Volume 47 , issue 1$-$2 ( 1995 ) | back |

Finding the boundary curves of the third order linear ordinary differential equation | 1$-$6 |

**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 |

**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 |

**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 |

**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 |

**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 |

**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 |

**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 |