This paper focuses on presenting several generalized fixed point theorems in 2-normed spaces. In particular, we consider an extension of the contractive conditions associated with Kannan and Chatterjea types. Our research leads to the establishment of new results and theorems that contribute to the understanding of fixed point theory, specifically in 2-normed spaces. These findings aim to enhance the existing knowledge and provide a more profound perspective on the behavior of fixed points in these generalized conditions.
This study presents a two-dimensional symbolic algebraic modeling for coupled heat and moisture transport across the three layers of the skin: epidermis, dermis, and subcutaneous tissue. The model combined Pennes’ bioheat equation with a diffusion-reaction equation. It accounts for evaporation and metabolic fluid generation, enabling a more realistic representation of skin physiology. The finite difference method discretizes the coupled equations, offering computational efficiency as well as numerical stability. The simulations yield physiologically realistic temperature and moisture distributions that capture depth-dependent variations across multiple skin layers. This method improves the scientific understanding of thermal and hydration connections in human skin. It supports applications in thermal diagnostics, burn management, drug delivery, and wearable healthcare technologies.
In this paper, we defined and investigated a generalized type of topological vector space known as h alpha-irresolute topological vector spaces by using the notion of h alpha-open sets, which was given by Abdullah et al. [2] in 2022. We explore and investigate several properties and characterizations of this new notion of h alpha-irresolute topological vector space. Also, we give several characterizations of h alpha-compact spaces and h alpha-Hausdorff spaces. Furthermore, we show that an hcti hcti-irresolute topological vector space is h alpha-hausdorff iff a one-point set in X is hcti hcti-closed in X.
A numerical simulation is designed to analyse the transport of heat and water within the dermal and subdermal regions of the human upper limb. The system incorporates key biophysical parameters, including Heat conduction ability, Heat produced by metabolism, Rate of blood circulation, Hydration diffusion, and Sweatinduced water transport. The model is formulated as a set of elliptic partial differential equations under steady-state conditions. Utilizing finite element simulations, the simulation domain is discretized into a structured mesh, and the resulting equations are discretized into a linear algebraic system. The derived systems are solved numerically using MATLAB to simulate the spatial distribution of temperature and water across the skin layers. The framework highlights the effectiveness of linear algebraic techniques in solving complex bio-heat and water transport problems in physiological tissue.
Soft set theory has numerous applications in various areas of life, including medical diagnosis, data mining, engineering, business, economics, and decision-making problems. The goal of this study is to put forward the concept of (is an element of, is an element of Yqk)-fuzzy soft interior ideals and explore its essential properties in detail. Also, the connection of (is an element of, is an element of Yqk)-fuzzy soft ideal with (is an element of, is an element of Yqk)-fuzzy soft interior ideals is elaborated. Moreover, semiprime (is an element of, is an element of Yqk)-fuzzy soft ideals and their essential properties are explained. Finally, upper and lower parts of (is an element of, is an element of Yqk)-fuzzy soft interior ideals are elaborated.
