International Journal Of Mathematics And Computer Research

〖 Δ〗_kl- Statistical Convergence via Neutrosophic Normed Spaces for Double Sequences

2025-03-01T11:53:23+00:00

In this paper, we present the extension of ∆-statistically convergent and ∆-statistically Cauchy sequences via neutrosophic normed space (NNS) to double sequences. The study in analogy also define and introduce for which lim or where denote set of all statistically convergent sequences. Furthermore, we present their feature utilizing double density and establish some inclusion relations between these concepts and prove some essentials analogous properties for double sequences.

Temperature Elliptic Sombor and Modified Temperature Elliptic Sombor Indices

2025-03-08T14:43:23+00:00

In this paper, we introduce the temperature elliptic Sombor index, modified temperature elliptic Sombor index and their corresponding exponentials of a graph. Also we compute these temperature indices for some standard graphs and HC₅C₇[p, q] nanotubes. Furthermore, we establish some properties of newly defined temperature elliptic Sombor index.

ON COMBINATORIAL IDENTITIES OF LUCAS AND FIBONACCI NUMBERS CONNECTED TO TCHEBYSHEV POLYNOMIALS

2025-03-13T08:57:56+00:00

The present paper is on derivation of many combinatorial identities of x_n = T_n (9), y_n = U_n-1 (9) , L_6n+k = L_k x_n +20 F_k y_n and F_6n+k = F_k x_n +4 L_k y_n , k=0,1,2,3,4,5 n=0,1,2,..., where T_n (x) and U_n-1 (x) are the well known Tchebyshev polynomials of first and second kind and L_n and F_n are the well known Lucas and Fibonacci numbers.

Implementation of Analytical Hierarchy Process (AHP) for Ranking Consumers Satisfaction Criteria in the Mathematics Dan Science Learning Center

2025-03-13T11:28:18+00:00

Customer satisfaction is defined as a measurement that determines the level of customer satisfaction with the products, services and capabilities of a service provider. In this article, we determine the priority order of criteria that influence the customer satisfaction in the mathematics and science learning center using the AHP method.

Based on the results of the AHP method, the main priority criterion is responsibility of providing information related to services with weight criterion is 0.216.

Proof of Goldbach’s Conjecture and Bertrand’s Postulate Using Prime Generator Theory (PGT)

2025-03-18T08:51:49+00:00

Goldbach’s Conjecture states every even integer n > 2 can be written as the sum of 2 primes, while Bertrand’s Postulate states for each n ≥ 2 there is at least one prime p such that n < p < 2n. I show both are essentially statements on the primes distribution, and their inherent properties when modeled and understood as the residues of modular groups Zn. In addition, a much tighter dynamic bound on p than given by the BP will be presented

Epidemic Modeling of Student Learning Behavior: A Novel Perspective

2025-03-18T11:06:18+00:00

This study introduces a groundbreaking approach to understanding student learning behavior by applying epidemic modeling. By analogizing the spread of diseases to the dissemination of knowledge, we modified the classic SIR model to create the Student Learning Behaviour (SLB) model. This model simulates the dynamics of student learning by capturing interactions between students, instructors, and learning materials, enabling knowledge acquisition and retention predictions. The study highlights the significance of social interactions outside the classroom and curricular activities in shaping students' learning behavior and motivation. It investigates the impact of students' learning behavior on their academic achievement, emphasizing the crucial role of self-motivation and appearance in driving improvement. This research provides educators and policymakers with a valuable tool for designing targeted interventions and optimizing instructional strategies, offering insights into the complex processes underlying student learning.

On Fixed Points of Expansion Mappings in Menger Spaces

2025-03-20T11:38:50+00:00

The aim of this paper is to establish a common fixed point theorem for expansion mappings involving six mappings in a Menger space, utilizing the concepts of semi-compatibility and weak compatibility while considering the continuity of the mappings.

A Comprehensive Review of Graph Theory Applications in Network Analysis

2025-03-20T11:22:24+00:00

This review paper investigates the extensive role of graph theory as a unifying framework for network analysis across diverse domains. The study begins by out- lining fundamental concepts, such as adjacency matrices, centrality measures, and community detection algorithms, which together enable systematic exploration of net- work topologies. Next, it examines pivotal applications, illustrating how graph-based techniques facilitate tasks like influencer detection in social media, energy-efficient routing in communication networks, and large-scale protein-interaction modeling in bioinformatics. Methodologically, the paper consolidates theoretical foundations with real-world case studies, highlighting both classical graph models (e.g., Erd˝os–R´enyi, Watts–Strogatz, Barab´asi–Albert) and advanced solutions (e.g., graph neural networks and quantum walks) that address emerging challenges of dynamic, multilayered, and high-dimensional data. The key findings demonstrate that graph theory consistently delivers actionable in- sights—enhancing traffic management in transportation, bolstering fault tolerance in critical infrastructures, and supporting cutting-edge cybersecurity anomaly detection. Moreover, the exploration of hypergraphs and quantum computing signals promising avenues for further research. In practical terms, the ability to handle massive datasets in near-real-time has positioned graph analysis as an essential tool for academia, indus- try, and public policy. Overall, this study underscores the versatility of graph theory and points to new interdisciplinary opportunities, emphasizing the need for continued innovation in handling computational complexity, data privacy, and dynamic network evolution.

Numerical Simulation of Convection flow in Warm Bath and Its Possible mixing Behaviour

2025-03-20T11:54:51+00:00

We have carried out an investigation of the mixing behaviour of fluid with different densities, were density was taken as a quadratic function of temperature and all flow parameters were kept fixed. The result showed that mixed dense fluid that have attained T_mor a temperature close to it was descending from the contact layer in the form of an inverted mushroom like structure towards the floor of the container. Most of the convection flow configurations considered in the past are such that the isothermal walls with heat generation are mostly the vertical walls or both the vertical and the horizontal walls. However, results by Cianfrini et al. 2015 with similar configuration appears similar as compared to ours as the authors also recorded the inverted mushroom like structure behaviour descending towards the floor of the container. Both vertical and horizontal velocity profiles were also considered at some point below the contact layer and plotted against the x-coordinate. The results as presented here are very good as they give insight into the mixing behaviour of a possible warm bath. Thus, it is true that whenever water of different densities come in contact, mixing will occur without any external mixing or perturbation: and any part of the fluid that have mixed up to the T_mwill descend to the floor of the container if only either of the temperature is above the temperature of maximum density until the entire ambient fluid is induced through convection flow.

The Effect of Two Stay – Two Stray (TS-TS) Model on Students’ Mathematical Connection Ability and Self Efficacy

2025-03-20T11:52:48+00:00

Mathematical connection ability and self-efficacy are two crucial aspects in mathematics learning that significantly influence students' academic achievement. In an effort to improve both aspects, an innovative learning model is needed. This study aims to investigate the effect of the Two Stay-Two Stray (TS-TS) model on students' mathematical connection ability and self-efficacy. This study uses a quantitative research method and a quasi-experimental research type with a One-Group Pretest-Posttest Design research design. The Two Stay-Two Stray (TS-TS) model is said to be influential if there is a significant difference between the pretest and posttest results. Data analysis was carried out in two stages: first, a paired sample multivariate analysis test (Hotelling's T2) was applied to examine the effect of the Two Stay-Two Stray (TS TS) model on both variables simultaneously. Second, a paired sample t-test was applied to evaluate the differences between the pretest and posttest in more detail on each variable individually. The results of the study showed that the TS-TS model had a significant effect on students' mathematical connection skills and self-efficacy simultaneously, as evidenced by the results of Hotelling's T2. In addition, the results of the paired sample t-test proved that there was an increase between the pretest and posttest in each variable after the application of the TS-TS model. This proves that the Two Stay-Two Stray (TS-TS) learning model has an effect on students' mathematical connection skills and self-efficacy.

Neighborhood Kepler Banhatti and Modified Neighborhood Kepler Banhatti Indices of Certain Dendrimers

2025-03-21T11:31:19+00:00

In this paper, we introduce the neighborhood Kepler Banhatti index, modified neighborhood Kepler Banhatti index and their corresponding exponentials of a graph. Also we compute these neighborhood Kepler Banhatti indices of certain dendrimers. Furthermore, we establish some properties of newly defined the neighborhood Kepler Banhatti index.

Mining Data for Music Recognition in Big Data Using Locality-Sensitive Hashing (LSH) Algorithm

2025-03-22T10:21:51+00:00

In the ever-evolving landscape of the music industry, the ability to efficiently recognize and categorize vast amounts of musical data is paramount. This study explores the application of data mining techniques for music recognition within the realm of Big Data, leveraging the Locality-Sensitive Hashing (LSH) algorithm. As the volume of digital music continues to grow exponentially, traditional methods of music recognition and classification face significant challenges in terms of scalability and efficiency. LSH, known for its ability to approximate nearest neighbor searches in high-dimensional spaces, offers a promising solution to these challenges.By implementing LSH, this research aims to improve the speed and accuracy of music recognition processes. The study delved into the mechanics of LSH, explaining how it hashes similar music data points into the same buckets with high probability, thereby facilitating quick and efficient retrieval. Through extensive experimentation and analysis, the effectiveness of LSH in handling large-scale music datasets is evaluated, highlighting its advantages over conventional methods. The findings of this study underscore the potential of LSH to revolutionize music recognition in Big Data environments, offering a scalable, efficient, and robust approach to managing and categorizing extensive musical archives. This research not only contributes to the academic discourse on data mining and music recognition but also provides practical insights for industry practitioners seeking to harness the power of Big Data in the music domain.

Dataset Generation and Cluster Creation for Adaptive E-Learning System Using the Rectilinear Technique of K-Means Clustering, Demonstrated Using Java

2025-03-29T11:18:44+00:00

Data is an essential element in research which can be challenging to obtain especially when such data is termed classified. Consequently, researchers depend on dataset or direct collection from respondents. The volume of data collected through this means is grossly limited and laborious putting into consideration, the resources involved in the collection and accuracy rate. In order to ease this, researches that requires demonstration, can rely on internally synthetic generated data. This work looks at how data can be generated using Java multi-dimensional array, and the classification of generated data into cluster using the k-means rectilinear technique, that is used to classify adaptiveness of learners in an eLearning environment. With the combination of simple and complex codes, the work adequately and accurately generated 125 elements, created 5 clusters based on the fusion of known and adopted learning pedagogies, which can be used to determine how learners learn different subject matters.

Classification of Maize (Zea May L) Leaf Diseases Variants Based on Sobel Edge Detection and Machine Learning Technique

2025-03-29T11:24:43+00:00

Zeae-maydis, also known as maize gray leaf spot, and porcinia sorghi, known as maize common rust, are the two most prevalent and dangerous diseases that harm maize crops in Nigeria. Plant diseases are difficult for Nigerian farmers to recognize correctly, and it is impossible to assess their severity with the unaided eye. Moreover, many support vector machine (SVM) classification models for maize leaf disease classification have been developed by different researchers. However, these existing models are impacted by imbalanced datasets, irrelevant feature selection, and difficulty in fine-tuning the hyperparameters of the SVM. Consequently, to resolve these problems, two optimized multiclass support vector machine classification models (BPSO-SVM and RSA-SVM) were trained to categorize maize leaves disease into Zeae-maydis and porcinia sorghi using 1,648 photos of maize leaves across all maize datasets, which included 574 photos of gray leaf spot disease, 574 photos of common rust disease, and 500 photos of healthy leaves obtained from the Kaggle village datasets. The images were subjected to preprocessing process such as resizing of the image, contrast enhancement and removal of noise before the affected area was segmented through the Sobel edge detection method. The Gray Level Spatial Dependence and colour moment were then used to extract texture, shape, and colour features. The comparative experiments demonstrate that the BPSO-SVM model outperforms the RSA-SVM model with a performance accuracy of 96.37% and 96.93% on the same datasets at a threshold value of 0.80. However, this study only identified two of the numerous diseases that affect maize.