Alternativity and reciprocity in the Cayley-Dickson algebra

We calculate the eigenvalue \rho of the multiplication mapping R on the Cayley-Dickson algebra A_n. If the element in A_n is composed of a pair of alternative elements in A_{n-1}, half the eigenvectors of R in A_n are still eigenvectors in the subspace which is isomorphic to A_{n-1}. The invariant under the reciprocal transformation A_n \times A_{n} \ni (x,y) -> (-y,x) plays a fundamental role in simplifying the functional form of \rho. If some physical field can be identified with the eigenspace of R, with an injective map from the field to a scalar quantity (such as a mass) m, then there is a one-to-one map \pi: m \mapsto \rho. As an example, the electro-weak gauge field can be regarded as the eigenspace of R, where \pi implies that the W-boson mass is less than the Z-boson mass, as in the standard model.Comment: To be published in J. Phys. A: Mathematical and Genera

Non-semisimple Lie algebras with Levi factor \frak{so}(3), \frak{sl}(2,R) and their invariants

We analyze the number N of functionally independent generalized Casimir invariants for non-semisimple Lie algebras \frak{s}\overrightarrow{% oplus}_{R}\frak{r} with Levi factors isomorphic to \frak{so}(3) and \frak{sl}(2,R) in dependence of the pair (R,\frak{r}) formed by a representation R of \frak{s} and a solvable Lie algebra \frak{r}. We show that for any dimension n >= 6 there exist Lie algebras \frak{s}\overrightarrow{\oplus}_{R}\frak{r} with non-trivial Levi decomposition such that N(\frak{s}% \overrightarrow{oplus}_{R}\frak{r}) = 0.Comment: 16 page

Contractions of Low-Dimensional Lie Algebras

Theoretical background of continuous contractions of finite-dimensional Lie algebras is rigorously formulated and developed. In particular, known necessary criteria of contractions are collected and new criteria are proposed. A number of requisite invariant and semi-invariant quantities are calculated for wide classes of Lie algebras including all low-dimensional Lie algebras. An algorithm that allows one to handle one-parametric contractions is presented and applied to low-dimensional Lie algebras. As a result, all one-parametric continuous contractions for the both complex and real Lie algebras of dimensions not greater than four are constructed with intensive usage of necessary criteria of contractions and with studying correspondence between real and complex cases. Levels and co-levels of low-dimensional Lie algebras are discussed in detail. Properties of multi-parametric and repeated contractions are also investigated.Comment: 47 pages, 4 figures, revised versio

Lowest dimensional example on non-universality of generalized In\"on\"u-Wigner contractions

We prove that there exists just one pair of complex four-dimensional Lie algebras such that a well-defined contraction among them is not equivalent to a generalized IW-contraction (or to a one-parametric subgroup degeneration in conventional algebraic terms). Over the field of real numbers, this pair of algebras is split into two pairs with the same contracted algebra. The example we constructed demonstrates that even in the dimension four generalized IW-contractions are not sufficient for realizing all possible contractions, and this is the lowest dimension in which generalized IW-contractions are not universal. Moreover, this is also the first example of nonexistence of generalized IW-contraction for the case when the contracted algebra is not characteristically nilpotent and, therefore, admits nontrivial diagonal derivations. The lower bound (equal to three) of nonnegative integer parameter exponents which are sufficient to realize all generalized IW-contractions of four-dimensional Lie algebras is also found.Comment: 15 pages, extended versio

Low-productivity boreal forests have high conservation value for lichens

1. Land set aside for preservation of biodiversity often has low productivity. As biodiversity generally increases with productivity, due to higher or more diverse availability of resources, this implies that some of the biodiversity may be left unprotected. Due to a lack of knowledge on the species diversity and conservation value of low-productivity habitats, the consequences of the biased allocation of low-productivity land for set-asides are unknown. 2. We examined the conservation value of boreal low-productivity forests (potential tree growth <1 m(3) ha(-1) year(-1)) by comparing assemblages of tree- and deadwood-dwelling lichens and forest stand structure between productive and low-productivity forest stands. We surveyed 84 Scots pine-dominated stands in three regions in Sweden, each including four stand types: two productive (managed and unman-aged) and two low-productivity stands (on mires and on thin, rocky soils). 3. Lichen species richness was the highest in low-productivity stands on thin soil, which had similar amounts and diversity of resources (living trees and dead wood) to productive unmanaged stands. Stands in low-productivity mires, which had low abundance of living trees and dead wood, hosted the lowest lichen richness. Lichen species composition differed among stand types, but none of them hosted unique species. The differences in both species richness and composition were more pronounced in northern than in southern Sweden, likely due to shorter history of intensive forestry. 4. Synthesis and applications. Boreal low-productivity forests can have as high conservation value as productive forests, which should be reflected in conservation strategies. However, their value is far from uniform, and conservation planning should acknowledge this variation and not treat all low-productivity forests as a uniform group. Some types of low-productivity forest (e.g. on rocky soil) are more valuable than others (e.g. on mires), and should thus be prioritized in conservation. It is also important to consider the landscape context: low-productivity forests may have higher value in landscapes where high-productivity forests are highly influenced by forestry. Finally, although low-productivity forests can be valuable for some taxa, productive forests may still be important for other taxa

Quantifying the Detrimental Impacts of Land-Use and Management Change on European Forest Bird Populations

The ecological impacts of changing forest management practices in Europe are poorly understood despite European forests being highly managed. Furthermore, the effects of potential drivers of forest biodiversity decline are rarely considered in concert, thus limiting effective conservation or sustainable forest management. We present a trait-based framework that we use to assess the detrimental impact of multiple land-use and management changes in forests on bird populations across Europe. Major changes to forest habitats occurring in recent decades, and their impact on resource availability for birds were identified. Risk associated with these changes for 52 species of forest birds, defined as the proportion of each species' key resources detrimentally affected through changes in abundance and/or availability, was quantified and compared to their pan-European population growth rates between 1980 and 2009. Relationships between risk and population growth were found to be significantly negative, indicating that resource loss in European forests is an important driver of decline for both resident and migrant birds. Our results demonstrate that coarse quantification of resource use and ecological change can be valuable in understanding causes of biodiversity decline, and thus in informing conservation strategy and policy. Such an approach has good potential to be extended for predictive use in assessing the impact of possible future changes to forest management and to develop more precise indicators of forest health

Applying an ecosystem services framework on nature and mental health to recreational blue space visits across 18 countries

The effects of ‘nature’ on mental health and subjective well-being have yet to be consistently integrated into ecosystem service models and frameworks. To address this gap, we used data on subjective mental well-being from an 18-country survey to test a conceptual model integrating mental health with ecosystem services, initially proposed by Bratman et al. We analysed a range of individual and contextual factors in the context of 14,998 recreational visits to blue spaces, outdoor environments which prominently feature water. Consistent with the conceptual model, subjective mental well-being outcomes were dependent upon on a complex interplay of environmental type and quality, visit characteristics, and individual factors. These results have implications for public health and environmental management, as they may help identify the bluespace locations, environmental features, and key activities, that are most likely to impact well-being, but also potentially affect recreational demand on fragile aquatic ecosystems

Variable strength of forest stand attributes and weather conditions on the questing activity of Ixodes ricinus ticks over years in managed forests

Given the ever-increasing human impact through land use and climate change on the environment, we crucially need to achieve a better understanding of those factors that influence the questing activity of ixodid ticks, a major disease-transmitting vector in temperate forests. We investigated variation in the relative questing nymph densities of Ixodes ricinus in differently managed forest types for three years (2008–2010) in SW Germany by drag sampling. We used a hierarchical Bayesian modeling approach to examine the relative effects of habitat and weather and to consider possible nested structures of habitat and climate forces. The questing activity of nymphs was considerably larger in young forest successional stages of thicket compared with pole wood and timber stages. Questing nymph density increased markedly with milder winter temperatures. Generally, the relative strength of the various environmental forces on questing nymph density differed across years. In particular, winter temperature had a negative effect on tick activity across sites in 2008 in contrast to the overall effect of temperature across years. Our results suggest that forest management practices have important impacts on questing nymph density. Variable weather conditions, however, might override the effects of forest management practices on the fluctuations and dynamics of tick populations and activity over years, in particular, the preceding winter temperatures. Therefore, robust predictions and the detection of possible interactions and nested structures of habitat and climate forces can only be quantified through the collection of long-term data. Such data are particularly important with regard to future scenarios of forest management and climate warming

Associations between green/blue spaces and mental health across 18 countries

Living near, recreating in, and feeling psychologically connected to, the natural world are all associated with better mental health, but many exposure-related questions remain. Using data from an 18-country survey (n= 16,307) we explored associations between multiple measures of mental health (positive well-being, mental distress, depression/anxiety medication use) and: (a) exposures (residential/recreational visits) to diferent natural settings (green/inland-blue/coastalblue spaces); and (b) nature connectedness, across season and country. People who lived in greener/ coastal neighbourhoods reported higher positive well-being, but this association largely disappeared when recreational visits were controlled for. Frequency of recreational visits to green, inland-blue, and coastal-blue spaces in the last 4 weeks were all positively associated with positive well-being and negatively associated with mental distress. Associations with green space visits were relatively consistent across seasons and countries but associations with blue space visits showed greater heterogeneity. Nature connectedness was also positively associated with positive well-being and negatively associated with mental distress and was, along with green space visits, associated with a lower likelihood of using medication for depression. By contrast inland-blue space visits were associated with a greater likelihood of using anxiety medication. Results highlight the benefts of multi-exposure, multi-response, multi-country studies in exploring complexity in nature-health associations.info:eu-repo/semantics/publishedVersio