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The triangle graph is not SPN
No full textA real symmetric matrix is copositive if for every nonnegative vector . A matrix is SPN if it is a sum of a real positive semidefinite matrix and a nonnegative matrix. Every SPN matrix is copositive, but the converse does not hold for matrices of order greater than . A graph is an SPN graph if every copositive matrix whose graph is is SPN. We show that the triangle graph is not SPN
Spectral analysis of saddle-point matrices from optimization problems with elliptic PDE constraints
No full textThe main focus of this paper is the characterization and exploitation of the asymptotic spectrum of the saddle--point matrix sequences arising from the discretization of optimization problems constrained by elliptic partial differential equations. They uncover the existence of an hidden structure in these matrix sequences, namely, they show that these are indeed an example of Generalized Locally Toeplitz (GLT) sequences. They show that this enables a sharper characterization of the spectral properties of such sequences than the one that is available by using only the fact that they deal with saddle--point matrices. Finally, they exploit it to propose an optimal preconditioner strategy for the GMRES, and Flexible--GMRES methods
Class, Crime, and Cannibalism in The String of Pearls; or, The Demon Barber as Bourgeois Bogeyman
No full textAlthough the tale of Sweeney Todd is one with significant cultural resonance, little has been written about the text itself, The String of Pearls. This article argues that the text engages with anxieties about class conflict through a narrative that enacts exaggerated versions of various interactions. In the nineteenth century, critics objected to the cheap fiction pejoratively known as penny dreadfuls, asserting that the genre’s exciting tales of bloodshed, villainy, and mayhem would seduce readers to lives of debauchery and crime, but I argue that this concern about cheap fiction was not for the preservation of the souls of the poor and working classes but rather for the preservation of the middle classes' own corporeal bodies and the system that privileged and protected them. While there is no question that the narrative enacts extreme manifestations of problems facing the urban poor—among them, contaminated or even poisonous foodstuffs and the perils of urban anonymity—it also features an intractable and rapacious lower class and a subversion of the master-servant dynamic on which the comforts of the middle class were constructed, and so, in addition to adventure, detection, and young love, The String of Pearls offers a dark revenge fantasy of class-based violence that the middle-class critics of the penny dreadful were perhaps justified in fearing. tl;dr: Eat the Rich
Nationalizing Realism in Dermot Bolger’s The Journey Home
No full textDermot Bolger’s third novel, The Journey Home, emerged in 1990 in the author’s home country of the Republic of Ireland, yet took 18 years to be republished in the United States in 2008. The novel’s graphic depiction of an array of abuses, including sexual, physical, political, and economic, not only illustrated the author’s intention to shock the reading public regarding the government’s conscious disregard for these struggles, but its publication also elucidated the aftereffects of exposing the differences between experiences with abuse and the ways in which both national and socio-economic processes mediate their interpretations. In this paper, I will argue that Bolger’s illustration of corruption and abuse does not only display a contrast between the public and those who represent their image, but also how socioeconomic paradigms are used to mediate perceptions of what constitutes ‘reality’
Confronting COVID-19 in ‘Social Class in America’: Research and Reflections by Working-Class Student-Scholars
No full textSilva, Jennifer (2019) We’re Still Here: Pain and Politics in the Heart of America, Oxford University Press, Oxford, UK.
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The Multiplicity of -eigenvalues of Graphs
No full textFor a graph and real number , the -matrix of is defined as where is the adjacency matrix of and is the diagonal matrix of the vertex degrees of . In this paper, the largest multiplicity of the -eigenvalues of a broom tree is considered, and all graphs with an -eigenvalue of multiplicity at least are characterized
Structure-preserving Diagonalization of Matrices in Indefinite Inner Product Spaces
No full textIn this work, some results on the structure-preserving diagonalization of selfadjoint and skewadjoint matrices in indefinite inner product spaces are presented. In particular, necessary and sufficient conditions on the symplectic diagonalizability of (skew)-Hamiltonian matrices and the perplectic diagonalizability of per(skew)-Hermitian matrices are provided. Assuming the structured matrix at hand is additionally normal, it is shown that any symplectic or perplectic diagonalization can always be constructed to be unitary. As a consequence of this fact, the existence of a unitary, structure-preserving diagonalization is equivalent to the existence of a specially structured additive decomposition of such matrices. The implications of this decomposition are illustrated by several examples
Mentoring for Faculty from Working-Class Backgrounds
No full textFaculty mentoring across gender, race, and culture is facilitated by formal mentoring programs. Mentoring across the cultural differences associated with social class, however, represents a largely unaddressed gap in the provision of formal faculty mentoring. Based on a pre-program needs survey, we designed and delivered a pilot program that served working-class faculty with mentoring on career self-efficacy. Assessment showed that working-class faculty mentees made gains in this important construct. Our concluding discussion reflects upon the role of mentoring in the experience of working-class faculty