We present a theoretical model for analyzing skeletal muscle contraction, explicitly incorporating the deformation characteristics of muscle tissue. Additionally, we propose an analytical framework to investigate the mechanical behavior and contraction dynamics of the modeled muscle system. This approach offers a refined understanding of muscle function by integrating both structural and functional aspects into a cohesive mathematical representation.

In this paper, we focus on calculating the Mellin transform of three types of trigonometric functions, namely, \(\displaystyle\sum_{k=0}^{n}c_{k}\sin(a_{k}x)\), \(\displaystyle\sum_{k=0}^{n}c_{k}\cos(a_{k}x)\) and \(\displaystyle\sum_{k=1}^{n}c_{k}(1-\cos(a_{k}x))\), where \(n\) is an integer, \(c_{k}\in\mathbb{R}^{*}\) and \(0<a_{0}<\cdots<a_{n}\). Our approach is based on the application of techniques from linear algebra, calculus, Laplace transform, and special functions. In particular, we give an evaluation of the integral \(\displaystyle\int_{0}^{\infty}\frac{\sin^{n}x}{x^{\alpha}}dx\), \(n\in\mathbb{N}^{*}\), \(0<\alpha<n+1\).

Aging is a complex, systemic process often driven by both intrinsic and extrinsic factors. Recent evidence suggests that secretions from aging organs may influence the function of distant tissues. This study investigates the impact of liver-derived secretions from oxidatively aged cells on induced pluripotent stem cell-derived cardiomyocytes (iCMs). Here, we exposed HepG2 liver cells to hydrogen peroxide at varying concentrations (25–300 \(\mu\)M) and durations with regular intervals to model aging. Post-treatment validation confirmed increased oxidative stress, lipofuscin accumulation, p21 expression, and senescence, particularly in the 15-day 100 \(\mu\)M group. Conditioned media from aged HepG2 cultures were then applied to healthy, differentiated iCMs at various dilutions including undiluted, 1:1, and 1:3 with iCM media. iCMs exposed to aged liver secretions exhibited significantly increased aging phenotypes, including elevated lipofuscin and p21 expression, as well as increased senescent cell populations, with the strongest effects observed in undiluted and 1:1 treatment conditions. While senescence levels peaked at the 1:1 dilution rather than in undiluted media, a dose-dependent response to secreted stress factors was observed. Control experiments with untreated liver media showed no significant effects, confirming that the aging phenotypes observed in iCMs were driven specifically by the secretome of aged liver cells. These findings reveal a clear mechanism by which hepatic aging can promote cardiac aging and dysfunction, offering insight into liver-heart crosstalk in the context of human aging.

This study presents a semi-analytical investigation of transient free convection flow of a viscous, incompressible fluid within a vertical channel subjected to third-kind thermal boundary conditions. These boundary conditions, representing convective heat exchange between the fluid and surroundings, offer a more realistic thermal model for practical systems such as heat exchangers and insulated enclosures. The governing partial differential equations are transformed into the Laplace domain using the Laplace transform technique, and closed-form solutions are obtained. These are subsequently inverted to the time domain via Riemann-sum approximation. To capture memory and hereditary effects inherent in complex fluid behavior, the model incorporates fractional derivatives in the Caputo-Fabrizio and Atangana-Baleanu senses. The study analyzes temperature distribution, velocity profiles, Nusselt number, and skin friction, with results validated numerically using MATLAB. Graphical and tabular analyses reveal the influence of key parameters, including Biot number, buoyancy forces, and various Prandtl numbers. The findings contribute to the broader understanding of transient free convection under realistic thermal conditions and have potential applications in the design and optimization of thermal systems in engineering and industry.

University campuses pose unique challenges in terms of environmental pollution and crowd management due to increasing human activity, expansive physical areas, and diverse sources of waste generation. Traditional monitoring systems often fall short in addressing these issues, as they lack the ability to deliver location-based, detailed, and real-time information. Situations such as waste accumulation and high crowd density present serious environmental and safety risks, demanding more sensitive, comprehensive, and dynamic solutions. This study presents an integrated drone-based monitoring system capable of real-time, location-aware tracking of environmental pollution and human density. The system consists of a drone that captures high-resolution imagery, a YOLOv8x model for waste detection, a YOLOv11n model for human detection, geolocation algorithms that utilize image metadata, and density maps generated using Kernel Density Estimation. Leveraging various open-source datasets, the models accurately detected waste and human objects from field-captured images. Experimental evaluations demonstrated detection accuracies of 85.87% for waste and 73.36% for humans. The detections were interactively visualized on the campus map, providing decision-makers with real-time, data-driven insights for sanitation and safety operations. The proposed system serves not only as a standalone object detection platform but also as a multi-layered decision support infrastructure that includes spatial and temporal analysis. Results indicate that the integration of UAV technology with AI-powered object detection offers a highly effective tool for environmental monitoring and operational planning in campus settings.