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.

Edge Induced V\(_4\)−Magic Labeling of Line Graphs

K. B. Libeeshkumar — 2026-05-05

Let V₄ = {0, a, b, c} be the Klein-4-group with the elements a, b, c have order 2 and 0 be the identity element. Let G = (V (G),E(G)) be a simple, connected, finite and undirected graph. Let f : E(G) → V₄∖{0} be an edge labeling and f⁺ : V (G) → V₄ denotes the induced vertex labeling of f defined by f⁺(u) = \( \begin{array}{c} \sum\\uv\epsilon E(G) \end{array}\) f(uv) for all u ∈ V (G). Then f⁺ again induces an edge labeling f⁺⁺ : E(G) → V₄ defined by f⁺⁺(uv) = f⁺(u)⁺f⁺(v), for all uv ∈ E(G). A graph G = (V (G),E(G)) is said to be an edge induced V4-magic graph (Libeeshkumar and Kumar, 2020a), if there exists an edge labeling f for which the function f⁺⁺ is a constant function. The function f, so obtained is called an Edge Induced V₄-Magic Labeling (EIML) of G. The present paper discusses some results related to the EIML of line graphs and provides a characterization of the EIML of line graphs for certain well-known named graphs.

An Explicit Bound for Product-Form Nonlinear Integral Inequalities

S. G. Latpate — 2026-05-09

In this article, we establish some product-form nonlinear integral inequalities and their applications. These inequalities can be employed as a notable tool in the study of certain integral and differential equations and epidemic models. Few applications are provided to demonstrate the significance of our results.

Refined Liouville-Type Results for the Three-Dimensional Stationary MHD Equations

Xiangyi Zhang — 2026-05-11

We prove refined Liouville-type theorems for smooth solutions to the three-dimensional stationary MHD equations. Under a mild growth condition involving a function g(ρ) (monotone, \(\rho^{-1 / 3} g(\rho) \rightarrow 0,\) and \(\left.\int^{\infty} \frac{d \rho}{\rho g(\rho)}=\infty\right)\), any solution with velocity and magnetic field growing at most like \(\rho^{\frac{2}{p}-\frac{1}{3}} g(\rho)^{\frac{3}{p}-1}\) for some 3/2 < p < 3 must be identically zero. This extends recent sharp Liouville theorems for the Navier-Stokes equations to the MHD case and allows for logarithmic or even weaker subcritical growth.

An Adaptive Two-Step Hybrid Block Method with Optimized Off-Step Points for Direct Solution of Third-Order Initial Value Problems

O. C. Akeremale — 2026-05-13

This paper introduces a new two-step hybrid block method for the direct numerical solution of third-order initial value problems (IVPs) without reduction to systems of first-order equations. The method is derived using collocation and interpolation techniques with a power series basis function, incorporating optimized -step points within each interval. The scheme is proven to be zero-stable, consistent, and converges at order nine, with an error constant of C10 ≈ 2.14 × 10−8, which confirms that the method is A-stable. Numerical experiments conducted on linear and nonlinear third-order IVPs demonstrate the method’s superior accuracy and computational efficiency compared to existing standard methods such as the classical Runge–Kutta fourth-order method (RK4), Adams–Bashforth–Moulton (ABM), and other hybrid block methods in the literature. The proposed method is self-starting, generates solutions simultaneously at multiple points, and is recommended for solving challenging third-order IVPs in engineering and physics.

Complex Inversion Formula for the Laplace-Carson Transform

Fasiyoddin I. Momin — 2026-05-16

Aims/ Objectives: To present a systematic study of the complex inversion formula for the Laplace–Carson transform.To establish convergence criteria and study detailed computational methodologies for both finite and infinite poles.

Study Design: Analytical study.

Place and Duration of Study: Research Center in Mathematics,Maulana Azad College of Arts, Science and Commerce, Chh. Sambhajinagar, Maharashtra,India. june 2025 to march 2026.

Methodology: The complex inversion formula is an extremely powerful method for calculating the inverse of an LC-transform. A practical post-inversion formula and a new inversion method, analogous to classical Laplace inversion techniques, are introduced. The LC-transform is a modified version of the classical Laplace transform and it offers distinct analytical advantages over the Laplace transform in various applied mathematical fields. Additionally, we discuss functions possessing branch points and deal with meromorphic functions containing infinitely many poles.

Results: Several illustrative examples and applications to partial differential equations demonstrate the analytical advantages of the Laplace–Carson transform over the classical Laplace transform.

Conclusion: In this paper,the complex inversion formula for LC-transform transform is rigorously established and its computational application extended to complex branch points and meromorphic functions with various poles.

Anti-Frobenius Algebras and Anti-Bialgebras

Gbêvèwou Damien Houndedji — 2026-05-16

We introduce the notion of q-generalized associative algebras, which unifies associative (q = 1) and antiassociative (q = −1) structures, and investigate their bimodule and matched pair theories. Specializing to antiassociative algebras, we develop the double construction of quadratic antiassociative algebras — termed anti-Frobenius algebras — by equipping the direct sum A⊕A∗ with a compatible antiassociative product and a non-degenerate symmetric invariant bilinear form.

We prove that such double constructions are equivalent to matched pairs of antiassociative algebras and to antisymmetric infinitesimal anti-bialgebras, characterized by suitable co-derivation and antisymmetry conditions on the comultiplication. Furthermore, we establish a direct link to Mock-Lie structures: the anticommutator of an anti-Frobenius algebra yields a Manin triple of Mock-Lie algebras, and the corresponding antisymmetric infinitesimal anti-bialgebra induces a Mock-Lie bialgebra via symmetrization of the comultiplication.

A detailed low-dimensional example and a relation analysis highlight the analogies and distinctions with classical Frobenius and Mock-Lie bialgebra theories.

A Note on Explicit Particular Solutions for Third and Fourth Order Generalized Leonardo-Type Recurrences with Polynomial-Exponential Input

Yüksel Soykan — 2026-05-16

Sequences, both classical and modern in scope, can be analyzed through a versatile framework that remains central to mathematics, namely recurrence relations. Previous investigations established explicit iterative procedures for constructing polynomial–exponential particular solutions of generalized Leonardotype sequences. Building upon that framework, this article develops illustrative examples for the cases m = 3, 4, where the forcing term is given by C(n) = p(n)dⁿ, with p(n) = \(\sum_{i=0}^s c_i n^i\) a polynomial in n. For such recurrences, we derive particular solutions of the form

\[W_n^{(C)}=n^r\left(\sum_{i=0}^s A_i n^i\right) d^n\]

and demonstrate the computation of the coefficients Ai via the established iterative scheme. These formulas not only provide constructive clarity but also demonstrate how the iterative procedure systematically determines the polynomial part of the solution. The examples reveal how the multiplicity r of the root d in the characteristic polynomial governs the structure of the solution, while resonance phenomena emerge when the forcing term interacts with repeated characteristic roots. Such resonance effects are highlighted in detail, showing their decisive role in shaping the solution’s form and complexity. In addition to the explicit constructions, a brief literature review is included to situate Leonardo-type sequences within their historical development and to highlight recent advances in generalized Leonardotype recurrences. This contextualization underscores the enduring role of recurrence relations in number theory, discrete mathematics, and symbolic computation. By presenting explicit cases, the paper offers a transparent and accessible illustration of the general theory, reinforcing the connection between abstract recurrence analysis and concrete symbolic computation, while also pointing toward potential applications in computational mathematics and combinatorial modeling.

Mathematical Modeling of COVID-19 Disease Dynamics Incorporating Quarantine and Vaccination

Rajat Kaushik — 2026-05-20

This article examines the dynamics of COVID-19 regarding transmission rates and loss of immunity, utilizing a system of ODEs that encompasses the impacts of quarantine and vaccination, including the incidence rate. Our methodology aims to understand the consequences of vaccination and quarantine through the utilization of the fundamental reproduction number (R0). The stability study indicates that if R0 < 1, the disease-free equilibrium points are locally and globally asymptotically stable, whereas the endemic point is stable for R0 > 1. Finally, we use Python software to draw some characteristics of the covid-19 virus and to identify the effective parameters for spreading this disease by sensitivity diagrams and the simulation results agree with our qualitative study.

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.