Simple mathematical expressions are given for the betweenness centrality of nodes in trees, forests and cycles. As application, a centrality test is given for when a network might be a forest.

This work investigates epoxy composites reinforced by randomly oriented, short glass fibres and silica microparticles. A full-factorial experiment evaluates the effects of glass fibre mass fraction (15 wt% and 20 wt%) and length (5 mm and 10 mm), and the mass fraction of silica microparticles (5 wt% and 10 wt%) on the apparent density and porosity, as well as the compressive and tensile strength and modulus of the hybrid composites. Hybrid epoxy composites present significantly higher tensile strength (9%) and modulus (57%), as well as compressive strength (up to 15%) relative to pure epoxy.

Effective small and medium enterprise (SME) leadership demands creative solutions to ensure organisations survive and thrive during the turbulent times that COVID-19 continues to bring. This paper explores how SME leaders (in micro and small organisations) prioritise and access the skills and development needed to provide effective and sustainable leadership to organisations, focusing on the role of resilience and the benefits it provides. Participants were selected through purposive and snowballing sampling. Online surveys and semi-structured interviews were conducted and provided qualitative data that contributes to an understanding of the role of resilience and the view of participants as to what is needed to effectively respond to a dynamic environment. Evidence shows that SME leaders prioritise learning and development opportunities that provide demonstrable benefits throughout the organisation. Building business resilience remains a fuzzy concept; however, viewing resilience as a multi-level construct offers benefits when designing and delivering development opportunities. It has been found that networking, partnerships, and relationship building promote resilience and may offer a solution to how to embed resilience building into development opportunities that SME leaders value and wish to engage with. This article contributes by illustrating and exploring leadership development within SMEs during a period of unexpected and untested uncertainty. The pandemic caused major shock waves within business communities, and SMEs were significantly affected. The research is limited in that it is expected to be a once-in-a lifetime event, and as such conditions may not be replicable, learning opportunities for other ‘shock’ events are possible. The findings of this paper have relevance to practice in that, while the event may be one-off, shocks to the business environment are not.

Green manufacturing is increasingly becoming popular, especially in lubricant manufacturing, as more environmentally friendly substitutes for mineral base oil and synthetic additives are being found among plant extracts and progress in methodologies for extraction and synthesis is being made. It has been observed that some of the important performance characteristics need enhancement, of which nanoparticle addition has been noted as one of the effective solutions. However, the concentration of the addictive that would optimised the performance characteristics of interest remains a contending area of research. The research was out to find how the concentration of green synthesized aluminum oxide nanoparticles in nano lubricants formed from selected vegetable oils influences friction and wear. A bottom-up green synthesis approach was adopted to synthesize aluminum oxide (Al₂O₃) from aluminum nitrate (Al(NO₃)₃) precursor in the presence of a plant-based reducing agent—Ipomoea pes-caprae. The synthesized Al₂O₃ nanoparticles were characterized using TEM and XRD and found to be mostly of spherical shape of sizes 44.73 nm. Al₂O₃ nanoparticles at different concentrations—0.1 wt%, 0.3 wt%, 0.5 wt%, 0.7 wt%, and 1.0 wt%—were used as additives to castor, jatropha, and palm kernel oils to formulate nano lubricants and tested alternately on a ball-on-aluminum (SAE 332) and low-carbon steel Disc Tribometer. All the vegetable-based oil nano lubricants showed a significant decrease in the coefficient of friction (CoF) and wear rate with Ball-on-(aluminum SAE 332) disc tribometer up to 0.5wt% of the nanoparticle: the best performances (e_COF = 92.29; e_WR = 79.53) came from Al₂O₃-castor oil nano lubricant and Al₂O₃-palm kernel oil; afterwards, they started to increase. However, the performance indices displayed irregular behaviour for both COF and Wear Rate (WR) when tested on a ball-on-low-carbon steel Disc Tribometer.

This comprehensive review explores the forefront of nanohybrid materials, focusing on the integration of coordination materials in various applications, with a spotlight on their role in the development of flexible solar cells. Coordination material-based nanohybrids, characterized by their unique properties and multifunctionality, have garnered significant attention in fields ranging from catalysis and sensing to drug delivery and energy storage. The discussion investigates the synthesis methods, properties, and potential applications of these nanohybrids, underscoring their versatility in materials science. Additionally, the review investigates the integration of coordination nanohybrids in perovskite solar cells (PSCs), showcasing their ability to enhance the performance and stability of next-generation photovoltaic devices. The narrative further expands to encompass the synthesis of luminescent nanohybrids for bioimaging purposes and the development of layered, two-dimensional (2D) material-based nanostructured hybrids for energy storage and conversion. The exploration culminates in an examination of the synthesis of conductive polymer nanostructures, elucidating their potential in drug delivery systems. Last but not least, the article discusses the cutting-edge realm of flexible solar cells, emphasizing their adaptability and lightweight design. Through a systematic examination of these diverse nanohybrid materials, this review sheds light on the current state of the art, challenges, and prospects, providing valuable insights for researchers and practitioners in the fields of materials science, nanotechnology, and renewable energy.