Fracture toughness is a critical mechanical property influencing the clinical durability of prosthodontic materials, especially those used in high-stress posterior regions. Differences in composition, microstructure, and fabrication technologies can significantly affect resistance to crack propagation. This experimental study evaluated the fracture toughness of three prosthodontic material groups (n = 10 each). Standardized samples were prepared and tested using the Vickers indentation technique under controlled laboratory conditions. Descriptive statistics were calculated for each group, and a one-way analysis of variance (ANOVA) was performed to determine significant differences among the groups. Post-hoc pairwise comparisons were conducted using Tukey’s Honest Significant Difference (HSD) test. Statistically significant differences in fracture toughness were observed among the three groups (p < 0.001). Group II demonstrated the highest mean fracture toughness (5.39 ± 0.34 MPa·m^1/2), followed by Group III (4.34 ± 0.36 MPa·m1/2). Group I recorded the lowest mean value (2.82 ± 0.56 MPa·m1/2). Tukey’s post-hoc analysis confirmed that all pairwise comparisons were significant (p < 0.001), indicating that each material group exhibited distinct mechanical performance profiles. The findings show that the fracture toughness of prosthodontic materials vary significantly depending on their composition and manufacturing technology. Materials in Group II outperformed the other groups, suggesting greater suitability for clinical situations where high resistance to fracture is required. Further studies incorporating additional mechanical tests and long-term clinical evaluation are recommended to validate these results under functional oral conditions. 

Abstract— This study examines the current state of conformity assessment (CA) in Libya, with a specific focus on the cement manufacturing sector as a case study. Conformity assessment, encompassing testing, inspection, certification, and accreditation, plays a critical role in ensuring product quality, safety, and market access. Libya faces challenges in implementing effective CA practices, hindering its economic diversification. This research evaluates stakeholder awareness, infrastructure adequacy, legal/institutional frameworks, and alignment with international standards using a mixed-methods approach. A stakeholder survey (N=54) and qualitative analysis of Libyan legal and regulatory documents were employed. Key findings reveal nominal CA awareness (82.69%), yet practical implementation gaps exist due to inadequate infrastructure (18.8% of respondents citing this as an obstacle), weak enforcement (18.8%), and limited technical expertise. The cement sector showed low Quality Management Systems (QMS) adoption (48%) and inconsistent adherence to the Libyan Portland Cement Standard LNS 340:2009. While support for aligning with international standards is strong (average rating 4.04/5), obstacles like lack of awareness (31.1%) and technical expertise (30.2%) impede progress. The study proposes actionable recommendations to strengthen Libya’s CA system, including developing a unified national framework, investing in accredited laboratories, and promoting collaboration.

Keywords— Conformity Assessment, Cement Industry, Libya, Quality Standards, Economic Diversification, Stakeholder Awareness.

In this paper, we consider the Bayesian estimation of the parameters and reliability function for a Cosine inverse log compound Rayleigh distribution under squared error and squared logarithmic loss functions. We use Lindley’s approximation to compute the Bayesian estimates. This method is evaluated using mean square error through simulation study with varying sample size.

The healthcare system in Libya faces significant challenges due to political instability, fragmented infrastructure, and inconsistent medical practices. Clinical Practice Guidelines (CPGs) serve as essential tools for standardising care, ensuring evidence- based treatment, and optimising healthcare resources. In Libya, the lack of structured guidelines has contributed to disparities in disease management, affecting patient outcomes and overall healthcare efficiency. This commentary explores the critical need for CPGs in Libya, highlighting their potential to improve healthcare delivery, minimise variability in treatment, and enhance patient safety. While implementation poses challenges, including centralisation, limited research capacity, and resource constraints, integrating CPGs through a phased implementation framework could be a transformative step toward a more resilient and equitable healthcare system. By fostering collaboration among policymakers, healthcare professionals, and international organisations, Libya can lay the foundation for a systematic approach to disease management, ultimately improving the quality of care for its population. Healthcare reform in Libya is urgently needed, and strategic investments in CPG development and dissemination could drive the necessary transformation in Libyan healthcare.

Abstract— Crime prediction has gained increasing attention due to the growing availability of historical crime data and the need for data-driven decision-making in public safety. This study presents a comparative analysis of Long Short-Term Memory (LSTM) architectures for predicting the exact occurrence time of crimes based on temporal patterns. Three LSTM-based models are evaluated: Vanilla LSTM, Stacked LSTM, and Bidirectional LSTM.

The proposed approach integrates time-based features and lag features to capture temporal dependencies within crime data. Model performance is assessed using standard regression metrics, including Mean Absolute Error (MAE), Mean Squared Error (MSE), and Root Mean Squared Error (RMSE). Experimental results indicate that deeper LSTM architectures combined with temporal lag information improve prediction accuracy compared to the baseline model.

This study demonstrates the effectiveness of LSTM-based models for crime occurrence prediction and provides insights into selecting suitable deep learning architectures for time-series crime analysis, supporting the development of more reliable tools for proactive crime prevention.

This paper introduces a finite topological space 𝜏𝑝 on the group of units modulo a prime 𝑝, defined by its basis of conjugate residue pairs {𝛼, 𝑝 − 𝛼} for all units 𝛼 ∈ 𝑈𝑝. We investigate the fundamental topological concepts such as point-set topology, separation axioms, and characterise the structure and behaviour of this topology. Additionally, we examine a function 𝑓 from 𝜏𝑝 to the topology of quadratic residues 𝜏𝑄, mapping each unit to its square modulo 𝑝. We analyse the continuity, openness of 𝑓, and explore its implications for separation properties. Furthermore, we define a quotient topology on 𝑈𝑝 based on the equivalence relation 𝑥 ∼ 𝑦 if and only if 𝑥2 ≡ 𝑦2 𝑚𝑜𝑑 𝑝, showing that the resulting quotient space is homeomorphic to (𝑄𝑝 , 𝜏𝑄 ).