Volume 47 , issue 1$-$2 ( 1995 ) back
 Finding the boundary curves of the third order linear ordinary differential equation 1$-$6 Zdravko F. Starc

Abstract

In this paper the boundary curves of the third order linear ordinary differential equations are given.

Keywords: Boundary curves.

MSC: 34A30

 On a theorem of Ky-Fan type 7$-$10 Milutin Dostanić

Abstract

We prove a statement of the Ky-Fan type which makes it possible in some situations to find the second term of the singular values asymptotics of a sum of two operators.

Keywords: Singular values, asymptotics.

MSC: 47B07

 Some properties of semi-continuous functions and quasi-uniform spaces 11$-$18 J. Ferrer, V. Gregori and I. L. Reilly

Abstract

This paper approaches the problem of characterizing the topological spaces that admit a unique compatible quasi-uniform structure by means of semi-continuous functions. The desired result is achieved by relating properties of the semi-continuous quasi-uniformity with a new characterization of hereditarily compact spaces via lower semi-continuous functions.

Keywords: Semi-continuous function, quasi-uniform space, hereditarily compact space.

MSC: 54E35, 54E55

 Banach spaces over topological semifields and common fixed points 19$-$22 Slobodan Č. Nešić

Abstract

In this paper we shall prove the existence of a common fixed point of two mappings of a Banach space over a topological semifield.

Keywords: Banach space over a topological semifield, common fixed point, Cauchy sequence and sequentially complete metric space.

MSC: 47H10, 54H25

 Convergence of finite-difference schemes for Poisson's equation with boundary condition of the third kind 23$-$30 Branislav Popović

Abstract

In this paper we study the convergence of finite-difference schemes to generalized solutions of the third boundary-value problem for Poisson's equation on the unit square. Using the generalized Bramble-Hilbert lemma, we obtain error estimates in discrete $H^1$ Sobolev norm compatible, in some cases, with the smoothness of the data. The outline of the paper is as follows. In section 1 notational conventions are presented. The stability theorem is proved in section~2. In section 3 we prove estimates of the energy of the operator $\Delta_h$. Finally, in section 4, we derive our main results.

Keywords: Finite-difference scheme, third boundary-value problem, Poisson's equation.

MSC: 65N12, 65N15

 On probability measure generated by spectral density estimate 31$-$37 Pavle Mladenović

Abstract

We study the periodogram based estimate of spectral density of a strictly stationary random sequence and consider this estimate as a random function on the whole domain of frequency. We renormalize the scale in this domain and investigate the probability measure generated by obtained process in the space of continuous functions.

Keywords: Stationary time series, spectral density, periodogram based estimate, cumulant spectral densities, weak convergence.

MSC: 62M15, 60G10, 60G15

 A word on the joint embedding property 39$-$47 Milan Z. Grulović

Abstract

A possible generalization has been considered of the notion of the joint embedding property. Some preliminary results are obtained.

Keywords: Joint embedding property, amalgamation property.

MSC: 03C52, 03C25, 03C62

 Kratka biografija profesora dr Zlatka Mamuzića 49$-$52 Slobodan Č. Nešić