On the Cardinality of Positively Linearly Independent Sets

Positive bases, which play a key role in understanding derivative free optimization methods that use a direct search framework, are positive spanning sets that are positively linearly independent. The cardinality of a positive basis in $\R^n$ has been established to be between $n+1$ and $2n$ (with both extremes existing). The lower bound is immediate from being a positive spanning set, while the upper bound uses {\em both} positive spanning and positively linearly independent. In this note, we provide details proving that a positively linearly independent set in $\R^n$ for $n \in \{1, 2\}$ has at most $2n$ elements, but a positively linearly independent set in $\R^n$ for $n\geq 3$ can have an arbitrary number of elements

The crystal structure of thiourea nitrate

The structure of thiourea nitrate has been determined by three-dimensional X-ray methods. Both Cu Ke and Mo K~ data were obtained with a single-crystal diffractometer and the final R values are 4.9% and 5.5% respectively. The space group is P211m and there are two molecules in the unit cell. All atoms, including hydrogen, lie on mirror planes. The whole structure is built up of layers of atoms, the atoms within each layer being linked by a network of hydrogen bonds

Berryogenesis: self-induced Berry flux and spontaneous non-equilibrium magnetism

Spontaneous symmetry breaking is central to the description of interacting phases of matter. Here we reveal a new mechanism through which a driven interacting system subject to a time-reversal symmetric driving field can spontaneously magnetize. We show that the strong internal ac fields of a metal driven close to its plasmon resonance may enable Berryogenesis: the spontaneous generation of a self-induced Bloch band Berry flux. The self-induced Berry flux supports and is sustained by a circulating plasmonic motion, which may arise even for a linearly polarized driving field. This non-equilibrium phase transition occurs above a critical driving amplitude, and may be of either continuous or discontinuous type. Berryogenesis relies on feedback due to interband coherences induced by internal fields, and may readily occur in a wide variety of multiband systems. We anticipate that graphene devices, in particular, provide a natural platform to achieve Berryogenesis and plasmon-mediated spontaneous non-equilibrium magnetization in present-day devices

Education, Job Search and Re-employment Outcomes among the Unemployed

This study assesses the effects of education on both job search intensity and re-employment success for unemployed workers. Given that the positive correlation between education and job search intensity or re-employment success is likely to be confounded by the endogeneity of education, we make use of data on compulsory schooling laws to create instrumental variables to assess the causal effects of education. Based on data from the Labour Force Survey and the Canadian Census, we find that education both significantly increases job search intensity and significantly improves re-employment success for the unemployed. The evidence on job search intensity provides insights into one potential mechanism through which education may increase the probability of re-employment following unemployment.education, adaptability, unemployment, job search, causal effects, compulsory schooling laws

The Role of Education in Technology Use and Adoption: Evidence from the Canadian Workplace and Employee Survey

Adoption of innovations by firms and workers is an important part of the process of technological change. Many prior studies find that highly educated workers tend to adopt new technologies faster than those with less education. Such positive correlations between the level of education and the rate of technology adoption, however, do not necessarily reflect the true causal effect of education on technology adoption. Relying on data from the Workplace and Employee Survey, this study assesses the causal effects of education on technology use and adoption by using instrumental variables for schooling derived from Canadian compulsory school attendance laws. We find that education increases the probability of using computers in the job and that employees with more education have longer work experiences in using computers than those with less education. However, education does not influence the use of computer-controlled and computer-assisted devices or other technological devices such as cash registers and sales terminals. Our estimates are consistent with the view that formal education increases the use of technologies that require or enable workers to carry out higher order tasks, but not those that routinize workplace tasks.technology use and adoption, education, causal effects, compulsory schooling laws, heterogeneity in technology