Volume 47 , issue 1$-$2 ( 1995 )back
Finding the boundary curves of the third order linear ordinary differential equation1$-$6
Zdravko F. Starc

Abstract

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

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Keywords: Boundary curves.

MSC: 34A30

On a theorem of Ky-Fan type7$-$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.

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Keywords: Singular values, asymptotics.

MSC: 47B07

Some properties of semi-continuous functions and quasi-uniform spaces11$-$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.

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

MSC: 54E35; 54E55

Banach spaces over topological semifields and common fixed points19$-$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.

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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 kind23$-$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.

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

MSC: 65N12; 65N15

On probability measure generated by spectral density estimate31$-$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.

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

MSC: 62M15; 60G10, 60G15

A word on the joint embedding property39$-$47
Milan Z. Grulović

Abstract

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

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Keywords: Joint embedding property, amalgamation property.

MSC: 03C52; 03C25, 03C62

Kratka biografija profesora dr Zlatka Mamuzića49$-$52
Slobodan Č. Nešić