This paper introduces and investigates D-soft compact spaces, a novel generalization of compactness in soft topological spaces using D-soft covers. We establish fundamental properties, characterizations, and relationships between D-soft compactness and other forms of soft compactness. Key results include the hereditary nature of D-soft compactness under specific conditions, the equivalence between D-soft and soft compactness in soft locally indiscrete spaces, and preservation under continuous mappings. The study provides new perspectives on compactness conditions in soft topology with potential applications in decision-making and uncertainty modeling. Several examples and counterexamples illustrate the theoretical developments, demonstrating that D-soft compactness is generally stronger than soft compactness.

In this paper, we introduce and investigate the concept of nearly α-compact topological spaces as a natural generalization of α-compact and countably α-compact spaces. We establish fundamental properties and characterizations of nearly α-compact spaces, demonstrating their relationship with various topological properties including α-continuity, separation axioms, and compactness-like properties. Several equivalent conditions for nearly α-compactness are provided, and we prove that the property is preserved under certain types of mappings. The behavior of nearly α-compact spaces under topological operations such as subspaces, products, and sums is thoroughly examined. We also introduce the notion of α-nearness and investigate its connection with nearly α-compact spaces. Additionally, we provide comprehensive examples and establish new theorems that demonstrate the richness and applicability of this concept.

This paper introduces new subclasses of bi-univalent functions of complex order linked with shell-like domains, formulated via the subordination principle and the q-analogue of Fibonacci numbers. Motivated by recent advances in q-calculus and its applications in geometric function theory, we construct and examine two distinct families of analytic bi-univalentfunctions. For these subclasses, coefficient estimates are derived for the initial Taylor–Maclaurin coefficients, together with sharp bounds for the Fekete–Szeg¨o functional expressed in terms of the involved parameters. The outcomes of this study extend and unify earlier results in the theory of bi-univalent functions, while providing new insights into the interaction between biunivalentfunction theory, the q-Fibonacci framework, and shell-like geometries. Furthermore, the subclasses established here may serve as a foundation for future studies in analytic function spaces, special functions, and their operator-theoretic connections.

This paper examines the mathematical model governing the behavior of a buoyant fluid column rising through a less buoyant ambient fluid within a confined region bounded by two vertical walls. The study represents a bounded-domain extension of the compositional plume model previously developed by Eltayeb and Loper for an unconfined environment. The system is characterized by five dimensionless parameters: (i) the Grashoff number, representing the ratio of buoyancy forces generated by concentration differences between the plume and the surrounding fluid to viscous forces; (ii) the Prandtl number, defined as the ratio of viscosity to thermal diffusivity; (iii) the plume thickness; (iv) the separation distance between the two vertical walls; and (v) the dimensionless distance between the plume and the nearest wall, with all length scales normalized using the salt-finger length scale. The principal aim of the study is to assess how the presence of boundaries modifies the solutions obtained for an unbounded ambient fluid, particularly in the high-Prandtl-number limit where thermal diffusion is drastically weaker than viscous diffusion. The analysis shows that the basic-state solution does not depend on either the Grashoff or Prandtl numbers. Unlike the unbounded case, where symmetry is preserved, the presence of sidewalls generally breaks this symmetry unless the plume is positioned exactly midway between the two boundaries. In an unbounded domain, the plume is always unstable and exhibits two independent modes of instability: the varicose (V) mode and the sinuous (S) mode. The introduction of sidewalls significantly changes the stability characteristics of the flow. This effect is heavily influenced by large Prandtl numbers, which narrow the thermal boundary layer and modify the spatial distribution of temperature perturbations. A strongly unstable region emerges when a thin plume is located near a boundary. In other areas of the parameter space, the instability growth rate remains comparable to that of the unbounded configuration but decreases as the distance between the walls becomes smaller. Instability continues to appear in two distinct classes of solutions related to the classical varicose and sinuous modes, although these modes are modified by both the high Prandtl number constraints and the plume’s position relative to the nearest sidewall.

This paper examines the mathematical model governing the behavior of a buoyant fluid column rising through a less buoyant ambient fluid within a confined region bounded by two vertical walls. The study represents a bounded-domain extension of the compositional plume model previously developed by Eltayeb and Loper [9 – 11] for an unconfined environment. The system is characterized by five dimensionless parameters: (i) the Grashoff number, representing the ratio of buoyancy forces generated by concentration differences between the plume and the surrounding fluid to viscous forces; (ii) the Prandtl number, defined as the ratio of viscosity to thermal diffusivity; (iii) the plume thickness; (iv) the separation distance between the two vertical walls; and (v) the dimensionless distance between the plume and the nearest wall, with all length scales normalized using the salt-finger length scale. The principal aim of the study is to assess how the presence of boundaries modifies the solutions obtained for an unbounded ambient fluid. The analysis shows that the basic-state solution does not depend on either the Grashoff or Prandtl numbers. Unlike the unbounded case, where symmetry is preserved, the presence of sidewalls generally breaks this symmetry unless the plume is positioned exactly midway between the two boundaries. In an unbounded domain, the plume is always unstable and exhibits two independent modes of instability: the varicose (V) mode and the sinuous (S) mode. The introduction of sidewalls significantly changes the stability characteristics of the flow. A strongly unstable region emerges when a thin plume is located near a boundary. In other areas of the parameter space, the instability growth rate remains comparable to that of the unbounded configuration but decreases as the distance between the walls becomes smaller. Instability continues to appear in two distinct classes of solutions related to the classical varicose and sinuous modes, although these modes are modified by the plume’s position relative to the nearest sidewall.