Asian Research Journal of Mathematics

Activation Energy and Chemical Reaction Effects on MHD Radiative Powell–Eyring Nanofluid Flow with Viscous Dissipation and Newtonian Heating over a Radially Stretching Surface

Obinna, Nwokorie — 2026-04-13

Non-Newtonian nanofluid flow over stretching surfaces is crucial in many industrial applications, where nanoparticles, magnetic fields, and thermal effects significantly enhance heat transfer and fluid behavior. Advanced models, particularly the Powell–Eyring fluid framework, effectively capture complex rheological behavior, making them essential for accurately analyzing flow and heat transfer over radially stretching surfaces in realistic engineering processes. This study investigates the unsteady magnetohydrodynamic (MHD) radiative flow of a Powell–Eyring nanofluid over a radially stretching surface, incorporating viscous dissipation, Newtonian heating, and chemical reactions with activation energy. Using similarity transformations, the boundary-layer equations for momentum, energy, and concentration are reduced to a nonlinear system and solved numerically via MATLAB’s bvp4c. Thermal radiation is modeled using the Rosseland approximation, and reaction kinetics follow a temperature-dependent Arrhenius expression. Parametric analysis shows that the magnetic field and Eckert number suppress velocity while enhancing temperature. Velocity decreases with higher Darcy number and material parameter, but rises with the Powell–Eyring parameter. Temperature increases with Brownian motion, temperature difference, radiation, and Biot number, but decreases with Prandtl number. Concentration decreases with temperature difference, chemical reaction, Brownian motion, and Schmidt number, while it increases with concentration slip, activation energy, and thermophoresis. Effects on skin friction, Nusselt, and Sherwood numbers are quantified, highlighting the influence of key dimensionless parameters on momentum, heat, and mass transfer. These results guide the optimization of reactive nanofluid systems in energy-intensive and chemical processes.

Perimetric Expansive Maps in Perturbed Metric Spaces

Ranjana Maravi — 2026-04-13

This paper develops a fixed point framework for mappings that expand triangular perimeters within the setting of perturbed metric spaces. By decomposing the distance structure into an exact metric and an adjustable perturbation, we show that surjectivity transforms forward perimetric expansion into backward contractive behavior, forcing geometric convergence of inverse orbits. This mechanism yields a powerful expansive analogue of classical triangular contraction principles and ensures the existence and uniqueness of fixed points under mild regularity and the absence of 2–cycles. Detailed examples reveal both borderline nonexpansive behavior and genuinely strict expansive regimes arising from hierarchical folding dynamics. Three applications demonstrate the breadth of the theory: (i)a nonlinear integral operator whose structural expansiveness ensures the existence of a unique equilibrium solution to a Volterra-type equation. (ii) a hierarchical deduplication model in which strict perimetric expansion enforces a unique canonical representative under repeated merging: and (iii) a cryptographic state–evolution scheme whose perimetric geometry captures collision resistance and guarantees a unique master seed. These results highlight the versatility of perimetric expansion in nonlinear analysis, structured data aggregation, secure computation, and integral-equation models.

Some New Lower Bounds for the Spread of a Nonnegative Matrix with a Zero Diagonal Element

Ram Asrey Rajput — 2026-04-20

Let \(\mathbb{N}\)\(_n\) (with n ≥ 2) be the family of all nonnegative n × n matrices A = [a_ij], where a₁₁ = 0 and the remaining entries a_ij ∈ [0, 1) with a spectral radius ρ(A) = 1. We can establish a lower bound for the additional spread s(A) ≥ \(\frac{k}{n-1}\), where k is the count of zero diagonal elements in matrix A. Furthermore, if matrix A possesses only two distinct eigenvalues, then it follows that s(A) ≥ \(\frac{n−2}{n−1}\). Additionally, we derived a few other lower bounds under a special family of matrices.

Spectra of Lower Triangular Double-Band Infinite Matrices with Oscillatory Entries on ℓ1

Laloo Prasad Yadav — 2026-04-23

This research investigates the spectral properties of a class of lower triangular double- band infinite matrices acting on the sequence space ℓ1. The matrix A is characterized by diagonal and sub-diagonal entries consisting of two oscillatory sequences, p and q possessing four and six distinct limit points, respectively. Through the application of functional analytic techniques and Goldberg’s subdivision, the spectrum, point spectrum, residual spectrum, and continuous spectrum are explicitly determined. The analysis demonstrates that while the point and continuous spectra are empty, the residual spectrum coincides with the entire spectrum, which is defined by a specific algebraic inequality involving the product of the oscillatory entries. These findings extend existing research in summability theory and provide a deeper understanding of the stability of linear operators in infinite-dimensional systems.

On the Infinitude of Primes of Certain Types

Aditi S. Phadke — 2026-04-23

Prime numbers and their patterns are a very important topic historically as well as in current times with applications to fields such as cryptography. In this paper, we give different proofs than those available in the literature of infinitude of primes of the type 4k + 3, 6k + 5, and 4k + 1. These are all special cases of the Dirichlet prime number theorem. We have used the technique of Saidak as well as divisibility properties, to give a constructive proof to prove infinitude of the primes of the form 4k + 3 and 6k + 5. The infinitude of primes of the type 3k + 2 is a corollary. In literature, these cases are proved by method of contradiction. To prove that there are infinitely many primes of the type 4k + 1, we show that every prime factor of a Fermat number Fn(n ≥ 1) is of the form 4k + 1 using a classical result on quadratic residues. Also any two Fermat numbers are coprime. Combining these two results has enabled us to prove that there are infinitely many primes of the type 4k + 1.

Structural Analysis of Quadrilateral Snake Graphs Variants via Reverse Sombor-Based Indices and their Polynomial Formulations

K. M. Saranya — 2026-04-24

Topological indices are widely used to describe the structural characteristics of graphs through numerical values. In this work, several variants of quadrilateral snake graphs are analyzed. For these graph classes, reverse degree-based indices including the reverse Sombor index, reverse Elliptic Sombor index, reverse Euler Sombor index, and reverse Harmonic index are computed using edge partition techniques. In addition, the reverse Sombor polynomial is formulated to provide a detailed description of the graph structure. Exlicit expressions are obtained for each class of graphs, and corresponding numerical values are presented to illustrate the results. The outcomes of this work contribute to the ongoing development of topological indices and provide further insight into the strucrtural behavior of quadrilateral snake graph models.

Unit Regular Elements in Transformation Semigroups and Continuous Transformation Spaces

J. Dasan — 2026-04-25

In the current literature, most works on transformation semigroups have shifted their attention to characterizing regular or unit regular elements in specialized sub-semigroups, such as those preserving partitions, invariant subspaces, or subspace structures. In this paper, the unit regular elements t of the semigroup T(X) of all transformations defined on an arbitrary set X are characterized. An important property of a unit regular element which states that an element t of T(X) is unit regular if and only if there exists a cross section X0 such that X − X0 and X − R(t) are of the same cardinality has been proved. This result reveals that any transformation t on X having finite range is always unit regular and shows that a transformation t in T(X) which is injective (but not surjective) or surjective (but not injective) can never be a unit regular element of T(X). As a consequence, an alternative proof of the fact that T(X) is a unit regular semigroup if and only if X is finite is given. Analogous characterization of unit regular elements of the semigroup space CT(X) of continuous transformations on a Hausdorff topological space X is also analyzed. The result shows that an element t in CT(X) is unit regular if and only if the range R(t) is a closed subset of X, t is a quotient map onto R(t) with kernel of t possessing continuous cross section X0 such that the closures of X − X0 and X − R(t) are homeomorphic which coincides with t on the boundary X0.

On SR-fuzzy Transportation Problem Models and their Solution Algorithm

S. K. Shukla — 2026-04-25

Businesses have been focusing on the need to increase profit by reducing operational costs. In operations research, the transportation problem is essentially a logistics puzzle focused on moving goods from various suppliers to their final destinations as efficiently as possible. By balancing availability constraints with customer requirement, this model identifies the specific shipping routes that will either drive down total costs or boost the bottom line. In this paper, we explore a transportation model where availability, requirement, and shipping costs are all treated as square root (SR)-fuzzy numbers. The majority of existing studies regarding fuzzy transportation issues revolve around intuitionistic, Pythagorean, and Fermatean fuzzy numbers, leaving other fuzzy frameworks less explored. However, the current study is the first to consider the fuzzy parameter as square root fuzzy numbers. A transportation problem is formulated along with the corresponding algorithms that are applicable to SR-fuzzy data. A key contribution of this work is the formulation of a unique score function designed to the specific characteristics of SR-fuzzy sets. Unlike the conventional score function, the proposed score function takes non-negative values. We integrate this score function with standard SR-fuzzy arithmetic to build a method for solving transportation problems in SR-fuzzy environment.

Combination of Fuzzy Vector Spaces and Fuzzy Topology: Foundations and Applications

Freddy Tsatsa Bakweno — 2026-04-30

This article proposes a unified mathematical framework combining the theory of fuzzy vector spaces and that of fuzzy topologies to model complex systems characterized by uncertainty and structural imprecision. We formally introduce the notion of a fuzzy topological vector space and study its fundamental algebraic and topological properties, including the continuity of vector operations, fuzzy separation axioms, and fuzzy compactness and connectivity. A constructive approach based on α-cuts is developed to establish a rigorous link between fuzzy structures and classical topological vector spaces. Furthermore, we extend this framework to fuzzy functional analysis, fuzzy Sobolev spaces, fuzzy partial differential equations, and fuzzy dynamical systems. Potential applications in optimal control, image processing, artificial intelligence, and mathematical physics are also discussed.

This work constitutes a theoretical contribution towards the coherent integration of algebra, topology and uncertainty, paving the way for the development of new mathematical tools for the analysis of complex systems. Future work could focus on integrating fuzzy topological vector spaces with fuzzy differential geometry, fuzzy manifolds, fuzzy neural networks, and advanced numerical methods, in order to develop a comprehensive analytical and computational theory.