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1

Some results on generalized finite operators and range kernel orthogonality in Hilbert spaces

Mesbah Nadia, Messaoudene Hadia, Alharbi Asma

Demonstratio Mathematica

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2021

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Vol. 54, nr 1

318--325

EN

Let be a complex Hilbert space and B(H) denotes the algebra of all bounded linear operators acting on H. In this paper, we present some new pairs of generalized finite operators. More precisely, new pairs of operators (A, B) ∈ B(H) × B(H) satisfying: ∥ AX – XB − I∥ ≥ 1, for all X ∈ B(H). An example under which the class of such operators is not invariant under similarity orbit is given. Range kernel orthogonality of generalized derivation is also studied.

2

Range-Kernel orthogonality and elementary operators on certain Banach spaces

Bachir Ahmed, Segres Abdelkader, Sayyaf Nawal Ali, Ouarghi Khalid

Demonstratio Mathematica

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2021

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Vol. 54, nr 1

272--279

EN

The characterization of the points in Cp:1≤p<∞(H) , the Von Neuman-Schatten p-classes, that are orthogonal to the range of elementary operators has been done for certain kinds of elementary operators. In this paper, we shall study this problem of characterization on an abstract reflexive, smooth and strictly convex Banach space for arbitrary operator. As an application, we consider other kinds of elementary operators defined on the spaces Cp:1≤p<∞(H), and finally, we give a counterexample to Mecheri’s result given in this context.

3

Relatively orthocomplemented skew nearlattices in Rickart rings

Cırulis J.

Demonstratio Mathematica

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2015

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Vol. 48, nr 4

493--508

EN

A class of (right) Rickart rings, called strong, is isolated. In particular, every Rickart *-ring is strong. It is shown in the paper that every strong Rickart ring R admits a binary operation which turns R into a right normal band having an upper bound property with respect to its natural order ≤; such bands are known as right normal skew nearlattices. The poset (R, ≤) is relatively orthocomplemented; in particular, every initial segment in it is orthomodular. The order ≤ is actually a version of the so called right-star order. The one-sided star orders are well-investigated for matrices and recently have been generalized to bounded linear Hilbert space operators and to abstract Rickart *-rings. The paper demonstrates that they can successfully be treated also in Rickart rings without involution.

4

Orthogonal Experiment Design Algorithm of a Distribution Network Reconfiguration

Yanli L., Dexiang Z., Hong S., Xue G.

Przegląd Elektrotechniczny

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2013

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R. 89, nr 4

120-122

EN

According to the operation characteristics of the power distribution network with tree structure and the reconfiguration power distribution network, this paper proposes the orthogonal experiment design algorithm of power distribution network reconfiguration by mending the switch of the ring net presented by the orthogonal table.

PL

W artykule przedstawiono propozycję algorytmu rekonfiguracji sieci dystrybucji energii. W metodzie zastosowano projektowanie ortogonalnego eksperymentu. Wykonanie operacji polega na przełączaniu (łączeniu) odpowiednich łączników w pierścieniu sieci, która zapisana jest w tablicy ortogonalnej.

5

Tangency and orthogonality in metric spaces

Pascali E.

Demonstratio Mathematica

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2005

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Vol. 38, nr 2

437--449

EN

We consider an abstract definition of tangency in metric spaces and study some of its properties. We introduce also a particular structure on metric spaces and define, with respect this structure, the notion of tangency and orthogonality. Some properties of continuous curves in such spaces are investigated.

6

Drgania belki Timoshenki-Kelvina

Cabański J.

Zeszyty Naukowe. Mechanika / Akademia Techniczno-Rolnicza w Bydgoszczy

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1999

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Z. 44 (221)

29-37

PL

W pracy przedstawiono analityczną metodę rozwiązania zagadnienia drgań swobodnych i wymuszonych belki Timoshenki. Założono, że belka jest wykonana z materiału lepko-sprężystego opisanego modelem reologicznym Voigta-Kelvina. W opracowanej metodzie użyto reguł operatorowych przedstawionych w pracy [2]. Istotą tej metody jest rozdzielenie zmiennych w przestrzeni zespolonej oraz własność ortogonalności zespolonych wektorów drgań własnych. Rozwiązania uzyskano w postaci uogólnionych szeregów Fouriera.

EN

In this paper an analytical method of solving the free and forced vibration problems of Timoshenko beam is presented. It's assumed, that the beam is carried out from a viscoelastic material, which is descriebed by the rheology Voigt-Kelvin model. The besis of the elaborate method are the operator principles [2]. The essence of this method is separation of variables in the conjugate space and the property of orthogonality of complex eigenvector of free vibration. The solution in the generalize form of the Fourier's series is obtained.