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Press, E. (2021). Dirty Work: Essential Jobs and the Hidden Toll of Inequality in America. Farrar, Straus, and Giroux
No full textThe American Poor and Working Class in Cross-National Comparison
No full textIn this paper the authors compare the American poor and working class with their counterparts around the world. They find that the earnings of the American working-class fare well in their analysis, while American poverty is closer to the middle of the pack
Banach spaces of GLT sequences and function spaces
No full textGeneralized locally Toeplitz (GLT) sequences of matrices originated from the spectral study of certain partial differential equations. To be more precise, such matrix sequences arise when we numerically approximate either partial differential equations or fractional differential equations using any discretization by local methods (finite differences, finite elements, finite volumes, isogeometric analysis, etc.). The study of the asymptotic spectral behavior of GLT sequences is important in analyzing the solution of the corresponding partial differential equations and in finding fast and efficient methods for the corresponding large linear systems. Approximating classes of sequences (a.c.s.) and spectral symbols are important notions connected to GLT sequences. Recently, G. Barbarino obtained some results regarding the theoretical aspects of such notions. He obtained the completeness of the space of matrix sequences with respect to pseudometric a.c.s. Also, he identified the space of GLT sequences with the space of measurable functions. In this article, we follow the same research line and obtain various connections between the subalgebras of matrix-sequence spaces and the subalgebras of function spaces. In some cases, these are identifications as Banach spaces and some of them are Banach algebra identifications. We also prove that the convergence notions in the sense of eigenvalue/singular value clustering are equivalent to the convergence with respect to the metrics introduced here. These convergence notions are related to the study of preconditioners in the case of matrix/operator sequences. As an application of our main results, we establish a Korovkin-type result in the setting of GLT sequences
On decompositions of matrices into products of commutators of involutions
No full textLet be a field and let be a natural number greater than . The aim of this paper is to prove that if contains at least three elements, then every matrix in the special linear group is a product of at most two commutators of involutions
An improved algorithm for solving an inverse eigenvalue problem for band matrices
No full textThe construction of matrices with prescribed eigenvalues is a kind of inverse eigenvalue problems. The authors proposed an algorithm for constructing band oscillatory matrices with prescribed eigenvalues based on the extended discrete hungry Toda equation (Numer. Algor. 75:1079--1101, 2017). In this paper, we develop a new algorithm for constructing band matrices with prescribed eigenvalues based on a generalization of the extended discrete hungry Toda equation. The new algorithm improves the previous algorithm so that the new one can produce more generic band matrices than the previous one in a certain sense. We compare the new algorithm with the previous one by numerical examples. Especially, we show an example of band oscillatory matrices which the new algorithm can produce but the previous one cannot
Stratifications of the ray space of a tropical quadratic form by Cauchy-Schwartz functions
No full textClasses of an equivalence relation on a module over a supertropical semiring, called rays, carry the underlying structure of 'supertropical trigonometry' and thereby a version of convex geometry which is compatible with quasilinearity. In this theory, the traditional Cauchy-Schwarz inequality is replaced by the CS-ratio, which gives rise to special characteristic functions, called CS-functions. These functions partite the ray space into convex sets and establish the main tool for analyzing varieties of quasilinear stars in . They provide stratifications of and, therefore, a finer convex analysis that helps better understand geometric properties
On the non-backtracking spectral radius of graphs
No full textGiven a graph with edges, the non-backtracking spectral radius of is the spectral radius of its non-backtracking matrix defined as the matrix where each edge is represented by two rows and two columns, one per orientation: and , and the entry of in row and column is given by , with being the Kronecker delta. A tight upper bound is given for the non-backtracking spectral radius in terms of the spectral radius of the adjacency matrix and minimum degree, and those connected graphs that maximize the non-backtracking spectral radius are determined if the connectivity (edge connectivity, bipartiteness, respectively) is given
A norm inequality for three matrices
No full textWe prove a Frobenius norm inequality for three matrices, analogous to the well-known Bottcher--Wenzel inequality. The situation is also similar: standard inequalities would yield an upper bound, which however can be reduced by means of further, detailed investigations
