This paper introduces a unified framework for fixed point theorems involving asymptotically regular mappings in \(b\)-metric spaces through the concept of contractive families. We establish a general fixed point theorem that encompasses various existing results, including those of Kannan-type and generalized contractive conditions, as special cases. In particular, we demonstrate that the recent results of Nagac and Tas [1] emerge naturally as special cases of our main theorem through appropriate parameter choices. The main result employs coefficient functions and a general auxiliary function with strengthened continuity conditions, providing flexibility that allows the derivation of numerous particular cases. Several corollaries with complete proofs are presented to demonstrate that our results properly generalize and extend well-known theorems in the literature.

This paper introduces the concept of edge sum labeling in hypergraphs, where the edges of a hypergraph \(\mathcal{H}\) are assigned distinct positive integers such that the sum of the labels of all edges incident to any vertex is itself an edge label of \(\mathcal{H}\). Moreover, if the sum of the labels of any collection of edges equals the label of another edge in \(\mathcal{H}\), those edges must be incident to at least one common vertex. Additionally, we define and investigate zero edge sum hypergraphs, exploring their unique properties and presenting various results related to this new class of hypergraphs.

The basic building block of a modern block cipher is the substitution box (S-box), which provides the nonlinearity that is required when fending off advanced cryptanalytic methods. The novel approach introduced in the present work is computationally efficient, but it is still a robust algorithm for generating an 8 8 S-box through an operation of a specifically defined bijective mapping over the Galois Field \(GF(2^{8})\). The proposed S-box was strictly tested on a broad range of standard security criteria to prove its cryptographic integrity. A good performance has been identified in the analysis with a nonlinearity of 112 and linear approximation probability (LAP) of 0.0625, and the outstanding element of differential approximation probability (DAP) of 0.0156. Using a strong cryptographic construction, the new AES structure implements an S-box whose avalanche-like properties are best shown by a low value of the strict avalanche criterion (SAC) 0.4995 and strong bit independence (BIC) scores. The experimental results have supported the hypothesis that the proposed S-box has a much greater resistance to both the differential and the linear attacks compared with the state-of-the-art algebraic, heuristic, and chaos-based designs. In order to show how applicable the S-box can be in practical terms, a framework of image encryption incorporates the use of the S-box in it, whereby it operates as the basis element of a block cipher. The resulting cipher image achieved an entropy of 7.9978, which demonstrates a very high degree of randomness and strong resistance to statistical attacks. The feature article introduces a significant step towards systematizing cryptographic design through the introduction of a sound and carefully defined framework for the construction of high-security S-boxes.

The present study investigates the phytochemical composition and biopesticidal efficacy of bark extracts from four medicinal plants—Terminalia arjuna, Neltuma juliflora, Saraca asoca, and Cinnamomum verum—against the stored-grain pest Tribolium castaneum (Herbst). Bark samples were taxonomically authenticated, extracted using standardized protocols, and subjected to qualitative phytochemical screening, revealing abundant alkaloids, flavonoids, terpenoids, phenolics, and other secondary metabolites. GC–MS profiling, supported by retention time, fragmentation patterns, and library match scores, identified several bioactive constituents, with T. arjuna and N. juliflora displaying the highest diversity and peak abundance. Repellency and toxicity bioassays, conducted with three independent replicates, demonstrated a significant concentration- and time-dependent response. One-way ANOVA followed by LSD post-hoc analysis confirmed statistically significant differences among treatments, while probit analysis provided LC₅₀ values with 95% confidence intervals, establishing T. arjuna as the most potent extract. In-silico molecular docking further highlighted compounds such as ellagic acid, catechin, quercetin, and luteolin as strong binders to key insect enzymatic targets, showing interaction energies comparable to or exceeding those of the synthetic insecticide malathion. Collectively, the integrated chemical, biological, and computational evidence underscores the promise of T. arjuna and N. juliflora bark extracts as effective, biodegradable, and environmentally safe biopesticide candidates. The findings support further purification, SAR-guided optimization, and field-scale validation of the active compounds for sustainable pest-management applications.

A series of novel substituted benzaldehyde derivatives of 4-Amino-7H-pyrrolo[2,3-d]pyrimidine (4A7HPP), designated as compounds 1a–1d, were synthesized under microwave irradiation, providing a safe, cost-effective, and efficient alternative to conventional procedures. The condensation of 4A7HPP with hydroxybenzaldehyde analogues in DMF afforded the corresponding imine derivatives in high yields (71.54–85.02%) with reduced reaction time and solvent consumption. The synthesized compounds were characterized by ¹H NMR, FT-IR, UV–Vis spectroscopy, and elemental analysis, confirming the presence of characteristic azomethine (–CH=N–) and aromatic proton signals. The compounds exhibited significant antibacterial activity against Staphylococcus aureus, Bacillus subtilis, Escherichia coli, and Pseudomonas aeruginosa (MIC: 7.5–28 mm), surpassing the standard drug streptomycin. Notably, antifungal evaluation against Candida albicans and Saccharomyces cerevisiae demonstrated activity up to 2.5 times greater than fluconazole. Molecular docking studies performed against target proteins—S. aureus DHFR (PDB ID: 2W9H), E. coli DHFR (PDB ID: 1RX2), and C. albicans ERG11 (PDB ID: 5TZ1)—revealed stronger binding affinities for compounds 1b and 1d (−8.3 to −9.0 kcal mol⁻¹) compared with reference ligands, supported by low RMSD values (0.655–0.785 Å). Brine shrimp lethality bioassay indicated moderate cytotoxicity (LD₅₀: 3.50–8.50 × 10⁻⁴ M). ADME analysis suggested favorable pharmacokinetic profiles, high gastrointestinal absorption, and compliance with Lipinski’s rule of five. These results highlight compounds 1a–1d as potential lead molecules for the development of new antimicrobial and antifungal agents, warranting further biological and pharmacological investigations.