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Generalized left and right Weyl spectra of upper triangular operator matrices
No full textIn this paper, for given operators A\in\B(\H) and B\in\B(\K), the sets of all C\in \B(\K,\H) such that M_C=\bmatrix{cc} A&C\\0&B\endbmatrix is generalized Weyl and generalized left (right) Weyl, are completely described. Furthermore, the following intersections and unions of the generalized left Weyl spectra \bigcup_{C\in\B(\K,\H)}\sigma^g_{lw}(M_C) \;\;\; \mbox{and} \;\;\; \bigcap_{C\in\B(\K,\H)}\sigma^g_{lw}(M_C) are also described, and necessary and sufficient conditions which two operators A\in\B(\H) and B\in\B(\K) have to satisfy in order for to be a generalized left Weyl operator for each C\in\B(\K,\H), are presented
The Enhanced Principal Rank Characteristic Sequence for Hermitian Matrices
No full textThe enhanced principal rank characteristic sequence (epr-sequence) of an n\x n matrix is a sequence , where each is , , or according as all, some, or none of its principal minors of order are nonzero. There has been substantial work on epr-sequences of symmetric matrices (especially real symmetric matrices) and real skew-symmetric matrices, and incidental remarks have been made about results extending (or not extending) to (complex) Hermitian matrices. A systematic study of epr-sequences of Hermitian matrices is undertaken; the differences with the case of symmetric matrices are quite striking. Various results are established regarding the attainability by Hermitian matrices of epr-sequences that contain two s with a gap in between. Hermitian adjacency matrices of mixed graphs that begin with are characterized. All attainable epr-sequences of Hermitian matrices of orders , , , and , are listed with justifications
Solutions of the system of operator equations via the *-order
No full textIn this paper, some necessary and sufficient conditions are established for the existence of solutions to the system of operator equations in the setting of bounded linear operators on a Hilbert space, where the unknown operator is called the inverse of along . After that, under some mild conditions, it is proved that an operator is a solution of if and only if , where the -order means . Moreover, the general solution of the equation above is obtained. Finally, some characterizations of via other operator equations, are presented
On the Location of Eigenvalues of Real Matrices
No full textThe research in this paper is motivated by a recent work of I. Barany and J. Solymosi [I. Barany and J. Solymosi. Gershgorin disks for multiple eigenvalues of non-negative matrices. Preprint arXiv no. 1609.07439, 2016.] about the location of eigenvalues of nonnegative matrices with geometric multiplicity higher than one. In particular, an answer to a question posed by Barany and Solymosi, about how the location of the eigenvalues can be improved in terms of their geometric multiplicities is obtained. New inclusion sets for the eigenvalues of a real square matrix, called Ger\v{s}gorin discs of the second type, are introduced. It is proved that under some conditions, an eigenvalue of a real matrix is in a Ger\v{s}gorin disc of the second type. Some relationships between the geometric multiplicities of eigenvalues and these new inclusion sets are established. Some other related results, consequences, and examples are presented. The results presented here apply not only to nonnegative matrices, but extend to all real matrices, and some of them do not depend on the geometric multiplicity
LIGHTS OUT! on Cartesian Products
No full textThe game LIGHTS OUT! is played on a 5 by 5 square grid of buttons; each button may be on or off. Pressing a button changes the on/o state of the light of the button pressed and of all its vertical and horizontal neighbors. Given an initial configuration of buttons that are on, the object of the game is to turn all the lights out. The game can be generalized to arbitrary graphs. In this paper, Cartesian Product graphs (that is, graphs of the form G\box H, where G and H are arbitrary finite, simple graphs) are investigated. In particular, conditions for which GH is universally solvable (every initial configuration of lights can be turned out by a finite sequence of button presses), using both closed neighborhood switching and open neighborhood switching, are provided
A modified NHPA Section 110 Class II inventory using LiDAR imagery to locate historic-era homesteads and irrigation features of the lower Gros Ventre River floodplain terrace and Ditch Creek alluvial fan within Grand Teton National Park, Teton County, WY
No full textGIS analysis of LiDAR imagery facilitated the completion of a modified NHPA Section 110 Class II survey and inventory. The identification and recordation of 58 new archaeological sites, 21 isolated finds, and 18 updated site records in the vicinity of the Mormon Row Historic District (MRHD; 48TE1444) has led to a recommendation that the landscape and the resources be collectively nominated and designated as a Rural Historic Landscape (RHL). The fieldwork was accomplished using a newly invented method called iterology that takes into account ideology, technology, historical ecology, and the archival/archaeological record in an iterative process (back and forth) across scales, dimensions, and intersections of cultural resources within a landscape in an effort to locate the object of Mormonideological desire in the archaeological record. One can locate the object of ideological desire in the archaeological record if certain assumptions are accepted and protocols followed. The result of the fieldwork and analysis is the location of the object as well as the production of a Doctoral dissertation outlining the methods and theory needed to arrive at the conclusions and results. The object is the Mormon Irrigation Pattern, first observed in LiDAR imagery at Mormon Row.
Featured photo by Tim Peterson on Unsplash. https://unsplash.com/photos/Ab6ksdu5Q7
From Betrayal to Resistance: Workingclass voices in Russia today
No full textThis article analyses three aspects of working-class life in Russia that add to the debate about global working-class responses to disenfranchisement and ‘crisis’. Firstly, it highlights how traditionally workers have been atomised as a group due to the demotivating effects of postcommunist transition itself. Nonetheless, there remains a coherence of shared values and grievances rooted in the still-living memory of the communist-era ‘social contract’, and workers’ current experience of harsh anti-labour industrial relations and state indifference. Thirdly, despite seemingly no outlet in oppositional politics, there are signs of resistance, if not revolt. These range from the informal ‘black’ economy as ‘exit’ from formal work, smallscale labour protests and the organising of new independent labour unions in transnational companies, and the rising political consciousness of working-class voters who look for any ‘alternative’ to the ruling party – including the popular-nationalist far right, and abstention from voting all together. The conclusions highlight the convergence of workers’ and ordinary people’s grievances in Russia in an unpredictable environment where multiple issues may coalesce and then spiral out of control. Recent examples of such issues have included labour unrest due to wage arrears, political corruption, road taxes on truckers, and the demolition of housing in city centres
Peralta, Dan-el Padilla (2015) Undocumented: A Dominican Boy’s Odyssey from a Homeless Shelter to the Ivy League, Penguin Books, New York, Ny. Vance, J.D. (2016) Hillbilly Elegy: A Memoir of a Family and Culture in Crisis, HarperCollins, New York, Ny.
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In Class, Sharing Class: Faculty Members from Low-Socioeconomic Status Backgrounds and Status Visibility
No full textLow-Socioeconomic status (low-SES) faculty members might be well-positioned to support lowSES students. However, research suggests that there are a number of hurdles to faculty members playing such a role. In this paper, we examine low-SES background faculty members’ selfdescribed levels of support for their low-SES students, including the likelihood and means of support, how they assess which students might need support, and their reservations about engaging in this work. We show that low-SES faculty members report supporting their low-SES students, most often through direct discussions of experiences that may be shared in common and drawing on their own memories of college experiences