Althammer polynomials, also called Legendre-Sobolev polynomials, constitute the first example of Sobolev orthogonal polynomials studied in the literature. Analytic properties of such polynomials and the location of their zeros have attracted attention in the last decades, both from a theoretical point of view as well as for their applications. The zeros of the Althammer polynomial An(x) of degree n interlace with those of other orthogonal polynomials, such as ultraspherical polynomials. In this work, we are focused on the computation of the zeros of An(x) using a variant of the Erlich-Aberth method. This is an iterative algorithm requiring good initial approximations of the zeros of An(x). We extend the interlacing properties of the zeros of An(x) to other classes of orthogonal polynomials, so that we can again use the Erlich-Aberth method to propose a fast computational technique for computing them. Numerical tests show the effectiveness of the proposed approach.
Elemental Tellurium gained particular attention in recent years due to its properties as high mobility, p-type semiconductor and strong infrared light absorber. Its van der Waals structure allows the combination with silicon as well as with two-dimensional materials giving rise to stacked structures with novel electronic and optical properties. Here we report a method to enhance photodetector performances, in terms of photocurrent and response speed at visible and infrared wavelengths, of Te/n-Si heterojunctions by introducing a topological insulator buffer layer of Bi2Se3 between Te and n-Si substrate. The photocurrent of the obtained stacked structure Te/Bi2Se3/n-Si results respectively 2.7 and 59 times higher than that shown by Bi2Se3/n-Si and Te/n-Si at 7 = 1550 nm when operating in self-powered mode. Moreover, the response time at visible wavelength decreases up to 6 times with respect to Te/n-Si and 2.9 times to Bi2Se3/n-Si. The obtained results are ascribed to the presence of the high mobility surface states of Bi2Se3 topological insulator. The research confirms the success in combining different nanomaterials for wide range wavelength optoelectronic devices and in the use of topological insulators for fast photodetectors.
Manganese-copper (Mn-Cu) mixed oxides are promising catalysts for abatement of incomplete combustion products from domestic wood burning, notably CO and Volatile Organic Compounds (VOCs). In this paper, the influence of the Mn/Cu molar ratio on structure, redox properties, and catalytic performances was investigated. Mixed oxides were synthesized by oxalate co-precipitation and calcined under air at 500 degrees C. Physicochemical characterization (XRD, Raman, N-2-physisorption, XPS, H-2-TPR) revealed strong Mn & horbar;Cu interaction. Catalytic tests for total oxidation of CO, toluene, and their mixture showed that copper-rich oxides, especially Cu1Mn0.25Ox, achieved the best performance at low temperature (T-50 = 49 degrees C and 230 degrees C for the oxidation of CO and toluene respectively). In alternating feeding, the presence of CO promotes the oxidation of toluene at low temperature, while an excess of Cu in the material ensures full CO2 selectivity. For mixed oxides, the linear correlation between Cu2+ -> Cu+ reducibility and T-50 for toluene oxidation in presence of CO demonstrates that the incorporation of Mn into Cu oxides enhances oxidation. Overall, tuning the Mn/Cu ratio enables efficient, selective, and simultaneous removal of CO and VOCs, providing a cost-effective solution for emission control from biomass combustion.
Introduction Afforestation is increasingly recognized as a key strategy to address climate change and ecological degradation, offering multiple ecosystem services. However, strategic planning is needed to ensure that afforestation actions are ecologically effective and economically efficient by targeting areas where ecosystem service provision is most significant.Objectives In this study, we provide a workflow to prioritize afforestation areas at national scale tailored to four distinct ecosystem service goals: ecological connectivity, human health, climate mitigation, and water regulation.Methods Using Italy as a case study, we applied goal-specific analysis to areas considered suitable for afforestation, integrating geospatial datasets of environmental and social factors. For each objective, spatial indicators were combined into a priority map at 1 km resolution, subsequently aggregated into composite maps. The top 20% priority areas for each objective were identified to inform national and regional planning.Results High-priority areas to improve ecological connectivity were focused around urban centers and extensive agricultural plains. Water regulation benefits were most relevant in urbanized and vineyard landscapes, while urban areas also emerged as priorities for human health. Climate mitigation potential was highest in moist temperate and mountain regions. Overlap among goals was limited, revealing significant trade-offs across ecosystem services.Conclusions The workflow provides a replicable approach to identify goal-specific afforestation priorities across diverse landscapes. It supports coordinated strategies to enhance ecosystem service provision and restoration effectiveness at national and regional levels.
Ensemble inequivalence, where a system's thermodynamic properties depend on the statistical ensemble used to describe it, is a well-established phenomenon in classical systems with long-range interactions. Here, we present a detailed analysis of a quantum ferromagnet spin model that exhibits this same behavior. We find that the microcanonical and canonical phase diagrams are identical at zero temperature (T = 0), but differ significantly at finite temperatures. Our results highlight a breakdown of ensemble equivalence in this quantum long-range model, contrasting with what is observed for short range. These findings have important implications for the study and manipulation of long-range interacting quantum platforms, such as those used in atomic, molecular, and optical physics.
