A Matroid Generalization of a Result on Row-Latin Rectangles

Let A be an m \times n matrix in which the entries of each row are all distinct. Drisko showed that, if m \ge 2n-1, then A has a transversal: a set of n distinct entries with no two in the same row or column. We generalize this to matrices with entries in a matroid. For such a matrix A, we show that if each row of A forms an independent set, then we can require the transversal to be independent as well. We determine the complexity of an algorithm based on the proof of this result. Lastly, we observe that m \ge 2n-1 appears to force the existence of not merely one but many transversals. We discuss a number of conjectures related to this observation (some of which involve matroids and some of which do not).Comment: 9 pages, 5 figure

Dynamical energy analysis on mesh grids: a new tool for describing the vibro-acoustic response of complex mechanical structures

We present a new approach for modelling noise and vibration in complex mechanical structures in the mid-to-high frequency regime. It is based on a dynamical energy analysis (DEA) formulation which extends standard techniques such as statistical energy analysis (SEA) towards non-diffusive wave fields. DEA takes into account the full directionality of the wave field and makes sub-structuring obsolete. It can thus be implemented on mesh grids commonly used, for example, in the finite element method (FEM). The resulting mesh based formulation of DEA can be implemented very efficiently using discrete flow mapping (DFM) as detailed in [1] and described here for applications in vibro-acoustics

Explorations in knowing: thinking psychosocially about legitimacy

This article has been made available through the Brunel Open Access Publishing Fund.In this paper, we look at what engaging with psychoanalysis, through psychosocial accounts of subjectivity, has contributed to our struggles for legitimacy and security within our ways of knowing. The psychosocial, with its insistence on the unconscious and the irrational, features as both a source of security and of insecurity. We use three examples drawn from our own empirical research to explore the entanglement of the researcher with the researched and how this can offer a re-imagined sense of legitimacy for our work. In elaborating our argument, we discuss our experiences of 'being captured' by data and participants, and of negotiating the ethics of analysing participants' accounts. © 2014 The Author(s). Published by Pedagogy, Culture & Society

The vector algebra war: a historical perspective

There are a wide variety of different vector formalisms currently utilized in engineering and physics. For example, Gibbs' three-vectors, Minkowski four-vectors, complex spinors in quantum mechanics, quaternions used to describe rigid body rotations and vectors defined in Clifford geometric algebra. With such a range of vector formalisms in use, it thus appears that there is as yet no general agreement on a vector formalism suitable for science as a whole. This is surprising, in that, one of the primary goals of nineteenth century science was to suitably describe vectors in three-dimensional space. This situation has also had the unfortunate consequence of fragmenting knowledge across many disciplines, and requiring a significant amount of time and effort in learning the various formalisms. We thus historically review the development of our various vector systems and conclude that Clifford's multivectors best fulfills the goal of describing vectorial quantities in three dimensions and providing a unified vector system for science.Comment: 8 pages, 1 figure, 1 tabl

Optimum Utilization of Alfalfa in Sheep Rations

The unique qualities of alfalfa as a forage afford the progressive sheep producer many opportunities to develop efficient sheep feeding programs. As a grazed sward, as hay or silage, alfalfa can be utilized in a variety of ways. The following points should be considered in developing programs using alfalfa

A history of public education in the City of Sacramento : with special emphasis upon the administration of Charles C. Hughes beginning in 1913

The influx of people into Sacramento during the days of the Gold Rush brought many problems to the citizens of this new community. One problem that manifested itself early was that of educating the children of the pioneer population