International Journal Of Mathematics And Computer Research

Static Spherical Fluid Models in Einstein–Cartan–Sciama–Kibble Theory A Study of Torsion, Spin–Gravity Coupling, And Self-Gravitating Configurations

Dr. Kanchan Singh — 2026-10-03

This paper develops a systematic framework for studying static, spherically symmetric perfect fluid configurations within the Einstein–Cartan– Sciama–Kibble (ECSK) theory of gravitation. The ECSK formalism extends classical general relativity by incorporating spacetime torsion as a geometrical field sourced by the intrinsic spin density of matter. We write down the governing field equations for the interior of a self-gravitating fluid sphere, exploit Hehl’s redefinition of effective thermodynamic variables to decouple the spin–torsion corrections, and derive a class of interior solutions by prescribing a barotropic equation of state together with a specific choice of one metric potential. The solutions are matched at the stellar surface to the Schwarzschild exterior via the Darmois–Israel junction conditions, yielding unique values for all integration constants. Explicit analytic expressions for the energy density, isotropic pressure, and spin density are presented and analysed. Physical viability is assessed through the standard energy conditions, regularity requirements, and monotonicity criteria. The investigation demonstrates that spin–torsion coupling introduces a repulsive pressure correction that can, under appropriate conditions, prevent the formation of central singularities and modify the mass–radius relationship of compact stellar objects. The astrophysical implications for neutron stars, quark stars, and other dense matter environments are discussed in detail.

A Machine Learning Framework for Mobile Money Fraud Detection Using Gaussian Naïve Bayes: A Transaction-Level Evaluation on the Synthetic Paysim Dataset

Davies Isobo Nelson — 2026-10-06

In Mobile money services are increasingly targeted by fraud, including SIM-related abuse such as SIM swapping, which undermines user trust, exposes sensitive financial data, and costs telecom operators and financial providers billions of dollars annually. Traditional rule-based detection systems have proven insufficient for identifying evolving fraud patterns, motivating the adoption of machine learning approaches. This study presents the design and implementation of a transaction-level mobile-money fraud screening system built around the Gaussian Naïve Bayes (GNB) classifier and evaluated on the synthetic PaySim dataset. The system was implemented following the Rapid Application Development (RAD) methodology using object-oriented design techniques. The dataset was split 80%/20% into training and held-out test sets; normalization was fitted on the training data, and the Synthetic Minority Oversampling Technique (SMOTE, sampling ratio 0.1) was applied to the training set only, leaving the test set at its natural class distribution. Furthermore, predicted fraud probabilities were converted to class labels using a decision threshold of 0.3 instead of the conventional 0.5. The developed model achieved 99.91% accuracy, 89.22% precision, 88.67% recall, 88.94% F1-score, 99.95% specificity, an AUC-ROC of 0.9425, and a false positive rate of 0.05%. The findings indicate that Gaussian Naïve Bayes provides an interpretable and computationally practical baseline for transaction-level fraud screening. However, becuase PaySim contains no SIM-specific signals such as SIM-swap events, device/IMSI changes, or OTP request patterns, the developed model should be understood as a general mobile-money transaction fraud screen rather than a dedicated SIM-fraud detector; the synthetic nature of the dataset and the conditional-independence assumption of Naïve Bayes further limit direct generalization to live telecommunications environments. Future work should incorporate real-world telecom and mobile-money data with genuine SIM-level features, adaptive fraud behaviour, deep learning or sequential models, and real-time stream processing.

Enhancing House Rent Prediction Using A Stacking Ensemble Model for Sustainable Community Development

Abiola, Oladimeji Arowolo — 2026-10-07

House rent estimation remains a challenge due to inconsistent pricing methods, reliance on manual valuation, and the absence of intelligent systems for determining fair rent values. Traditional approaches used by house agents and property owners often result in price variations and inaccurate rent estimations. This study developed a House Rent Prediction System using stack ensemble to estimate annual house rent values based on housing characteristics. The dataset used for the study was obtained from house agents and secondary sources and was preprocessed through data cleaning, encoding, and feature scaling using StandardScaler. The developed system was implemented using Streamlit and included functionalities such as manual prediction, property visualization, house comparison, prediction history, market analytics, and property carousel display. Model evaluation was carried out using MAE, MSE, RMSE, R² Score, and K-Fold Cross Validation. The results showed that the developed system was effective in predicting house rent values and can support intelligent housing valuation and decision-making in community development.

Lecturers’ Awareness and Attitudes Towards the Use of Artificial Intelligence Tools at the University of Nigeria, Nsukka

Lysa Ifunanya Ollowu — 2026-10-09

The increasing availability of artificial intelligence (AI) tools presents new opportunities and challenges for teaching and learning in higher education. This study examined lecturers’ awareness of and attitudes towards the use of AI tools at the University of Nigeria, Nsukka. A descriptive survey design was adopted. Four research questions and two hypotheses guided the study. The population comprised academic staff in the Department of Science Education, University of Nigeria, Nsukka, from whom 49 lecturers participated in the study. Data were collected using a researcher-developed instrument titled Questionnaire on Lecturers’ Awareness Level and Attitude to AI Tools (QLALAAIT). The instrument was subjected to face validation and trial testing, and its overall reliability coefficient, determined using Cronbach’s alpha, was 0.83. Data were analysed using mean and standard deviation to answer the research questions, while analysis of variance (ANOVA) was used to test the hypotheses at the 0.05 level of significance. The findings indicated that lecturers demonstrated awareness of selected AI tools, including ChatGPT, Turnitin, and QuillBot, and generally expressed positive attitudes towards their use in educational contexts. Further analysis showed that years of teaching experience did not significantly influence lecturers’ awareness of or attitudes towards AI tools. The study highlights the need for structured professional development, institutional support, and access to appropriate resources to facilitate informed and effective use of AI tools in university teaching and related academic activities.

ChatGPT Awareness and Utilization Among Undergraduate Biology Education Students at the University of Nigeria, Nsukka: Implications for Mathematics Education

Euphemia Ebubechukwu ONAH — 2026-10-12

The rapid diffusion of generative artificial intelligence (GenAI) into higher education has created new opportunities for learning while also raising concerns about accuracy, academic integrity, digital inequality, and overreliance on automated outputs. This study examined awareness, utilization, challenges, and perceived institutional responses to ChatGPT among undergraduate Biology Education students at the University of Nigeria, Nsukka. A descriptive survey design was adopted. Eighty questionnaires were distributed to students across 100–400 levels, and 67 usable responses were returned, representing an 83.75% response rate. Data were collected using a researcher-developed Questionnaire on the Extent of Awareness and Usage of ChatGPT (QEAUC), which demonstrated an overall Cronbach’s alpha of .798. Frequency and percentage were used to analyse awareness items, while mean and standard deviation were used for utilization, challenges, and proposed solutions. The findings showed substantial

awareness of ChatGPT: respondents demonstrated awareness on seven of eight awareness items, although only 25.4% recognized that ChatGPT uses natural language processing to understand and respond to queries. Overall utilization was high (M = 2.81, SD = 0.81 on a 4-point scale), with particularly high use for content creation, academic research, education, assignments, brainstorming, and conversation practice. Respondents also agreed that important barriers included inadequate internet access (M = 3.64), training costs (M = 3.46), and rote or superficial use (M = 3.51). The strongest proposed solutions were free internet access (M = 3.85), free Wi-Fi (M = 3.82), curriculum integration (M = 3.76), and guided learning activities (M = 3.58). The study concludes that ChatGPT is already embedded in the academic practices of many participating Biology Education students, but effective integration requires AI literacy, reliable digital infrastructure, explicit institutional guidance, and assessment practices that preserve student thinking and academic integrity.

Efficiency of the Pooled Logistic Regression Approach as an Alternative to the Cox Proportional Hazard Model

Precious O. Ibeakuzie — 2026-10-16

The Cox proportional hazards (CPH) model and the exponential Cox model are foundational tools in survival analysis, yet they impose structural assumptions; proportional hazards and constant baseline hazard, respectively that frequently fail in practice. This paper proposes and evaluates pooled logistic regression (PLR) applied to survival-piled (stacked) data as an alternative discrete-time survival estimator. Right-censored survival data are restructured into a long-format person-time binary classification dataset, and three models are compared: the exponential Cox model, the classical semi-parametric CPH model, and PLR. Monte Carlo simulations with 1,000 replications at each of six sample sizes (n = 25, 50, 100, 150, 200, 250) are conducted to assess stability, discrimination, and goodness-of-fit. Performance is measured by Harrell's concordance index (C-index) and the Akaike information criterion (AIC). Simulation results show that PLR maintains consistently high and stable C-index values (0.742–0.784) across all sample sizes, whereas the CPH model exhibits high variability (0.575–0.884) and the exponential Cox model underperforms throughout (0.532–0.671). AIC comparisons further demonstrate PLR's competitive goodness-of-fit at moderate and large sample sizes. Real-data validation using the NCCTG lung cancer dataset corroborates these findings. PLR's theoretical connection to the Cox partial likelihood is established formally, and its compatibility with machine-learning classification pipelines is discussed. The findings support PLR as a robust, flexible, and interpretable alternative for discrete-time survival analysis.

A Robust Database Model for Specific Number Types and an Implementation of a Huge Database for First 1 Trillion Prime Numbers

Neeraj Anant Pande — 2026-10-20

Numbers of different specific types are of importance in study of mathematics. For many types of numbers, a general formula for n^th number either doesn’t exist or although it exists, it becomes impracticable to apply in view of large resource overheads required in its computation. For such numbers, there is need of database of these types of numbers which stores these numbers in succession. This work suggest a robust model database for storing such numbers and highlights various desired features it incorporates. In fact, one such implementation of this database on a huge scale is very recently implemented which is going to be of immense use for researchers in respective domain.

Generalized Area and Arc Length of Sine Function in Polar Coordinate

Sudarno Sudarno — 2026-10-22

Polar coordinate is formed by the radius and rotation angle. The radius indicates distance of a point from pole, while the rotation angle is angle from which starting point moves to ending point relative to the axis-x. Because polar coordinate is affected by two variables, polar coordinate is defined on a plane. This research aims to find a general formula for determining area and length of a curve. The curve equation is a sine function, which is circular and cardioid. The graph of circle is affected by constant and positive or negative sign on the sine function. The constant determines the size of the graph, while positive or negative sign indicates position of the graph in the quadrant. Similarly, the graph of cardioid is affected by constant and positive or negative sign on the sine function. The constant determines the size of the graph, while positive or negative sign indicates the direction of the cardioid. The area of circle is directly proportional to the square of constant. The arc length of circle is directly proportional to the constant. The area of cardioid is directly proportional to the square of constant. The arc length of cardioid is equal to eight times the constant. The general formula for the area and arc length of the curve is used as a predictive tool.