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 G are ∅, each singleton {u} (u∈V(G)), and V(G). The graph G is indecomposable if all its modules are trivial; otherwise it is decomposable. For a graph G with at least four vertices, the decomposability dimension of G, denoted by dimdec(G), is the minimum number of successive subgraph complementations needed to transform G into an indecomposable graph. (A subgraph complementation replaces an induced subgraph by its complement.) For every integer n≥4, we define dimdec(n) as the maximum value of dimdec(G) over all n-vertex graphs G. We prove that dimdec(n)=dimdec(Kn)=dimdec(K‾n)=⌈log2(n+1)⌉.
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.
The development of biodegradable polymers presents a promising solution to the environmental challenges posed by non-biodegradable, petroleum-based plastics. This study investigated the development of sustainable and bioactive packaging films based on gelatin and pectin, incorporating date syrup as a natural antioxidant. Date syrup, a readily available and cost-effective by-product of date palm cultivation, was characterized by LC-HESI-MS and found to be rich in phenolic compounds, with gentisic acid identified as a major compound. Six film formulations with varying date syrup concentrations (1—10
