Ninety years of k-tridiagonal matrices

2020 ◽  
Vol 57 (3) ◽  
pp. 298-311
Author(s):  
Carlos M. da Fonseca ◽  
Victor Kowalenko ◽  
László Losonczi
Keyword(s):  
Spectral Theory ◽  
Trigonometric Polynomials ◽  
Structured Matrices ◽  
Tridiagonal Matrices ◽  
Seminal Article

AbstractThis survey revisits Jenő Egerváry and Otto Szász’s article of 1928 on trigonometric polynomials and simple structured matrices focussing mainly on the latter topic. In particular, we concentrate on the spectral theory for the first type of the matrices introduced in the article, which are today referred to as k-tridiagonal matrices, and then discuss the explosion of interest in them over the last two decades, most of which could have benefitted from the seminal article, had it not been overlooked.

To the spectral theory of partially ordered sets

2018 ◽  
Vol 60 (3) ◽  
pp. 578-598
Author(s):  
Yu. L. Ershov ◽  
M. V. Schwidefsky
Keyword(s):  
Spectral Theory ◽  
Partially Ordered Sets ◽  
Ordered Sets ◽  
Partially Ordered

SPECTRAL THEORY OF 2-D PHOTONIC CRYSTALS: ANALYTICAL GROUNDS

2016 ◽  
Vol 75 (16) ◽  
pp. 1417-1433 ◽  
Author(s):  
Yurii Konstantinovich Sirenko ◽  
K. Yu. Sirenko ◽  
H. O. Sliusarenko ◽  
N. P. Yashina
Keyword(s):  
Photonic Crystals ◽  
Spectral Theory

Approximation of Unbounded Functions by Trigonometric Polynomials

2017 ◽  
Vol 13 (4) ◽  
pp. 106-116
Author(s):  
Alaa A. Auad ◽  
◽  
Mousa M. Khrajan
Keyword(s):  
Trigonometric Polynomials

Approximate Solution Of A Singular Integral Equation With A Multiplicative Cauchy Kernel In The Half-Plane

2008 ◽  
Vol 8 (2) ◽  
pp. 143-154 ◽  
Author(s):  
P. KARCZMAREK
Keyword(s):  
Integral Equation ◽  
Approximate Solution ◽  
Singular Integral Equation ◽  
Half Plane ◽  
Singular Integral ◽  
Trigonometric Polynomials ◽  
Cauchy Kernel

AbstractIn this paper, Jacobi and trigonometric polynomials are used to con-struct the approximate solution of a singular integral equation with multiplicative Cauchy kernel in the half-plane.

From Littoral to Ozone: On Mike Pearson’s Contributions to Indian Ocean History

2019 ◽  
Vol 2 (1) ◽  
pp. 12-24
Author(s):  
Edward A. Alpers
Keyword(s):  
New York ◽  
Indian Ocean ◽  
Great Circle ◽  
Historical Scholarship ◽  
The Indian Ocean ◽  
Seminal Article

In this article I examine two of Michael Pearson’s most important contributions to our understanding of Indian Ocean history: the concept of the littoral, which he first articulated in his seminal article on “Littoral society: the case for the coast” in The Great Circle 7, no. 1 (1985): 1-8, and his comment in The Indian Ocean (London and New York: Routledge, 2003, p. 9) that “I want it to have a whiff of ozone.” Accordingly, I review Pearson’s publications to see how he has written about these two notions and how they have influenced historical scholarship about the Indian Ocean.

Duality beyondPersons and Groups

2020 ◽  
pp. 391-413
Author(s):  
Sophie Mützel ◽  
Ronald Breiger
Keyword(s):  
Social Network ◽  
Social Network Analysis ◽  
Network Analysis ◽  
Network Data ◽  
Future Directions ◽  
Affiliation Networks ◽  
The Social ◽  
Recent Developments ◽  
Principle Of Duality ◽  
Seminal Article

This chapter focuses on the general principle of duality, which was originally introduced by Simmel as the intersection of social circles. In a seminal article, Breiger formalized Simmel’s idea, showing how two-mode types of network data can be transformed into one-mode networks. This formal translation proved to be fundamental for social network analysis, which no longer needed data on who interacted with whom but could work with other types of data. In turn, it also proved fundamental for the analysis of how the social is structured in general, as many relations are dual (e.g. persons and groups, authors and articles, organizations and practices), and are thus susceptible to an analysis according to duality principles. The chapter locates the concept of duality within past and present sociology. It also discusses the use of duality in the analysis of culture as well as in affiliation networks. It closes with recent developments and future directions.

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