On commuting UU-operators in Jordan algebras

Recently J.A.Anquela, T.Cort\'es, and H.Petersson proved that for elements $x, y$ in a non-degenerate Jordan algebra $J$, the relation $x \circ y = 0$ implies that the $U$-operators of $x$ and $y$ commute: $U_xU_y = U_yU_x$. We show that the result may be not true without the assumption on non-degeneracity of $J$. We give also a more simple proof of the mentioned result in the case of linear Jordan algebras, that is, when $char\, F\neq 2$

The Story of Safe2Tell

This publication highlights the Safe2Tell program, including the far-reaching impact of providing students in all Colorado schools an increased ability to both prevent and report violence by making anonymous calls to 1-877-542-SAFE. It also illustrates through stories and interviews the value of Safe2Tell among families and communities, necessary steps and resources to implement the program, and the hotline's long-term sustainability achieved through legislation

Carbon Sources to Microbes and Cryoconite on Alaskan Alpine Glacier Surfaces

Cryoconite are depressions in the ice surface filled with diverse microorganisms and dark debris, which are reducing albedo and increasing glacier melt. In order to understand cryoconite carbon composition and carbon sources to microorganisms living on glacier surfaces, bulk organic carbon and microbial lipids from supraglacial cryoconite sediment within the ablation zones of Spencer, Matanuska, and Mendenhall glaciers in southern Alaska have been coupled with radiocarbon (14C) analyses. The microbial lipids analyzed in these studies, phospholipid fatty acids (PLFA), are components of microbial membranes, quickly degrade after cell death, and give a snapshot of the viable microbial community. PLFA structure distributions indicated autotrophic and heterotrophic microorganisms in the supraglacial environment, in an abundance similar to surrounding Alaskan soils. The 14C content of PLFA indicated that microbes were incorporating carbon that was recently in equilibrium with the atmosphere, which suggests autotrophic predominance or the use of modern carbon by heterotrophs. The 14C content of bulk cryoconite organic carbon on Matanuska and Spencer glaciers was depleted relative to the modern atmosphere, where it was modern and in some cases enriched on Mendenhall glacier. This difference was hypothesized to originate from surrounding geology. These results reveal two distinct carbon pools: a highly abundant microbial community, which uses young carbon as a carbon source, living within and minimally interacting with a larger, sometimes old carbon pool. Ultimately, this study highlights the carbon isotopic heterogeneity of cryoconite material

Regional Human Rights Regimes and Environmental Protection: A Comparison of European and American Human Rights Regimes’ Histories, Current Law, and Opportunities for Development

This work reviews the Inter-American and European human rights regimes and their abilities to respond to point-source pollution, climate change, and ecosystem conservation. It begins by reviewing leading human rights theories and the development of the relationship between human rights and the environment. It then focuses on European human rights, both under the ECHR and the CFREU, and highlights the ECHR’s ability to respond to instances of point-source-pollution though the right to privacy. The work then looks at the Inter-American human rights regime, its structure, history and ability to respond to environmental challenges. It reviews the regime’s tendency to use the right to property to protect the environments of indigenous populations and provides a detailed analysis of the regime’s potential ability to respond to climate change based on the recent Athabaskan Petition. Finally this work looks at how environmental protection can be developed within both regimes, comparing their abilities to adapt and progressively interpret each regime’s human rights laws. It concludes that the European regime is in a better position to expand its human rights, potentially to the degree of recognizing a right to a healthy environment

The Role of Identities in Jordan AIgebras

Born of quantum mechanics, but abandoned at birth by physicists, Jordan algebras recovered to lead a productive life in a variety of mathematical fields

Albert algebras over curves of genus zero and one

Albert algebras and other Jordan algebras are constructed over curves of genus zero and one, using a generalization of the Tits process and the first Tits construction due to Achhammer.Comment: 37 page