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On spectra of a certain class of quadratic operator pencils with one-dimensional linear part

On spectra of a certain class of quadratic operator pencils with one-dimensional linear part

We consider a class of quadratic operator pencils that occur in many problems of physics. The part of such a pencil linear with respect to the spectral parameter describes the viscous friction in problems of small vibrations of strings and beams. Patterns in location of eigenvalues of such pencils...

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Main Author: Pivovarchik, V.N.
Format: Article
Language:English
Published: Інститут математики НАН України 2007
Series:Український математичний журнал
Subjects:
Статті
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/164188
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spelling irk-123456789-1641882020-02-09T01:27:01Z On spectra of a certain class of quadratic operator pencils with one-dimensional linear part Pivovarchik, V.N. Статті We consider a class of quadratic operator pencils that occur in many problems of physics. The part of such a pencil linear with respect to the spectral parameter describes the viscous friction in problems of small vibrations of strings and beams. Patterns in location of eigenvalues of such pencils are established. If the viscous friction (damping) is pointwise, then the operator in the linear part of the pencil is one-dimensional. For this case, rules in the location of the purely imaginary eigenvalues are found. Розглянуто певний клас квадратичних операторних в'язок, що виникають у багатьох задачах фізики. Лінійна за спектральним параметром частина в'язки описує в'язке тертя в задачах про малі коливання струн та стержнів. Встановлено закономірності в розташуванні власних значень таких в'язок. Якщо в'язке тертя зосереджене в одній точці, то оператор у лінійній за параметром частині в'язки є одновимірним. Для цього випадку знайдено порядок розташування суто уявних власних значень. 2007 Article On spectra of a certain class of quadratic operator pencils with one-dimensional linear part / V.N. Pivovarchik // Український математичний журнал. — 2007. — Т. 59, № 5. — С. 702–716. — Бібліогр.: 45 назв. — англ. 1027-3190 http://dspace.nbuv.gov.ua/handle/123456789/164188 517.5 + 517.43 en Український математичний журнал Інститут математики НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
topic Статті
Статті
spellingShingle Статті
Статті
Pivovarchik, V.N.
On spectra of a certain class of quadratic operator pencils with one-dimensional linear part
Український математичний журнал
description We consider a class of quadratic operator pencils that occur in many problems of physics. The part of such a pencil linear with respect to the spectral parameter describes the viscous friction in problems of small vibrations of strings and beams. Patterns in location of eigenvalues of such pencils are established. If the viscous friction (damping) is pointwise, then the operator in the linear part of the pencil is one-dimensional. For this case, rules in the location of the purely imaginary eigenvalues are found.
format Article
author Pivovarchik, V.N.
author_facet Pivovarchik, V.N.
author_sort Pivovarchik, V.N.
title On spectra of a certain class of quadratic operator pencils with one-dimensional linear part
title_short On spectra of a certain class of quadratic operator pencils with one-dimensional linear part
title_full On spectra of a certain class of quadratic operator pencils with one-dimensional linear part
title_fullStr On spectra of a certain class of quadratic operator pencils with one-dimensional linear part
title_full_unstemmed On spectra of a certain class of quadratic operator pencils with one-dimensional linear part
title_sort on spectra of a certain class of quadratic operator pencils with one-dimensional linear part
publisher Інститут математики НАН України
publishDate 2007
topic_facet Статті
url http://dspace.nbuv.gov.ua/handle/123456789/164188
citation_txt On spectra of a certain class of quadratic operator pencils with one-dimensional linear part / V.N. Pivovarchik // Український математичний журнал. — 2007. — Т. 59, № 5. — С. 702–716. — Бібліогр.: 45 назв. — англ.
series Український математичний журнал
work_keys_str_mv AT pivovarchikvn onspectraofacertainclassofquadraticoperatorpencilswithonedimensionallinearpart
first_indexed 2023-10-18T22:13:09Z
last_indexed 2023-10-18T22:13:09Z
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