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1

Hyponormal differential operators with discrete spectrum

Ismailov Z. I., Unluyol E.

Opuscula Mathematica

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2010

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Vol. 30, no. 1

79-94

EN

In this work, we first describe all the maximal hyponormal extensions of a minimal operator generated by a linear differential-operator expression of the first-order in the Hilbert space of vector-functions in a finite interval. Next, we investigate the discreteness of the spectrum and the asymptotical behavior of the modules of the eigenvalues for these maximal hyponormal extensions.

2

Curvilinear finite difference method (CFD) approximation of differential operators

Lara-Dziembek S., Siedlecki J.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

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2009

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Vol. 8, nr 1

97-103

EN

Curvilinear finite difference method is a one of variants of generalized finite difference method. Geometrical mesh can be created by the optional set of points for which the n-points stars are defined. In this paper the 9-points stars are considered (2D task) and the method of differential operators approximation is presented. In the final part of the paper the example of computations is shown.

3

On the tolerance overaging for differential operators with periodic coefficients

Borowska J., Łaciński Ł., Rychlewska J., Woźniak C.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

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2008

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Vol. 7, nr 1

17-21

EN

The aim of this contribution is to propose the tolerance averaging for differential operators with periodic coefficients. The averaging technique presented in this paper is based on proper limit passages with tolerance parameter to zero. This approach is a certain generalization of that presented in [1].

4

Spectra of the operator of the first difference in salpha, s)/alpha and lp (alpha) (1

Fares A., Malafosse B.

Demonstratio Mathematica

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2008

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Vol. 41, nr 3

661-676

EN

In this paper we deal with the spectrum of the operator of the first difference A considered as an operator from E to itself where E is one of the sets [...].We apply these results to characterize matrix transformations mapping in E [...] or N. This paper generalizes some results given in [8] and [3].

5

Filippov Lemma for certain differential inclusion of third order

Bartuzel G., Fryszkowski A.

Demonstratio Mathematica

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2008

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Vol. 41, nr 2

337-352

EN

We propose a version of the Filippov Lemma for differential inclusions of the type y'" + k2y' is an element of F(x,y) defined on [—1,1] with boundary conditions y(-1)=y(1)=y'(1)=0.

6

Some inequalities involving differential operators and their applications to certain multivalent functions

Dziok J., Huseyin I., Piejko K.

Journal of Mathematics and Applications

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2007

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Vol. 29

109-120

EN

The main object of the present paper is to investigate several results of certain differential operators which were recently introduced and (or) studied in a series of papers by Chen et et al. [1-3], Irmak et al. [8, 10, 11], Dziok et al. [5, 6] and Liu et al. [14]. In addition, some applications of our results involving certain differential inequalities of multivalently analytic and (or) multivalently raeromorphic functions are given. Our certain results also include some recent results in [5, 6, 9, 11, 12].

7

Robust 4D segmentation of cells in confocal images

Mischler D., Romaniuk B., Benassarou A., Bittar E.

Machine Graphics and Vision

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2006

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Vol. 15, No. 3/4

515-524

EN

We present a method to automatically extract the evolution of the cell envelope in 4D confocal images. Our method is based on 4D ReAM, a tracking system consisting of a previously presented deformable surface model, which can change its topology. The process consists in attracting the model for each volume of a 4D series towards an iso-surface of interest, and towards the image gradients. We then statistically estimate the characteristics of the cell surface on the nodes of the model, and reconstruct it. We show detailed results on the segmentation of the cell envelope during the mitosis.

8

Generating functions of orthogonal polynomials and Szegö-Jacobi parameters

Asai N., Kubo I., Kuo H.-H.

Probability and Mathematical Statistics

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2003

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Vol. 23, Fasc. 2

273--291

EN

In this paper, we present a more direct way to compute the Szegö-Jacobi parameters from a generating function than that in [5] and [6]. Our study is motivated by the notions of one-mode interacting Fock spaces defined in[1] and Segal-Bargmann transform associated with non-Gaussian probability measures introduced in [2]. Moreover, we examine the relationships between the representations of orthogonal polynomials in terms of differential or difference operators and our generating functions. The connections provide practical criteria to determine when functions of a certain form are orthogonal polynomials.

9

Absence of eigenvalues for integro-differential operators

Cojuhari P. A., Stanescu M.M.

Opuscula Mathematica

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2003

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Vol. 23

5-14

EN

Sufficient conditions for the absence of eigenvalues of integro-differential operators are presented.

10

Certain operators and inequalities and their applications to meromorphically multivalent functions

Dziok J., Irmak H.

Demonstratio Mathematica

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2003

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Vol. 36, nr 4

839--846

EN

In the present paper, making use of certain operators, some theorems involving inequalities on meromorphically multivalent functions in the punctured unit disk are obtained. Moreover, some of the results which are important for geometric function theory are also included.

11

A remark on the Poisson kernels on homogeneous manifolds of negative curvature

Urban A.

Probability and Mathematical Statistics

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2002

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Vol. 22, Fasc. 2

289-291

EN

In this note we give an improvement of the estimate of the Poisson kernels for second order differential operators on homogeneous manifolds of negative curvature obtained for the first time, using some probabilistic techniques, in [1] and then improved by the author in [4].