Localized Transfunctions

A transfunction is a function which maps between sets of finite measures on measurable spaces. Push-forward operators form one important class of examples of transfunctions and are identified with their respective measurable functions. In this regard, transfunctions are a generalization of measurable functions between measurable spaces. Additionally, there are naturally arising transfunctions with nice properties which are not measurable functions. Transfunctions which are weakly $\sigma$-additive (commutable with addition over countable sequences of orthogonal measures) between second-countable metric spaces are of particular interest and are primarily developed in this paper. We study such transfunctions which are localized: sending source measures carried by small open sets to target measures also carried by small open sets. With the right settings and assumptions, we develop some theorems which characterize continuous functions and measurable functions, and show that the behavior of localized transfunctions can be approximated by measurable functions and by continuous functions, but only up to some error. We also characterize transfunctions that correspond to Markov operators. In our investigation of transfunctions we are motivated by several potential applications, including Monge-Kantorovich transportation problem or population dynamics that will be presented in some detail in this paper.Comment: 23 page

Derivations on Pseudoquotients

A space of pseudoquotients denoted by B(X, S) is defined as equivalence classes of pairs (x, f); where x is an element of a nonempty set X, f is an element of S; a commutative semigroup of injective maps from X to X; and (x, f) ~ (y, g) for gx = fy: If X is a ring and elements of S are ring homomorphisms, then B(X, S) is a ring. We show that, under natural conditions, a derivation on X has a unique extension to a derivation on B(X, S): We also consider (α, β) -Jordan derivations, inner derivations, and generalized derivations.Введено означення простору псевдочасток B(X, S) як класів еквiвалентностi пар (x, f), де x — елемент непорожньої множини X, f — елемент комутативної напівгрупи S ін'єктивних відображень із X у X; та (x, f) ~ (y, g), якщо gx = fy. Якщо X — кільце та елементи S є гомоморфізмами кільця, то B(X, S) є кільцем. Показано, що за природних умов похідна на X має єдине розширення до похідної на B(X, S). Також розглянуто (α, β)-жорданові похідні, внутрішні похідні та узагальнені похідні

On De Graaf spaces of pseudoquotients

A space of pseudoquotients, $\mathcal{B}(X,S)$, is defined as equivalence classes of pairs $(x,f)$, where $x$ is an element of a non-empty set $X$, $f$ is an element of $S$, a commutative semigroup of injective maps from $X$ to $X$, and $(x,f) \sim (y,g)$ if $gx=fy$. In this note, we consider a generalization of this construction where the assumption of commutativity of $S$ is replaced by Ore type conditions. As in the commutative case, $X$ can be identified with a subset of $\mathcal{B}(X,S)$, and $S$ can be extended to a group, $G$, of bijections on $\mathcal{B}(X,S)$. We introduce a natural topology on $\mathcal{B}(X,S)$ and show that all elements of $G$ are homeomorphisms on $\mathcal{B}(X,S)$

Spared, shared and lost—routes for maintaining the Scandinavian Mountain foothill intact forest landscapes

Intact forest landscapes harbor significant biodiversity values and pools of ecosystem services essential for conservation, land use and rural development. Threatened by fragmentation and loss by transitions to industrial clear-cut forestry, those landscapes are of pivotal interest for protection that secures their intact character. With wall-to-wall land-cover data, we explored opportunities for maintaining intact forest landscapes through comprehensive spatial planning across a 2.5 million hectares boreal to sub-alpine forest region along the eastern slopes of the Scandinavian Mountain range. We analyzed forest and woodland types that are protected, need protection or potentially can be subject to continued forest management. We established that the fraction of already clear-cut forest is very small and that the forest landscape of the Scandinavian Mountain foothills contains a high proportion of protected high conservation value forests, covering almost 2 million ha, and that over 500,000 ha (27%) remains unprotected and may be subject to future protection or continued adapted forest management. We found evident north to south differences with respect to forest landscape configuration, distribution of unprotected forests and land ownership. With a focus on non-industrial private landowners, we conclude that sustainable land-use requires integrative, multi-functional approaches that rely on further protection, forest, and forest landscape restoration and a much larger share of continuous cover forestry than presently. Our results provide input into ongoing policy implementation and green infrastructure planning in the context of securing intact forest values and integrative opportunities for rural livelihood and regional development based on multiple value chains.publishedVersio

Biodiversity’s contributions to sustainable development

International concern to develop sustainably challenges us to act upon the inherent links between 23 our economy, society and environment, and is leading to increasing acknowledgement of 24 biodiversity’s importance. This Review discusses the breadth of ways in which biodiversity can 25 support sustainable development. It uses the Sustainable Development Goals (SDGs) as a basis for 26 exploring scientific evidence of the benefits delivered by biodiversity. It focuses on papers that 27 provide examples of how biodiversity components (i.e. ecosystems, species and genes) directly 28 deliver benefits that may contribute to the achievement of individual SDGs. It also considers how 29 biodiversity’s direct contributions to fulfilling some SDGs may indirectly support the achievement of 30 other SDGs to which biodiversity does not contribute directly. How the attributes (e.g. diversity, 31 abundance or composition) of biodiversity components influence the benefits delivered is also 32 presented, where described by the papers reviewed. While acknowledging potential negative 33 impacts and trade-offs between different benefits, the study concludes that biodiversity may 34 contribute to fulfilment of all SDGs

Gone with the forest: Assessing global woodpecker conservation from land use patterns

As a result of their ecological traits, woodpeckers (Picidae, Aves) are highly sensitive to forest cover change. We explored the current land cover in areas of high species richness of woodpeckers to determinate regions where urgent conservation actions are needed. In addition, we identified woodpecker species that are sensitive to forest loss and that have high levels of human habitat modification and low levels of protection (through protected areas) in their distribution ranges. Location: Global. Methods: We joined available range maps for all extant 254 woodpecker species with information of their conservation status and tolerances to human habitat modifications and generated a richness map of woodpecker species worldwide. Then, we associated this information (the richness pattern and individual species’ maps) with land cover and protected areas (PAs) maps. We found that the foremost woodpecker species richness hotspot is in Southeast Asia and is highly modified. At the second species richness hotspot in the eastern Andes, we observed a front of deforestation at its southern extreme and a greater deforested area in its northern extreme but most of its area remains with forest coverage. At the species level, 17 species that are sensitive to forest modification experience extensive deforestation and have low extents of PAs in their ranges.The most diverse woodpecker hotspots are mostly occupied by human-modified landscapes, and a large portion of the species there avoids anthropogenic environments. The level of representation of woodpecker species in PAs is low as a global general pattern, although slightly better in Asia. Our global analysis of threats to woodpecker from land use patterns reiterates the urgent conservation needs for Southeast Asian forests. Finally, based on our results, we recommend a re-evaluation for inclusion in the Red List of five woodpecker species.Fil: Vergara Tabares, David Lautaro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Diversidad y Ecología Animal. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas Físicas y Naturales. Instituto de Diversidad y Ecología Animal; ArgentinaFil: Lammertink, J. Martjan. Cornell University; Estados Unidos. Provincia de Entre Ríos. Centro de Investigaciones Científicas y Transferencia de Tecnología a la Producción. Universidad Autónoma de Entre Ríos. Centro de Investigaciones Científicas y Transferencia de Tecnología a la Producción. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Centro de Investigaciones Científicas y Transferencia de Tecnología a la Producción; ArgentinaFil: Verga, Ernesto Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto Multidisciplinario de Biología Vegetal. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas Físicas y Naturales. Instituto Multidisciplinario de Biología Vegetal; ArgentinaFil: Schaaf, Alejandro Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro de Investigaciones y Transferencia de Jujuy. Universidad Nacional de Jujuy. Centro de Investigaciones y Transferencia de Jujuy; ArgentinaFil: Nori, Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Diversidad y Ecología Animal. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas Físicas y Naturales. Instituto de Diversidad y Ecología Animal; Argentin

Exact and explicit probability densities for one-sided Levy stable distributions

We study functions g_{\alpha}(x) which are one-sided, heavy-tailed Levy stable probability distributions of index \alpha, 0< \alpha <1, of fundamental importance in random systems, for anomalous diffusion and fractional kinetics. We furnish exact and explicit expression for g_{\alpha}(x), 0 \leq x < \infty, satisfying \int_{0}^{\infty} exp(-p x) g_{\alpha}(x) dx = exp(-p^{\alpha}), p>0, for all \alpha = l/k < 1, with k and l positive integers. We reproduce all the known results given by k\leq 4 and present many new exact solutions for k > 4, all expressed in terms of known functions. This will allow a 'fine-tuning' of \alpha in order to adapt g_{\alpha}(x) to a given experimental situation.Comment: 4 pages, 3 figures and 1 tabl