The eight Cayley-Dickson doubling product

The purpose of this paper is to identify all eight of the basic Cayley-Dickson doubling products. A Cayley-Dickson algebra \cda{N+1} of dimension $2^{N+1}$ consists of all ordered pairs of elements of a Cayley-Dickson algebra \cda{N} of dimension $2^N$ where the product $(a,b)(c,d)$ of elements of \cda{N+1} is defined in terms of a pair of second degree binomials $\left(f(a,b,c,d),g(a,b,c,d)\right)$ satisfying certain properties. The polynomial pair$(f,g)$ is called a `doubling product.' While \cda{0} may denote any ring, here it is taken to be the set $\mathbb{R}$ of real numbers. The binomials $f$ and $g$ should be devised such that \cda{1}=\mathbb{C} the complex numbers, \cda{2}=\mathbb{H} the quaternions, and \cda{3}=\mathbb{O} the octonions. Historically, various researchers have used different yet equivalent doubling products.Comment: 32 candidates for alternate Cayley-Dickson doubling products are winnowed down to 8 products. Author now finds that 4 of those 8 should also be discarded: each allows zero divisors at the eight dimensional stage. The 4 remaining products are denoted in the paper as P0,P3(the standard doubling product),P4,P7. Those four produce algebras isomorphic to the standard Cayley-Dickson algebra

Slavery and its definition

Had the abolitionists of the past, the likes of Abraham Lincoln or William Wilberforce, been able to see into the twenty-first century, what might have struck them as very strange was that while they had come far in ending slavery and suppressing human exploitation, they seemed to have lost sight of what the term "slavery" means. This, despite the fact that for more than eighty-five years there has been a consensus in international law as to the legal definition of slavery. In the case of slavery the element of possession is fundamental. It allows people to drain the swamp and leave the definitional quagmire which has marginalised the legal definition of slavery. With the legal definition of slavery marginalised, people looked elsewhere to define slavery. A survey of the academic literature on contemporary slavery -- including much of the legal literature on the subject -- would show that, in the main, it has turned to the work of Kevin Bales and his sociological reading of what constitutes slavery

No One Shall Be Held in Slavery or Servitude: A critical analysis of international slavery conventions

Traces the development of slavery definitions in international agreements from 1815 to 2001. Overview of slavery definitions in international law; Historical analysis of the evolution of slavery definitions in international agreements; Analysis of the main characteristics of slavery in international agreements; Types of social theory that can be used in illuminating slavery; Discussion on the dimensions of slavery

Slavery is bad for business: analyzing the impact of slavery on national economies

Public discourse on human trafficking and modern-day slavery is reaching a tipping point -- it is coming to be understood as a global problem with economic and policy implications far beyond simple reports of cross-border human trafficking. A decade ago most educated citizens considered slavery a phenomenon of the past, relegated to history textbooks. Today a strong narrative has reached global proportions: activists, epistemic communities, NGOs, IGOs, and governments are acknowledging the scope and extent of slavery in the twenty-first century. One need only point to Nicholas Kristof and Sheryl Wu Dunn’s bestseller Half the Sky, President Barack Obama’s 2012 speech at the Clinton Global Intiative, or the awareness that celebrities such as Mira Sorvino and Jada Pinkett Smith are raising about the subject to illustrate how far the antislavery movement has progressed.1 Yet despite such civic mindedness, surprisingly little data and empirically driven research exist on slavery today. Although some headway has been made in estimating its prevalence -- most notably in the form of contributions by Kevin Bales and by the International Labor Organization (ILO) -- apart from a rough estimate of how many slaves exist in the world today (21 to 27 million), scholars and policy makers know little about the risk factors -- let alone the business impact -- that contemporary slavery has on the global community.2 Indeed, most extant research, although useful, is qualitative, not allowing for statistical models.3 To what extent is slavery empirically bad for business? For whom is the business of slavery profitable, and for whom is it economically burdensome

Slavery is bad for business: analyzing the impact of slavery on national economies

Public discourse on human trafficking and modern-day slavery is reaching a tipping point -- it is coming to be understood as a global problem with economic and policy implications far beyond simple reports of cross-border human trafficking. A decade ago most educated citizens considered slavery a phenomenon of the past, relegated to history textbooks. Today a strong narrative has reached global proportions: activists, epistemic communities, NGOs, IGOs, and governments are acknowledging the scope and extent of slavery in the twenty-first century. One need only point to Nicholas Kristof and Sheryl Wu Dunn’s bestseller Half the Sky, President Barack Obama’s 2012 speech at the Clinton Global Intiative, or the awareness that celebrities such as Mira Sorvino and Jada Pinkett Smith are raising about the subject to illustrate how far the antislavery movement has progressed.1 Yet despite such civic mindedness, surprisingly little data and empirically driven research exist on slavery today. Although some headway has been made in estimating its prevalence -- most notably in the form of contributions by Kevin Bales and by the International Labor Organization (ILO) -- apart from a rough estimate of how many slaves exist in the world today (21 to 27 million), scholars and policy makers know little about the risk factors -- let alone the business impact -- that contemporary slavery has on the global community.2 Indeed, most extant research, although useful, is qualitative, not allowing for statistical models.3 To what extent is slavery empirically bad for business? For whom is the business of slavery profitable, and for whom is it economically burdensome

Weather, climate, and hydrologic forecasting for the US Southwest: A survey

As part of a regional integrated assessment of climate vulnerability, a survey was conducted from June 1998 to May 2000 of weather, climate, and hydrologic forecasts with coverage of the US Southwest and an emphasis on the Colorado River Basin. The survey addresses the types of forecasts that were issued, the organizations that provided them, and techniques used in their generation. It reflects discussions with key personnel from organizations involved in producing or issuing forecasts, providing data for making forecasts, or serving as a link for communicating forecasts. During the survey period, users faced a complex and constantly changing mix of forecast products available from a variety of sources. The abundance of forecasts was not matched in the provision of corresponding interpretive materials, documentation about how the forecasts were generated, or reviews of past performance. Potential existed for confusing experimental and research products with others that had undergone a thorough review process, including official products issued by the National Weather Service. Contrasts between the state of meteorologic and hydrologic forecasting were notable, especially in the former's greater operational flexibility and more rapid incorporation of new observations and research products. Greater attention should be given to forecast content and communication, including visualization, expression of probabilistic forecasts and presentation of ancillary information. Regional climate models and use of climate forecasts in water supply forecasting offer rapid improvements in predictive capabilities for the Southwest. Forecasts and production details should be archived, and publicly available forecasts should be accompanied by performance evaluations that are relevant to users