On periodic solutions of 2-periodic Lyness difference equations

We study the existence of periodic solutions of the non--autonomous periodic Lyness' recurrence u_{n+2}=(a_n+u_{n+1})/u_n, where {a_n} is a cycle with positive values a,b and with positive initial conditions. It is known that for a=b=1 all the sequences generated by this recurrence are 5-periodic. We prove that for each pair (a,b) different from (1,1) there are infinitely many initial conditions giving rise to periodic sequences, and that the family of recurrences have almost all the even periods. If a is not equal to b, then any odd period, except 1, appears.Comment: 27 pages; 1 figur

Temperature contour maps at the strain-induced martensitic transition of a Cu–Zn–Al shape-memory single crystal

We study temperature changes at the reverse strain-induced martensitic transformation in a Cu–Zn–Al single crystal. Infrared thermal imaging reveals a markedly inhomogeneous temperature distribution. The evolution of the contour temperature maps enables information to be extracted on the kinetics of the interface motion

Temperature and magnetic field dependences of the elastic constants of Ni-Mn-Al magnetic Heusler alloys

We report on measurements of the adiabatic second order elastic constants of the off-stoichiometric Ni$_{54}$Mn$_{23}$Al$_{23}$ single crystalline Heusler alloy. The variation in the temperature dependence of the elastic constants has been investigated across the magnetic transition and over a broad temperature range. Anomalies in the temperature behaviour of the elastic constants have been found in the vicinity of the magnetic phase transition. Measurements under applied magnetic field, both isothermal and variable temperature, show that the value of the elastic constants depends on magnetic order, thus giving evidence for magnetoelastic coupling in this alloy system.Comment: 7 pages, 5 figures. Accepted for publication in Physical the Review

Martensitic transition and magnetoresistance in a Cu-Al-Mn shape memory alloy. Influence of aging

We have studied the effect of ageing within the miscibility gap on the electric, magnetic and thermodynamic properties of a non-stoichiometric Heusler Cu-Al-Mn shape-memory alloy, which undergoes a martensitic transition from a $bcc$-based ($\beta$-phase) towards a close-packed structure ($M$-phase). Negative magnetoresistance which shows an almost linear dependence on the square of magnetization with different slopes in the $M$- and $\beta$-phases, was observed. This magnetoresistive effect has been associated with the existence of Mn-rich clusters with the Cu$_2$AlMn-structure. The effect of an applied magnetic field on the martensitic transition has also been studied. The entropy change between the $\beta$- and $M$-phases shows negligible dependence on the magnetic field but it decreases significantly with annealing time within the miscibility gap. Such a decrease is due to the increasing amount of Cu$_2$MnAl-rich domains that do not transform martensitically.Comment: 9 pages, 9 figures, accepted for publication in PR

Some properties of the k-dimensional Lyness' map

This paper is devoted to study some properties of the k-dimensional Lyness' map. Our main result presentes a rational vector field that gives a Lie symmetry for F. This vector field is used, for k less or equal to 5 to give information about the nature of the invariant sets under F. When k is odd, we also present a new (as far as we know) first integral for F^2 which allows to deduce in a very simple way several properties of the dynamical system generated by F. In particular for this case we prove that, except on a given codimension one algebraic set, none of the positive initial conditions can be a periodic point of odd period.Comment: 22 pages; 3 figure

First-principles study of lattice instabilities in the ferromagnetic martensite Ni2_2MnGa

The phonon dispersion relations and elastic constants for ferromagnetic Ni$_2$MnGa in the cubic and tetragonally distorted Heusler structures are computed using density-functional and density-functional perturbation theory within the spin-polarized generalized-gradient approximation. For $0.9<c/a<1.06$, the TA$_2$ tranverse acoustic branch along $[110]$ and symmetry-related directions displays a dynamical instability at a wavevector that depends on $c/a$. Through examination of the Fermi-surface nesting and electron-phonon coupling, this is identified as a Kohn anomaly. In the parent cubic phase the computed tetragonal shear elastic constant, C$^\prime$=(C$_{11}-$C$_{12}$)/2, is close to zero, indicating a marginal elastic instability towards a uniform tetragonal distortion. We conclude that the cubic Heusler structure is unstable against a family of energy-lowering distortions produced by the coupling between a uniform tetragonal distortion and the corresponding $[110]$ modulation. The computed relation between the $c/a$ ratio and the modulation wavevector is in excellent agreement with structural data on the premartensitic ($c/a$ = 1) and martensitic ($c/a$ = 0.94) phases of Ni$_2$MnGa.Comment: submitted to Phys. Rev.

Causes of Morbidity in Wild Raptor Populations Admitted at a Wildlife Rehabilitation Centre in Spain from 1995-2007: A Long Term Retrospective Study

Background: Morbidity studies complement the understanding of hazards to raptors by identifying natural or anthropogenic factors. Descriptive epidemiological studies of wildlife have become an important source of information about hazards to wildlife populations. On the other hand, data referenced to the overall wild population could provide a more accurate assessment of the potential impact of the morbidity/mortality causes in populations of wild birds. Methodology/Principal Findings: The present study described the morbidity causes of hospitalized wild raptors and their incidence in the wild populations, through a long term retrospective study conducted at a wildlife rehabilitation centre of Catalonia (1995-2007). Importantly, Seasonal Cumulative Incidences (SCI) were calculated considering estimations of the wild population in the region and trend analyses were applied among the different years. A total of 7021 birds were analysed: 7 species of Strigiformes (n = 3521) and 23 of Falconiformes (n = 3500). The main causes of morbidity were trauma (49.5%), mostly in the Falconiformes, and orphaned/young birds (32.2%) mainly in the Strigiformes. During wintering periods, the largest morbidity incidence was observed in Accipiter gentillis due to gunshot wounds and in Tyto alba due to vehicle trauma. Within the breeding season, Falco tinnunculus (orphaned/young category) and Bubo bubo (electrocution and metabolic disorders) represented the most affected species. Cases due to orphaned/young, infectious/parasitic diseases, electrocution and unknown trauma tended to increase among years. By contrast, cases by undetermined cause, vehicle trauma and captivity decreased throughout the study period. Interestingly, gunshot injuries remained constant during the study period. Conclusions/Significance: Frequencies of morbidity causes calculated as the proportion of each cause referred to the total number of admitted cases, allowed a qualitative assessment of hazards for the studied populations. However, cumulative incidences based on estimated wild raptor population provided a more accurate approach to the potential ecological impact of the morbidity causes in the wild populations

DNA metabarcoding reveals modern and past eukaryotic communities in a high-mountain peat bog system

Peat bogs located in high mountains are suitable places to study local environmental responses to climate variability. These ecosystems host a large number of eukaryotes with diverse taxonomic and functional diversity. We carried out a metabarcoding study using universal 18S and COI markers to explore the composition of past and present eukaryotic communities of a Pyrenean peat bog ecosystem. We assessed the molecular biodiversity of four different moss micro-habitats along a flood gradient in the lentic Bassa Nera system (Central Pyrenees). Five samples collected from different sediment depths at the same study site were also analysed, to test the suitability of these universal markers for studying paleoecological communities recovered from ancient DNA and to compare the detected DNA sequences to those obtained from the modern community. We also compared the information provided by the sedimentary DNA to the reconstruction from environmental proxies such as pollen and macro-remains from the same record. We successfully amplified ancient DNA with both universal markers from all sediment samples, including the deepest one (~ 10,000 years old). Most of the metabarcoding reads obtained from sediment samples, however, were assigned to living edaphic organisms and only a small fraction of those reads was considered to be derived from paleoecological communities. Inferences from ancient sedimentary DNA were complementary to the reconstruction based on pollen and macro-remains, and the combined records reveal more detailed information. This molecular study yielded promising findings regarding the diversity of modern eukaryotic peat bog communities. Nevertheless, even though information about past communities could be retrieved from sediment samples, preferential amplification of DNA from living communities is a caveat for the use of universal metabarcoding markers in paleoecology

Birds of prey as limiting factors of gamebird populations in Europe: a review

Whether predators can limit their prey has been a topic of scientific debate for decades. Traditionally it was believed that predators take only wounded, sick, old or otherwise low-quality individuals, and thus have little impact on prey populations. However, there is increasing evidence that, at least under certain circumstances, vertebrate predators may indeed limit prey numbers. This potential role of predators as limiting factors of prey populations has created conflicts between predators and human hunters, because the hunters may see predators as competitors for the same resources. A particularly acute conflict has emerged over the past few decades between gamebird hunters and birds of prey in Europe. As a part of a European-wide research project, we reviewed literature on the relationships between birds of prey and gamebirds. We start by analysing available data on the diets of 52 European raptor and owl species. There are some 32 species, mostly specialist predators feeding on small mammals, small passerine birds or insects, which never or very rarely include game animals (e.g. hares, rabbits, gamebirds) in their diet. A second group (20 species) consists of medium-sized and large raptors which prey on game, but for which the proportion in the diet varies temporally and spatially. Only three raptor species can have rather large proportions of gamebirds in their diet, and another seven species may utilise gamebirds locally to a great extent. We point out that the percentage of a given prey species in the diet of an avian predator does not necessarily reflect the impact of that predator on densities of prey populations. Next, we summarise available data on the numerical responses of avian predators to changing gamebird numbers. In half of these studies, no numerical response was found, while in the remainder a response was detected such that either raptor density or breeding success increased with density of gamebirds. Data on the functional responses of raptors were scarce. Most studies of the interaction between raptors and gamebird populations give some estimate of the predation rate (per cent of prey population taken by predator), but less often do they evaluate the subsequent reduction in the pre-harvest population or the potential limiting effect on breeding numbers. The few existing studies indicate that, under certain conditions, raptor predation may limit gamebird populations and reduce gamebird harvests. However, the number and extent of such studies are too modest to draw firm conclusions. Furthermore, their geographical bias to northern Europe, where predator–prey communities are typically simpler than in the south, precludes extrapolation to more diverse southern European ecosystems. There is an urgent need to develop further studies, particularly in southern Europe, to determine the functional and numerical responses of raptors to gamebird populations in species and environments other than those already evaluated in existing studies. Furthermore, additional field experiments are needed in which raptor and possibly also mammalian predator numbers are manipulated on a sufficiently large spatial and temporal scale. Other aspects that have been little studied are the role of predation by the non-breeding part of the raptor population, or floaters, on the breeding success and survival of gamebirds, as well as the effect of intra-guild predation. Finally there is a need for further research on practical methods to reduce raptor predation on gamebirds and thus reduce conflict between raptor conservation and gamebird management.The work was financially supported by the EuropeanCommission, and is part of project REGHAB (ReconcilingGamebird Hunting and Biodiversity; contract no.EVK2-CT-2000-200004).Peer reviewe

Morbidity, outcomes and cost-benefit analysis of wildlife rehabilitation in Catalonia (Spain)

Background There are few studies of careful examination of wildlife casualties in Wildlife Rehabilitation Centers. These studies are essential for detecting menaces to wild species and providing objective criteria about cost-benefit of treatments in those centers. The release rate is considered the main outcome indicator, but other parameters such as length of stay at the center and a cost-benefit index expressed as number of released animals per euro and day, could be used as reliable estimators of the rehabilitation costs. Methodology A retrospective study based on 54772 admissions recorded from 1995-2013 in the database of the Wildlife Rehabilitation Center of Torreferrussa (Catalonia, NW Spain) assessed the morbidity, outcomes and cost-benefits of the rehabilitation practices. Results Three hundred and two species were included: 232 birds (n = 48633), 37 mammals (n = 3293), 20 reptiles (n = 2705) and 13 amphibians (n = 141). The most frequent causes of admission were: 39.8% confiscation of protected species (89.4% passerines), 31.8% orphaned young animals (35.3% swifts, 21.7% diurnal raptors and owls) and 17.4% trauma casualties (46.7% raptors and owls). The highest proportion of releases was found in the captivity confiscation category [87.4% passerines (median time of stay: 12 days)], followed by the orphaned category [78% owls (66 days), 76.5% diurnal birds of prey (43 days), 75.6% hedgehogs (49 days), 52.7% swifts (19 days) and 52% bats (55 days)]. For the trauma group, 46.8% of releases were hedgehogs (44 days) and 25.6% owls (103 days). As regards the cost-benefit index, the trauma casualties and infectious diseases had the worse values with 1.3 and 1.4 released animals/euro/day respectively, and were particularly low in raptors, waders, marine birds and chiroptera. On the contrary, captivity (4.6) and misplacement (4.1) had the best index, particulary in amphibian, reptiles and passerines. Conclusions/significance Cost-benefit studies including the release rate, the time of stay at the center and the costbenefit index should be implemented for improving management efficiency of the Wildlife Rehabilitation Centers