Mathematics and Computer Science: Research Updates Vol. 12

6G-Enabled NB-IoT Framework for Satellite-Integrated Industrial IoT

2026-06-20T11:54:49+00:00

This study develops a 6G-enabled NB-IoT framework for satellite-integrated Industrial Internet of Things (IIoT) applications, with emphasis on signal generation, routing, and cloud service enablement for device-centric industrial and smart-city environments. The proposed framework is aligned with the ISRO-RESPOND Basket 2024 requirements for NB-IoT in satellite communication and considers IEEE 802.15.4-based wireless sensor networking, 3GPP-oriented cellular access, and edge-cloud platform services. The manuscript presents a conceptual architecture in which wireless sensor nodes, relay links, base station interfaces, and cloud resources support producer-consumer data flows between device, machine, and application layers. At the physical layer, the study discusses SC-FDMA uplink and OFDMA downlink operation, pulse-shaping, cyclic-prefix use, sub-carrier mapping, and RF power-amplifier design to minimise peak-to-average power ratio and intersymbol interference. The proposed use of a Zener-diode-assisted RF power-amplifier circuit is positioned as a mechanism for maintaining voltage stability and supporting energy-aware transmission in narrowband channels. At the networking layer, the framework incorporates TCP/IP encapsulation, link-state routing, BGP, OSPF, RIP, ZRP, VLAN/WLAN/PAN connectivity, and packet retransmission logic to support end-to-end data transport. The service layer maps NB-IoT and wireless-sensor data flows to cloud and edge orchestration for fire services, waste management, transport, street lighting, emergency medical services, and smart-meter applications. It also organises assumptions on topology, data acquisition, quality of experience, and routing resilience for later technical evaluation. The chapter therefore provides an integrated design-oriented description of a satellite-assisted NB-IoT/IIoT framework that combines waveform considerations, routing procedures, data acquisition, and cloud-based service access. The work is primarily architectural and is intended to inform subsequent simulation, implementation, and validation.

Contextualised Pedagogy in Teaching Integrals: Evidence from Goma Secondary Schools

2026-06-20T11:56:57+00:00

Integral calculus is a fundamental area of mathematics that supports the calculation of areas, volumes and averages, as well as the modelling of phenomena in several scientific and technical fields. In secondary schools in Goma, Democratic Republic of the Congo (DRC), the teaching and learning of integrals take place in a socio-educational context marked by limited resources, insufficient continuing teacher training and weak contextualisation of textbooks and classroom activities. This study analysed the conditions under which integrals are taught and learned in Goma secondary schools, with particular attention to contextualised pedagogy and educational innovation. A descriptive mixed-method design was used. Data were collected from 16 mathematics teachers and 295 students drawn from 16 schools through textbook analysis, questionnaires and diagnostic tests. Quantitative data were processed using descriptive statistics, while open-ended responses and textbook content were examined through thematic content analysis. The findings show that the textbooks used in the schools introduce integrals mainly after derivatives and present them predominantly as inverse operations, with exercises that are largely procedural and weakly connected to local situations. Teachers reported limited access to continuing training and teaching resources, and classroom practice remained mainly lecture-based. Students perceived integral calculus as difficult and abstract, frequently confused the integral with the primitive, and encountered substantial difficulty when solving contextualised problems. However, many students indicated that practical examples, guided exercises and visual or digital supports could improve their understanding. The study concludes that improving the teaching and learning of integrals in Goma requires stronger didactic transposition, locally contextualised resources and sustained support for mathematics teachers.

Mapping the Memory Landscape: Understanding RAM

2026-06-20T11:59:57+00:00

This chapter presents a practical, hardware-oriented explanation of random-access memory (RAM) and its relationship to low-level programming concepts. It is designed for learners who encounter difficulty with pointers, dynamic memory, stack behaviour, heap allocation, and the apparent abstraction of program storage in C and C++. The discussion begins by describing RAM as a linear sequence of byte-addressable cells, each identified by a unique address commonly represented in hexadecimal form. This model is then used to explain how variables, arrays, strings, objects, compiled instructions, and pointers occupy specific regions within memory. The chapter further examines the distinction between stack and heap memory, emphasising their different lifetimes, management models, growth directions, and roles in function execution and dynamic allocation. It also connects these software-level ideas with hardware-level organisation by comparing stack and heap concepts with the internal RAM structure of the 8051 microcontroller and the segmented memory architecture of the 8086 microprocessor. In addition, the chapter discusses processor registers, cache hierarchy, RAM, and secondary storage as layers of a memory-speed hierarchy, explaining why access time varies across these storage locations and why global variables may incur higher access costs than register-resident local values. By linking programming abstractions to the physical and architectural organisation of memory, the chapter offers a structured conceptual map for understanding pointer arithmetic, stack frames, heap management, register use, cache effects, embedded-system memory constraints, and low-level program behaviour. The overall aim is to support clearer reasoning about memory management and performance without treating memory-related errors as mysterious or disconnected from hardware reality.

Approximation of Lipschitz Functions via Product Summability Methods

2026-06-20T12:01:44+00:00

Product summability methods provide a useful framework for studying the approximation of Fourier series when ordinary convergence does not fully capture the behaviour of functions with limited smoothness. This study examines the degree of approximation of periodic functions belonging to the Lipschitz class by applying the product mean obtained from the Cesàro and Euler summability methods to the associated Fourier series. The work is placed within summability theory and harmonic analysis, where the control of approximation error is central to understanding the convergence of transformed trigonometric series. The manuscript first reviews the relevant notions of degree of approximation, Lipschitz continuity, Cesàro summability, Euler summability and product means, and then establishes the principal theorem for functions that are Lebesgue integrable on the stated interval and periodic with period 2π. The theorem gives an estimate for the approximation error in relation to the smoothness parameter of the Lipschitz class and the order of the Fourier approximation. The analysis indicates that the combined Cesàro–Euler product mean provides a structured procedure for obtaining approximation estimates for functions whose regularity is controlled but not necessarily differentiable. The results contribute to the study of summability-based Fourier approximation by clarifying how a product method can be used in the Lipschitz setting. The discussion further notes the relevance of such approximation techniques to areas in which Fourier representations are used, including signal analysis, numerical methods and computational modelling. Overall, the study presents a mathematically focused treatment of product summability as a tool for estimating the approximation of Lipschitz functions through Fourier series, without extending the conclusion beyond the established theorem.

Schizophrenia Detection with EEG Signal Using EEGNet and Attention Mechanism

2026-06-29T06:31:12+00:00

Schizophrenia is a severe psychiatric disorder that affects cognition, perception, emotion and behaviour, and timely diagnosis is important for planning appropriate clinical management. Conventional diagnostic approaches are mainly based on clinical interviews and behavioural assessment, which may be influenced by subjectivity and inter-clinician variation. This study proposes an automated EEG-based schizophrenia detection framework that integrates EEGNet, an attention mechanism and Bidirectional Long Short-Term Memory (BiLSTM) networks. EEG recordings from healthy individuals and patients diagnosed with schizophrenia were preprocessed using filtering, Independent Component Analysis-based artefact removal, epoch segmentation and normalisation. Subject-wise data splitting was used to reduce the risk of data leakage during model evaluation. EEGNet was applied to extract spatial and spectral features from multichannel EEG signals, while the attention mechanism assigned greater weight to informative EEG channels and temporal regions. BiLSTM layers were then used to model bidirectional temporal dependencies in the extracted EEG feature sequences. The proposed framework achieved a reported classification accuracy of 99.41% within the described experimental setting. The findings indicate that combining EEGNet-based feature extraction, attention-based feature weighting and BiLSTM-based sequence learning may improve automated schizophrenia classification from EEG signals. However, further validation using independent datasets and detailed reporting of experimental conditions are required before clinical application can be considered.

Student Orientation Piloted by Artificial Intelligence Using Filtering Collaborative Base on Memory

2026-07-04T13:36:26+00:00

Traditional student orientation in universities and higher education institutions in the Democratic Republic of Congo, particularly at the National Pedagogical University, often depends on personal choice, social influence, perceived employment opportunities and ease of enrolment rather than on candidates' demonstrated academic skills. This practice may contribute to academic failure, uneven distribution of students across departments and weak alignment between graduates' training and labour-market expectations. This study proposes a memory-based collaborative filtering algorithm for recommending university courses according to students' prior academic performance. The model uses two main matrices: one containing candidates' average marks in subjects studied at secondary-school level and another containing the weighting of those subjects in university programmes. The product of these matrices provides a compatibility structure that supports comparison between candidate profiles and programme requirements. Cosine similarity is then used to identify the programme with the strongest alignment for each candidate. The algorithm was implemented in Python using Jupyter Notebook within the Anaconda environment and tested on a sample drawn from the Faculty of Sciences. The results show candidate placement across Biology, Geography, Petrochemistry, Physics, Mathematics and Statistics, and Hospitality, with recommendation scores indicating the relative strength of alignment. The proposed approach offers a structured decision-support tool for academic guidance while retaining the need for institutional interpretation and validation.

Survival Models Based on Clinical and Demographic Covariates of Haemodialysis Patients

2026-07-04T13:45:09+00:00

Background and Objective: Patients with chronic kidney disease (CKD) in Tanzania may avoid modern medical care because of limited knowledge and fear of treatment costs, which may increase mortality even among younger patients. Survival models for CKD and end-stage kidney disease (ESKD) patients based on clinical, demographic and laboratory covariates may help physicians intervene earlier and prolong patients' survival. This study aimed to develop parametric and non-parametric survival models for haemodialysis patients and to determine the covariates influencing mortality among dialysis patients. Although machine-learning models are increasingly used and can be efficient, they may not always be appropriately interpreted or implemented in some clinical situations.

Materials and Methods: This retrospective cohort study included 171 dialysis patients admitted to Muhimbili Hospital, Dar es Salaam, in 2015 and followed up to 2018. The hospital is a primary referral health centre for kidney diseases, and its nephrology department manages many ESRD patients, mainly through dialysis and transplantation. Basic prevalence was determined, and patient survival time was analysed using five parametric models. The Cox proportional hazards model and Kaplan-Meier model were used to identify significant survival patterns related to smoking, alcohol intake and HIV status.

Results: Of the 171 patients, 148 survived for 0-500 days, 20 survived for 501-1000 days, and only 3 patients survived for more than 1000 days. The factors associated with survival were sex, the number of dialysis sessions, blood transfusion and alcohol consumption. The lognormal distribution was the best parametric fit for the data, and the estimated average survival time was 268 days. The Cox proportional hazards model identified alcohol intake and the number of dialysis sessions as significant covariates. The Kaplan-Meier curve and mortality-rate curve showed significant differences according to smoking status, alcohol consumption and HIV infection, and these differences were supported by log-rank tests.

Conclusion: CKD and dialysis treatment were more common among males in Tanzania, and few patients survived beyond three years of treatment and follow-up. The number of dialysis sessions, lack of hygienic blood transfusion and alcohol intake were associated with mortality among CKD patients undergoing dialysis.

Machine Learning Algorithms for Intrusion Detection: A Comparative Analysis

2026-07-11T07:35:53+00:00

Network intrusion has remained one of the most persistent and critical threats to computer networks for several decades. To reduce the severity of network intrusions, network intrusion detection systems have proved effective. This study undertakes a comparative examination of machine learning algorithms used for intrusion detection, addressing the escalating challenge of safeguarding networks from malicious attacks in an era characterised by the proliferation of network-related applications. Given the limitations of conventional security tools in combating intrusions effectively, the adoption of machine learning has emerged as a promising avenue for strengthening detection capabilities. The research evaluates the efficacy of three distinct machine learning algorithms - Convolutional Neural Networks (CNN), Recurrent Neural Networks (RNN), and Naive Bayes - in identifying diverse attack categories, including Denial of Service (DoS), Probe, Remote to Local, and User to Root. This research adopts an experimental research design. The NSL-KDD dataset consists of several attributes that provide the features of network-based intrusion detection systems. Conducted on the NSL-KDD dataset, the analysis identifies CNN and RNN as stronger performers than Naive Bayes, particularly in terms of detection accuracy. The CNN algorithm achieved an accuracy rate of 96.55%. The Naive Bayes algorithm, although having a lower accuracy of 91.30%, still demonstrated acceptable performance in detecting DoS attacks. While CNN demonstrated strong performance in attack detection, its slightly lower Receiver Operating Characteristic scores compared with RNN indicate a nuanced difference in discriminatory power. In contrast, Naive Bayes, while computationally efficient, exhibited lower accuracy and F1 scores because of its assumption of feature independence. These findings are useful to researchers and practitioners in intrusion detection systems, offering insights into algorithmic choices. Overall, this study contributes to ongoing efforts to strengthen network security and supports the development of safer technological systems.