Logarithmic interpolation methods and measure of non-compactness

We derive interpolation formulae for the measure of non-compactness of operators interpolated by logarithmic methods with [θ] = 0; 1 between quasi-Banach spaces. Applications are given to operators between Lorentz-Zygmund spaces

The equivalence theorem for logarithmic interpolation spaces in the quasi-Banach case

We study the description by means of the J-functional of logarithmic interpolation spaces (A0, A1) 1, q, A in the category of the p-normed quasi-Banach couples (0 < p ≤ 1). When (A0, A1) is a Banach couple, it is known that the description changes depending on the relationship between q and A. In our more general setting, the parameter p also has an important role as the results show

enmpa: An R package for ecological niche modeling using presence-absence data and generalized linear models

Here, we present the new R package “enmpa,” which includes a range of tools for modeling ecological niches using presence-absence data via logistic generalized linear models. The package allows users to calibrate, select, project, and evaluate models using independent data. We have emphasized a comprehensive search for ideal predictor combinations, including linear, quadratic, and two-way interaction responses, to provide more detailed and robust model calibration processes. We demonstrate the use of the package with an example of a simulated pathogen and its niche. Since enmpa is designed specifically to work with presence-absence data, our tools are particularly useful for studies with data derived from a detection or non-detection sampling universe, such as pathogen testing results. enmpa can be downloaded from CRAN, and the source code is freely available on GitHub

Associate spaces of logarithmic interpolation spaces and generalized Lorentz-Zygmund spaces

We determine the associate space of the logarithmic interpolation space (X0, X1)1,q,A where X0 and X1 are Banach function spaces over a σ-finite measure space (Ω, µ). Particularizing the results for the case of the couple (L1, L∞) over a non-atomic measure space, we recover results of Opic and Pick on associate spaces of generalized Lorentz-Zygmund spaces L(∞,q;A). We also establish the corresponding results for sequence spaces

La formación para la acreditación de líderes escolares

Los líderes escolares deben adaptar sus actuaciones a los retos actuales, desempeñando funciones vinculadas a su perfil profesional, acorde a las líneas estratégicas establecidas en el marco normativo vigente. De ahí que sea necesario formar directivos que sepan liderar y gestionar los cambios que la escuela demanda, al tiempo que se favorece el desarrollo de sus correspondientes competencias tanto genéricas como específicas. Así, desde el marco de formación permanente, se gestiona el “Curso sobre el desarrollo de la función directiva” de ámbito regional andaluz, mediante el cual, se promueven competencias esenciales para el desempeño directivo relativas al liderazgo, relaciones humanas, gestión del aprendizaje y evaluación institucional. En este trabajo, presentaremos datos obtenidos en la última convocatoria realizada, describiendo la muestra de participantes, estructura y diseño de la propuesta formativa e instrumentos de recogida de evidencias con los que realizar análisis valorativo de los participantes, extracto de perfiles de género, años de docencia y de experiencia en el desempeño de la función directiva. En los resultados se presentan conclusiones alcanzadas en torno al liderazgo escolar, competencias profesionales directivas, dificultades y logros aportados para la gestión y organización escolar y la propia valoración del directivo en cuanto al procedimiento de acreditación.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Noise-Aware Variational Eigensolvers: A Dissipative Route for Lattice Gauge Theories

We propose a novel variational ansatz for the ground-state preparation of the ℤ2 lattice gauge theory (LGT) in quantum simulators. It combines dissipative and unitary operations in a completely deterministic scheme with a circuit depth that does not scale with the size of the considered lattice. We find that, with very few variational parameters, the ansatz can achieve >99% precision in energy in both the confined and deconfined phase of the ℤ2 LGT. We benchmark our proposal against the unitary Hamiltonian variational ansatz showing a reduction in the required number of variational layers to achieve a target precision. After performing a finite-size scaling analysis, we show that our dissipative variational ansatz can predict accurate critical exponents without requiring a number of layers that scales with the system size, which is the standard situation for unitary ansätze. Furthermore, we investigate the performance of this variational eigensolver subject to circuit-level noise, determining variational error thresholds that fix the error rate below which it would be beneficial to increase the number of layers. In light of these quantities and for typical gate errors � in current quantum processors, we provide a detailed assessment of the prospects of our scheme to explore the ℤ2 LGT on near-term devices

Interpolation of the measure of non-compactness of bilinear operators among quasi-Banach spaces

Working in the setting of quasi-Banach couples, we establish a formula for the measure of non-compactness of bilinear operators interpolated by the general real method. The result applies to the real method and to the real method with a function parameter

Function spaces of Lorentz-Sobolev type: Atomic decompositions, characterizations in terms of wavelets, interpolation and multiplications

We establish atomic decompositions and characterizations in terms of wavelets for Besov-Lorentz spaces Bsq Lp,r (Rn) and for Triebel-Lizorkin-Lorentz spaces Fsq Lp,r (Rn) in the whole range of parameters. As application we obtain new interpolation formulae between spaces of Lorentz-Sobolev type. We also remove the restrictions on the parameters in a result of Peetre on optimal embeddings of Besov spaces. Moreover, we derive results on diffeomorphisms, extension operators and multipliers for Bsq Lp,∞ (Rn). Finally, we describe Bsq Lp,r (Rn) as an approximation space, which allows us to show new sufficient conditions on parameters for Bsq Lp,r (Rn) to be a multiplication algebra