the paper was printed. In order to correct this error, we give the correct end of the paper, starting from the eight line on page 218 (after the end of Proof of Theorem 1). We apologize to the authors and to the readers.

MSC: 42C05