South East Asian Journal of Mathematics and Mathematical Sciences
Bibliographic information ISSN: 0972-7752 (Print) ISSN: 2582-0850 (Online) DOI: 10.56827/SEAJMMS
Ramanujan Society of Mathematics and Mathematical Sciences
CERTAIN IDENTITIES DEDUCED FROM SEARS TRANSFORMATION
In this paper certain identities have been deduced from the Sears Transformation formula.
Copyright (c) 2026 South East Asian Journal of Mathematics and Mathematical Sciences
A subset $S$ of vertex set $V(G)$ of a graph $G$ of order $n\geq 2$ is a geodetic hub set of $G$ if $S$ is both a geodetic set and a hub set of $G$. The minimum cardinality of a geodetic hub set of $G$ is called the geodetic hub number of $G$, denoted by $h_{geo}(G)$. In this paper, we initiate the study of geodetic hub number of a graph. The geodetic hub number of several classes of graphs are determined and its value for some graph operations are studied.
CERTAIN RESULTS ON $q$-STARLIKE FUNCTIONS WITH RESPECT TO SYMMETRIC AND CONJUGATE POINTS
In the present paper, we introduce two Subclasses $\displaystyle S_{s}^{\ast}(\delta , \theta , q) $ and $\displaystyle S_{c}^{\ast}(\delta , \theta , q)$ of analytic and $q$-starlike functions with respect to symmetric and conjugate points in the open unit disk $\displaystyle {\Delta}$. For functions belonging to these Classes, we obtain estimates coefficient and sufficient Condition.
$q$-Starlike with respect to symmetric points
SOME COUPLED FIXED POINT RESULTS ON $N_p$-CONE METRIC SPACES OVER BANACH ALGEBRA
The main aim of this paper is to introduce the notion of $N_p$-cone metric spaces over Banach algebra. We define $T$-contraction map and study some coupled common fixed point theorems in the new setup. Finally, we state an example as an application to illustrate our obtained results. Our results generalize and extend some well-known results in the literature.
$N_p$-cone metric spaces over Banach algebra
A nonempty subset of the edge set of a graph $G$ is called an edge open packing set if no two edges of it have a common edge. The edge open packing number $\rho_e^o(G)$ of a graph $G$ is the maximum number of edges in an edge open packing set. In this paper, a number of results are presented concerning lower and upper bounds of $\rho_e^o(G)$ for graphs such as trees, split graphs and unicyclic graphs. Some open problems are proposed.
ENERGY AND LAPLACIAN ENERGY ON INVERSE FUZZY GRAPH
Real-time problems involving uncertain or indeterminate information can be effectively addressed using fuzzy graphs (FGs). However, the problems in which the edge membership values have a significant impact due to the combination of its corresponding vertices remain unsolved. To address this, inverse fuzzy graph (IFG) was introduced. In this article, the energy ($E^{I}$) and the Laplacian energy ($LE$) on inverse fuzzy graph (IFG) $G^{I}$ have been newly introduced. Further, various lower and upper bounds are derived for $E^{I}(G^{I})$ and $LE(G^{I})$. Additionally the sharp bound is estimated for $E^{I}(G^{I})$ which aids in determining the minimum and maximum bounds for $E^{I}(G^{I})$. Furthermore, for the newly defined $l-$ regular IFG, the equality condition $E^{I}(G^{I})=LE(G^{I})$ holds true.
GEOMETRICAL PROPERTIES OF GENERALIZED QUASI-CONFORMAL CURVATURE TENSOR
This paper examines the generalized quasi-conformal curvature $\mathcal{G}$, which generalizes the concept of conformal curvature tensor $\mathcal{C}$, quasi-conformal curvature tensor $\mathcal{\widetilde{C}}$, projective curvature tensor $\mathcal{P}$, pseudo projective curvature tensor $\mathcal{\widetilde{P}}$, and pseudo $W_2-$curvature tensor $\mathcal{\widetilde{W}}_2$. Initially, we acquire some geometrical features. Subsequently, we examine pseudo generalized conformal symmetric manifolds. Divergence-free generalized quasi-conformal curvature tensor is derived from the Gray's decomposition. Additionally, we also examine Einstein $(P\mathcal{G}S)_n$ manifolds. A study of generalized quasi-conformal has been conducted as the four-dimensional spacetime of general relativity $\widetilde{GR}$. Ultimately, we examine a non-trivial Lorentzian metric of $(P\mathcal{G}S)_4$.
Quasi-conformal curvature tensor $\mathcal{\widetilde{C}}$
pseudo projective curvature tensor $\mathcal{\widetilde{P}}$
conformal curvature tensor $\mathcal{ C }$
projective curvature tensor $\mathcal{ P }$
concircular curvature tensor $\mathcal{ L }$
generalized quasi conformal curvature tensor $\mathcal{ G }$
INTERPOLATIVE HARDY-ROGERS TYPE CONTRACTION ON PARTIAL FUZZY METRIC SPACES AND RELATED FIXED POINT RESULTS
In this paper, we introduce a new class of fuzzy interpolative Hardy– Rogers type contractions in the frameworks of fuzzy metric spaces and partial fuzzy metric spaces. We establish fixed point theorems guaranteeing the existence and uniqueness of fixed points under suitable contractive conditions involving control parameters. The obtained results extend and unify several known results in the literature, including classical Hardy–Rogers type contractions in fuzzy and partial fuzzy settings. Illustrative examples are also provided to demonstrate the applicability of the proposed results.
A GEOMETRIC STUDY OF $f(r)$-GRAVITY SPACETIMES THROUGH PROJECTIVE CURVATURE TENSOR
This research investigates spacetime with projective curvature tensor in $f(r)$ gravity. It explores projectively flat and projectively flat perfect fluid spacetime, determining isotropic pressure ($p$) and energy density ($\sigma$). The study extends to energy conditions and reveals that spacetimes with divergence-free projective curvature tensor may represent a dark energy dominated era or have constant isotropic pressure and energy density, especially when the energy-momentum tensor is recurrent or bi-recurrent.
ON APPROXIMATE SOLUTIONS OF FRACTIONAL ORDER SMOKING EPIDEMIC MODEL USING SUMUDU DECOMPOSITION METHOD
In this paper, an approximate analytical solution of a fractional-order smoking epidemic model is obtained by employing the Sumudu Decomposition Method (SDM). To validate the effectiveness and reliability of the proposed method, the obtained SDM solutions are compared with numerical solutions computed via the classical Runge–Kutta method. A detailed error and convergence analysis is presented to assess the accuracy of the method. The results demonstrate that the SDM provides highly accurate approximations, particularly for small and moderate time intervals. Graphical simulations are included to illustrate the dynamical behavior of the model for different parameter values. The study confirms that the SDM is a simple, efficient, and reliable technique for solving nonlinear fractional-order epidemic models and can be effectively applied to analyze short-term dynamics in smoking-related population systems.
PNN - COCOSO FOR MULTI ATTRIBUTE GROUP DECISION MAKING
Decision making in real-world situations is highly challenging during evaluation of a set of alternatives with conflicting criteria. Although there exists a vast body of literature covering different Multi-Attribute Decision Making (MADM) frameworks under single or group decision making (MAGDM), most of them are limited to fuzzy or neutrosophic environments capturing limited uncertainty. To address these limitations, this paper proposes an extension of the Combined Compromise Solution (COCOSO) strategy for group decision making within the framework of Pentapartitioned Neutrosophic Numbers (PNNs), which we name as PNN - COCOSO strategy. Unlike classical fuzzy or single-valued neutrosophic approaches, pentapartitioned neutrosophic numbers allow decision makers to distinguish among truth, falsity, contradiction, and ignorance, providing a comprehensive picture of uncertainty in decision making. Furthermore, this paper utilizes COCOSO's mechanism of multiple compromise measures through a distinguished parameter $\Omega$, combining additive and multiplicative aggregation simultaneously to enhance ranking stability.To illustrate the developed strategy, a benchmark problem of group decision making is selected from literature and analyzed for any alteration of ranking. Additionally, a secondary illustration is also provided to present the case of single decision maker. A comprehensive sensitivity analysis is performed to ascertain the stability of rankings across the ranges of the distinguished parameter $\Omega \in [0.1,1.0]$, enhancing the robustness of the proposed method in decision making.
Multi-Attribute Group Decision Making (MAGDM)
Pentapartitioned Neutrosophic Number (PNN)
ON RECENT PARTITION FUNCTION OF KAUR AND RANA
Recently, Kaur and Rana introduced the partition function denoted by $\rho(n)$, where the largest part $\lambda$ appears exactly once, and the remaining parts constitute a partition of $\lambda$. In this paper, we establish new generating functions for certain variants of $\rho(n)$. Further, we obtain a linear recurrence relation for our new generating function.
QUANTUM CODES THROUGH CONSTACYCLIC CODES OVER $\mathcal{F}_{p}+{\mu}\mathcal{F}_{p}+{\nu}\mathcal{F}_{p}+{\varpi}\mathcal{F}_{p}+{\mu}{\nu}\mathcal{F}_{p}+{\nu}{\varpi}\mathcal{F}_{p}+{\mu}{\varpi}\mathcal{F}_{p}+{\mu}{\nu}{\varpi}\mathcal{F}_{p}$
The purpose of this paper is to identify the structural characteristics and construction of quantum codes over $\mathcal{F}_p$ using $\alpha_1+\alpha_2 {\mu}+\alpha_3 {\nu}+\alpha_4 {\varpi}+\alpha_5 {\mu}{\nu}+\alpha_6 {\nu}{\varpi}+\alpha_7 {\mu}{\varpi}+\alpha_8 {\mu}{\nu}{\varpi}- $constacyclic codes over ring $\mathcal{R} ~= ~\mathcal{F}_p[{\mu},{\nu},{\varpi}]/<{\mu}^2-{\mu}, {\nu}^2-{\nu}, {\varpi}^2-{\varpi}~, {\mu}{\nu}-{\nu}{\mu}, {\nu}{\varpi}-{\varpi}{\nu}, {\mu}{\varpi}-{\varpi}{\mu}>$, here $\mathcal F_{p}$ is a finite field with p elements. We define a Gray map from $\mathcal{R}$ to $\mathcal{F}_p^{8}$, a distance-preserving map. Breaking down constacyclic codes into cyclic and negacyclic codes results in the creation of quantum codes over the finite field $\mathcal{F}_p$. As an application, some examples are illustrated to obtain the quantum codes of different parameters.
AN APPLICATION OF SOMBOR INDEX OF HESITANCY FUZZY GRAPHS IN MOBILE NETWORKS
Pathinathan T., J. Jon Arockiaraj, and J. Jesintha Rosline [5] introduced the concept of Hesitancy Fuzzy Graphs (HFGs). In this work, we discuss an application of the Sombor index of a HFG in mobile networks. This work includes the comparison of the performance levels of mobile companies --- Jio, BSNL, Airtel, and Vodafone Idea --- in a selected area. Then, we investigate how these mobile companies can improve their performance.
GENERALIZED $M$-CONTINUOUS AND $M$-IRRESOLUTE MAPPINGS IN FERMATEAN NEUTROSOPHIC TOPOLOGICAL SPACES
In this paper, we introduce and investigate Fermatean Neutrosophic generalized $M$-continuous mappings and Fermatean Neutrosophic generalized $M$-irresolute mappings within the framework of Fermatean Neutrosophic topological spaces. We systematically study the fundamental topological properties of these newly defined classes of mappings, analyze their behavior under set-theoretic operations, and establish their interrelations with other well-known classes in Fermatean Neutrosophic topology. Several illustrative examples are provided to clarify the concepts and demonstrate the applicability of the proposed framework. Additionally, we examine the structural aspects and role of these mappings in preserving Fermatean Neutrosophic generalized $M$-closed sets. The results significantly enrich the theoretical foundation of Fermatean Neutrosophic topology by extending classical ideas of open and closed mappings, and provide potential applications in decision sciences and information systems where uncertainty and vagueness are inherent.
Fermatean Neutrosophic generalized $M$-closed
Fermatean Neutrosophic generalized $M$-continuous and Fermatean Neutrosophic generalized $M$-irresolute mappings
ON $\Psi_{\alpha,\beta}$--EXPANSIVE MAPPINGS WITH DISPLACEMENT CONTROL AND FIXED POINT CONSEQUENCES
In this paper, we introduce a new class of nonlinear expansive mappings governed by a rational displacement--distance gauge $\Psi_{\alpha,\beta}$, which simultaneously depends on the interpoint distance and the individual self--displacements of the operator. This framework extends classical Wang--type expansive models that are based solely on interpoint distances. Under a natural domination condition linking displacement and distance, we establish the existence, uniqueness, and global convergence of fixed points for $\Psi_{\alpha,\beta}$--expansive mappings in complete metric spaces. The proposed approach yields a displacement--sensitive expansive mechanism that enables the treatment of operators not covered by classical expansive conditions, thereby overcoming limitations of existing theories and providing a more flexible framework for applications in nonlinear analysis. Several nontrivial examples are presented to illustrate the applicability, strength, and novelty of the proposed theory.
PARTITION DIMENSION OF EXTENDED ZERO DIVISOR GRAPHS
The ordered partition $\Pi=\{S_1,S_2,...,S_k\}$ of the vertices of the connected graph $G$ is a resolving partition, if for any vertex $x\in V$ with respect to the partition $\Pi$ is the vector $\zeta(x|\Pi)=(d(x,S_1),d(x,S_2),...,d(x,S_k))$ where $d(x,S_j), 1\leq j \leq k$ represents the distance between the vertex $x$ and the set $S_j$, is different for every pair of vertices and is denoted by $pd(G)$. The partition dimension is the minimum of $k$ for which there is a resolving partition. In this paper, we investigate the partition dimension of the extended zero divisor graphs of certain finite commutative rings.
SHOCK WAVE PROPAGATION IN A SELF-GRAVITATING DUSTY GAS WITH MAGNETIC FIELD IN A ROTATING MEDIUM
This study investigates the propagation of exponential shock wave in a self-gravitating, rotating, perfectly conducting mixture of perfect gas and small solid particles (dusty gas) subjected to an axial or azimuthal magnetic field for both the adiabatic and isothermal flow conditions. The analysis incorporates the components of the vorticity vector, and both the isothermal and adiabatic compressibilities. In the present model, the solid particles are assumed to be continuously dispersed throughout the mixture, and flow equilibrium is maintained across the entire flow-field region behind the shock front. The impact of the variations in the physical parameters of the problem on the flow behavior is also investigated. It is worth to notice that, due to an increase in the gravitational parameter or the ratio of the solid-particle density to the initial gas density, the strength of the shock wave increases, while an increment in the adiabatic index or the shock Cowling number results reduction in the shock strength. The presence of an axial magnetic field enhances the shock strength in comparison to that of azimuthal magnetic field. Also, the shock wave is weaker in the isothermal flow condition as compared to the adiabatic flow condition
CONTROLLED $K$-FRAMES IN $2$-HILBERT SPACES
In this paper, we introduce a new generalization of controlled $K$-frames to the context of $2$-Hilbert spaces, thereby extending beyond classical Hilbert space theory. We develop foundational results by examining the operator-theoretic properties of controlled $K$-frames in this setting, establishing equivalent conditions that characterize them, and exploring their stability under suitable transformations. This builds directly on prior work introducing controlled $K$-frames in Hilbert $C^*$-modules, where the concept was first defined, equivalent conditions were established, relationships between $K$-frames and controlled $K$-frames were revealed, and invariance and perturbation properties were analyzed. Our work elevates these ideas by adapting them to the richer structure of 2-Hilbert spaces-a framework extending Hilbert spaces through inner products valued in $C^*$-algebras.
UNSTEADY SECOND GRADE ALIGNED MHD FLUID THROUGH POROUS MEDIA IN A ROTATING FRAME: A CLASS OF EXACT SOLUTIONS USING INVERSE METHOD
This study presents exact analytical solutions for the unsteady plane flow of an electrically conducting second-grade fluid within a rotating frame, permeating a porous medium under the action of a magnetic field. The analysis employs the inverse method, wherein suitable $a~ priori$ assumptions for the vorticity and stream function yield consistent forms of the velocity field and pressure distribution. Closed-form expressions for the governing flow variables are derived, ensuring compliance with both the fundamental equations and physical constraints. The influence of critical parameters, such as rotational effects, magnetic field intensity, porous medium resistance, and non-Newtonian fluid characteristics, is examined in detail. Graphical illustrations highlight the role of these parameters in shaping the flow dynamics, offering deeper insight into the complex interplay between rotation, magnetohydrodynamic forces, and porous medium interactions.
COMMUTATIVITY DEGREE AND GRAPHS RELATED TO CONJUGACY CLASSES OF SOME NON-ABELIAN GROUPS
Let $G$ be a finite group. The commutativity degree of $G$ is the probability that two randomly chosen elements of the group commute. This paper explores the commutativity degrees and the properties of graphs relating to conjugacy classes associated with various group and group products, focusing on dihedral, generalized quaternion, and symmetric groups. We find that the conjugacy class graph of $Q_{4n}\times Q_{4m}$ and $S_n \times S_m$ are connected and non-planar. Furthermore, we examine the generalized conjugacy class graphs of generalized dihedral and generalized quaternion group, providing insights into their graph structures and connectivity properties. Our findings highlight the intricate relationships between group elements, their conjugacy classes, and the resulting graph-theoretic representations.
SOME PROPERTIES OF HARMONIC UNIVALENT FUNCTIONS USING Q-CALCULUS AND ERROR FUNCTION
This paper investigates a subclass of harmonic univalent functions using q-calculus and error functions. We determine the necessary condition for the complex valued harmonic, univalent and sense-preserving function $f$ to be the class of harmonic error functions. Further, the necessary and sufficient conditions for functions $f$ to be a member of the subfamily and its characterization, followed by extreme points of the class are determined. Additionally, we prove that the class is closed under convex combinations, indicating that linear combinations of functions within the class also belong to the class. These estimates illuminate the growth and deformation of functions within the unit disk. These findings enhance our understanding of the geometric and analytic properties of harmonic error functions and their significance in the field of geometric function theory.
DEGREE-BASED TOPOLOGICAL INDICES IN RANDOM POLYGONAL AND SPIRO CHAINS
A topological descriptors is a numerical quantity associated with the chemical structures which play an essential role in the chemical graph theory. In this work, we state and prove the expected values of the degree- based topological indices and generalized $ ISI_{(\alpha, \beta)} $ index for the random $ l $-polygonal chain and random $ l $-polygonal spiro chain. Based on the results above, we present the average values of the $ TIs $ with respect to the set of all polygonal and spiro polygonal chains with $ n $ polygons. As applications, we apply the affiliated formulae to obtain the expected values of the $ TIs $ of some special polygonal chains and spiro polygonal chains. Furthermore, we present diverse representations of graph that highlights the correlations between expected mean of indices and structural parameters.
Copyright (c) 2025 South East Asian Journal of Mathematics and Mathematical Sciences
MODIFIED TYPE-1 DIRICHLET AVERAGES OF THE THREE-PARAMETER MITTAG-LEFFLER FUNCTION THROUGH FRACTIONAL INTEGRALS AND SPECIAL FUNCTIONS
The classical power means of Hardy, Littlewood and Polya, which contains the harmonic mean, arithmetic mean and geometric mean, is generalized to the $Y$-mean and hypergeometric mean by Carlson. Carlson's hypergeometric mean is to average a function over a type-1 Dirichlet measure, and this term in the current literature is known as the Dirichlet average of that function. The present paper introduces a new Dirichlet average, associated with the modified type-1 Dirichlet measures called modified type-1 Dirichlet averages. This paper also investigates the modified type-1 Dirichlet averages of a three-parameter Mittag-Leffler type function, which is expressed using Riemann-Liouville integrals and hypergeometric functions with multiple variables.
generalized type-1 and type-2 Dirichlet models
hyper-geometric functions of one and many variables
$L(3, 2, 1)$-LABELING OF SOME CYCLE RELATED GRAPHS
Let $G=(V(G), E(G))$ be a connected graph. For $i,j,k\in \mathbb{N}$ with $i\geq j \geq k$, $L(i, j, k)$-labeling of graph $G$ is an integer labeling of the vertices of graph $G$ such that labels of adjacent vertices differ by at least $i$, labels of vertices at distance two differ by at least $j$ and labels of vertices at distance three differ by at least $k$. In this paper, we discuss $L(3, 2, 1)$-labeling for crown, arm crown, tadpole, and closed helm graphs.
FEKETE-SZEG\"{O} INEQUALITY FOR ANALYTIC AND BI-UNIVALENT FUNCTIONS RELATED WITH HORADAM POLYNOMIALS
In this research article, by making use of S$\check{a}$l$\check{a}$gean differential operator, we introduce and investigate a new subclass of analytic and bi-univalent functions using the Horadam polynomial. We derive the coefficient estimate and obtain Fekete-Szeg\"{o} inequality for functions in this subclass.
S$\check{a}$l$\check{a}$gean differential operator
RESULTS ON UNIQUENESS OF CERTAIN TYPE OF NON-LINEAR DIFFERENTIAL POLYNOMIALS SHARING A VALUE
In the paper we discuss the distribution of uniqueness and its elements over the extended complex plane from different polynomials of view. We obtain a new result regarding the structure and position of uniqueness. This new result has immense application like classifying different expressions to be or not to be unique. The principle objective of the paper is to study the uniqueness of meromorphic functions when sharing a value with weight $l(\geq 0)$ and its nonlinear differential polynomials. We prove a result which significantly generalize the result of Waghamore and Maligi [Commun. Math. {\bf 28} (2020), 289-299] by considering the difference polynomials of the form $f^n(f -1)^mP[f]$ and citing two proper examples we have shown that the result is true only for a particular case. Finally we present the compact version of the same result as an improvement.
GENERALIZATIONS OF WEAKER FORMS OF OPEN MAPS IN FERMATEAN FUZZY TOPOLOGICAL SPACES AND THEIR APPLICATIONS
In this paper, we study Fermatean fuzzy $Z$-open and Fermatean fuzzy $Z$-closed functions within the framework of Fermatean fuzzy topological spaces. We investigate several significant properties of these functions and examine their relationships. In addition, we present a real-life decision-making application based on an entropy measure for Fermatean fuzzy sets, illustrating their practical usefulness in real-world situations.
$\delta$-CONTINUOUS AND IRRESOLUTE MAPS IN PYTHAGOREAN FUZZY NANO TOPOLOGICAL SPACES AND ITS APPLICATION
In this paper, we develop the concept of Pythagorean fuzzy nano (resp. $ \delta $, $ \delta \mathcal{P} $, $ \delta \mathcal{S} $, $ \delta \alpha $ $ \& $ $ \delta \beta $ or $ e^{*} $)-continuity in Pythagorean fuzzy nano topological spaces and specialize some of their basic properties with examples. Also, we discuss about properties and characterization of Pythagorean fuzzy irresolute maps and application of Multiple Criteria Decision Making (MCDM) techniques to the real-world problem using a proposed similarity measure in Pythagorean fuzzy nano topological spaces.
$\mathcal{PF} \mathfrak{N} \delta \mathcal{S} Cts $
$\mathcal{PF} \mathfrak{N} \delta \mathcal{S} Irr$ and Zhang similarity measure
PARTITION DIMENSION OF BENZENOID SYSTEMS AND HEXAGONAL CACTUS CHAINS
This paper determines the partition dimension of selected hexagonal graph structures, namely pericondensed benzenoid systems $R_n$, $B_n$, and hexagonal cactus chains $PC_n$, $OC_n$, and $MC_n$. Using combinatorial techniques, we obtain exact partition dimensions for these classes. Our findings provide valuable insights into their structural properties and have applications in areas such as molecular chemistry and computational biology.