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Volume 4 Issue 2: Editorial Special Issue: Social Haunting, Classed Affect, and the Afterlives of Deindustrialization
No full textTwisted Seams: A Gendered Social Haunting
No full textThe starting point for this article is the bitterly fought UK Miners' Strike of 1984-1985 in which women played a significant role. The concept of 'social haunting', as developed by Avery Gordon and applied in the Manchester Metropolitan University Social Haunting project, is used to suggest that the strike activism involved a mobilisation and confrontation with the 'ghosts' of the mining past that involved complex and interwoven experiences of class and gender relations of power. The discussion focuses upon what is normally unspoken and unwritten about the impact of living with coal mining on the inter-generational subjectivities of women from mining families. I argue that the strike raised the ghosts of the injustices of mining history but that its defeat subverted the process that had begun of dealing particularly with the ghosts of gender inequality. The experience of the strike now constitutes a further dimension to the complexity of this haunting. Taking inspiration from Gordon's efforts to transcend disciplinary boundaries, I use a variety of sources and approaches, including sociological and historical research, memoir and the participatory learning achieved in a voluntary arts organisation in the ex-mining town of Seaham, to address this gendered haunting from my own, female perspective, and seek ways of raising, and transcending the ghosts through conscious art practice in a local settin
Friedman, Sam, and Laurison, Daniel (2018) The Class Ceiling: Why It Pays to Be Privileged, Policy Press, Bristol, UK. Markovits, Daniel (2019) The Meritocracy Trap: How America’s Foundational Myth Feed Inequality, Dismantles the Middle Class, and Devours
No full textAbsolutely compatible pairs in a von Neumann algebra
No full textLet a, b be elements in a unital C∗-algebra with 0 ≤ a, b ≤ I. The element a is absolutely compatible with b if |a − b| + |I − a − b| = I. In this note, some technical characterizations of absolutely compatible pairs in an arbitrary von Neumann algebra are found. These characterizations are applied to measure how far are two absolute compatible positive elements in the closed unit ball from being mutually orthogonal or commuting. In the case of 2 by 2 matrices, the results admit a geometric interpretation. Namely, non-commutative matrices of the form a = ( t α ) and b = ( x β ) with x, t ∈ (0, 1)\{ 1 }, |α|2 < t(1 − t) α¯ 1 − t β 1 − x 2 and |β|2 < x(1 − x), are absolutely compatible if, and only if, the corresponding point b = (x, lRe(β), S'm(β)) in R3 lies in the ellipsoid Ea = {x ∈ R3 : d2(x, a) + d2(x, a,) = 1}, where d2 denotes the Euclidean distance in R3, and the elements a and a, are (t, lRe(α), S'm(α)) and (1 − t, −lRe(α), −S'm(α)), respectively. The description of absolutely compatible pairs of positive 2 by 2 matrices is applied to determine absolutely compatible pairs of positive elements in the closed unit ball of Mn
On the Block Structure and Frobenius Normal Form of Powers of Matrices
No full textThe Frobenius normal form of a matrix is an important tool in analyzing its properties. When a matrix is powered up, the Frobenius normal form of the original matrix and that of its powers need not be the same. In this article, conditions on a matrix and the power are provided so that for any invertible matrix , if is block upper triangular, then so is when partitioned conformably. The result is established for general matrices over any field. It is also observed that the contributions of the index of cyclicity to the spectral properties of a matrix hold over any field. The article concludes by applying the block upper triangular powers result to the cone Frobenius normal form of powers of a eventually cone nonnegative matrix
The sum of the first two largest signless Laplacian eigenvalues of trees and unicyclic graphs
No full textLet be a graph on vertices with edges. The sum of eigenvalues of graphs has been receiving a lot of attention these years. Let be the sum of the first two largest signless Laplacian eigenvalues of , and define . Oliveira et al. (2015) conjectured that with equality if and only if , where is the -vertex unicyclic graph obtained by attaching pendent vertices to a vertex of a triangle. In this paper, it is proved that S_2(G) < e(G) + 3 -\frac{2}{n} when is a tree, or a unicyclic graph whose unique cycle is not a triangle. As a consequence, it is deduced that the conjecture proposed by Oliveira et al. is true for trees and unicyclic graphs whose unique cycle is not a triangle
In-sphere property and reverse inequalities for matrix means
No full textThe in-sphere property for matrix means is studied. It is proved that the matrix power mean satisfies in-sphere property with respect to the Hilbert-Schmidt norm. A new characterization of the matrix arithmetic mean is provided. Some reverse AGM inequalities involving unitarily invariant norms and operator monotone functions are also obtained
Condensed Forms for Linear Port-Hamiltonian Descriptor Systems
No full textMotivated by the structure which arises in the port-Hamiltonian formulation of constraint dynamical systems, structure preserving condensed forms for skew-adjoint differential-algebraic equations (DAEs) are derived. Moreover, structure preserving condensed forms under constant rank assumptions for linear port-Hamiltonian differential-algebraic equations are developed. These condensed forms allow for the further analysis of the properties of port-Hamiltonian DAEs and to study, e.g., existence and uniqueness of solutions or to determine the index. It can be shown that under certain conditions for regular port-Hamiltonian DAEs the strangeness index is bounded by
Cone-constrained rational eigenvalue problems
No full textThis work deals with the eigenvalue analysis of a rational matrix-valued function subject to complementarity constraints induced by a polyhedral cone . The eigenvalue problem under consideration has the general structure where denotes the dual cone of . The unconstrained version of this problem has been discussed in [Y.F. Su and Z.J. Bai. Solving rational eigenvalue problems via linearization. \emph{SIAM J. Matrix Anal. Appl.}, 32:201--216, 2011.] with special emphasis on the implementation of linearization-based methods. The cone-constrained case can be handled by combining Su and Bai's linearization approach and the so-called facial reduction technique. In essence, this technique consists in solving one unconstrained rational eigenvalue problem for each face of the polyhedral cone
Generalization of real interval matrices to other fields
No full textAn interval matrix is a matrix whose entries are intervals in . This concept, which has been broadly studied, is generalized to other fields. Precisely, a rational interval matrix is defined to be a matrix whose entries are intervals in \Q. It is proved that a (real) interval matrix with the endpoints of all its entries in \Q contains a rank-one matrix if and only if it contains a rational rank-one matrix, and contains a matrix with rank smaller than if and only if it contains a rational matrix with rank smaller than ; from these results and from the analogous criterions for (real) inerval matrices, a criterion to see when a rational interval matrix contains a rank-one matrix and a criterion to see when it is full-rank, that is, all the matrices it contains are full-rank, are deduced immediately. Moreover, given a field and a matrix \al whose entries are subsets of , a criterion to find the maximal rank of a matrix contained in \al is described