By using a certain general conic domain as well as the quantum (or q-) calculus, here we define and investigate a new subclass of normalized analytic and starlike functions in the open unit disk $\mathbb{U}$ . In particular, we find the Hankel determinant and the Toeplitz matrices for this newly-defined class of analytic q-starlike functions. We also highlight some known consequences of our main results.

Extreme climatic events, such as floods, are becoming increasingly frequent and severe worldwide, including in Pakistan. The Swat River Catchment (SRC), located in the eastern Hindukush region of Pakistan, is highly susceptible to flooding due to its unique geographical and climatic conditions. However, despite the region’s susceptibility, comprehensive flood risk assessments that integrate hazard, vulnerability, and exposure components remain limited. To address this gap, this study assesses flood risk in the SRC using 22 indicators distributed across the three core dimensions of flood risk: hazard, vulnerability, and exposure. Flood hazard was modeled using 11 indicators, broadly categorized into environmental, hydrological, and geographical aspects, while vulnerability was evaluated through socio-economic factors, geographical proximity, and land use characteristics. Exposure was analyzed based on population metrics and critical infrastructure. All data were converted into thematic layers in GIS, systematically weighted using the Analytical Hierarchy Process (AHP) and combined to produce hazard, vulnerability, and exposure maps respectively. These maps were then integrated through a risk equation to generate the final flood risk map. The results reveal that 31% of the study area is in a high flood risk zone, 27% in moderate risk zones, 23% in low risk, and 19% are safe areas. The results were validated using the Area Under the Curve (AUC) technique, yielding a value of 0.92, which indicates high reliability. By presenting the first integrated flood risk assessment for the SRC, this study provides valuable insights into flood-prone areas and risk distribution. These results highlight the urgent need for enhanced flood risk management, especially in urban areas. The developed methodology serves as a valuable tool for disaster management authorities and planners, helping them make risk-informed decisions, allocate resources efficiently, and implement targeted flood mitigation strategies.

In the title compound, [Fe(C(5)H(5))(C(18)H(14)NO)], the unsubstituted cyclo-penta-dienyl ring is disordered over two sets of sites with occupancy ratio of 0.55 (1):0.45 (1). One conformation has the rings eclipsed and the other staggered. An intra-molecular C-H⋯O hydrogen bond forms an S(6) ring motif. In the crystal, inter-molecular C-H⋯O and N-H⋯O hydrogen bonds lead to R(2) (1)(7) ring motifs. The mol-ecules are linked into polymeric chains extending along the b axis.

In recent years, special functions such as Bessel functions have been widely used in many areas of mathematics and physics. We are essentially motivated by the recent development; in our present investigation, we make use of certain conic domains and define a new class of analytic functions associated with the Dini functions. We derive inclusion relationships and certain integral preserving properties. By applying the Bernardi-Libera-Livingston integral operator, we obtain some remarkable applications of our main results. Finally, in the concluding section, we recall the attention of curious readers to studying the q-generalizations of the results presented in this paper. Furthermore, based on the suggested extension, the $(\mathfrak{p},q)$-extension will be a relatively minor and unimportant change, as the new parameter $\mathfrak{p}$ is redundant.

In this paper, we define new subclasses of $k$-uniformly Janowski starlike and $k$-uniformly Janowski convex functions associated with $t$-symmetric points. The integral representations, convolution properties and coefficient bounds for these classes are studied.