University of Wyoming Open Journals
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Rethinking Class and Contemporary Working-Class Studies
No full textThe field of working class studies is forming in the context of dramatic changes in the labor process and crises in capitalist economies. Workers have historically been slow to adjust to such changes with new organizing strategies. As we seek our bearings among the changes in order to develop the field in ways that enhance the organizational and intellectual capacity of working people, we should hold onto a key point of continuity: whatever the new labor processes or changes in the economy, the working class continues to exist in capitalist societies, within capitalist class dynamics, in which the organization of production underlies material, cultural, and political experience. Race and class continue to be mutually determined. While each is distinct, neither can be properly understood or challenged in isolation from the other
On the Principal Permanent Rank Characteristic Sequences of Graphs and Digraphs
No full textThe principal permanent rank characteristic sequence is a binary sequence r_0 r_1 · · · r_n, where r_k = 1 if there exists a principal square submatrix of size k with nonzero permanent and r_k = 0 otherwise, and r_0 = 1 if there is a zero diagonal entry. A characterization is provided for all principal permanent rank sequences obtainable by the family of nonnegative matrices as well as the family of nonnegative symmetric matrices. Constructions for all realizable sequences are provided. Results for skew-symmetric matrices are also included
On the Matrix Square Root via Geometric Optimization
No full textThis paper is triggered by the preprint [P. Jain, C. Jin, S.M. Kakade, and P. Netrapalli. Computing matrix squareroot via non convex local search. Preprint, arXiv:1507.05854, 2015.], which analyzes gradient-descent for computing the square root of a positive definite matrix. Contrary to claims of Jain et al., the authorâs experiments reveal that Newton-like methods compute matrix square roots rapidly and reliably, even for highly ill-conditioned matrices and without requiring com-mutativity. The author observes that gradient-descent converges very slowly primarily due to tiny step-sizes and ill-conditioning. The paper derives an alternative first-order method based on geodesic convexity; this method admits a transparent convergence analysis (< 1 page), attains linear rate, and displays reliable convergence even for rank deficient problems. Though superior to gradient-descent, ultimately this method is also outperformed by a well-known scaled Newton method. Nevertheless, the primary value of the paper is conceptual: it shows that for deriving gradient based methods for the matrix square root, the manifold geometric view of positive definite matrices can be much more advantageous than the Euclidean view
On the matrix equations U_iXV_j W_{i j} for 1 \leq i; j \leq k with i +j \leq k
No full textConditions for the existence of a common solution X for the linear matrix equations U_iXV_j ô° W_{ij} for 1 \leq ô° i,j \leq ô° k with i\leq ô° j \leq ô° k, where the given matrices U_i,V_j,W_{ij} and the unknown matrix X have suitable dimensions, are derived. Verifiable necessary and sufficient solvability conditions, stated directly in terms of the given matrices and not using Kronecker products, are also presented. As an application, a version of the almost triangular decoupling problem is studied, and conditions for its solvability in transfer matrix and state space terms are presented
Spatial patterns and sources of atmospheric nitrogen deposition in the Greater Yellowstone Ecosystem, Wyoming determined from lichens
No full textIncreased anthropogenic nitrogen (N) deposition can lead to N saturation of ecosystems, altering water quality, biogeochemical cycling and biodiversity. Although some N deposition (Ndep) is natural, there has been an increase of Ndep in the Greater Yellowstone Ecosystem (GYE), largely due to local and regional intensification of agricultural activity, which releases ammonia (NHx), and transportation and industrial processes, which release nitrogen oxides (NOx). The climate, topography, and sources of Ndep in the region likely create heterogeneous patterns of Ndep in the GYE, where nutrient-limited alpine ecosystems are especially susceptible to Ndep. Epiphytic lichens obtain their nutrients from the air and record local scale patterns of Ndep. We collected 162 lichen samples (Usnea lapponica and Letharia vulpina) and analyzed them for %N and δ15N at 15 sites in the GYE to understand patterns and sources of Ndep in the GYE at small spatial scales. We found that lichen \%N was higher closer to the Snake River Plains and at higher elevations, which indicates higher deposition at those sites. This is likely because N is more likely to be deposited closer to major sources and because N is often deposited in precipitation so deposition patterns follow precipitation patterns. Additionally, the mean δ15N value was -11.8 ± 3.2‰, which suggests an agricultural source of Ndep, but δ15N values increased with higher %N, which indicated sites with high deposition were receiving more N from combustion sources. However, the large amount of variation in lichens collected at a single site suggest that future work needs to address how microhabitat factors influence lichen N incorporation.
Featured photo by Kathryn Robertson, taken from the AMK Ranch photo collection
Right gut-majorization on M_{n,m}
No full textLet M_{n,m} be the set of all n-by-m matrices with entries from R, and suppose that R^n is the set of all 1-by-n real row vectors. A matrix R is called generalized row stochastic (g-row stochastic) if the sum of entries on every row of R is 1. For X, Y â M_{n,m}, it is said that X is rgut-majorized by Y (denoted by X âº_{rgut} Y ) if there exists an m-by-m upper triangular g-row stochastic matrix R such that X = Y R. In this paper, the concept right upper triangular generalized row stochastic majorization, or rgut- majorization, is investigated and then the linear preservers and strong linear preservers of this concept are characterized on R^n and M_{n,m}
Characterizations of linear mappings through zero products or zero Jordan products
No full textLet be a unital algebra and be a unital -bimodule. A characterization of generalized derivations and generalized Jordan derivations from into , through zero products or zero Jordan products, is given. Suppose that is a unital left -module. It is investigated when a linear mapping from into is a Jordan left derivation under certain conditions. It is also studied whether an algebra with a nontrivial idempotent is zero Jordan product determined, and Jordan homomorphisms, Lie homomorphisms and Lie derivations on zero Jordan product determined algebras are characterized
Norm Retrievable Frames in
No full textâThis paper is concerned with the norm retrievable frames in â. âWe present some equivalent conditions to the norm retrievable frames in â. âWe will also show that the property of norm retrievability is stable under enough small perturbation of the frame set only for phase retrievable framesâ
A new error bound for linear complementarity problems for B-matrices
No full textA new error bound for the linear complementarity problem is given when the involved matrix is a -matrix. It is shown that this bound improves the corresponding result in [M. Garc\'{i}a-Esnaola and J.M. Pe\~{n}a. Error bounds for linear complementarity problems for -matrices. {\em Appl. Math. Lett.}, 22:1071--1075, 2009.] in some cases, and that it is sharper than that in [C.Q. Li and Y.T. Li. Note on error bounds for linear complementarity problems for -matrices. {\em Appl. Math. Lett.}, 57:108--113, 2016.]
Preservers of term ranks and star cover numbers of symmetric matrices
No full textLet denote the set of symmetric matrices over some semiring, \s. A line of is a row or a column of . A star of is the submatrix of consisting of a row and the corresponding column of . The term rank of is the minimum number of lines that contain all the nonzero entries of . The star cover number is the minimum number of stars that contain all the nonzero entries of . This paper investigates linear operators that preserve sets of symmetric matrices of specified term rank and sets of symmetric matrices of specific star cover numbers. Several equivalences to the condition that preserves the term rank of any matrix are given along with characterizations of a couple of types of linear operators that preserve certain sets of matrices defined by the star cover number that do not preserve all term ranks