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
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.
Copyright (c) 2026 South East Asian Journal of Mathematics and Mathematical Sciences
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.
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.
$\delta$-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.
A HYBRID ITERATIVE APPROACH FOR SOLVING NONLINEAR TIME-FRACTIONAL DIFFERENTIAL EQUATIONS WITH APPLICATIONS TO FRACTIONAL REACTION-TRANSPORT MODELS
This paper proposes a novel hybrid iterative method for the numerical solution of nonlinear fractional differential equations (FDEs) in the Liouville-Caputo sense. The methodology integrates the Formable integral transform with a new algorithm based on the Daftardar-Gejji and Jafari iterative method to provide accurate approximations for complex FDEs. The efficacy of the approach is demonstrated through applications to the chemical Schnakenberg model and the coupled one-dimensional time-fractional Keller-Segel chemotaxis model. Numerical results confirm the convergence of fractional-order solutions towards their corresponding integer-order formulations, thereby validating the precision and reliability of the proposed technique. This study contributes significantly to the computational analysis of fractional reaction-transport phenomena and offers novel insights into the dynamic characteristics of nonlinear fractional models.
ON SOME COLOR PARTITION IDENTITIES OF SCHUR-TYPE OVERPARTITIONS
Motivated by the work of Broudy and Lovejoy, who investigated arithmetic properties of an overpartition counting function $S(n)$ that arose in connection with Schur’s partition theorem and a universal mock theta function. In this article, we present a few Ramanujan-type color partition identities of $S(n)$. Our proof relies on basic identities of theta-functions.
PARA-KENMOTSU MANIFOLDS ADMITTING QUARTER-SYMMETRIC METRIC CONNECTION
In this article, we examine para - Kenmotsu manifolds equipped with a quarter-symmetric metric connection, focusing on various geometric and curvature properties and we construct an example of a 3-dimensional para-Kenmotsu manifold which confirms the specified metric and structure fulfill the para-Kenmotsu curvature conditions. A unique relation between the curvature tensors of Para-Kenmotsu manifolds with respect to the quarter-symmetric metric connection and the Levi-Civita connection has been established. We explore the characteristics of the locally $\phi$-symmetric para-Kenmotsu manifold with respect to the quarter-symmetric metric connection and show that a para-Kenmotsu manifold admitting the quarter-symmetric metric connection $\tilde \nabla$ is locally $\phi$-symmetric if and only if it is so with respect to the Levi-Civita connection. In addition, we studied $\phi$-recurrent para-Kenmotsu manifolds with respect to the quarter-symmetric metric connection and proved that if a para-Kenmotsu manifold is $\phi$-recurrent with respect to the quarter-symmetric metric connection, then the manifold is an $\eta$-Einstein manifold with respect to the Levi-Civita connection.
$\phi$-recurrent para-Kenmotsu manifolds
$\phi$-symmetric para-Kenmotsu manifolds
GENERALIZED KOTHE-TOEPLITZ DUALS OF A NEW CLASS OF SEQUENCE SPACES
In this paper, we determine the $p\alpha$-duals of certain newly introduced difference sequence spaces, namely $\ell_{\infty}(u,\triangle_{v}^{m},q), c_{0}(u,\triangle_{v}^{m},q),$ and $c(u,\triangle_{v}^{m},q)$. Furthermore, we investigate their topological properties and establish the conditions under which these spaces are perfect.
ON WARPED PRODUCT QUASI GENERALIZED RECURRENT MANIFOLDS
Recurrent manifold is one of the important curvature restricted geometric structure and quasi generalized recurrent manifold is a proper generalization of such manifolds. The object of the present paper is to study the properties of quasi generalized recurrent warped product manifolds and to determine the necessary and sufficient conditions for a warped product manifold to be a quasi generalized recurrent manifold. Finally as a support of the main result, we present an example of warped product quasi generalized recurrent manifold.
MAPPING PROPERTIES OF PLANAR HARMONIC FUNCTIONS VIA MILLER-ROSS FUNCTIONS
In this paper, we investigate the relationship between a novel class of harmonic univalent functions and the harmonic starlike and convex functions defined in the open unit disk, using a convolution operator associated with the Miller-Ross function. The importance of this investigation lies in the fact that convolution operators generated by special functions, such as the Miller–Ross function, provide powerful tools for constructing and characterizing new subclasses of harmonic mappings with rich geometric behavior. Several corollaries and related consequences of the main results are also established.
ON NANO SOFT $^{s}(\mathscr{I})$-CONTINUOUS FUNCTIONS
In this paper, we introduce new ideas of nano soft $^{s}(\mathscr{I})$-open sets and examine a few characteristics of nano soft $^{s}(\mathscr{I})$-openess. Furthermore, we study nano soft $^{s}(\mathscr{I})$-continuous functions. Likewise, some characterization and properties are given. We compare our framework with some other well-known ones that are present in the literature.
nano soft $^{s}(\mathscr{I})$-closed set
nano soft $^{s}(\mathscr{I})$-continuity
POLYNOMIAL-TIME APPROACHES TO FUZZINESS IN RATIO LABELLED GENERAL GRAPHS
In classical fuzzy graph theory, fuzziness is introduced by freely assigning membership values to vertices and edges, which makes every crisp graph trivially fuzzy. To avoid this limitation, we propose ratio labeling (RL), a structured labelling scheme in which vertex and edge memberships are linked by a fixed functional relationship. This approach provides a meaningful and non-trivial criterion for deciding when a graph can truly be considered fuzzy. We derive necessary and sufficient conditions under which a crisp graph becomes a fuzzy graph under ratio labelling and characterize the class of general graphs that admit fuzziness in this framework. We also present deterministic polynomial-time algorithms to label the vertices and edges of a general graph and to determine whether a given graph admits fuzziness under ratio labelling. These results offer an efficient and systematic method for studying fuzziness in general graphs and highlight the potential of ratio labelling for applications in connectivity analysis.