International Journal of Mathematical Sciences and Computing @ijmsc
Journal articles - International Journal of Mathematical Sciences and Computing
All articles: 294
Exact Analytical Solution of Boundary Value Problem in a Form of an Infinite Hypergeometric Series
Scientific article
This paper proposes an exact solution of the classical Graetz problem in terms of an infinite series represented by a nonlinear partial differential equation considering two space variables, two boundary conditions and one initial condition. The mathematical derivation is based on the method of separation of variables whose several stages were illustrated to reach the solution of the Graetz problem.
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Exploring Approaches for Curve Similarity: A Comprehensive Review
Scientific article
Curve similarity plays a crucial role in various domains where comparing functional or dynamic shapes is essential, including bioassay analysis, trajectory studies, spectroscopy, medical signal interpretation, and functional genomics. Despite its broad impact, research on curve similarity methods remains fragmented across statistical, computational geometry, and signal processing communities, leading to a lack of unified terminology and systematic comparison. To address this gap, this study adopts a structured literature review methodology, in which relevant studies are identified through a comprehensive search of major academic databases and selected based on predefined inclusion criteria, including peer-reviewed publications focusing on similarity measures for curves and time series. The review systematically examines mathematical and statistical approaches to curve similarity, focusing on their theoretical foundations, statistical properties, and practical applications. The selected methods are categorized into five groups: distance-based, alignment-based, topology-oriented, statistical and hypothesis testing, and learning-based approaches. For each category, key aspects such as mathematical formulation, invariance properties, robustness to sampling variability, and computational characteristics are analyzed. In addition, application domains, method comparisons, and common limitations are discussed, along with available software tools that support curve similarity analysis. By providing a structured and methodologically grounded synthesis, this review assists researchers in selecting appropriate techniques and highlights potential directions for developing more robust and scalable similarity assessment frameworks.
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Ferrer diagram based partitioning technique to decision tree using genetic algorithm
Scientific article
Decision tree is a known classification technique in machine learning. It is easy to understand and interpret and widely used in known real world applications. Decision tree (DT) faces several challenges such as class imbalance, overfitting and curse of dimensionality. Current study addresses curse of dimensionality problem using partitioning technique. It uses partitioning technique, where features are divided into multiple sets and assigned into each block based on mutual exclusive property. It uses Genetic algorithm to select the features and assign the features into each block based on the ferrer diagram to build multiple CART decision tree. Majority voting technique used to combine the predicted class from the each classifier and produce the major class as output. The novelty of the method is evaluated with 4 datasets from UCI repository and shows approximately 9%, 3% and 5% improvement as compared with CART, Bagging and Adaboost techniques.
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Fixed Point Results in the Fuzzy Multiplicative Metric Spaces and Application
Scientific article
This paper presents the development of fuzzy multiplicative metric spaces, an extended framework that combines the principles of multiplicative metric spaces with fuzzy logic to better address uncertainty and imprecision inherent in many real-world problems. By replacing additive distance measures with multiplicative ones, this approach proves particularly effective in contexts where relative variations or proportional relationships are more meaningful than absolute differences. Within this generalized setting, we establish a series of fixed-point theorems of Banach, Kannan, and Chatterjee types, along with related corollaries, each supported by concrete examples. The theoretical results are further validated through their application to the solution of nonlinear integral equations, demonstrating the versatility and applicability of the proposed framework across mathematical analysis and applied disciplines.
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Forecasting Natural Gas Prices Using Nonlinear Autoregressive Neural Network
Scientific article
When forecasting time series, It was found that simple linear time series models usually leave facets of economic and financial unknown in the forecasting time series due to linearity behavior, which remains the focus of empirical and applied study. The study suggested the Nonlinear Autoregressive Neural Network model and a comparison was made using the ARIMA model for forecasting natural gas prices, as obtained from the analysis, NAR models were better than the completed ARIMA model, measured against three performance indicators. The decision criterion for the selection of the best suited model depends on MSE, RMSE and R2. From the results of the criterion it has found that both the models are providing almost closed results but NAR is the best suited model for the forecasting of natural gas prices.
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Forecasting the Environmental Situation at Mining Company Treatment Facilities Based on Fuzzy Logic
Scientific article
This study analyzes wastewater treatment processes at a mining company in the Almaty region, Kazakhstan. Four treatment schemes were developed and assessed, with a focus on optimizing efficiency. The discharged water quality from different technological lines was evaluated using integral functions for a quantitative comparison of each scheme's performance. Additionally, an expert system was developed to validate the results and support future research in wastewater treatment.
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Scientific article
The one-dimensional non-homogeneous wave equation subject to non-homogeneous boundary and initial conditions presents significant analytical challenges, particularly when external forcing and irregular boundary data are simultaneously present. Classical methods such as separation of variables are restricted to homogeneous settings and fail to accommodate non-homogeneous terms in a unified framework. This study employs the Fourier transform method to derive an exact analytical solution by decomposing the total wave displacement into two components: u(x,t) = V(x,t) + ψ(x), where V(x,t) is the oscillatory component satisfying the homogeneous wave equation and ψ(x) is the spatially adjusted component encoding the influence of non-homogeneous boundary conditions and external forcing. The analytical solution is verified by direct substitution and benchmarked against a second-order explicit finite-difference scheme on a grid of 500 spatial points, yielding a maximum point-wise absolute error below 8×10⁻³, consistent with the second-order truncation error of the numerical scheme. For the representative test case with unit wave speed, unit domain length, constant spatial forcing F(x) = 2, and initial displacement u₀(x) = sin(πx), the steady-state component is recovered exactly as ψ(x) = x − x², and the dominant Fourier coefficient is A₁ ≈ 0.742. A direct point-by-point comparison with published benchmark values further quantifies the sensitivity of wave solutions to boundary condition specification. The proposed framework accommodates both finite and infinite spatial domains and offers a systematic, closed-form alternative to purely numerical approaches for this class of wave propagation problems, with relevance to acoustics, structural dynamics, and materials science.
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From Pixels to Processes: A Process Mining- Inspired Approach to Image Steganalysis
Scientific article
Steganography attempts to conceal messages in plain sight while steganalysis seeks to identify them or, more importantly, to extract the embedded data. Low-payload and spatially localized steganographic embedding is increasingly used to evade detection by classical steganalysis methods. While such strategies preserve global image statistics and remain visually imperceptible, they can disrupt natural pixel-level behavior. This work proposes a behavioral steganalysis framework inspired by process mining that detects image steganography by analyzing localized behavioral deviation using regional behavioral contrast and behavioral amplification. Experiments on lossless grayscale PNG images from the USC SIPI database and 10,000 images from the BOWS2 dataset using 1-bit LSB embedding show that the proposed framework reliably identifies steganographic embedding. On the USC SIPI dataset, conventional statistical detectors, including chi-square analysis and the StegExpose tool, showed limited detection capability under the evaluated localized embedding settings. Despite high perceptual quality of stego images (PSNR > 55 dB), significant behavioral deviation is consistently observed within embedded regions. These results demonstrate that the proposed process mining-inspired framework provides an interpretable and complementary direction for image steganalysis, particularly under low-payload and localized embedding scenarios.
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Future Possible Age of the Universe with Density Variation
Scientific article
A fundamental principle and assumption of cosmology says that the universe is homogeneous and isotropic when viewed on a large scale. According to the cosmological principle, space might be flat, or have a negative or positive curvature in cosmological model. Positively curved universe denotes the closed universe and negatively curved universe denotes the open universe. Our universe type is flat because it expands in every direction neither curving positively nor negatively. We have observed that the progression of the universe is based on radiation and matter domination. In this paper we also have observed that future possible upper limit age of the universe is 9.4203×〖10〗^10 years which varies with density.
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Scientific article
Regression testing is used to check that changes in the some functionality of the software to not affect its old behaviours. Test case prioritization is essential for reducing the cost of regression testing. In this paper a test cases prioritization model based on fuzzy logic is presented. State machine diagram is used to capture the behaviour of the system. Risk information is associated with the states. After change in the functionality of the system new state machine diagram is designed. This new state machine diagram is converted into Weighted Extended Finite State Machine (WEFSM). Weights are assigned to nodes and edges based on change and risk exposure. Risk exposure and change information of each test case is used as input to fuzzy model. Test cases are categorized in retestable, reusable and obsolete.
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Generalized Algorithm on idiosyncrasy of Numbers
Scientific article
In this paper, using computer algebra system a new generalized algorithm is developed to study and generalize the Kaprekar’s operation which can be used for desired numbers of iterations and is also applicable to any n-digits number which is greater than or equal to two. Existing relevant results are verified with the available results in literature and further extended to examine the difference (kernel) of the obtained number during the process with the number obtained in preceding iteration after each step. Sum of the digits of an acquired number obtained after each step is also noticed and found that sum of its digits is divisible by 9. A detailed investigation is conducted for all two-digit number and the output acquired is exhibited in tabular form which has not been studied in earlier. An 8-digits number also considered and found that it does not converges to a unique kernel like 3-digits and 4-digits, but follows a regular pattern after initial iteration. Analytical illustrations are provided along with pictorial representations for 2-digits, 3-digits 4-digits and 8-digits number. This algorithm can further be employed for numbers having any number of digits.
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Graph Dynamic Threshold Model Resource Network: Key Features
Scientific article
In this paper, we describe a graph dynamic threshold model called resource network, and briefly present the main results obtained during several years of research. Resource Network is represented by a connected oriented with weighted graph with an arbitrary topology. Weights of edges denote their throughput capacities for an abstract resource. The resource is stored in vertices, which can contain its unlimited amount. Network operates in discrete time. The total amount of resource is constant, while pieces of resource are reallocating among vertices every time step, according to certain rules with threshold switching. The main objective of our research is to define for a network with an arbitrary topology all its basic characteristics: the vectors of limit state and flow for every total amount of resource W; the threshold value of total recourse T, which switches laws of operating of the network; description of these laws. It turned out that there exists several classes of networks depending on their topologies and capacities. Each class demonstrates fundamentally different behavior. All these classes and their characteristics will be reviewed below.
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Green Computing: An Era of Energy Saving Computing of Cloud Resources
Scientific article
Cloud computing is a widely acceptable computing environment, and its services are also widely available. But the consumption of energy is one of the major issues of cloud computing as a green computing. Because many electronic resources like processing devices, storage devices in both client and server site and network computing devices like switches, routers are the main elements of energy consumption in cloud and during computation power are also required to cool the IT load in cloud computing. So due to the high consumption, cloud resources define the high energy cost during the service activities of cloud computing and contribute more carbon emissions to the atmosphere. These two issues inspired the cloud companies to develop such renewable cloud sustainability regulations to control the energy cost and the rate of CO2 emission. The main purpose of this paper is to develop a green computing environment through saving the energy of cloud resources using the specific approach of identifying the requirement of computing resources during the computation of cloud services. Only required computing resources remain ON (working state), and the rest become OFF (sleep/hibernate state) to reduce the energy uses in the cloud data centers. This approach will be more efficient than other available approaches based on cloud service scheduling or migration and virtualization of services in the cloud network. It reduces the cloud data center's energy usages by applying a power management scheme (ON/OFF) on computing resources. The proposed approach helps to convert the cloud computing in green computing through identifying an appropriate number of cloud computing resources like processing nodes, servers, disks and switches/routers during any service computation on cloud to handle the energy-saving or environmental impact.
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Handling Numerical Missing Values Via Rough Sets
Scientific article
Many existing industrial and research data sets contain missing values. Data sets contain missing values due to various reasons, such as manual data entry procedures, equipment errors, and incorrect measurements. It is usual to find missing data in most of the information sources used. Missing values usually appear as "NULL" values in the database or as empty cells in the spreadsheet table. Multiple ways have been used to deal with the problem of missing data. The proposed model presents rough set theory as a technique to deal with missing data. This model can handle the missing values for condition and decision attributes, the web application was developed to predict these values.
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Hive-Based Data Encryption for Securing Sensitive Data in HDFS
Scientific article
Big Data is a new class of technology that gives businesses more insight into their massive data sets, allowing them to make better business decisions and satisfy customers. Big data systems are also a desirable target for hackers due to the aggregation of their data. Hadoop is used to handle large data sets through reading and writing application programs on a distributed system. Hadoop Distributed File System is used to store massive data. Since HDFS does not safeguard data privacy, encrypting the file is the right way to protect the stored data in HDFS but takes a long time. In this paper, regarding privacy concerns, we use different compression-type data storage file formats with the proposed user-defined function (XOR-Onetime pad with AES) to secure data in HDFS. In this way, we provide a dual level of security by masking the selective data and whole data in the file. Our experiment demonstrates that the whole process time is significantly smaller than that of a conventional method. The proposed UDF with ORC, Zlib file format gives 9-10% better performance results than 2DES and other methods. Finally, we decreased the load time of secure data and significantly improved query processing time with the Hive engine.
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Scientific article
The amount of data that is transmitted across the internet is continuously increasing. With the transmission of this huge volume of data, the need of an encryption algorithm that guarantees the data transmission speedily and in a secure manner is a must. Hence, to achieve security in wireless networks, cryptography plays a very important role. In this paper, several hybrid combinations, which combines both symmetric and asymmetric cryptographic techniques to offer high security with minimum key maintenance is presented. This hybrid combination offers several cryptographic primitives such as integrity, confidentiality and authentication, thereby enhancing the security. Various combinations of Advanced Encryption Standard (AES), Elliptical Curve Cryptography (ECC) and Rivest, Shamir and Adleman (RSA) algorithms are used to provide hybrid encryption. Secure Hash Algorithm (SHA-256) is also used to provide authentication and integrity. The experimental results show that the proposed hybrid combinations gives better performance in terms of computation time compared to individual cryptographic schemes.
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Scientific article
This research focuses on developing an automated framework for evaluating distress on flexible and rigid pavement surfaces through deep learning and algorithms, enhancing infrastructure monitoring by efficiently identifying, assessing, and measuring road distresses. The methodology begins with identifying road stretches from ground-level images, followed by capturing photos of distresses and applying algorithms to measure their dimensions accurately. A YOLOv5 model is developed to evaluate the length and width of identified distresses, with an exploration of the relationship between camera position and measurement accuracy. Physical measurements using tape are employed for validation, ensuring that the automated results align with real-world dimensions. Results indicate that the average errors of 26.1% for length and 26.9% for width for flexible pavement and the average percentage error in length is about 29% and average percentage error in width is about 1% for rigid pavement. This highlights the importance of precise measurements for effective road rehabilitation. The integration of computer vision in road maintenance, validated through physical measurements, promises significant improvements in the accuracy, efficiency, and resilience of road networks.
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Implementation of Fast and Efficient Mac Unit on FPGA
Scientific article
Floating-point arithmetic operations on digital systems have become an important aspect of research in recent times. Many architecture have been proposed and implemented by various researchers and their merits and demerits are compared. Floating point numbers are first converted into the IEEE 754 single or double precision format in order to be used in the digital systems. The arithmetic operations require various steps to be followed for the correct and accurate steps. In the proposed approach a fast and area efficient Carry Select Adder are implemented along with the parallel processing of various units used in the architecture. The result also verifies the proposed approach that shows a decrement of 27 % in the combinational path delay with an increment of around 8% in the number of LUTs used.
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Scientific article
The mortuary industry in most developing countries are in need of improvement on the receiving and releasing of deceased persons. Paper-based mortuary systems lack reliability, timely information retrieval, accountability, data security and access control; compared to computer-based, mortuaries are the norm in advanced countries. This study reports the development of a fingerprint-based biometric mortuary system for deceased identification and claiming. The system design methodology was based on the object-oriented analysis and design approach using the UML. The system was implemented with Java as the frontend and processing logic, interacting with MySQL Server at the backend for transaction management. As generated from the University of Calabar Teaching Hospital Calabar, the result of this study shows that, with the fingerprint verification technique, mortuary establishments in Nigeria and related countries can enhance the deceased claimant verification process to avoid releasing the deceased to wrong persons and reduce deceased identification anomalies. The study has shown that biometrics technology can enhance deceased identification and release in resource-constrained settings like Nigeria.
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Inhomogeneous Assessment of New Mechanism of Adaptive Detection of Partially-correlated χ2-Targets
Scientific article
Owing to its merits in fluctuating radar targets detection, the scenario of fusion structure has rapidly become a methodology of choice. The base goal of this paper is to analyze the linear type of this methodology, which is termed as linear fusion (LF). The target of interest along with fallacious ones is assumed to be fluctuating obeying χ2-model of two-degrees of freedom in their fluctuation, with particular attention on partially-correlated target returns. Closed-form expression is derived for the detection performance of the proposed processor. The analytical results are validated with computer simulation. Our simulation results demonstrate that the LF model yields impressive detection performance in terms of detection performance and CFAR loss, in comparison with the conventional schemes in the case where the operating environment is free of or contaminated with interferers. Additionally, the LF homogeneous performance outweighs that of Neyman-Pearson (N-P) detector, which is the yardstick of the CFAR world. Moreover, the LF structure has the capability of holding the rate of false alarm fixed against the presence of interferers. The ability to obtain improved performance compared to existing models is the major contribution of this research.
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