Mathematics and Computer Science: Research Updates Vol. 7

A Geometric Study of Garner Cancerous Model

2025-10-21T08:26:21+00:00

In cell proliferation, a cancer cell copies its DNA and divides into two cells. If this division is more rapid, then we can say that cancer is the fastest growing or it may be highly graded effective cancer. It is necessary to differentiate cancer stem cells from healthy stem cells. In the present paper, Garner’s cancer model (GCM) has been geometrically studied by using the KCC-Jacobi theory. In the KCC theory, the second-order dynamical system and the geodesic equation associated with the Finsler space are topologically equivalent. The Jacobi stability based on the KCC theory and the Lyapunov linear stability of the model are discussed in detail. The particular value of parameters has been chosen to compare the Jacobi and Lyapunov linear stability, and it has been found that the Jacobi stability on the basis of KCC theory is global than the linear stability. The critical values of the bifurcating parameters are found and their effects on the model have been investigated. This study will be helpful in measuring and preventing cancer cell growth. In this study, it has been observed that an unstable stage of cancer/tumor occurs only when there is a severe effect of any parameter present.

Mathematical Modelling and Analysis of Malaria Transmission Dynamics among Children under Five with Early and Late Treatment Interventions

2025-10-21T09:01:56+00:00

Malaria, a life-threatening disease caused by Plasmodium parasites transmitted through the bites of infected Anopheles mosquitoes, poses a persistent public health challenge in Nigeria due to its complex transmission dynamics. Mathematical modeling provides a robust framework to unravel the complexities of malaria transmission, enabling predictions of disease dynamics and evaluation of control measures. This study develops a compartmental SEIIR-SEI model to evaluate the impact of early (λ1) and late (λ2) treatment interventions on malaria transmission among children under 5, aiming to guide effective control strategies. Parameterized with Nigerian malaria case data (2007–2021), the model integrates human and mosquito populations to examine how treatment timing affects the basic reproduction number (R0) and disease prevalence. The methodology encompasses model formulation, assumptions, parameter estimation, analytical methods, and numerical simulations. Using stability analysis, sensitivity analysis, and numerical simulations, we find a baseline R0 = 2.24, indicating endemicity. Early treatment reduces this to R0,λ1 = 1.46, outperforming late treatment (R0,2 = 1.65). Sensitivity analysis highlights mosquito biting rates ((b) and λ1 as key drivers of R0. Simulations show that 60–80% early treatment coverage (λ1 ≥ 0.6) within 24 hours significantly lowers prevalence within 120 days, unlike 100% late treatment (λ2 = 1.0). The disease-free equilibrium is stable when R0 < 1, achievable with high λ1. Rapid diagnosis, Artemisininbased Combination Therapies, and vector control are critical for eradication. Policymakers should enhance healthcare access and surveillance to reduce Nigeria’s malaria burden. These findings provide a rigorous, data-driven foundation for policymakers to optimize malaria control programs, reducing morbidity, mortality, and economic burdens in endemic regions. Future studies should explore fractionalorder models or spatial dynamics to further refine intervention strategies.

Implementation of Agile Methodology in an iOS-Based Travel Planning Application with Route Optimization

2025-10-21T09:08:22+00:00

Background: Generation Z is known for its high curiosity, adventurous spirit, and passion for hobbies such as traveling. Gen Z individuals often face challenges in travel planning, including suitable tourist destinations near their location.

Aims: This study aimed to develop Find Your Way, an iOS-based travel planning application designed to address user needs through the Agile development approach, with a focus on optimizing multi-destination routes for more efficient travel planning.

Methodology: This study was conducted in Indonesia over a five-month period, from December 2024 to April 2025. It applied Agile methodology, consisting of six iterative phases such as planning, design, development, testing, deployment, and review, executed over two development cycles to refine the application based on user feedback. Interviews were conducted with four participants aged 18–35 to gather functional requirements. The data were analyzed using thematic analysis to identify key user needs, which guided the design and implementation of the application using Swift and MVVM Clean Architecture. A distinctive contribution of this study was the integration of Particle Swarm Optimization (PSO) for route optimization, enabling more accurate predictions of both travel time and duration at destinations. The core features developed included destination recommendations, route management, and customizable map settings. Testing was performed using blackbox and whitebox methods, while deployment was conducted via TestFlight with CI/CD integration through Xcode Cloud. In the review phase, 30 users aged 18–25 completed a User Acceptance Test (UAT) to evaluate the app’s usability and performance.

Results: The study successfully produced Find Your Way, a travel planning application tailored to functional requirements identified by users. Five key features were implemented, including destination information, location and route recommendations, as well as storage and map display settings. The application achieved a UAT score of 97.33%, a result that underscores both the system’s reliability and the practical effectiveness of combining Agile development with PSO-driven route optimization. Testing confirmed the application’s functionality and program logic through blackbox and whitebox methods.

Conclusion: The Find Your Way application was successfully developed and met user functional requirements. The high UAT score of 97.33% highlights the practical significance of the application, demonstrating that it effectively fulfilled its intended purpose while validating the Agile development approach and the integration of PSO as a distinct optimization method.

Path Finding and Pattern Spotting in Toroidal Topologies: A Study on de Bruijn Structures, k-ary n-Cubes, and Toroidal k-ary Grids

2025-10-21T09:12:34+00:00

This paper examines toroidal layouts with a focus on their roles in pattern spotting and path-finding strategies. While de Bruijn structures provide a precise method to locate specific patterns, k-ary n-cubes and toroidal k-ary grids enable efficient path finding through different node organization principles. The study compares these structures by modeling their underlying strategies and presenting algorithmic solutions in pseudocode. The results highlight the complementary strengths of each approach, offering useful insights for applications in network routing, parallel computing, and data organization.

Beta Distribution Goodness of Fit: A Comparative Study of Anderson-Darling, Kolmogorov-Smirnov, Shapiro-Francia and Chi-Square Tests

2025-10-21T09:17:55+00:00

The Beta Distribution is widely used in statistical applications. It has numerous applications in various fields, including reliability applications and manufacturing quality control. In this study, Beta Distribution Goodness-of-fit procedures are illustrated. A comparative study between the Anderson-Darling, Kolmogorov-Smirnov, Shapiro-Francia, and Chi-square goodness-of-fit test in testing for Beta distribution is performed using simulation. Performance of Kolmogorov–Smirnov test is more consistent than other tests considered.

A Study on Radio Harmonic Mean Labeling of Various Classes of Star Graphs

2025-10-24T13:03:51+00:00

Graph labelling is one of the fascinating areas of graph theory with wide-ranging applications. Labelled graphs serve as useful models for a broad range of applications, such as X-ray, crystallography, radar, coding theory, astronomy, circuit design, channel assignments of FM radio stations and communication network addressing. Motivated by the problem of channel assignment of FM radio stations, the concept of radio labelling of graph and the notion of radio mean labelling of graph have been introduced. Motivated by the notion of radio mean labelling and its noteworthy results, the concept of radio harmonic mean labelling has been introduced. In this work, most of the results focus on particular classes of star graphs and utilise ad hoc methods. The methodology is used in this study, the vertices are assigned the labels with N, finding the span of a mapping f and finding the lowest spans taken over all radio harmonic mean labeling of the graph G.A radio harmonic mean labeling of a connected graph G is a one to one map f from the vertex set V(G) to the set of natural numbers N such that for any two distinct vertices u and v of G, \(d(u, v)+\left\lceil\frac{2 f(u) f(v)}{f(u)+f(v)}\right\rceil \geq 1+\operatorname{diam}(G)\). The radio harmonic mean number of f, rhmn(f) is the maximum number assigned to any vertex of G. The radio harmonic mean number of G, rhmn(G) is the minimum value of rhmn(f) taken over all radio harmonic mean labelling f of G. In this paper, we have determined the radio harmonic mean number of some star-related graphs.

Negative Definite Functions on Sobolev Type Spaces with Fractional Fourier Transform

2025-10-25T03:58:45+00:00

Non-archimedean pseudo-differential operators have gained popularity in recent years due to their utility in studying certain equations associated with new physical models in physical form. Main aim of this paper is to define non-archimedean pseudo-differential operator associted with fractional Fourier transform in this manuscript. In this manuscript, we discuss some classes of p-adic complete inner product spaces, B_ϕ, _k(Q_p), 0 ≤ k < ∞, connected to negative definite, radial and continuous functions ϕ : Q_p → C. In this article, we also introduce the non-archimedean pseudo-differential operator A_ϕ,k involving fractional Fourier transform connected to negative definite functions. We find the convolution Kernel Kk of these operators and the Green function related to fractional Fourier transform.

Application of Self-starting CUSUM (Cumulative Sum) Control Charts for Monitoring Process Performance

2025-10-30T11:04:55+00:00

Statistical process control (SPC) charts are important tools for detecting process shifts. SPC enables operations to run smoothly and consistently produce goods that meet quality standards. It is widely used in manufacturing and can also be applied to any process where quality and change monitoring are priorities, including in service industries, environmental management, economics, healthcare, and more. The control chart is an important statistical technique that is used to monitor the quality of a process. The most accepted control charts are the Shewhart charts, CUSUM charts and the EWMA charts. Shewhart control charts help to detect larger shifts in the process parameters, but Cumulative Sum (CUSUM) and Exponentially Weighted Moving Average (EWMA) charts are expected for smaller and moderate changes. The CUSUM control chart is normally used in industry for the result of small and moderate shifts in process stability and disparity. It can be shown that if there are sharp, irregular changes to a process, these types of charts are highly effective. On the other hand, if one is involved in a small, persistent shift in a process, other types of control charts may be chosen, for instance, the CUSUM control chart. In this study, a Self-Starting CUSUM control chart was used for monitoring the moisture level of the paper sheet. For monitoring the process, 30 samples were collected from the ongoing process. The results demonstrate that CUSUM charts can detect process shifts as early as the 21st observation, whereas traditional Shewhart charts showed no change. This early detection can help the decision maker to proactively respond to the output and correct the problems in time. The Self-Starting – CUSUM chart is very easy to use, and it quickly detects both small and large shifts in the process mean and /or standard deviation.