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1

Structure of n-quasi left m-invertible and related classes of operators

Duggal Bhagwati Prashad, Kim In Hyun

Demonstratio Mathematica

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2020

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Vol. 53, nr 1

249--268

EN

Given Hilbert space operators T, S ∈ B(H), let Δ and δ ∈ B(B (H)) denote the elementary operators ΔT,S(X) = (LT RS − I) (X) = TXS - X and δT,S(X) = (LT – RS)(X) = TX - XS. Let d = Δ or δ. Assuming T commutes with S∗, and choosing X to be the positive operator S∗nSn for some positive integer n, this paper exploits properties of elementary operators to study the structure of n-quasi [m, d]-operators dm T,S (X) = 0 to bring together, and improve upon, extant results for a number of classes of operators, such as n-quasi left m-invertible operators, n-quasi m-isometric operators, n-quasi m-self-adjoint operators and n-quasi (m, C) symmetric operators (for some conjugation C of H). It is proved that Sn is the perturbation by a nilpotent of the direct sum of an operator Sn1 = (…)n satisfying dmT1S1(I1) = 0 , T1 = (…) , with the 0 operator; if S is also left invertible, then Sn is similar to an operator B such that dmB∗,B(I) = 0. For power bounded S and T such that ST∗ - T∗S = 0 and ΔTS(S∗nSn) = 0, S is polaroid (i.e., isolated points of the spectrum are poles). The product property, and the perturbation by a commuting nilpotent property, of operators T, S satisfying dmT,S (I) = 0, given certain commutativity properties, transfers to operators satisfying S∗ndmT,S (I)Sn = 0.

2

Słupy z łącznikami w linii średniego napięcia

Zawodniak J. J.

Automatyka, Elektryka, Zakłócenia

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2018

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Vol. 9, Nr 2(32)

38--42

PL

W artykule przedstawiono problematykę związaną z wymianą słupa z łącznikiem. Opisano proces zbierania danych do przeprowadzenia analiz kierunkowych przed podjęciem ostatecznej decyzji. Omówiono zagadnienia wpływające na ostateczny wybór nowego słupa z łącznikiem.

EN

This article presents selected problems related to the design and execution of medium voltage power line earthworms that affect later operation. The problem was also discussed economically from the perspective of the whole life of the earth ground and not only the initial design and construction.

3

Widmo Page'a jako narzędzie analizy anten liniowych

Walkowiak M., Witenberg A.

Przegląd Telekomunikacyjny + Wiadomości Telekomunikacyjne

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2016

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nr 8-9

1072--1075, CD

PL

Na prostych przykładach pokazano zastosowanie widma Page’a do analizy zjawisk przejściowych zachodzących w antenach liniowych pobudzanych impulsowo. Transformacja Page’a przenosi sygnał z dziedziny czasu w dziedzinę czas-częstotliwość. Transformata jest przyczynowa, spełnia twierdzenie Parsevala na brzegach obszaru określoności i nie generuje składowych o częstotliwościach różnicowych. Narzędzie umożliwia powiązanie zachowania się anteny z elementami struktury.

EN

On straight examples is shown the use of the Page spectrum to the analysis of phenomena of transients in linear antennas with impulse excitation. The Page transform converts a signal from the time domain into the timefrequency domain. The transform is causal, fulfils the Parseval boundary conditions and does not generate cross terms. This tool makes possible the association of the property of an antenna with elements of its structure.

4

Optimal Control of Electric Network Chain

Górecki H.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2001

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vol. 49, nr 1

149-159

EN

In the paper optimal control of an R, L, C, G electric network chain is considered. For the unloaded RC-chain the gains of the proportional optimal controllers are calculated. The optimal value of the functional is given. The proposed method is alternative to the method of solving Riccati equations for the calculation of the optimal gains.

5

Floating-point roundoff errors of second-order state-space digital filters.

Świder Z.

Systems Science

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2000

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Vol. 26, nr 1

67-81

EN

An expression for the output roundoff error variance of second-order state-space digital filter implemented in floating-point arithmetic is derived. The expression is further specified to white-noise and constant inputs which are common in feedback systems. Numerical results are presented for four typical realizations, i.e., controller and observer canonical forms, balanced realization, and minimum-noise-gain filter. All possible realizations are examined by means of a parametric approach. It is demonstrated that a simple modal realization involving poles and residues of the filter transfer function generates error not much larger than that of the minimum-noise-gain realization.

6

An electric network chain with feedbacks

Górecki H.

Control and Cybernetics

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2000

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Vol. 29, no 1

111-118

EN

In the paper an R, L. C, G electric network chain with feedbacks is considered. The formulas for the transfer function, for its poles and for the integral square error value are given.