Conicoid Mirrors

The first order equation relating object and image location for a mirror of arbitrary conic-sectional shape is derived. It is also shown that the parabolic reflecting surface is the only one free of aberration and only in the limiting case of distant sources.Comment: 9 page

Some asymptotics for Sobolev orthogonal polynomials involving Gegenbauer weights

AbstractWe consider the Sobolev inner product 〈f,g〉=∫−11f(x)g(x)(1−x2)α−12dx+∫f′(x)g′(x)dψ(x),α>−12, where dψ is a measure involving a Gegenbauer weight and with mass points outside the interval (−1,1). We study the asymptotic behaviour of the polynomials which are orthogonal with respect to this inner product. We obtain the asymptotics of the largest zeros of these polynomials via a Mehler–Heine type formula. These results are illustrated with some numerical experiments

Field and temperature dependence of magnetization in FeCu-based amorphous alloys

In this paper, the production of FeCu-based FeCuZr amorphous alloys by ball milling is reported. The thermal dependence of magnetization for the [Fe_(0.5)Cu_(0.5)]_85Zr_(15) (at. %) amorphous alloy has been found to show a dramatic field dependence of the kink point of the magnetization. This kink corresponds to a temperature different from the Curie temperature, above 400 K, of the ferromagnetic phase, which, according to spin waves fitting, can be induced by applying external fields. Just above 235 K, the thermoremanence increases sharply, and this feature strongly suggests an increase of the ferromagnetic ordering under zero field heating. Neutron diffraction experiments seem to confirm the enhancement of spin alignment. The thermal expansion above the compensation temperature is proposed to be the origin of the thermoremanence enhancement through the anti-Invar effect as might be explained within the framework of recent ab initio calculations [M. van Schilfgaarde et al., Nature (London) 400, 46 (1999)]

Asymptotics for Jacobi–Sobolev orthogonal polynomials associated with non-coherent pairs of measures

AbstractWe consider the Sobolev inner product 〈f,g〉=∫−11f(x)g(x)dψ(α,β)(x)+∫f′(x)g′(x)dψ(x), where dψ(α,β)(x)=(1−x)α(1+x)βdx with α,β>−1, and ψ is a measure involving a rational modification of a Jacobi weight and with a mass point outside the interval (−1,1). We study the asymptotic behaviour of the polynomials which are orthogonal with respect to this inner product on different regions of the complex plane. In fact, we obtain the outer and inner strong asymptotics for these polynomials as well as the Mehler–Heine asymptotics which allow us to obtain the asymptotics of the largest zeros of these polynomials. We also show that in a certain sense the above inner product is also equilibrated

Fractal dimension of lightning discharge

International audienceUsing a stochastic model, we simulate the process of dielectric breakdown in the atmosphere and calculate the fractal dimension of 3-dimensional lightning patterns. Finite-size effects have been studied. The projections of our patterns on vertical planes fit the experimental fractal dimension obtained from photographic analysis. This work is inspired by a previous work by A.A. Tsonis

Thermoremanence anomaly in Fe-Zr(B,Cu) Invar metallic glasses: Volume expansion induced ferromagnetism

We report the existence of a thermally induced sharp increase of thermoremanence around the Curie temperature of Invar-like Fe-Zr(B,Cu) soft magnetic glasses. Neutron-diffraction measurements indicate that a true enhancement of the average local magnetic moment, rather than only a change in the domain structure, occurs. Such enhancement has been tentatively attributed to the increasing volume expansion that takes place beyond the Curie temperature and reinforces ferromagnetism in some low-density clusters

Temporal dynamics of soil fungal communities after partial and total clear-cutting in a managed Pinus sylvestris stand

Forest management aimed to maximize timber production might impact soil fungi, especially those symbiotically associated to tree roots. In this study, we analyse the temporal dynamics of soil fungi along five sampling years after tree removal in a managed Pinus sylvestris stand in northern Spain, where timber production is combined with regular mushroom harvesting. Two management methods were tested: total and partial clear-cutting leaving retention trees for seedling regeneration. Undisturbed, uncut plots were also included in the experiment as a control treatment. The whole fungal community (phylotypes and ecological guilds) were analysed by high-throughput Illumina MiSeq sequencing of fungal ITS1 amplicons. We hypothesized that (1) ectomycorrhizal fungal communities will decrease after both clear-cutting treatments with a concurrent increase in the abundance of saprotrophs, (2) the abundance and diversity of the ectomycorrhizal guild will be more preserved in partially clear-cut than in total clear-cut plots, and (3) the overall fungal diversity will decrease in the cut plots leading to major losses of ectomycorrhizal species. Our results show that soil fungal composition changed across the five years after clear-cutting by decreasing ectomycorrhizal fungi and increasing saprotrophs. However, these changes did not significantly affect fungal diversity and there were taxa-specific responses to tree harvest treatments. Boletus edulis, the most abundant ectomycorrhizal species fruiting in the study area and a valuable local non-forest resource, was negatively affected by either clear-cutting treatments. Soil fungal community composition in partially clear-cut areas was not different from that of total clear-cut areas. Our results indicate a strong effect of tree harvest on the relative abundance of ectomycorrhizal fungi along the first years after clear-cutting. However, levels of fungal diversity were comparable to the undisturbed forest, thus suggesting a potential further recovery of ectomycorrhizal fungi through the colonization of the regenerated seedlings.info:eu-repo/semantics/acceptedVersio