ABSTRACT. This paper introduces a new class of sets, called R_(i^* )-open sets, within the framework of ideal topological spaces. In addition, it defines several types of R_(i^* )-open and R_(i^* )-closed functions and develops a generalized notion of continuity based on these sets. The main focus of this study is the concept of continuity, where new classes of 〖R 〗_(i^* )-continuous functions are introduced, examined, and systematically analyzed. The paper thoroughly investigates the fundamental properties of these functions and explores the relationships between these newly defined forms of continuity and other well-known types in topology. Furthermore, it demonstrates that R_(i^* )-open sets play a significant and central role in characterizing, extending, and unifying the concept of continuity in ideal topological spaces. Several illustrative results and observations are provided to clarify these relationships. The findings reveal that this approach not only generalizes classical continuity but also offers a broader and more flexible framework for studying functions and their behavior. This contributes to a deeper understanding of topological structures and opens new avenues for further research in this field

ABSTRACT. This study investigates the structural, mechanical, and thermal properties of epoxy composites reinforced with eggshell powder to develop sustainable and cost-effective industrial materials. Utilizing a simple hand-molding technique, epoxy was reinforced with varying weight fractions of eggshell waste and subjected to different thermal treatments ranging from 7°C to 150°C. Mechanical evaluations revealed that small additions of eggshell powder, specifically between 1 and 3 wt%, significantly improved the impact resistance, hardness, tensile strength, and compressive strength of the matrix. The optimal mechanical performance was consistently observed at a curing temperature of 50°C, where the material achieved maximum cross-link density. Conversely, higher filler concentrations led to particle agglomeration and structural defects, which degraded mechanical integrity. Morphological and structural analyses using SEM, EDX, and XRD confirmed the homogeneous distribution of the filler at low concentrations and verified the presence of the thermally stable calcite phase of calcium carbonate. Furthermore, thermal conductivity increased alongside temperature and filler addition. These eco-friendly composites demonstrate immense potential for applications in lightweight automotive parts and sustainable construction materials.

ABSTRACT. This study introduces and investigates SRT-open sets as a new class of generalized open sets in ideal topological spaces. Their fundamental properties are established and supported by illustrative examples that clarify their behavior within the ideal framework. Several associated classes of functions are also examined, including SRI-continuous, strongly SRI-continuous, and SRI-irresolute mapping, together with their essential properties and relationships. Furthermore, new covering properties, namely SRI-compactness and SRI-Lindelöff spaces, are introduced and investigated, and their connections with the corresponding classical topological concepts are established. In addition, a new notion of connectedness, called connectedness via SRI-open sets, is defined and characterized through several equivalent results. The relationships between this generalized connectedness and classical connectedness are also discussed. The obtained results enrich the theory of ideal topological spaces, extend existing generalized topological structures, and provide a broader framework for studying generalized open sets, generalized continuity, covering properties, and connectedness, offering promising directions for future research in topology.

ABSTRACT. Ultraviolet C radiation (275 nm) is a potent genotoxic agent that induces DNA strand breaks, cyclobutane pyrimidine dimers, and 6–4 photoproducts in exposed cells. Red light photobiomodulation (PBM), delivered via light-emitting diodes (LEDs) at 633–655 nm, has emerged as a promising non-invasive strategy to stimulate DNA repair. This study investigated and compared the cytoprotective efficacy of red LED irradiation applied either before (Red+UV) or after (UV+Red) UVC exposure in rat embryonic fibroblast (REF) cells, using the alkaline comet assay and the MTT colorimetric assay as quantitative endpoints. UVC irradiation (10 mJ/cm2) induced a significant increase in medium- and high-damage comets (p < 0.0001) and reduced cell viability by ~43% relative to untreated controls. These findings demonstrate that post-irradiation PBM is the superior therapeutic modality.