International Journal of Mathematical Sciences and Computing @ijmsc
Journal articles - International Journal of Mathematical Sciences and Computing
All articles: 294
Scientific article
Water loss in water distribution systems (WDS) is a serious problem in Tanzania and the third world countries at large. A lot of water is lost on its way before reaching the consumers. This causes a shortage of water supply which leads to loss of revenues of the concerned water authorities. The control or reduction of water loss in the WDS is closely dependent on the commitment of the decision-makers and on the strategies and budget, they set for that purpose. This paper presents a combined model of Multi-Criteria Decision Making (MCDM) and Numerical optimization techniques which may help decision-makers to prioritize and select the best strategies to be used in the management of water loss in the WDS at Moshi Urban Water Supply and Sanitation Authority (MUWSA), Tanzania. The Multi-Criteria Decision Making family methods namely the Multi-Attribute Value Theory (MAVT), Simple Multi-Attribute Rating Technique Exploiting Ranks (SMARTER), and Complex Proportional Assessment (COPRAS) were used to evaluate and prioritize the strategies, whereas the Integer Linear Programming (ILP) technique a numerical optimization technique was used to select the best strategies or alternatives to be employed in water loss management. The results show that the most preferable alternative is replacement of dilapidated pipes while the least preferable alternative is network zoning. The model selects thirteen out of sixteen alternatives, which cost 97% (TZS 235.71 million) of the total budgets set by the water authority to form a portfolio of the best alternatives for water loss management. Furthermore, the model showed robustness as the selected portfolio of alternatives remained the same even when the weights of the evaluation criteria changed.
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Scientific article
This study extends the one-dimensional anharmonic oscillators by implementing physics-informed transformer networks (PINNs) for multi-dimensional quantum systems. We develop a novel computational framework that combines transformer architecture with physics-informed neural networks to solve the Schrodinger equation for 2D and 3D anharmonic oscillators, addressing both perturbative and non-perturbative regimes. The methodology incorporates attention mechanisms to capture long-range quantum correlations, orthogonal loss functions for eigenfunction discovery, and adaptive training protocols for progressive dimensionality scaling. Our approach successfully computes eigenvalues and eigenfunctions for quartic anharmonic oscillators in multiple dimensions with coupling parameters ranging from weak (λ = 0.01) to strong (λ = 1000) regimes. Results demonstrate superior accuracy compared to traditional neural networks, with mean absolute errors below 10-6 for ground state energies and the successful capture of symmetry breaking in anisotropic systems. The transformer-based architecture requires 60% fewer trainable parameters than conventional feedforward networks while maintaining comparable accuracy. Applications to molecular vibrational systems and solid-state physics demonstrate the practical utility of this approach for realistic quantum mechanical problems beyond the scope of perturbative methods.
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Multiobjective artificial bee colony based job scheduling for cloud computing environment
Scientific article
Cloud computing has become the hottest issue due to its wide range of services. Due to a large number of users, it becomes more significant to provide high availability of services to cloud users. The majority of existing scheduling techniques in the cloud environment is NP-Complete in nature. Many researchers have utilized meta-heuristic techniques to schedule the jobs in cloud data centers. The majority of existing techniques such as Genetic Algorithm, Ant colony optimization, Non-dominated Sorting Genetic Algorithm (NSGA-III), etc. suffer from poor convergence speed. Also, most of these techniques are either based upon scheduling or load balancing. Therefore, to overcome these issues, a new Variance Honey Bee Behavior with multi-objective optimization method (VHBBMO) is proposed in this paper. Extensive experiments have been conducted by considering the various set of jobs. The experimental results have shown that the proposed method provides more significant results than available methods.
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Scientific article
Nowadays, there are many organizations and institutions have realized the significant effect of the Internet of Things (IoT). The IoT technologies can enhance the quality of processes and services that make organizations seek to integrate these technologies to their products especially their smart devices. The IoT can be considered as one of the most important requirements that influences on detecting the best supplier. Therefore, every organization should take into account the effect of IoT on detecting the best supplier. So that, there is a need to a framework to help organizations for detecting the suitable supplier based on the effect of IoT. This work aims to introduce a proposed framework using trapezoidal neutrosophic numbers to detect the suitable supplier for purchasing smart systems based on the effect of IoT. The proposed framework consists of six phases. The proposed framework integrates the values and ambiguities index method with Single Valued Trapezoidal Neutrosophic Numbers (SVTN-numbers) which generalized fuzzy set and intuitionistic fuzzy to give more accurate results. The proposed framework is applied with a case study and the results concluded that the proposed framework can handle unclear information which exists in the purchasing process for detecting the suitable supplier of smart devices based on the effect of IoT. Also, the proposed framework can handle uncertainty in decision making and link between customers and suppliers which can improve Supply Chain Management (SCM).
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Non-singular Transformation Based Encryption Scheme
Scientific article
In this paper, we propose a novel variant of the Hill cipher based on vector spaces. In the classical Hill cipher, a non-singular matrix is used for encryption but it is well known that this cipher is vulnerable to the known-plaintext attack. In our proposed cryptosystem, we eradicate this problem by encrypting each plaintext block with a new invertible key matrix. This makes our scheme immune to all existing attacks in literature on this type of ciphers and so the resulting cipher can be used as other state-of-art block cipher. To generate the invertible matrices which serve as the dynamic keys, we make use of the vector spaces along with randomly generated basis and non-singular linear transformation. In addition to this, we also study the computational complexity of the proposed cryptosystem and compare this with the computational complexities of other schemes based on Hill cipher.
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Novel Quantum Random Number Generator with the Improved Certification Method
Scientific article
Random numbers play an important role in many areas, for example, encryption, cryptography, static analysis, simulations. It is also a fundamental resource in science and engineering. There are algorithmically generated numbers that are similar to random distributions, but are not actually random, called pseudo random number generators. In many cases the tasks to be solved are based on the unpredictability of random numbers, which cannot be guaranteed in the case of pseudo random number generators, true randomness is required. In such situations, we use real random number generators whose source of randomness is unpredictable random events. Quantum Random Number Generators (QRNGs) generate real random numbers based on the inherent randomness of quantum measurements. Our goal is to generate fast random numbers at a lower cost. At the same time, a high level of randomness is essential. Through quantum mechanics, we can obtain true numbers using the unpredictable behavior of a photon, which is the basis of many modern cryptographic protocols. It is essential to trust cryptographic random number generators to generate only true random numbers. This is why certification methods are needed which will check both the operation of the device and the quality of the random bits generated. We present the improved novel quantum random number generator, which is based the on time of arrival QRNG. It uses the simple version of the detectors with few requirements. The novel QRNG produces more than one random bit per each photon detection. It is rather efficient and has a high level of randomness. Self-testing as well as device independent quantum random number generation methods are analyzed. The advantages and disadvantages of both methods are identified. The model of a novel semi self-testing certification method for quantum random number generators (QRNG) is offered in the paper. This method combines different types of certification approaches and is rather secure and efficient. Finally, the novel certification method is integrated into the model of the new quantum random number generator. The paper analyzes its security and efficiency.
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Numerical Double Integration for Unequal Data Spaces
Scientific article
Numerical integral is one of the mathematical branches that connect between analytical mathematics and computer. Numerical integration is a primary tool used by engineers and scientists to obtain an approximate result for definite integrals that cannot be solved analytically. Numerical double integration is widely used in calculating surface area, the intrinsic limitations of flat surfaces and finding the volume under the surface. A wide range of method is applied to solve numerical double integration for equal data space but the difficulty is arisen when the data values are not equal. In this paper we have tried to generate a mathematical formula of numerical double integration for unequal data spaces. Trapezoidal rule for unequal space is used to evaluate the formula. We also verified our proposed model by demonstrating some numerical examples and compared the numerical result with the analytical result.
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Scientific article
This dissertation presents a numerical investigation of the two-dimensional incompressible Navier-Stokes equations, focusing on the classic Lid-Driven Cavity problem. The study develops a computational fluid dynamics (CFD) solver from first principles using the Finite Difference Method (FDM) on a structured Cartesian grid, providing a funda- mental understanding of the pressure-velocity coupling in viscous flows. The numerical framework employs the Projec- tion Method, originally proposed by Chorin, to enforce the incompressibility constraint. This operator-splitting technique solves an intermediate velocity field which is subsequently projected onto a divergence-free space via a Pressure Poisson Equation (PPE). The governing equations are discretized using second-order central differences for spatial derivatives and a first-order explicit Euler scheme for time integration. The solver is validated at a Reynolds number of Re = 100. The simulation results successfully capture the characteristic flow features, including the primary central vortex and the corner recirculation eddies. Quantitative validation is performed by comparing the vertical centerline velocity profiles against the established benchmark data of Ghia et al. The results demonstrate excellent agreement with the benchmark solutions, confirming that the developed solver correctly resolves the physics of wall-bounded shear flows. This work establishes a robust foundational framework for simulating viscous incompressible flows and highlights the efficacy of the Projection Method for fundamental CFD applications.
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Scientific article
In this paper, we studied to obtain numerical solutions of partial differential equations with fractional variable coefficient by MAPLE 18 software algorithm on New Iterative Method. We examined and investigated behaviours of the fractional variable coefficients (Even and Odd) on first order partial differential equation; we obtain numerical solution and plot 2D/3D graphs representation of eight (8) cases for the study of the sequential trend of the fractional coefficients. The simplicity and the accuracy of the proposed numerical scheme are verified. More numerical examples will be used in the future for further testing the ability of the proposed scheme for solving some classical problems in engineering sciences.
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On E–Optimality Design for Quadratic Response Surface Model
Scientific article
In response surface methodology, optimality criteria is a major tools used to measure the goodness of a design. Optimal experimental designs (or optimum designs) are a class of experimental designs that are optimal with respect to some statistical criterion. E – Optimality criterion is one of the traditional alphabetical criterion used to explore the right choice of a design in both linear and quadratic response surface models. In this paper, we investigated E – optimal experimental designs for a quadratic response surface model with two factor predictors. We developed an algorithm and a flowchart in line with a program to obtain E – optimal design and compare the result with an existing method. Two designs were formulated each with six points to illustrate the usefulness of the new method. The result revealed that the new technique outperformed better than the existing method. The significance of the later to the former technique is that, it minimizes error due to approximation and also make the computation of the aforementioned optimality easier. We, therefore recommended this method to be used at all length of points when E – optimality is to be evaluated.
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Scientific article
This paper aims at providing in-depth refinement to switching time-variant autoregressive processes via the mode as a stable location parameter in adopted noisy Fisher’s z-distribution that was impelled in a Bayesian setting. Explicitly, a four-parameter Fisher’s z-distribution of Bayesian Mixture Autoregressive (FZBMAR) process was proposed to congruous k-mixture components of Fisher’s z-switching mixture autoregressive processes that was based on shifting number of modes in the marginal density of any switching time-variant series of interest. The proposed FZBMAR process was not only used to seize what is term “most likely mode value” of the present conditional modal distribution given the immediate past but was also used to capture the conditional modal distribution of the observations given the immediate past that can either be perceived as an asymmetric or symmetric distributed varieties. The proposed FZBMAR process was compared with the existing Student-t Mixture Autoregressive (StMAR) and Gaussian Mixture Autoregressive (GMAR) processes with the demonstration of monthly average share prices (stock prices) of sixteen (16) swaying European economies. Based on the findings, the FZBMAR process outperformed the existing StMAR and GMAR processes in explaining the sixteen (16) swaying European economies share prices via a minimum Pareto-Smoothed Important Sampling Leave-One-Out Cross-Validation (PSIS-LOO) error process performance in comparison with AIC, HQIC by the latters. The same singly truncated student-t prior distribution was adopted for the noisy adoption of Fisher’s z hyper-parameters and the embedded autoregressive coefficients in the proposed FZBMAR process; such that their resulting posterior distributions gave the same singly truncated student-t distribution (conjugate) with an embedded Gamma variate.
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On the Relations between Lucas Sequence and Fibonacci-like Sequence by Matrix Methods
Scientific article
In the present paper first and foremost we introduce a generalization of a classical Fibonacci sequence which is called a Fibonacci-Like sequence and at hindmost we obtain some relationships between Lucas sequence and Fibonacci-Like sequence by using two cross two matrix representation to the Fibonacci-Like sequence. The most worth noticing cause of this article is our proof method, since all the identities are proved by using matrix methods.
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On the number of Perfect Matchings of Tubular Fullerene Graphs
Scientific article
The perfect matchings counting problem of graphs has important applications in combinatorial optimization, statistical physics, quantum chemistry and other fields. A perfect matching of a graph G is a set of non-adjacent edges that covers all vertices of G . The number of perfect matchings of a graph is closely related to its number of vertices. A fullerene graph is a 3-connected cubic planar graphs all of whose faces are pentagons and hexagons. Došlić obtained that a fullerene graph with P vertices has at least P/2+1 perfect matchings, Zhang et al. proved a better lower bound 3(p+2)/4 of the number of perfect matchings of a fullerene graph. We have known that the fullerene graph has a nontrivial cyclic 5-edge-cut if and only if it is isomorphic to the graph Tn for some integer n >=1, where Tn is the tubular fullerene graph Tn comprised of two caps formed of six pentagons joined by n concentric layers of hexagons. In this paper, the perfect matchings of the graph Tn is classified by matching a certain vertex, and recursive relations of a set of perfect matching numbers are obtained. Then the calculation formula of the number of perfect matchings of the graph Tn is given by recursive relationships. Finally, we get the number of perfect matchings of Tn with P vertices.
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Scientific article
It has been of concern for the most appropriate control mechanism associated with the growing complexity of dual HIV-HBV infectivity. Moreso, the scientific ineptitude towards an articulated mathematical model for co-infection dynamics and accompanying methodological application of desired chemotherapies inform this present investigation. Therefore, the uniqueness of this present study is not only ascribed by the quantitative maximization of susceptible state components but opined to an insight into the epidemiological identifiability of dual HIV-HBV infection transmission routes and the methodological application of triple-dual control functions. Using ODEs, the model was formulated as a penultimate 7-Dimensional mathematical dynamic HIV-HBV model, which was then transformed to an optimal control problem, following the introduction of multi-therapies in the presence of dual adaptive immune system and time delay lags. Applying classical Pontryagin’s maximum principle, the system was analyzed, leading to the derivation of the model optimality system and uniqueness of the system. Specifically, following the dual role of the adaptive immune system, which culminated into triple-dual application of multi-therapies, the investigation was characterized by dual delayed HIV-HBV virions decays from infected double-lymphocytes in a biphasic manner, accompanied by more complex decay profiles of infectious dual HIV-HBV virions. The result further led to significant triphasic maximization of susceptible double-lymphocytes and dual adaptive immune system (cytotoxic T-lymphocytes and humeral immune response) achieved under minimal systemic cost. Therefore, the model is comparatively a monumental and intellectual accomplishment, worthy of emulation for related and future dual infectivity.
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Scientific article
An innovative and creative docking technique known as cross- docking (CD) strategy was initiated in 1930s to make supply chain fast and productive. However, it only became popular from 1980s. Vehicle routing between suppliers/customers to CD terminal (CDT) is one of operational level problems at CDT. Moreover, moving unloaded products from indoors to outdoors of CDT is one of the internal operations inside a CDT. The main difference between this study and the existing studies which find in the literature is that to consider the activities inside CDT. Also, loading or unloading shipments at all the nodes including CDT are taken into account. Moreover, homogenous fleets of vehicles within pickup or delivery process are assumed, but heterogeneous fleets of vehicles between pickup and delivery processes are assumed in this study. A mixed integer non-linear programming model is developed to address this problem. In our proposed model, costs of transportation between nodes, service at nodes including CDT, moving shipments inside CDT and vehicle operation are considered as the contributors to the total cost. The proposed model was tested for fifteen randomly generated small scale problems using Branch and Bound algorithm and the algorithm was run using LINGO (version 18) optimization software. The average computational time to reach the optimal solution is estimated. The study revealed that for small scale problems, the convergence rate of the problems rises to polynomial with degree 6. Also, the study shows that for moderately large and large scale problems the computational time to reach the optimal solution is exponential. Therefore, this study recommends using a suitable evolutionary algorithm to reach a near optimal solution for moderately large and large scale problems. It further recommends that, this model can be used for last time planning for similar small scale problems.
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Optimal bounding function for GNR-enumeration
Scientific article
The proposed pruning technique by Gama-Nguyen-Regev for enumeration function makes this pruned enumeration (GNR-enumeration) as a claimant practical solver for SVP. The total cost of GNR-enumeration over a specific input lattice block with pre-defined enumeration radius and success probability would be minimized, just if this enumeration uses an optimal bounding function for pruning. Unfortunately, the running time of the original proposed algorithm of searching optimal bounding function by the work of Chen-Nguyen (in 2011) is not analyzed at all, so our work in this paper tries to introduce some efficient searching algorithms with exact analysis of their time/space complexity. In fact, this paper proposes a global search algorithm to generate the optimal bounding function by a greedy idea. Then, by using our greedy strategy and defining the searching steps based on success probability, a practical search algorithm is introduced, while it’s time-complexity can be determined accurately. Main superiorities of our algorithm include: complexity analysis, using high-performance version of each sub-function in designing search algorithm, jumping from local optimums, simple heuristics to guide the search, trade-off between quality of output and running time by tuning parameters. Also by using the building blocks in our practical search algorithm, a high-quality and fast algorithm is designed to approximate the optimal bounding function.
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Optimal control dynamics: control interventions for eradication of ebola virus infection
Scientific article
In affirmation of the existence of control interventions for the eradication of Ebola virus infection as a remedy to complete lack of outright medical cure, the present study seek and formulated using continuous ordinary differential equations an extended BEB-SEIR 4-Dimensional mathematical Ebola dynamic model vested with the scope of establishing the epidemiological impact of identified structured Ebola control measures. Derived model was presented as an optimal control problem subjected to structured dual treatment functions. Moreso, following the validity of model state components as representatives of living organisms and the establishment of existence of boundedness of solutions; we performed our analysis using classical Pontryagin’s maximum principle with which the optimality system of the model was established. Numerical simulations of derived model via Runge-Kutter of order 4 in a Mathcad surface were conducted. Result clearly indicated enhanced impact of intermediary and secondary control interventions as Ebola virus treatment functions with high significant maximization of susceptible population devoid of Ebola infection. Both the exposed and infectious classes were maximally reduced to near zero with possibilities of achieving complete eradication if time interval could be extended exceeding the of Ebola life-cycle. Furthermore, recovery rate of removed class justified the formulation and application of the model. The study therefore suggests further articulation of the model to account for possible intracellular delay in the biological mechanism.
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Optimizing Cybersecurity and Risk Management for Intrusion Mitigation in IoT Applications
Scientific article
This study presents a C*-algebraic framework for optimizing intrusion mitigation in Internet of Things (IoT) networks by integrating mathematical models for cyberattack propagation with optimization-based security strategies. Theoretical results demonstrate that the spectral radius of the attack operator ρ(A) governs the recovery of IoT networks under attack, where ρ(A) < 1 ensures system recovery, and ρ(A) ≥ 1 leads to persistent or growing attack impact. The framework combines blockchain-based trust, AI-driven intrusion detection systems (IDS), and Zero-Trust Architecture (ZTA) to provide a multi-layered, adaptive defence system. Unlike probabilistic models that simplify attack dynamics, this approach rigorously models threats using bounded linear operators, thereby offering scalability and robustness. Optimization ensures computational efficiency, making the model suitable for resource-constrained IoT environments, with the operator norm and the spectral radius acting as key constraints. Validation on real-world datasets such as CIC-IoT2023, UNSW-NB15, and BoT-IoT revealed that the AI-IDS models achieved near-perfect performance, while the unified model integrating blockchain, IDS, and ZTA showed an accuracy of 51.0
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Scientific article
Optimizing load balancing in cloud-based healthcare systems is critical for improving system performance, particularly in terms of reducing latency, increasing throughput, and enhancing task completion time. This study investigates the impact of optimization algorithms, specifically Genetic Algorithm (GA) and Simulated Annealing (SA), on the efficiency of cloud resource allocation in healthcare applications. Additionally, we incorporate queuing theory and stochastic processes to model the task arrival and server load dynamics. By applying these optimization techniques, the system performance was evaluated, showing significant improvements in the key performance metrics. The results highlighted a 50% improvement in latency, 50% increase in throughput, and 25% reduction in task completion time. The optimized system demonstrated enhanced resource utilization, ensuring more efficient real-time data processing in cloud healthcare environments. The proposed approach shows promising results for future applications in dynamic healthcare workload management.
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Outlier Detection Algorithm Based on Fuzzy C-Means and Self-organizing Maps Clustering Methods
Scientific article
Data mining and machine learning methods are important areas where studies have increased in recent years. Data is critical for these areas focus on inferring meaningful conclusions from the data collected. The preparation of the data is very important for the studies to be carried out and the algorithms to be applied. One of the most critical steps in data preparation is outlier detection. Because these observations, which have different characteristics from the observations in the data, affect the results of the algorithms to be applied and may cause erroneous results. New methods have been developed for outlier detection and machine learning and data mining algorithms have been provided with successful results with these methods. Algorithms such as Fuzzy C Means (FCM) and Self Organization Maps (SOM) have given successful results for outlier detection in this area. However, there is no outlier detection method in which these two powerful clustering methods are used together. This study proposes a new outlier detection algorithm using these two powerful clustering methods. In this study, a new outlier detection algorithm (FUSOMOUT) was developed by using SOM and FCM clustering methods together. With this algorithm, it is aimed to increase the success of both clustering and classification algorithms. The proposed algorithm was applied to four different datasets with different characteristics (Wisconsin breast cancer dataset (WDBC), Wine, Diabetes and Kddcup99) and it was shown to significantly increase the classification accuracy with the Silhouette, Calinski-Harabasz and Davies-Bouldin indexes as clustering success indexes.
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