scholarly journals Orthogonal similarity transformation of a symmetric matrix into a diagonal-plus-semiseparable one with free choice of the diagonal

2005 ◽  
Vol 102 (4) ◽  
pp. 709-726 ◽  
Author(s):  
Raf Vandebril ◽  
Ellen Van Camp ◽  
Marc Van Barel ◽  
Nicola Mastronardi
2020 ◽  
Vol 128 (11) ◽  
pp. 1614
Author(s):  
В.А. Кузьмицкий

Based on algebraic methods, we have found an accurate solution for the inverse task for the vibronic analogue of the complex Fermi resonance, i.e. the determination from the spectral data (energies Ek and transition intensities Ik of the observed conglomerate of lines, k = 1, 2, ..., n; n > 2) energies of the «dark» states Am and the matrix elements of their coupling Bm with the «bright» state. The algorithm consists of two stages. At the first stage, the Jacobi plane rotations are used to construct an orthogonal similarity transformation matrix X, for which the elements of the first row obey the requirement (X1k)^2 = Ik, which corresponds to that fact that there is only one non-perturbed «bright» state. At the second stage, the quantities Am and Bm are obtained after solving the eigenvalue problem for block of «dark» states of the matrix Xdiag({Ek})X-1.


2001 ◽  
Vol 11 (08) ◽  
pp. 2277-2285 ◽  
Author(s):  
M. J. FRIEDMAN

The Continuation of Invariant Subspaces (CIS) algorithm [Demmel et al., 2001; Dieci & Friedman, 2001] produces a smooth orthogonal similarity transformation to block triangular form of a parameter dependent matrix A(s). The CIS algorithm is an adaptation of an iterative refinement technique for improving the accuracy of computed invariant subspaces. On the basis of the CIS algorithm, new test functions are defined for an improved, more reliable detection of bifurcations in problems with simple bifurcations near multiple bifurcations, problems with multiple bifurcations, and problems with symmetries. Illustrative examples are given.


Author(s):  
Glen E. Bodner ◽  
Rehman Mulji

Left/right “fixed” responses to arrow targets are influenced by whether a masked arrow prime is congruent or incongruent with the required target response. Left/right “free-choice” responses on trials with ambiguous targets that are mixed among fixed trials are also influenced by masked arrow primes. We show that the magnitude of masked priming of both fixed and free-choice responses is greater when the proportion of fixed trials with congruent primes is .8 rather than .2. Unconscious manipulation of context can thus influence both fixed and free choices. Sequential trial analyses revealed that these effects of the overall prime context on fixed and free-choice priming can be modulated by the local context (i.e., the nature of the previous trial). Our results support accounts of masked priming that posit a memory-recruitment, activation, or decision process that is sensitive to aspects of both the local and global context.


Author(s):  
А.В. Мацук

В статье исследуются события бескоролевья 1733 г. в Речи Посполитой. Согласно «трактату Левенвольде» компромиссным кандидатом на избрание монархом Речи Посполитой был португальский инфант дон Мануэль, которого предложила Австрия. Россия больше склонялась к кандидатуре «пяста». Россия оказалась не подготовленной к началу бескоролевья. Бывшие российские союзники магнаты ВКЛ рассорились с российским послом Фридрихом Казимиром Левенвольде и перешли на сторону Франции. В конце февраля 1733 г. в ВКЛ направили Юрия Ливена, который от имени российской царицы предложил поддержку в получении короны Михаилу Вишневецкому и Павлу Сангушке. Принятое на конвокационном сейме решение об избрании королем «пяста» и католика показало популярность Станислава Лещинского. В результате вслед за Австрией Россия поддержала кандидатом на корону Фридриха Августа. Магнаты ВКЛ до последнего оставались конкурентами о короне. Оппозиция Лещинскому объединилась под лозунгом защиты «вольного выбора» и поэтому в ней остались кандидаты «пясты», которые не могли уступить друг другу, и согласились на компромисс – кандидатуру Фридриха Августа. Для противодействия возможному избранию Лещинского Россия создала в ВКЛ новоградскую конфедерацию. Ее организатором стал новоградский воевода Николай Фаустин Радзивилл. Эта конфедерация становится основой Генеральной Варшавской конфедерации, которая 5 октября 1733 г. избирает королем саксонского курфюрста. The article examines the events of the «kingless» year of 1733 in the Polish-Lithuanian Commonwealth. According to the Levenwolde Treaties the compromise candidate for the Commonwealth’s throne was the Portuguese Infante Don Manuel, who’s candidacy was proposed by Austria. Russia, in turn, leaned towards the «pyasta» candidate. The Russian Empire was clearly unprepared for the start of the kingless period. Russia’s former allies – magnates of the Grand Duchy of Lithuania – came into conflict with the Russian ambassador Frederick Kazimir Levenwolde and sided with France. In late February of 1733, Empress Anna Ioanovna of Russia sent Yuri Liven to the Grand Duchy of Lithuania, who offered official support in the struggle for the crown to Mikhail Vishnevetsky and Pavel Sangushka. The electoral decision made at the Sejm proved the popularity of the «pyast» and Catholic candidates, specifically – Stanislaus Leschinsky. In turn, Russia – following Austria – showed its support for the candidacy of Frederick August. The magnates of the Grand Duchy of Lithuania remained in opposition in the crown issue until the very last. Opposition to Leschinsky was united under the motto of «free choice». For that reason, it was comprised of «pyasta» candidates, who were in a deadlock with one another, and were now ready for the compromise candidacy of Frederick Augustus. In order to counter the possible election of Leschinsky, Russia created the Novograd Confederation in the Grand Duchy of Lithuania. It was organized by the Novograd Voevoda Faustin Radzivill. This confederation became the core of the General Warsaw Confederation that – on October 5th 1733 – elected the Saxon King to the throne of the Polish-Lithuanian Commonwealth.


Sign in / Sign up

Export Citation Format

Share Document