Volume 52 , issue 1$-$2 ( 2000 )back
Anwendung der Methode von Šapkarev zum Auflosen einige Randwertaufgaben für die lineare Komplexe Differentialgleichung II Ordnung1$-$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.

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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 $\Cal F_{\alpha}$, $\alpha>0$.

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

MSC: 30E20; 30D50, 30D55

A note on positive and positive definite Colombeau's generalized functions13$-$17
Z. Lozanov Crvenković and S. Pilipović

Abstract

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

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Keywords: Colombeau's generalized function.

MSC: 60G20

Einige Ergebnisse zur Theorie polyanalytischer Differentialgleichungen19$-$25
M. Čanak und Lj. Protić

Keywords: Polyanalitic differential equation.

MSC: 34M99; 32W50

Conditional estimation in exponential models27$-$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.

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

MSC: 62H12; 62H15

A note on the Hurwitz zeta function47$-$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~$n$.

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

MSC: 11M35; 11B68

On characterization of some covering properties in L-fuzzy topological spaces55$-$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.

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

MSC: 54A40