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A note on the boundary of the Birkhoff-James ε-orthogonality sets
No full textThe Birkhoff-James -sets of vectors and vector-valued polynomials (in one complex variable) have recently been introduced as natural generalizations of the standard numerical range of (square) matrices or operators and matrix or operator polynomials, respectively. Corners on the boundary curves of these sets are of particular interest, not least because of their importance in visualizing these sets. In this paper, we provide a characterization for the corners of the Birkhoff-James -sets of vectors and vector-valued polynomials, completing and expanding upon previous exploration of the geometric propertiesof these sets. We also propose a randomized algorithm for approximating their boundaries
Spectral upper bound on the quantum -independence number of a graph
No full textA well known upper bound for the independence number of a graph , due to Cvetkovi ́c, is that \begin{equation*}\alpha(G) \le n^0 + \min\{n^+ , n^-\}\end{equation*}where is the inertia of . We prove that this bound is also an upper bound for the quantum independence number (G), where and for some graphs . We identify numerous graphs for which , thus increasing the number of graphs for which is known. We also demonstrate that there are graphs for which the above bound is not exact with any Hermitian weight matrix, for and . Finally, we show this result in the more general context of spectral bounds for the quantum -independence number, where the -independence number is the maximum size of a set of vertices at pairwise distance greater than
Strong cospectrality and twin vertices in weighted graphs
No full textWe explore algebraic and spectral properties of weighted graphs containing twin vertices that are useful in quantum state transfer. We extend the notion of adjacency strong cospectrality to Hermitian matrices, with focus on the generalized adjacency matrix and the generalized normalized adjacency matrix. We then determine necessary and sufficient conditions such that a pair of twin vertices in a weighted graph exhibits strong cospectrality with respect to the above-mentioned matrices. We also determine when strong cospectrality is preserved under Cartesian and direct products of graphs. Moreover, we generalize known results about equitable and almost equitable partitions and use these to determine which joins of the form , where is either the complete or empty graph, exhibit strong cospectrality
Missing Men? Precarity and Declining Labor Force Participation Among Working-Class Men
No full textRecent research has noted declining labor force participation among working class men in the United States, but with little attention to the mechanisms underlying such withdrawal. In this article—drawing on in-depth interviews with 61 working-class men from rural Pennsylvania—I address this gap in the literature by prodding respondents on the sequential character of their employment experiences, their perceived vulnerabilities, and the calculations they make in the contexts in which they live. Findings reveal fluctuations in their engagement with work, something I refer to as participation churn. However, respondents’ labor force narratives also show how they adapt to local employment conditions and personal circumstances, a phenomenon referred to as adaptive nonparticipation. The results highlight key mechanisms underlying labor force dropout and have implications for how declining labor force participation should be understood. These findings advance the sociological understanding of how workers—even in precarious positions—assert agency
‘Mister Speaker! I therefore have no claim’ – Agda Östlund’s Entrance in the Parliamentary Debate in March 1922 in a Historical and Rhetorical Perspective
No full textIn March 1922 the Social Democrat Agda Östlund (1870–1942) speaks as the first female member of Swedish Parliament in the Second Chamber due to her own proposal for the state to take responsibility for arranging suitable work for tuberculosis patients when they leave the sanatorium, so that they can complete their convalescence. It may seem that democracy was once and for all established when women were finally included in the Parliament. But that was not the case. The question is how Agda Östlund acts in a formative historical stage after the first democratic election, how she finds a speaking position and how her speech can be understood in relation to the negotiation of the meaning of women’s civil and democratic rights.
This article includes a contextualisation and a text analysis where I go into how the text relates to a rhetorical situation. I see Agda Östlund’s utterances as rhetorical in accordance with the theoretical perspectives established by Lloyd F. Bitzer where the key concepts are rhetorical situation, problem, restrictions and audience. Agda Östlund uses the mother role as a rhetorical strategy, connects the issue of tuberculosis to the home and everyday environment and nursing, which are traditionally female spheres, and highlights class injustice in the possibility of completing convalescence after sanitation. The mother role and the factual and low-key argumentation have two purposes in this speech – partly to adapt to the Parliament order, and partly to present the actual issue. The rhetorical strategy is about using the mother role as a persona to make the class perspective a matter of care, nursing and compassion.
Östlund’s entry into the Parliament debate can be described as a rhetorically fragile situation because she speaks for the very substance of her own motion while at the same time following the committee’s line, in which she herself is a part, and demands a rejection of it
Giunta, E. and Trasciatti, M., eds. (2022) Talking to the Girls: Intimate and Political Essays on the Triangle Shirtwaist Factory Fire. New Village Press.
No full textOn the eigenvalues of matrices with common Gershgorin regions
No full textThis paper is a study of the eigenvalues of a complex square matrix with one variable nondiagonal entry expressed in polar form. Changing the angle of the variable entry while leaving the radius fixed generates an algebraic curve; as does the process of fixing an angle and varying the radius. The authors refer to these two curves as eigenvalue orbits and eigenvalue trajectories, respectively. Eigenvalue orbits and trajectories are orthogonal families of curves, and eigenvalue orbits are sets of eigenvalues from matrices with identical Gershgorin regions. Algebraic and geometric properties of both types of curves are examined. Features such as poles, singularities, and foci are discussed