International Journal Of Mathematics And Computer Research

A Unified Xgboost-Based Framework for Detecting Full-Lifecycle Attacks in Containerized Cluster Environments

GANIYU Waheed Oyekunle, Joshua Ayobami Ayeni, Olufemi Samuel Ojo — Tue, 05 May 2026 16:59:21 +0000

The approval of containerized applications in cloud-native environments has significantly improved application scalability, portability, and resource efficiency. However, this development has also introduced complex security challenges across all stages of the application lifecycle, from build-time, deployment-time, and runtime phases. Traditional security solutions are often based on isolated phases of the container lifecycle, but their solutions work on single-source monitoring and, which limits their ability to detect sophisticated multi-stage attacks. This study developed a Unified XGBoost-Based framework for detecting Full-lifecycle attacks in Containerized Cluster Environments. The framework integrated heterogeneous security data from multiple sources, including audit logs of Kubernetes, events in Docker, and Falco runtime alerts, to provide comprehensive reflectivity across the application lifecycle. Collected logs were preprocessed and transformed into structured feature vectors using feature extraction and engineering techniques. The extracted features were used to train an XGBoost classifier for multi-class attack detection, categorizing events into build-time attacks, deployment-time attacks, runtime attacks, and normal behavior. Experimental evaluation indicated strong performance, achieving an average precision of 96.9%, recall of 97.0%, and F1-Score of 96.9%, with runtime attacks recording the highest detection rate due to the rich behavioral indicators available in runtime logs. Comparative analysis further identified that the developed XGBoost-based model outperformed baseline machine learning algorithms, which are Logistic Regression, Decision Tree, Random Forest, and LightGBM. The findings confirm that integrating multi-source logs significantly improves full-lifecycle attack detection in a containerized cluster environment. This research contributes to the field of cybersecurity and containerized applications by providing a scalable and effective machine learning-based structure for comprehensive intrusion detection and threat monitoring.

Reinforcement Learning-Based Adaptive Auto encoder for Energy-Efficient Boll Rot and Pathogen Detection in IoT Networks

Aminu Adamu, Babangida Zubairu, Sagir Ibrahim, Aisha Ibrahim Gide — Thu, 07 May 2026 00:00:00 +0000

The increasing prevalence of crop diseases such as boll rot and other pathogen infections poses a significant threat to agricultural productivity, particularly in resource-constrained farming environments. This study proposes a Reinforcement Learning-Based Adaptive Auto encoder (RL-AAE) framework for energy-efficient detection of boll rot and related pathogens within Internet of Things (IoT)-enabled agricultural networks. The model integrates an adaptive auto encoder for feature extraction and dimensionality reduction with a reinforcement learning (RL) agent that dynamically optimizes sensing, data transmission, and decision-making processes to minimize energy consumption while maintaining high detection accuracy. The adaptive auto encoder is designed to learn compressed representations of high-dimensional sensor and image data collected from distributed IoT nodes, enabling efficient processing and anomaly detection. The reinforcement learning component continuously interacts with the network environment to select optimal actions, such as adjusting sampling rates, transmission intervals, and node participation, thereby prolonging network lifetime and reducing redundant energy usage. The proposed approach is evaluated using key performance metrics including detection accuracy, energy consumption, network lifetime, and latency. Experimental results demonstrate that the RL-AAE model significantly outperforms traditional machine learning and static IoT detection approaches by achieving higher classification accuracy for boll rot and pathogen detection while reducing energy consumption and extending network operational lifespan. This work highlights the potential of combining deep learning and reinforcement learning techniques to address critical challenges in smart agriculture, providing a scalable and intelligent solution for real-time disease monitoring in IoT-based farming systems.

Financial Mathematics in the Valuation of Financial Assets: An Analysis of Present Value, Discount Rates and Expected Return

Alberto Merced Castro Valencia, Caribert Toussaint — Thu, 07 May 2026 00:00:00 +0000

This paper examines the application of financial mathematics to the valuation of financial assets, with particular emphasis on present value, discount rates and expected return as core inputs in investment decision-making. The methodology is quantitative, document-based and analytical: classical and contemporary contributions on the time value of money, the risk–return trade-off and bond valuation are reviewed, and a hypothetical case is developed to illustrate the practical use of financial formulae. The analysis shows that the discount rate is not a secondary parameter but the variable that links risk, opportunity cost and asset price. In the applied example, a bond with a 10% annual coupon, a five-year maturity and a required return of 12% yields a theoretical price of 92,790.45 monetary units, below par value, confirming that when the required return exceeds the coupon rate the instrument trades at a discount. The paper concludes that financial mathematics is indispensable to valuation, asset selection and the internal consistency of corporate investment and financing decisions.

MULTI-OBJECTIVE STOCK PORTFOLIO OPTIMIZATION USING THE PARTITIONING AROUND MEDOIDS (PAM) APPROACH ON THE IDXESGL INDEX

Herni Herawati, Abdul Hoyyi, Yuciana Wilandari — Fri, 08 May 2026 06:35:47 +0000

Investment refers to allocating funds into financial assets, including stocks, to increase future value. To reduce potential losses, investors apply diversification through portfolio formation. This study optimizes stock portfolio construction within the IDXESGL index, which comprises 30 stocks, by combining Partitioning Around Medoids clustering and multi-objective optimization. Clustering employed 2024 financial ratios Return on Assets, Earnings per Share, and Debt to Equity Ratio while considering outliers. Portfolio optimization used daily closing prices from June 20 to November 30, 2025. The multi-objective approach balanced expected return and risk based on investor preferences, with risk measured using Value at Risk under the Historical Simulation method. PAM produced three optimal clusters with a higher silhouette coefficient. MAPA and BBNI represented Clusters 1 and 2, while Cluster 3 was excluded due to negative expected return. For risk seekers, the portfolio was dominated by MAPA (0.939) and BBNI (0.061), generating an expected return of 0.001155026 and a 1-day VaR of -4.9182%. Risk neutral investors obtained more balanced weights, yielding an average expected return of 0.000617052 and a 1-day VaR between -3.0614% and -2.2197%. For risk averters, BBNI (0.759) and MAPA (0.241) produced an expected return of 0.000534355 and a 1-day VaR of -2.218%.

Multidimensional Generalized Geometric Progressions of Multiplicity One

Dharmendra Kumar Yadav — Tue, 05 May 2026 00:00:00 +0000

This paper is a review article to expose the extended advanced concepts of geometric progressions made by applying the basic concepts of an arbitrary dimension and a fixed multiplicity (one which can be expanded for more than one also) applied on different common ratios, which was earlier published in chapter seven and eight in two books on multidimensional geometric progressions cited in the references. In this article we will report the advanced geometric progressions with multiplicity one of different dimensions from one to r and will discuss the formulae to find their general terms and the sums of first n terms. The formulae for infinite number of terms for different dimensions and multiplicities have also been discussed. We have left the discussion on the formulae to find the geometric means between any two arbitrary terms of such generalized geometric progressions so that mathematics teachers and learners can find it useful in teaching with a new look and a research-oriented approach. The article also opens many new areas of research and its applications.

Explicit Evaluations of Quintic theta function

Ravi G. N., Roja R., Praveenkumar . — Sat, 16 May 2026 08:14:50 +0000

Recently, B. C. Berndt and ¨ Ors Reb´ak have obtained several evaluations of cubic theta function [7]. Motivated by their work, in this article we present several evaluations of quintic theta function identities.

Reciprocal Teaching as a Participatory Teaching Method to Improve Mathematical Reasoning and Self-Confidence in Middle School Students

Farah Adibah, Dhoriva Urwatul Wutsqa, Puja Asti Ananta, Nadya Rahmah — Sat, 16 May 2026 11:45:57 +0000

This study investigates the effect of the Reciprocal Teaching (RT) model, implemented as a Participatory Teaching Method, on Grade VII middle school students' mathematical reasoning ability and self-confidence. A quasi-experimental one-group pretest-posttest design was employed with 32 students from SMP Negeri 6 Yogyakarta, selected through purposive sampling. The intervention consisted of four structured instructional sessions on quadrilateral and triangle geometry, incorporating the four RT strategies: predicting, questioning, clarifying, and summarizing. Data were collected using expert-validated instruments: a mathematical reasoning essay test and a Likert-scale self-confidence questionnaire, with reliability confirmed via Cronbach's alpha. Results showed statistically significant improvements in mathematical reasoning (M = 51.43 to 71.78) and self-confidence (M = 35.40 to 39.50), both indicating large effect sizes. Analysis by reasoning indicator revealed gains across conjecture-making, logical argumentation, and conclusion drawing. These findings suggest that RT effectively enhances both cognitive and affective dimensions of mathematics learning. Practical implications for mathematics educators and directions for future research are discussed.