International Journal of Mathematics And its Applications

Blood Flow Through Stenosed Arteries in the Presence of Silica $(SiO_2)$ Nano Particles

Nitin. S. Bodke — 2025-12-31

The numerical investigation of blood flow through stenosed human arteries in the presence of Silica $(SiO_2)$ nanoparticles (NPs) is carried out. The governing equations are discretized using the finite difference method, and the simulations are performed in MATLAB. The study focuses on analyzing the influence of Silica $(SiO_2)$ nanoparticles on velocity distribution, volumetric flow rate, and resistive impedance. Results indicate that the inclusion of nanoparticles significantly alters these hemodynamic parameters, with a marked impact on velocity, flow rate, and impedance.

Analyzing Complexities in Decision-Making using Rough Intuitionistic Fuzzy Diagraphs

Kamesh Kumar — 2026-01-01

This research article introduces a hybrid approach which integrates a rough set with an intuitionistic fuzzy set. A rough intuitionistic fuzzy architecture is formed to study the vagueness, incompleteness, and ambiguity based information systems in some real life problems by using this hybridization. This study basically extends the existing rough fuzzy hybrid approach by generalizing some of its definitions and theorems. Finally, application of the proposed hybrid mechanism to decision-making problems underscores the potential of our method. Present article provides an efficient and effective tool for dealing complexities in decision-making. In particular, an efficient algorithm is developed to solve decision-making problem. Time complexity of proposed algorithm is also computed.

Hilbert Graceful Labeling on the Eight Sprocket Graph

J. Suresh Kumar — 2026-01-01

Let $ G $ be a simple, finite, connected, undirected, non-trivial graph with $ p $ vertices and $ q $ edges. Let $ V(G) $ be the vertex set and $ E(G) $ be the edge set of $ G $. The $ n^{\text{th}} $ Hilbert number is denoted by $ H_n $ and is defined by $H_n = 4(n - 1) + 1, \quad \text{where } n \ge 1$. A \emph{Hilbert graceful labeling} is an injective function $H : V(G) \rightarrow \{x : x = 4(i - 1) + 1, \, 1 \le i \le 2q\}$ which induces a bijective function $H^* : E(G) \rightarrow \{1, 2, 3, 4, \ldots, q\}$ defined by $H^*(uv) = \frac{1}{4} \, |H(u) - H(v)|$, $\forall \, uv \in E(G), \, u, v \in V(G)$. A graph that admits a Hilbert graceful labeling is called a \emph{Hilbert graceful graph}. This paper focuses on the Eight Sprocket Graph $ SC_n $ and demonstrates its Hilbert gracefulness. It also investigates related graph families formed from copies of $ SC_n $, proving that the path union, cycle, and star of the Eight Sprocket Graph are all Hilbert graceful.

On the Stability of the Quadratic Functional Equation $f(2x+y) + f(x+2y)$ $= 4f(x+y) + f(x) + f(y)$ in $2$-Banach Space

Bhavin Mansukhlal Patel — 2026-01-01

In this research paper, we investigate the Hyers-Ulam stability of the functional equation $f(2x+y) + f(x+2y) = 4f(x+y) + f(x) + f(y)$ in $2$-Banach space.

Fixed Point Theorem of Generalized Contraction for Multi-valued Mapping on Fuzzy Metric Spaces

Arjun Singh Yadav — 2026-01-01

We prove a Generalized type fixed point theorem for multi-valued mappings on G-complete fuzzy metric spaces. The proof uses the Hausdorff fuzzy metric space which was introduced by Rodriguez-Lopez and Romaguera \cite{Lopez}. We also generalized previous known results.

Application of m-Ranking to Node Analysis in Complex Networks

Shibu Manuel — 2026-01-01

Identifying influential nodes in complex networks has gained considerable attention because of its significant theoretical importance and broad range of applications. The m-Ranking method incorporates both the degree of nodes and the weights of edges to rank nodes with varying importance levels. This approach can also be applied to unweighted networks by simply setting the weight parameter $\alpha= 1$. Furthermore, we illustrate the effectiveness of the proposed method using a real-world air traffic network, where the rankings produced are shown to be more meaningful compared to those obtained through existing methods.