Given a graph G, a subset M of V(G) is a module of G if every vertex outside M is either adjacent to all vertices in M or to none. The trivial modules of Gare empty set, each singleton {u}(u is an element of V(G)), and V(G). The graph Gis indecomposable if all its modules are trivial; otherwise it is decomposable. For a graph Gwith at least four vertices, the decomposability dimension of G, denoted by dim(dec)(G), is the minimum number of successive subgraph complementations needed to transform Ginto an indecomposable graph. (A subgraph complementation replaces an induced subgraph by its complement.) For every integer n >= 4, we defifine dim(dec)(n) as the maximum value of dim(dec)(G) over all n-vertex graphs G. We prove that dim(dec)(n) = dim(dec) (K-n) = dim(dec)(K-n)=[log(2)(n+1)]. (c) 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
Contingency analysis is essential to the reliability and resilience of modern power systems, especially as grids face rising demand, broader interconnections and increasing renewable penetration. This review presents a global synthesis of N-1 and N-2 contingency studies performed on real transmission networks (2015–2025). By examining outage behaviors and operational vulnerabilities in emerging grids, the study highlights recurrent weaknesses and convergence issues under stressed conditions. The review provides a structured overview of contingency analysis methods, covering classical power-flow techniques and sensitivity-based indices. It also documents the major simulation platforms for modeling line outages, tracking overload propagation, and assessing voltage-regulation. By mapping these constraints to the mitigation strategies commonly applied, this review proposes a unified constraint-to-mitigation framework for planners and operators. The synthesis of results from diverse regional grids offers the largest cross-country comparative reference, supporting enhanced grid security, reduced cascading-failure risks, and the development of reliable and future-ready transmission networks.
α-Aminophosphonates are of considerable interest due to their potential pharmacological properties. The Kabachnik–Fields reaction, a one-pot, three-component condensation, is a prevalent method for the synthesis of α-aminophosphonates. Microwave irradiation has emerged as a popular technique owing to its efficiency, versatility, and environmentally benign nature, and has been successfully applied to the Kabachnik–Fields reaction. This approach offers significant advantages, including reduced reaction times, higher yields, and improved product purity. The present review provides a comprehensive overview of the synthesis of α-aminophosphonate derivatives via the Kabachnik–Fields reaction under microwave irradiation as a versatile, efficient, and green methodology. Various synthetic protocols and reaction conditions are discussed, encompassing the use of different catalysts, solvents, and starting materials, along with the diverse biological activities exhibited by the resulting α-aminophosphonates.
This study investigates the effect of climate risk on corporate employment decisions. Using a large sample from 41 countries, we find a positive association between climate risk and underinvestment in labor, notably manifesting as excessive employee layoffs. This indicates that climate risk leads to suboptimal employment decisions through labor cost reduction to mitigate the impact on firm performance. However, firms with higher commitment to social responsibility exhibit less suboptimal underinvestment in their workforce. Finally, we find that companies with greater financial constraints, those operating in highly polluting sectors, and those in countries with weak investor protection are more likely to underinvest in labor. Our study underscores the necessity for managers to integrate climate risk considerations into strategic planning to avoid suboptimal labor investments, whereas regulators are urged to enforce transparent climate risk disclosures and encourage CSR initiatives for sustainable employment practices.
Olive oil industry is generating significant quantities of wastes, such as pomace, that pose challenges to the circular economy strategies. Therefore, implementing sustainable technologies to develop ecofriendly products from those wastes can concurrently enhance sustainable agriculture and the bioeconomy. Our study aims to evaluate the effects of lignin nanoparticles (LNPs) derived from olive mill solid wastes (pomace) on pomegranate tree (Punica granatum L.) physiological and biochemical responses, as well as soil-related attributes. Pomegranate plants of two cultivars (Gabsi and Kalaii) grown under greenhouse conditions, were subject of -in soil- treatments with two doses of LNPs (C1 = 25 mg L− 1 and C2 = 75 mg L− 1) extracted from pomace. To assess the effects of these treatments, a range of phytochemical and mineral analyses were performed on plant leaves and soil samples. Pomegranate plants of two cultivars (Gabsi and Kalaii) grown under greenhouse conditions, were subject of -in soil- treatments with two doses of LNPs (C1 = 25 mg L− 1 and C2 = 75 mg L− 1) extracted from pomace. To assess the effects of these treatments, a range of phytochemical and mineral analyses were performed on plant leaves and soil samples. the outcomes of this study showed that LNPs, enhanced dry matter content, relative water content (RWC), Phi2, photosynthetic pigment, total flavonoid content (TFC), antioxidant activity (DPPH), and mineral contents; phosphorus, potassium, calcium and zinc (P, K, Ca and Zn) for both cultivars. However, LNPs application reduced malondialdehyde (MDA) and hydrogen peroxide (H2O2) contents in leaf tissues. Both treatments increased soil organic matter and enzymatic activities by fostering beneficial microorganisms. Our findings suggested the beneficial impact of LNPs application on pomegranate tree agro-physiological responses, by acting as biostimulant and biofertilizer. Those beneficial actions deserve more attention for the up-coming researches to introduce LNPs for a greener agriculture.
