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Characterization of the Response Maps of Alternating-Current Networks
No full textIn an alternating-current network, each edge has a complex conductance with positive real part. The response map is the linear map from the vector of voltages at a subset of boundary nodes to the vector of currents flowing into the network through these nodes. In this paper, it is proved that the known necessary conditions for a linear map to be a response map are sufficient, and we show how to construct an appropriate network for a given response map
Using Markov Chains to Determine Expected Propagation Time for Probabilistic Zero Forcing
No full textZero forcing is a coloring game played on a graph where each vertex is initially colored blue or white and the goal is to color all the vertices blue by repeated use of a (deterministic) color change rule starting with as few blue vertices as possible. Probabilistic zero forcing yields a discrete dynamical system governed by a Markov chain. Since in a connected graph any one vertex can eventually color the entire graph blue using probabilistic zero forcing, the expected time to do this is studied. Given a Markov transition matrix for a probabilistic zero forcing process, an exact formula is established for expected propagation time. Markov chains are applied to determine bounds on expected propagation time for various families of graphs
Symmetry of cyclic weighted shift matrices with pivot-reversible weights
No full textIt is proved that every cyclic weighted shift matrix with pivot-reversible weights is unitarily similar to a complex symmetric matrix
A Note on Parallel Distinguishability of two Quantum Operations
No full textIn this work, the authors consider a homogeneous system of linear equations of the form arising from the distinguishability of two quantum operations by uses in parallel, where the coefficient matrix depends on a real parameter . It was conjectured by Duan et al. that the system has a non-trivial nonnegative solution if and only if lies in a certain interval depending on . The authors affirm the necessity part of the conjecture and establish the sufficiency of the conjecture for by presenting explicit non-trivial nonnegative solutions for the linear system
Zero-nonzero Patterns that Allow or Require an Inertia Set Related to Dynamical Systems
No full textThe inertia of an real matrix , denoted by , is the ordered triple , , in which , and are the numbers of its eigenvalues (counting multiplicities) with positive, negative and zero real parts, respectively. The inertia of an zero-nonzero pattern is the set . For , let
An zero-nonzero pattern allows if and requires if . In this paper, it is shown that there are no zero-nonzero patterns for order that require . Also, a complete characterization of zero-nonzero star patterns of order that allow is given
Post-Industrial Industrial Gemeinschaft: Northern Brexit and the Future Possible
No full textThe high vote for Brexit in England’s former industrial areas is often, reflecting historic classbased stereotypes, presented as a result of the incapacity of the working class to act in its own interests. Based on ethnographic research in a former milling town and a former mining town in northern England, this article articulates a logic for Brexit that cross-cuts ideological divisions within the working class. We highlight the affective afterlives of industry and, drawing on the classical sociology of Ferdinand Tönnies, argue that places such as these are characterised by a post-industrial industrial gemeinschaft whose centrepiece is industrial work, and which is reinforced in the very absence of that industrial work. In turn, we argue, the popularity of Brexit relates significantly to that political project's potential, whether real or illusory, to offer a future of work, and industrial work in particular
Are We All ‘BBC Dad’ Now? What Covid19 Restrictions Reveal About Comedy, Class, Paid Work, Parenting and Gender
No full textThe meme ‘BBC Dad’ first emerged in 2017 in response to an ‘embarrassing’ moment where a Professor was interrupted by his family during a live interview with BBC news TV. At the time the incident was circulated around the world as a curiosity, as the worlds of work, domestic (family) life and gender politics combined in a way that was apparently so unacceptable that it was comedic. The expectation was that the ‘victim’, the Professor, should somehow be ashamed of how his two roles as ‘professional’ and ‘parent’ had been shown to be in competition in that moment. Although this competition is often played out, especially by women and working-class workers, it is rarely shown in public, let alone discussed. However, during the global pandemic in 2020 many workers and parents are being placed in this situation and forced to juggle their dual responsibilities often in the same space and in real time. By asking ‘Are we all ‘BBC Dad’ now?’, this article questions how we consider those who conduct paid work and parent simultaneously, noting how previously accepted class and gender divides have shifted culturally as a result of the physical restraints posed by COVID-19 restrictions. The ’comedy’ that the original meme provided, and the way its meaning has shifted, shows how expectations have changed and hopefully how attitudes to normally hidden workers may also shift
Two Review Essays: Anti-Union Clichés float On the Waterfront: Rhetorical Analysis of the Film Citizen Kane and How Green was My Valley: Have We Sold Ourselves Short?
No full textSmarsh, S. (2020) She Come By it Natural: Dolly Parton and the Women Who Lived Her Songs. Simon and Schuster.
No full textTree Cover Number and Maximum Semidefinite Nullity of Some Graph Classes
No full textLet be a graph with a vertex set and an edge set consisting of unordered pairs of vertices. The tree cover number of , denoted , is the minimum number of vertex disjoint simple trees occurring as induced subgraphs of that cover all the vertices of . In this paper, the tree cover number of a line graph is shown to be equal to the path number of . Also, the tree cover numbers of shadow graphs, corona and Cartesian product of two graphs are found.
The graph parameter is related to another graph parameter , called the maximum semidefinite nullity of . Suppose denotes the collection of positive semidefinite real symmetric matrices associated with a given graph . Then is the maximum nullity among all matrices in . It has been conjectured that . The conjecture is shown to be true for graph classes considered in this work