Volume 52 , issue 1$-$2 ( 2000 ) back
 Anwendung der Methode von Šapkarev zum Auflosen einige Randwertaufgaben für die lineare Komplexe Differentialgleichung II Ordnung 1$-$6 Lj. Protić und M. Čanak

Abstract

Jetzt stellen wir die Frage: Unter welchen Bedingungen geht die allgemeine komplexe Differentialgleichung $$D^2w+\alpha(z,\bar z)Dw+\beta(z,\bar z)w=\gamma(z,\bar z)$$ durch Anwendung der $\Cal F$-Transformation in sie selbst. Diese Frage für reellen Differentialgleichungen II Ordnung hat I. Šapkarev in seiner Arbeit [2] gestellt.

Keywords: Linear complex differential equation, eigenproblem, method of Šapkarev.

MSC: 34M99

 Inclusion theorems for the spaces $\Cal F_{\alpha}$ 7$-$11 Stojan Duborija

Abstract

We give a new proof of one known inclusion theorem for the space $\Cal F_0$ that enables us to extend this theorem from the unit disc in $C$ to the unit ball in $C^n$, $n>1$. We also improve an inclusion relation between Bergman spaces and the spaces $\Cal F_{\alpha}$, $\alpha>0$.

Keywords: Fractional Cauchy integral, Hardy space, BMOA, Bergman space.

MSC: 30E20, 30D50, 30D55

 A note on positive and positive definite Colombeau's generalized functions 13$-$17 Z. Lozanov Crvenković and S. Pilipović

Abstract

The positivity and the positive definitness of Colombeau's generalized functions are investigated.

Keywords: Colombeau's generalized function.

MSC: 60G20

 Einige Ergebnisse zur Theorie polyanalytischer Differentialgleichungen 19$-$25 M. Čanak und Lj. Protić

Keywords: Polyanalitic differential equation.

MSC: 34M99, 32W50

 Conditional estimation in exponential models 27$-$45 Smail Mahdi

Abstract

A two-sided conditional confidence interval for the parameter of an exponential probability distribution is constructed. The construction relies on a decision following a preliminary test of significance for the equality of two exponential population means. The coverage probability, the expected length together with the coefficient of variation of this interval are studied. A shrinkage version of the interval is also proposed. Furthermore, a numerical study on the accuracy of the interval estimator is performed.

Keywords: Exponential distribution, interval estimator, coverage probability, expected length, shrinkage estimator, simulation.

MSC: 62H12, 62H15

 A note on the Hurwitz zeta function 47$-$54 Djurdje Cvijović and Jacek Klinowski

Abstract

We show that the Hurwitz zeta function and polylogarithm, $\zeta(\nu,a)$ and $\operatorname{Li}_{\nu}(z)$, form a discrete Fourier transform pair for $\Re\nu>1$. Many formulae, the majority of them previously unknown, are obtained as a corollary to this result. In particular, the transformation relation allows the evaluation of $\zeta(\nu,a)$ at rational values of the parameter~$a$. It is also shown that, by making use of the transform pair, various known results can be deduced easily and in a unified manner. For instance, $$2\zeta(2n+1,1/3)=(3^{2n+1}-1)\zeta(2n+1)+(-1)^{n- 1}3^{2n}\sqrt3\dfrac{(2\pi)^{2n+1}}{(2n+1)!}B_{2n+1}(1/3),$$ $n\ge1$, where $B_n(\cdot)$ stands for the Bernoulli polynomial of degree~$n$.

Keywords: Hurwitz zeta function, polylogarithms, discrete Fourier transform.

MSC: 11M35, 11B68

 On characterization of some covering properties in L-fuzzy topological spaces 55$-$61 H. Aygün and S. R. T. Kudri

Abstract

In this work, various characterizations of some weaker and stronger forms of $L$-fuzzy compactness are obtained in $L$-fuzzy topological spaces, where $L$ is a fuzzy lattice.

Keywords: $L$-fuzzy topology, fuzzy lattice, fuzzy compactness, almost compactness, near compactness, $S$-closedness, strong compactness, $\alpha$-nets.

MSC: 54A40