Zernike polynomials are widely used in optics and ophthalmology due to their direct connection to classical optical aberrations. While orthogonal on the unit disk, their application to discrete data or non-circular domains--such as ellipses, annuli, and hexagons--presents challenges in terms of numerical stability and accuracy. In this work, we extend Zernike-like orthogonal functions to these non-standard geometries using diffeomorphic mappings and construct sampling patterns that preserve favorable numerical conditioning. We provide theoretical bounds for the condition numbers of the resulting collocation matrices and validate them through extensive numerical experiments. As a practical application, we demonstrate accurate wavefront interpolation and reconstruction in segmented mirror telescopes composed of hexagonal facets. Our results show that appropriately transferred sampling configurations, especially Optimal Concentric Sampling and Lebesgue points, allow stable high-order interpolation and effective wavefront modeling in complex optical systems. Moreover, the Optimal Concentric Samplings can be computed with an explicit expression, which is a significant advantage in practice.
The increasing accumulation of plastic waste (PW) and its low recycling rates pose serious environmental challenges. This study investigates the replacement of coarse aggregate (CA) with polycarbonate PW at levels of 20%, 30%, and 40% in concrete prisms (100x50x400 mm), tested under drop-weight impact loading and validated with finite element method (FEM) simulations. PW incorporation reduced workability (slump from 165 mm to 35 mm) and bulk density (2215 to 1930 kg/m3), alongside compressive strength losses of 25-49% and modulus reductions of 15-34%. However, PW30% demonstrated the highest impact resistance, with a peak Tup load of 14,170 kN at 0.6 ms, bending load of 4152 kN, and inertial load of 5084 kN, confirming its superior energy absorption. Dynamic-to-static ratios also improved with PW, with fracture energy increasing from 3.05 to 10.1. FEM results confirmed these behaviors, particularly for PW30%. Overall, PW30% offers an optimal balance of ductility and toughness, suggesting its suitability for impact-resistant and lightweight applications.
The phytochemical profile and antioxidant capacity of Ruta graveolens L. leaves, collected from Msallata, Libya, are investigated in this study. Four solvents were used to extract the bioactive compounds: petroleum ether, ethanol, water, and chloroform. Moisture, ash, total proteins, total alkaloids, total phenols, total flavonoids, antioxidant activity, and mineral content in the leaves were measured. Ethanol was the extract with the highest extraction efficiency (16.32%) and the highest concentrations of antioxidant activity (6.47 mg/g), total flavonoids (3.77 mg/g), and total phenols (37.65 mg/g). According to phytochemical screening, all extracts lacked saponins but contained proteins, carbohydrates, phenols, flavonoids, alkaloids, coumarins, glycosides, steroids, and terpenes. Copper was the least common element, according to mineral analysis, whereas calcium, sodium, and magnesium were the most abundant. Iron was the most prevalent heavy metal, followed by zinc, with the overall order being Ca > Na > Mg > Fe > Zn > Cu. These results show the abundance of bioactive chemicals and natural antioxidants in R. graveolens L. leaves, demonstrating their potential uses in the production of functional foods and health promotion.
This grammatical and rhetorical study investigates the rulings on clauses that have no place in grammatical analysis (lā maḥalla lahā min al-i‘rāb), focusing specifically on the disconnected clause (al-jumla al-munqaṭi‘a) as articulated in Al-Shumunni’s gloss "Al-Munsif" on Ibn Hisham’s "Mughni Al-Labib". The research defines the disconnected clause as one whose grammatical and structural connection to what precedes it is severed, either phonetically or semantically. It analyzes the parenthetical clause of supplication, which maintains a semantic link while lacking a literal connector, and addresses the problematic absence of explicit or implicit ties in certain Quranic verses. Furthermore, the study explores the rhetorical approach to specialized resumption (al-isti’nāf al-bayānī) as a precise response to implicit contextual questions, categorizing them into general causative inquiries, specific causative inquiries, and inquiries for emphasis and negation. It examines the rulings on clauses following implicit prepositions and the mechanics of coordination based on syntactic locus. Additionally, the analysis addresses structural connectors in nominal circumstantial clauses and reviews the major scholarly disagreements concerning introductory or resumptive clauses following the particle of extent (ḥattā).
The purpose of this study is to address the critical challenge of insider threats and privacy risks in Human Resource Management (HRM) employee data systems by developing a secure and scalable framework for authorized data access and threat detection. The proposed methodology integrates Artificial Intelligence (AI), Machine Learning (ML), and blockchain technologies, where redundant employee records are removed, sensitive information is extracted using the Fuzzy Basis Cubic Spline Rule (FBCSR), and privacy is preserved through the R & ouml;ssler Attractor K-Anonymity (RAKA) approach. In the unified workflow, RAKA first anonymizes sensitive employee attributes, HSMPC then encrypts and securely stores the protected data on the blockchain for authorized sharing, and finally FBCSR enables real-time insider threat detection from user access activities, providing an end-to-end security solution for HRM applications. Employee data are further partitioned using Fuzzy C-Means (FCM) clustering and securely encrypted via Hybrid Secure Multi-Party Computation (HSMPC) before being stored on a blockchain supported by the PoSABS consensus mechanism and context-aware smart contract access control. Experiments conducted using the Employee dataset and the EventSim dataset demonstrate that the proposed framework achieves an insider threat detection accuracy of 96.19% while effectively preventing unauthorized access with improved scalability and encryption efficiency. The study provides an important implication for HRM organizations and policy makers by recommending blockchain-enabled privacy-preserving access governance to strengthen employee data protection and insider threat monitoring in real-world enterprise environments. The originality of this research lies in the novel integration of FBCSR-based threat detection with HSMPC encryption and scalable PoSABS blockchain consensus, offering a robust contribution toward secure employee data management in modern HRM systems.
