Asian Journal of Mathematical Sciences(AJMS)

On Computational Review of the Block Schaeffer’s Iteration Formula for Strongly Pseudocontractive Maps of the System of Linear Equations

2025-10-08T06:28:06+00:00

This work reviews the background concepts of the Block Schaeffer’s fixed point iteration for- mula, states
and proves its associated theorems before applying the method in the solution of a given system of linear
equation, the aim of which is to computationally confirm that the traditional Block Schaeffer’s iteration
formula is strongly Pseudo-contractive on convergence. Again this research seeks to computationally
reaffirm that the choice of any initial guess closer to the solution for an iteration formula converges faster
to the solution. The obviousness of this is reflected in the main result highlighted in our computation which
showed that a slight ad- justment in the initial guess becoming x¯∗ = x¯0 ± x¯0 10−1 ; x¯0 ̸ = ¯0 produces
faster convergence automatically, no matter how close x¯0 is to the solution, x∗.

Two problems of number theory

2025-10-08T06:36:27+00:00

In the article, the author shows the transition from the ternary Goldbach problem to the binary and then to
the solution of the problem of the infinity of twins. This article is the final one, in which the errors and
shortcomings of his previous articles on this topic are corrected.

Algebraic solution of Fermat's theorem

2025-10-08T06:42:11+00:00

Fermat's Last Theorem (or Fermat's last theorem) is one of the most popular theorems in mathematics.
Formulated in French mathematician Pierre Fermat in 1637. Despite the simplicity of the formulation,
literally, at the “school” arithmetic level, proof of the theorem sought by many mathematicians for more
than three hundred years. And only in 1994 year the theorem was proven by the English mathematician
Andrew Wilson with colleagues; The proof was published in 1995. [1]-[5] With this article, the author
completes his research on the given topic, makes corrections and eliminates the errors of the previous ones.

Detecting Fraud Transactions in Financial Institutions

2025-10-08T07:02:29+00:00

Detecting fraud and anomalies in financial transactions is crucial in safeguarding institutional assets,
maintaining regulatory compliance and ensuring customers trust in financial system. This study
investigated methods of detecting frauds or anomalies in transactions within financial institutions, a vital
task to prevent financial losses, reduce investigative costs, and comply with regulatory standards. We
compared the efficiency of three statistical models: Logistic Regression, Linear Discriminant analysis
(LDA).and Quadratic Discriminant (QDA), in identifying fraudulent activity. Secondary data of over
280,000 financial transactions from an online website (Kaggle) was used to evaluate each model based on
accuracy, precision, and error rates, for both fraudulent and non-fraudulent classifications. The results
indicated that Logistic Regression outperformed LDA, and QDA, achieving the highest accuracy and
lowest error rate, making it the most effective model among the models considered in the study for fraud
detection in this context.

Spectral Signatures of Distributed Software Systems: Eigenvalue Profiling for Enterprise-Scale Proactive Resilience Engineering

2025-10-08T07:06:10+00:00

This paper develops a rigorous spectral framework for profiling distributed software systems at enterprise
scale. We represent a distributed system as a discretized assemblage of computational elements and
construct complexity- aware stiffness and mass matrices. By performing spectral decomposition of the
resulting generalized eigenproblem, we extract spectral signatures — normalized sets of eigenvalues and
derived statistics — which uniquely characterize system resilience, bottlenecks, and failure propagation
dynamics. We define a Spectral Resilience Index (SRI) and vertical-grade functions for different enterprise
domains (finance, healthcare, retail, telco). To improve robustness and adaptivity, we overlay a Hidden
Markov Model (HMM) that maps observed telemetry to latent resilience states and refines deterministic
spectral predictions. We validate the methodology using public datasets (DORA metrics, Death Star Bench
traces, and Google SRE reports), present synthetic and trace-driven examples, and show how spectral
fingerprints can be used for early-warning, prediction, and proactive resilience engineering — reducing the
need for ad-hoc chaos engineering

Resource-Constrained Multi-objective Optimization Model for Global Warming Resilient Emergency Response and Welfare Networks

2025-10-08T07:12:21+00:00

This study introduces an uncertain multi-objective, multi-commodity, multi-period, and multi-vehicle
mixed-integer programming model with social equity designed for the critical response phase of
humanitarian operations. The framework strategically addresses the complexities of disaster relief by
integrating five key echelons: affected regions, distribution centers, hospitals, temporary
accommodation facilities, and temporary care centers. The model is driven by four primary objectives:
the minimization of overall costs associated with facility location, resource allocation, social equity and
crucially, the reduction of relief supply shortages. Uncertainty inherent in disaster scenarios is robustly
managed through a probabilistic scenario-based approach. Significant strategic decisions facilitated by
the model encompass the optimal siting of temporary care and accommodation centers, the efficient
allocation of affected populations to designated centers and hospitals, and the effective distribution of
supplies from major hubs to temporary shelters. Furthermore, the model determines optimal flows for
injured individuals and commodities between facilities, specifies the required number of vehicles for
inter-facility transport, and manages both shortage and inventory levels at all centers. A comprehensive
set of constraints ensures practical applicability, covering aspects such as demand fulfillment, relief
commodity flow, facility capacities, transportation logistics for both people and goods, and the
utilization of backup centers across multiple planning periods.
The developed model’s efficacy was demonstrated through its application to a real-world case
study: the city of Warri and its environs in Nigeria, a region significantly impacted by floods exacerbated
by global warming. To solve this complex problem, three distinct methods were employed: the epsilon-
constraint method, the Non-Dominated Sorting Genetic Algorithm-II (NSGA-II), and a modified multi-
objective particle swarm optimization (MMOPSO). Perfor- mance analysis, utilizing various multi-
objective evaluation metrics, confirmed the superior performance of MMOPSO. A significant
innovation of this model is its inherent integration of social equity principles, ensuring that the allocation
of resources and services prioritizes the most vulnerable populations within the affected area. A
preferred solution, selected from the MMOPSO-generated non-dominated set based on these equity
considerations and expert judgment, was thoroughly analyzed to exemplify the model’s practical
implications for resilient and equitable disaster response.