Fundamental Solutions for Abstract Fractional Evolution Equations with Generalized Convolution Operators

We investigate a class of abstract fractional evolution equations governed by convolution-type derivatives associated with Sonine kernels. These generalized derivatives encompass several known fractional operators, including the Caputo--Dzhrbashyan and distributed-order derivatives. We analyze the Cauchy problem $$\partial_t(k \ast (u - u_0))(t) = -A^\alpha u(t),$$ where $k$ is a Sonine kernel, $A$ is a closed linear operator generating a bounded analytic semigroup, and $\alpha \in (0,1)$. Using functional analytic techniques and subordination theory, we establish well-posedness in the space of infinitely smooth vectors and derive explicit representations for the solution via Laplace transforms and fractional semigroup theory. Several examples involving the Laplacian on different function spaces are discussed to illustrate the theory

El uso educativo y social del smartphone de los jóvenes universitarios

El smartphone se ha convertido en un elemento esencial en la vida de los jóvenes, desempeñando un papel clave en actividades sociales y educativas. Este estudio exploratorio, de diseño no experimental y enfoque cuantitativo, analiza cómo los estudiantes universitarios utilizan el smartphone a nivel educativo y social, así como los espacios en los que lo emplean. La muestra incluyó a 282 estudiantes. El análisis de los datos empleó estadísticas descriptivas y pruebas paramétricas, como la correlación de Pearson y la prueba t de Student. Los resultados revelan que los estudiantes valoran de manera equitativa el uso educativo y social del dispositivo. Aunque actividades como la búsqueda de información y las redes sociales son comunes, el uso educativo predomina en contextos tranquilos como el hogar o el transporte, mientras que el uso social es más frecuente en espacios públicos. Estos hallazgos refuerzan la polivalencia del smartphone en la vida universitaria

Comparison on the Use of Hybrid and Plugin Hybrid Electric Buses for Sustainable Urban Transportation–Split Use Case

Urban livability faces significant challenges due to traffic congestion, noise, and vehicle emissions. Electric buses offer a promising solution to reduce noise and tailpipe emissions in cities. However, their limited range, constrained by battery capacity, can hinder operational flexibility. As an alternative, plug-in hybrid electric buses (PHEB) and hybrid buses (HB) provide a more versatile option by combining zero-emission capabilities with conventional diesel engines. Their efficiency depends on battery capacity and the strategic allocation of electric drive sections along routes. Yet, existing electric drive assignment systems remain suboptimal, as they do not fully exploit the potential of hybrid propulsion

Maximal regularity of solutions for the tempered fractional Cauchy problem

Let $X$ be a Banach space. Given a closed linear operator $A$ defined on $X$ we show that, in vector-valued H\"older spaces $C^{\alpha}(\R,X)\, \, (0<\alpha<1)$, maximal regularity for the abstract Cauchy problem can be characterized solely in terms of a spectral property of the operator $A$, when we equip the Cauchy problem with the tempered fractional derivative. In particular, we show that generators of bounded analytic semigroups admit maximal regularity

Optimal control strategy based on differential evolution algorithm for seamless transition between islanded and grid-connected operation modes in microgrid clusters

The increasing integration of renewable energy sources and distributed energy resources is accelerating the transformation of traditional power systems into smart grids. This transformation relies heavily on the deployment of microgrids (MGs), which offer enhanced flexibility, resilience, and sustainability. However, ensuring the stable and efficient synchronization of MGs, especially during transitions between islanded and grid-connected modes, remains a critical and unresolved challenge. This challenge is further amplified in MG clusters (MGCs), where coordinated operation is essential to maintain power quality and system reliability. Driven by the need to address this challenge, this study proposes a real-time synchronization control method to enhance the dynamic performance and operational reliability of MGCs. The main objective is to design and validate an optimal control strategy capable of minimizing frequency deviations and improving power sharing during the synchronization process. To achieve this, an optimal seamless synchronization control based on a differential evolution (DE) algorithm is developed. This controller optimizes a frequency error control objective function in real time and is tested on an MGC architecture combining grid-forming (GFM) and grid-feeding (GFD) inverters. This work addresses the lack of robust, fast, and quantifiable synchronization methods for hybrid inverter-based MGCs, a gap that this study aims to fill. The proposed method enables accurate optimization of the transition between islanded and grid-connected modes. Simulation results demonstrate substantial performance gains: a 66.33% reduction in the ITSE compared to a synchronization strategy based on the fmincon optimization algorithm, and a 37.91% improvement over a conventional approach that adjusts synchronization by modifying the droop control coefficients. Furthermore, a comparative analysis with the particle swarm optimization (PSO) algorithm demonstrated that the DE-based approach reduces computation time by 20.29%, highlighting its superior efficiency and suitability for real-time embedded implementation. A sensitivity analysis involving 500 different scenarios, including evaluations under fault conditions, confirms the robustness of the approach. The average ITSE for these 500 simulations was 0.2459, with a standard deviation of 0.041, demonstrating consistent and reliable performance under varying load conditions. Moreover, a second sensitivity analysis, conducted over 250 simulations, identified the optimal DE parameters, enabling the selection of an effective combination of population size, mutation factor, and crossover rate. Finally, experimental validation using a Hardware-in-the-Loop setup, with an OPAL-RT4512 unit and a dSPACE MicroLabBox, verifies the effectiveness and real-time performance of the proposed control strategy

Dynamical Visualization and Qualitative Analysis of the (4+1)-Dimensional KdV-CBS Equation Using Lie Symmetry Analysis

This study investigates novel optical solitons within the intriguing (4+1)-dimensional Korteweg–de Vries–Calogero–Bogoyavlenskii–Schiff (KdV-CBS) equation, which integrates features from both the Korteweg–de Vries and the Calogero–Bogoyavlenskii–Schiff equations. Firstly, all possible symmetry generators are found by applying Lie symmetry analysis. By using these generators, the given model is converted into an ordinary differential equation. An adaptive approach, the generalized exp(-S(χ)) expansion technique has been utilized to uncover closed-form solitary wave solutions. The findings reveal a range of soliton types, including exponential, rational, hyperbolic, and trigonometric functions, represented as bright, singular, rational, periodic, and new solitary waves. These results are illustrated numerically and accompanied by insightful physical interpretations, enriching the comprehension of the complex dynamics modeled by these equations. Our approach’s novelty lies in applying a new methodology to this problem, yielding a variety of novel optical soliton solutions. Additionally, we employ bifurcation and chaos techniques for a qualitative analysis of the model, extracting a planar system from the original equation and mapping all possible phase portraits. A thorough sensitivity analysis of the governing equation is also presented. These results highlight the effectiveness of our methodology in tackling nonlinear problems in both mathematics and engineering, surpassing previous research efforts

EuPPollNet: A European Database of Plant-Pollinator Networks

Motivation: Pollinators play a crucial role in maintaining Earth's terrestrial biodiversity. However, rapid human-induced environmental changes are compromising the long-term persistence of plant-pollinator interactions. Unfortunately, we lack robust, generalisable data capturing how plant-pollinator communities are structured across space and time. Here, we present the EuPPollNet (European Plant-Pollinator Networks) database, a fully open European-level database containing harmonised taxonomic data on plant-pollinator interactions referenced in both space and time, along with other ecological variables of interest. In addition, we evaluate the taxonomic and sampling coverage of EuPPollNet, and summarise key structural properties in plant-pollinator networks. We believe EuPPollNet will stimulate research to address data gaps in plant-pollinator interactions and guide future efforts in conservation planning. Main Types of Variables Included: EuPPollNet contains 1,162,109 interactions between plants and pollinators from 1864 distinct networks, which belong to 52 different studies distributed across 23 European countries. Information about sampling methodology, habitat type, biogeographic region and additional taxonomic rank information (i.e. order, family, genus and species) is also provided. Spatial Location and Grain: The database contains 1214 different sampling locations from 13 different natural and anthropogenic habitats that fall in 7 different biogeographic regions. All records are geo-referenced and presented in the World Geodetic System 1984 (WGS84). Time Period and Grain: Species interaction data was collected between 2004 and 2021. Major Taxa and Level of Measurement: The database contains interaction data at the species level for 94% of the records, including a total of 1411 plant and 2223 pollinator species. The database includes data on 6% of the European species of flowering plants, 34% of bees, 26% of butterflies and 33% of syrphid species at the European level. Software Format: The database was built with R and is stored in ‘.rds’ and ‘.csv’ formats. Its construction is fully reproducible and can be accessed at: https://doi.org/10.5281/zenodo.14747448

3D-Printing of Highly Piezoelectric Barium Titanate Polymer Nanocomposites with Surface-Modified Nanoparticles at Low Loadings

This work describes the development and characterization of tetragonal barium titanate nanoparticles (BTO NPs) and their surface functionalization with dopamine dodecylamine (DDA), a lipophilic organic ligand. The so-obtained lipophilic NPs (BTO-DDA) are then formulated at low loadings (< 5 wt.%) into liquid photocurable resins for vat photopolymerization (VP) and 3D printed into solid objects. The printed composites are mechanically characterized in order to assess the effect of the nanomaterial on the mechanical properties of the 3D printed polymer, revealing no significant variations in the mechanical properties (tensile or flexural) of the nanocomposites compared to the original polymer matrix. In light of these results, the printed nanocomposites are studied in terms of their capacity to generate a separation of charge by the piezoelectric effect, typical of the BTO crystal structure. This study reveals that BTO-loaded nanocomposites display outstanding piezoelectric coefficients as high as 50 pC/N when BTO-DDA is formulated at 3.0 wt.%, only slightly less than one-third of the piezoelectric coefficient previously reported for bulk BTO, while preserving the mechanical properties of the polymer matrix

Conocimiento Didáctico Matemático de profesores de educación primaria en formación para enseñar probabilidad

La formación de los profesores de educación primaria en probabilidad es fundamental para desarrollar en sus estudiantes una comprensión temprana de los conceptos probabilísticos. El objetivo de este trabajo es evaluar el conocimiento didáctico-matemático para enseñar probabilidad de profesores españoles de educación primaria en formación. Para ello, se propone a 156 futuros profesores un cuestionario con tres tareas, cada una con cuatro apartados. El primero consiste en la resolución y justificación de la tarea y evalúa el conocimiento común de la probabilidad; en el segundo se pide identificar los objetos matemáticos requeridos en la solución y evalúa la faceta epistémica del conocimiento didáctico; el tercero requiere discriminar las respuestas correctas e incorrectas de estudiantes ficticios a la tarea, analizando así la faceta cognitiva; y el cuarto consiste en sugerir acciones para superar los errores de los estudiantes, evaluando así las facetas mediacional e interaccional. Los participantes muestran buen conocimiento común del contenido e identifican correctamente las respuestas correctas e incorrectas de los estudiantes ficticios. Es menor el desempeño en la identificación de objetos matemáticos, la explicación de los errores de los estudiantes y la sugerencia de acciones didácticas. Estos resultados sugieren puntos que se requieren reforzar en la formación de los profesores de educación primaria para enseñar probabilidad

Prototype Instrumentation for the Spatial and Temporal Characterisation of Voltage Supply Based on Two-Dimensional Higher-Order Statistics

This paper presents a proof-of-concept of a versatile Power Quality (PQ) analyser for tracking the voltage supply in industrial and residential sectors. It implements 2D Higher-Order Statistics (HOS) to assess voltage quality, based more on the sinusoidal waveform than on power fluctuations. Beyond the second-order parameters and permissible deviations regulated by the norm, EN 50160, the two-dimensional traces and probability density functions, along with a previously studied differential index, manage to identify different states of the electrical grid. Waveforms were measured in the wall plugs of a public building. In regard to analysing reliability and voltage waveform, the results corroborate that incorporating skewness and kurtosis indicators improves the characterisation, as well as extracting the customers’ supply behaviour under normal and anomalous operations. The instrument showed good behaviour in site characterisation, and the implemented method was considered as a probabilistic approach for the risk assessment of an installation. The prototype was tested in the facilities of a public building of the university, being able to detect deviations in 10 s traces of 3.9% in variance and 0.6% in kurtosis