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.
Our primary objective is to develop new characterizations of the MPDMP matrix, which was recently defined as the product of the Moore-Penrose inverse and the Drazin inverse. In particular, we present the MPDMP matrix as a solution of several systems of matrix equations and some equations with constraints. Different expressions for the MPDMP matrix are established in terms of projectors, the DMP and MPD inverses, and full-rank decompositions. We give the most general representation form and the canonical form for the MPDMP matrix. Also, we consider the MPDMP matrix of upper triangular block matrices. As applications of the MPDMP matrix, the solvability of certain linear equations is verified, and their solutions are represented.
In this paper, we analyze and visualize the arches of the athletic track on the high school playground near the Faculty of Geodesy in Zagreb based on surveying methods. A total of 129 numbered points were observed by the terrestrial method (tachymetry), and the final coordinates were obtained by subsequent data processing. We apply and compare three least squares methods of curve fitting on the data set to obtain equations of ellipses that are closest to observed points and visualize them using Grasshopper and Rhinoceros 3d. After finding the coefficients of the ellipse equations, we estimate five ellipse geometrical parameters along with their error assessments.
In this paper, by using S-norms, we define and study certain properright derivation BCC-ideals, and fuzzy derivation BCC-ideals of BCC-algebras. Next, we characterize them and subalgebras, BCC-ideals, left derivation BCC-ideals, right derivation BCC-ideals and derivation BCC-ideals of BCC-algebras, respectively. Later, we define the concepts of direct sum and union of them, and we prove that direct sum and union of them will also be fuzzy subalgebras, fuzzy BCC-ideals, fuzzy left derivation BCC-ideals, fuzzy right derivation BCC-ideals, and fuzzy derivation BCC-ideals of BCC-algebras, respectively. Finally, we investigate the image and pre-image of them under homomorphisms of BCC-algebras.
In this work, curve pairs with stationary acceleration on the SE(3) group are investigated. Considering that the Frenet frame of a spatial curve represents the rotational component of the spatial motion, while the translational component corresponds to an arbitrary spatial curve, a curve on SE(3) is defined using these two components. Characterizations are provided for these curves to have a stationary acceleration. By employing specific special curves, such as the Salkowski curve, Euler spiral, Cornu spiral, and logarithmic spiral, it is demonstrated that a curve defined on SE(3) can possess stationary acceleration. Furthermore, when the Bishop frame is used instead of the Frenet frame, characterizations for curve pairs with stationary acceleration are also presented.
In this work, we introduce Balancing, Balancing-Lucas polynomials, and k-Balancing, k-Balancing-Lucas polynomials. We exhibit some important theorems: Cassini, Catalan, Vajda, d'Ocagne, and Honsberger identities for Balancing, BalancingLucas polynomials, and k-Balancing, k-Balancing-Lucas polynomials. We give the concepts of recurrence relation, characteristic equation, roots of the characteristic equation, Binet formula, and generating function for polynomials, which are important for number sequences.
This article discusses the transmission dynamics of malaria disease between the human and mosquito populations in a periodically varying environment. Predominant vectors for malaria transmission are female Anopheles mosquitoes. We subdivided the human population into two distinct classes, high-immunity and low-immunity groups, within a periodic malaria compartmental framework to enhance the host heterogeneity. The global dynamics of the model are examined, which are influenced by a threshold parameter defined as the spectral radius of an associated linear integral operator. The next-generation matrix method is used to derive the basic reproduction number R0, representing the transmission potential. Furthermore, a sensitivity analysis is conducted to evaluate biological parameters to assess their influence on the spread of the disease. The findings provide a valuable understanding of how periodic environmental changes and host immunity impact the persistence and prevention of malaria.
A new system of general equations is introduced and investigated, which can be used to study the odd-order, non-positive and nonsymmetric boundary value problems. Some important and interesting results, such as the Riesz-Frechet representation theorem, Lax-Milgram lemma and system of absolute value equations can be obtained as special cases. It is shown that the system of general equations is equivalent to a nonlinear optimization problem. The auxiliary principle technique is used to prove the existence of a solution to the system of general equations. This technique is also used to suggest some new iterative methods for solving the system of general equations. The convergence analysis of the proposed methods is analyzed. Ideas and techniques of this paper may stimulate further research.
The Exeter point of a triangle is the perspector of its circum-medial triangle and its tangential triangle. Its construction can be done in the following way: Let the triangle ABC be given. Let X-2 be its centroid and A(t)B(t)C(t) its tangential triangle, and let A ', B ', C ' be the intersection points of the circumcircle and the medians through A, B, C, respectively. The lines A(t)A ', BtB ' and CtC ' intersect in a point X-22, called the Exeter point of the triangle ABC. In this paper we show that such a point also exists in an isotropic plane. Moreover, we study loci of Exeter points in the pencils of triangles. A triangle pencil consists of triangles that have the same circumcircle, i.e., two vertices are fixed, and the third vertex runs along the circumcircle, a non-isotropic line or isotropic line. The results obtained on the loci of its Exeter point are given.
In this paper, we establish the universal property of derivations between two Weil algebras, and we describe tangent vectors at a point and vector fields on the Weil bundle in terms of derivations. We reformulate the notion of vector fields on the Weil bundle in terms of derivations. We use the algebra of dual numbers, which is a Weil algebra and we prove the existence of the canonical Liouville vector field on the tangent bundle.
We study the global existence and other properties of solutions of a nonlinear implicit Volterra integrodifferential equation with finite delay in a Banach space. The technique used in our analysis is based on an application of the topological transversality theorem known as the Leray-Schauder alternative and the integral inequality, which provides an explicit bound on the unknown function.
In this paper, we define a new part of spectrum called the essential $\overline{\gamma}$-pseudospectrum of a linear operator via the measure of noncompactness of Kuratowski $\overline{\gamma}$. Our aim is to characterize the essential $\overline{\gamma}$-pseudospectrum of a bounded (an unbounded) linear operator. Moreover, we study the invariance of the $\overline{\gamma}$-pseudospectrum under perturbations.
In this work, the fundamental equations of generalized $\varphi(Ric)$-vector fields in both classical and hyperbolic K\"ahler spaces are derived and expressed as systems of linear partial differential equations in the Cauchy-type covariant derivative. Additionally, the specific form of the Ricci tensor $Ric$ for these spaces is determined.
In this paper, we classify the Ricci solitons and the Ricci bi-conformal vector fields on model space $Sol^{4}_{0}$. We also show which of them are gradient vector fields and which one of those are Killing vector fields.
In the present paper we introduce generalized extended $C$-Bochner curvaturetensor on $(\grave{k},\grave{\mu})$-contact metric manifolds. Also, we study $\grave{\hbar}$-generalized extended $C$-Bochner semisymmetric and $\psi $%-generalized extended $C$-Bochner semisymmetric non-Sasakian $(\grave{k},%\grave{\mu})$-contact metric manifolds.
In this paper, we discuss the existence of renormalized and entropy solutions of nonlinear elliptic problems governed by the general p(.)-Leray-Lions type operator with a natural growth term subject to L-1 data in the interior of the domain and Fourier type condition on the boundary. We first introduce a sequence of approximated problems by regularizing the data via truncation and Yosida's method. Then, using the technique of maximal monotone operators in Banach spaces, we prove that the approximated problem is well-posed in terms of a weak solution. Finally, we pass to the limit and prove that the sequence of approximated solutions converges to the entropy or renormalized solutions of the initial given problem.
