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A lower bound for the number of Egyptian fractions
Full text linkAn Egyptian fraction is a sum of the form 1/n1 +···+ 1/nr where
n1, ..., nr are distinct positive integers. We prove explicit lower bounds for
the cardinality of the set EN of rational numbers that can be represented by
Egyptian fractions with denominators not exceeding N. More precisely, we
show that for every integer k ≥ 4 such that lnk N ≥ 3/2 it holds
ln |EN |
ln 2 ≥
2 − 3
lnk N
N
ln N
k
j=3
lnj N,
where lnk denotes the k-th iterate of the natural logarithm. This improves on
a previous result of Bleicher and Erd ̋os [Illinois J. Math. 20 (1976), pp. 598–
613] who established a similar bound but under the more stringent condition
lnk N ≥ k and with a leading constant of 1.
Furthermore, we provide some methods to compute the exact values of
|EN | for large positive integers N, and we give a table of |EN | for N ≤ 154
Investigation of PCL/Bioactive Glass and PCL/Alumina-Toughened Zirconia Composites for Bone Tissue Engineering
No full textL'abstract è presente nell'allegato / the abstract is in the attachmen
Pathways to sustainability or collapse in inland small-scale aquaculture systems: insights from a social–ecological systems model
Full text linkDespite the promise of small-scale aquaculture for improving food security and alleviating poverty, its long-term sustainability remains poorly understood, particularly in contexts where economic and ecological processes reinforce each other. This paper develops a stylized social-ecological model that captures feedbacks between producer wealth, fish biomass, and nutrient dynamics in pond aquaculture. The model reveals how these intertwined feedbacks shape the long-term dynamics of the system and lead to monostability, bistability, or multistability. These regimes correspond to collapse, a high-yield but high-risk, and a sustainable equilibrium in fish production. Using bifurcation and stability analysis, we identify six dynamic scenarios: Clearwater, Overload, Flux, Knife-edge, Tipping pond and Decay, that represent qualitatively different long-term outcomes. Rather than predicting specific outcomes, the model gives a structural understanding of small-scale aquaculture dynamics and highlights the importance of local context and producers' heterogeneity in shaping the outcomes. It also provides a theoretical foundation for scenario-based management and empirical model development
Multiscale characterization of Ti-induced grain refinement in additively manufactured austenitic stainless steel
Full text linkIn-situ inoculation of grain-refining elements can effectively mitigate columnar grain growth and alleviate mechanical anisotropy in additively manufactured metals, while enhancing strength via the Hall-Petch effect. However, the refinement mechanism of Ti in austenitic stainless steel remains unclear. This study investigates Mn-assisted Ti inoculation in 316L stainless steel (SS316L), followed by annealing. Despite near-full densification, localized Ti enrichment formed coarse, brittle FeTi and C14 Laves intermetallic clusters, encapsulated by ultrafine ferritic grains within an austenitic matrix. Elevated annealing temperatures dissolved Laves phases and promoted Ti diffusion, resulting in dispersed TiO particles and ferritic domains. Refined Laves phases were redistributed to grain boundaries and triple junctions. Mechanical testing showed improved ductility with increasing annealing temperature: ultimate tensile strength decreased from 650 MPa to 610 MPa, while elongation rose from 13 % to 38 %. Hardness mapping revealed a more uniform distribution, though the maximum hardness dropped from 370 HV to 210 HV. Electrochemical corrosion tests in saline solution indicated that phase transformations induced by Ti-Mn co-inoculation undermined the corrosion resistance of SS316L, rendering it more susceptible to degradation in aggressive environments
Recent advances in lithium extraction from brine via solar-driven interfacial evaporation: Advanced strategies and challenges
No full text: In the framework of the green transition, the rising demand for electric vehicles and renewable energy technologies has substantially increased the need for efficient lithium extraction methods. Traditional lithium extraction methods from natural or synthetic brine are generally faced with challenges, such as high energy consumption and low efficiency, making it difficult to meet the demands for sustainable resource development. Solar interfacial evaporation technology has demonstrated substantial potential in lithium extraction due to its solar-driven process, efficient localized thermal management, and micro-interface regulation characteristics. In this review, the main methods of extracting lithium from brine and the latest progress and existing problems of lithium extraction by solar interfacial evaporation are reviewed, including coupling mechanisms between photothermal evaporation and lithium ion transport. In particular, design strategies of high-performance photothermal substrate and lithium selective functional layer, as well as the optimization path of anti-pollution and long-term stability are discussed. Furthermore, the advantages of multilayer device configurations and the optimization of three-dimensional evaporators in improving lithium extraction efficiency are analyzed. Finally, opportunities for future developments and challenges in this emerging research field are presented
Zero patterns in multi-way binary contingency tables with uniform margins
Full text linkWe study the problem of transforming a multi-way contingency table into an equivalent table with uniform margins and same dependence structure. This is an old question which relates to recent advances in copula modeling for discrete random vectors. In this work, we focus on multi-way binary tables and develop novel theory to show how the zero patterns affect the existence of the transformation as well as its statistical interpretability in terms of dependence structure. The implementation of the theory relies on combinatorial and linear programming techniques, which can also be applied to arbitrary multi-way tables. In addition, we investigate which odds ratios characterize the unique solution in relation to specific zero patterns. Several examples are described to illustrate the approach and point to interesting future research directions
Experimental validation and fracture mechanics analysis of an innovative UHPC-based material for structural strengthening
No full textThis study presents an experimental and fracture mechanics analysis of an innovative composite material engineered for structural strengthening, which is based on ultra-high performance concrete (UHPC) enhanced with a high dosage of steel fibres. The effectiveness of this material is evaluated on reinforced concrete (RC) beams that had been subjected to 24 years of sustained loading, representing a realistic, pre-damaged substrate. Combining four-point bending tests with acoustic emission (AE) monitoring, the research analyzes crack propagation, failure modes, and the interplay between mechanical response and AE parameters across micro-, meso‐, and macro-scales from a fracture mechanics perspective. Key findings include a 18% increase in ductility coefficient for beams with deeper UHPC layers, and AE-based precursors such as the b-value evolution and natural time variance reliably identified macro-fracture initiation. The RA-AF analysis quantified a meso‐scale transition from shear to tensile cracking with increased UHPC depth. The UHPC-RC vertical interface acts as a critical meso‐scale fracture process zone governing failure modes, with deeper UHPC applications enhancing ductility by promoting a tensile-dominated cracking mechanism. These results validate the superior performance of the proposed UHPC-based material in rehabilitating severely aged infrastructure and demonstrate that AE techniques, interpreted through fracture mechanics principles, offer unique insights into real-time multiscale damage progression beyond conventional measurements
Sol-Gel complements conventional strategies for the synthesis of self-extinguishing hybrid silica-epoxy nanocomposites
Full text linkSimplified vs Detailed Procedures to Assess the Energy Performance of Heating Storage Systems
No full textThe efficiency of the various technical building subsystems - such as emission, control, distribution, storage, and generation - significantly impacts overall building energy performance. Accurate calculation methods are essential for assessing subsystem heat losses and efficiencies. However, modelling these components while considering the interactions with each other, the building enve-lope and users is a complex issue, limiting the widespread use of highly accurate procedures. Therefore, numerical approaches that balance simplicity and accu-racy in the modelling of the subsystems are needed. Following the publication of Mandate M/480 EN, efforts have been made to improve the assessment of heating and cooling system performance. Nevertheless, several procedures still require improvements to maximize the efficacy of energy assessment. This work specifically focuses on the analysis of thermal storage systems. Current methods often oversimplify heat loss complexities, by simplifying the modelling of the water convective motes in the storage tank. As a result, simplified procedures show dis-crepancies compared to detailed calculations, highlighting the need for validated approaches. This research analyses simplified calculation methods for assessing thermal storage performance, identifying key parameters that influence energy losses, and aiming for a comprehensive validation. The study includes a compar-ative analysis of different simplified and detailed methods applied to a residential case study
