Research Updates in Mathematics and Computer Science Vol. 6

Developing a thoughtful attitude toward technology and the digital environment is central to the idea of IT mindfulness. Instead of relying on reflexive and automatic behaviours, it emphasizes the importance of being mindful and purposeful in our interactions with technology. We may improve our well-being, lessen stress and overwhelm, and develop a positive relationship with technology by engaging in IT mindfulness practices. This entails establishing boundaries, becoming more cognizant of our digital habits, and selecting how we interact with technology. IT mindfulness challenges us to consider our priorities and values, consider how and why we utilize technology, and make deliberate decisions that are consistent with our beliefs and objectives. The goal of IT mindfulness is to assist people in keeping a positive, balanced connection with technology while avoiding any potential drawbacks. Engaging in IT mindfulness involves establishing boundaries, being conscious of our digital habits, and making deliberate choices that align with our values and goals. By prioritizing meaningful interactions and limiting mindless consumption of technology, we can enhance our well-being and reduce stress. This approach encourages us to reflect on the role of technology in our lives, enabling us to foster a positive and balanced relationship with digital tools while avoiding potential negative impacts. By consciously setting boundaries and being mindful of our digital behaviours, we can align our technology use with our values and well-being. Prioritizing purposeful interactions and intentional engagement with digital tools allows us to maintain a positive and balanced relationship with technology. This practice empowers us to make thoughtful decisions that support our goals and beliefs while avoiding the potential negative effects of excessive or unconscious technology use. Embracing IT mindfulness fosters a healthier and more fulfilling digital lifestyle.

The SIMPLEX METHOD (SM) is a fundamental technique in the optimization field [1, 2], designed specifically to solve linear programming problems manually with high efficiency and accuracy by understanding limitations, specifying decision variables,creating objective functions and defining the feasible region by using slack variables, tableaus, and pivot variables as a means of finding the optimal solution to an optimization problem.

Topological Graph Theory (TGT) is a branch of mathematics that studies the interplay between graphs and topology. We discuss how embeddings and extensions affect multiple exports and minimal in minor-closed two-sum families of graphs—charts with limited treewidth that use recursive edge replacement fall under this category. We improve upon the TGT prior upper limit of fourteen established and, showing that any graph eliminating  K4 as a minor and described by Seymour, in particular parallel-series graphs, may be embedded into L1 was recently discovered with a distortion of at most two, the upper bound of two is optimum.

The development of a single sampling plan indexed with Maximum Allowable Proportion Defective (MAPD) and Probability of Allowable Risk (PAR) represents a novel approach to acceptance sampling plans. Previous sampling plans typically relied on two points on the Operating Characteristic (OC) curve or one point on the OC curve along with an outgoing quality or constraint. In this new plan, emphasis is placed on a single point, specifically the point of inflection of the OC curve. The MAPD corresponds to the p-axis of this point, while PAR is represented on the Pa(p) axis, ensuring that all lots inspected with a specified incoming quality MAPD will be accepted if Pa(p) \(\ge\) PAR. The primary aim of this research is to establish a sampling plan based on a single point on the OC curve. A significant quality MAPD, paired with the corresponding probability Pa(p*), leads to a decreasing operating ratio that defines a unique sampling plan. Furthermore, the complement probability to PAR (PRR) and the ratio PAR/PRR are introduced to identify sampling plans and the discriminant angle \(\theta\). The most discriminating operating ratio among all is given by PAR/PRR. A switching rule for sampling plans within a feasible interval of sample size, which can be inspected by manufacturers without affecting the Acceptable Quality Level (AQL), has been devised. OC curves illustrating PAR, PRR, the angle of discrimination, and the optimum sampling plan have been constructed. Additionally, tables with examples have been provided to aid in understanding. A conversion table for identifying other quality indices has also been included.

Using Lie’s Infinitesimal continuous parameter similarity transformation method of solving nonlinear coupled partial differential equations is used to find two new exact solutions of Wu-Yang-t’ Hooft-Julia-Zee ansatz reduced SU(2) Yang-Mills-Higgs field equations at Prasad-Sommerfield limits. These new solutions are with trigonometric circular functions unlike known hyperbolic functions. A general method of solving coupled nonlinear partial differential equations by reducing the number of independent variables by one, this method is explained.

In IoT-based home/enterprise network applications, an advanced security system is desirable for resource-constrained devices. Feature selection significantly affects the performance of a Machine Learning-based Intrusion Detection System (ML-IDS) to which data of the highest quality should be fed. An appropriate feature selection with sufficient features increases the accuracy of the Intrusion Detection System (IDS) classification. In addition, the consistent use of the same metrics in feature selection and detection algorithms further enhances classification accuracy. First, this paper studies two feature selection algorithms, Information Gain, a metric of entropy, and PSO-based feature selection, a metric of misclassification, to select a minimum number of attack feature subsets for resource-constrained IoT devices. Then, the detection algorithms for multi-classifications, Tree and Ensemble, are evaluated regarding non-consistent and consistent metrics. For specific performance comparison, the same metrics for feature selection and detection algorithm are utilized and compared with non-consistent use of feature selection and detection algorithm, e.g., feature selection by Information Gain (entropy) and Tree detection algorithm by classification.

Congestion in sensor network is one of the significant elements this should be suitably addressed to propel the reception of remote sensor organizations. In this work, an Energy-Proficient Directing Convention is introduced to send the hubs to their objective really. To control blockage, a Versatile Cradle compromise and further developed Trust-based Energy Productive Steering convention is first introduced, this strategy distinguishes the clog freeways and the Support compromise handles the cushion successfully. To course the convention, a Cross-Layer Security-Based Fluffy Rationale Energy Effective Parcel Misfortune Preventive Steering Convention has been created. The proposed convention courses the hubs and the convention embraces a steering convention that bestows security as far as staying away from malignant hubs and forestalling information misfortune. Thus, to work on the lifetime of the organization, a Thickness Mindful Ideal Grouping Approach is introduced. The proposed strategy is assessed in light of the Mat lab programming and the QoS execution measurements are Energy Utilization, Bundle Conveyance Proportion, Trust Worth Calculation, dormancy, unwavering quality, energy productivity, start to finish delay, Normal Throughput, exactness and organization lifetime. The viability of the exploration is assessed by contrasting it and other existing methods, including Trust Mindful Secure Steering Convention, Counterfeit Greenery Calculation Based Help Vector Machine, Efficient Trust Assessment Based Directing Plan, LionFuzzyBee, and BatFuzzyBee Calculation. Appropriately, the recommended strategy's presentation is 3%, 8%, 4%, 7%, and 2% higher than the current techniques for Parcel conveyance proportion, throughput, network lifetime, energy effectiveness, and unwavering quality. Thus, the proposed technique further develops the clog control execution in an energy-productive way, in future; an as of late high level method is proposed to individually successfully further develop the organization execution.

This research proposed a methodology for identifying the student's learning style and student’s performance prediction in the online learning environment using Machine Learning (ML) techniques. Identification of the student's learning style and performance prediction in the teaching and learning environment is important in improving both teaching and learning perspectives. The intention of the research was to investigate about applying Machine Learning Techniques for the identification of the Learning style of the students and the prediction of the student’s performance in an online learning environment based on the Felder Silverman Learning Style (FSLSM) identification model. The significance of this experiment is that the proposed methodology considers the combination of access frequency (f) of course materials and total time (T) students spent on each course activity to reduce the limitations that occur due to accessing the course modules randomly without any preference in the online learning environment in learning style identification. A reusable Moodle time-tracking plugin was created for the data collection procedure. Three-course modules that were created in accordance with the FSLSM model's features were used to prepare a real-time dataset. Seven criteria were chosen, and the features were verified using the Pearson Correlation Coefficient approach. Each of these course modules had 150 enrolled students. Machine learning is a widely used technology for the identification of the learning style and analyzing the data for making predictions. Once the data set was prepared, the data set was preprocessed and applied five Supervised Classification Machine learning algorithms as Decision Tree, Logistic Regression, Random Forest, Support Vector Machine and K-Nearest Neighbors algorithm. The models were evaluated using Accuracy, Precision, Recall and F1 values. Of the five algorithms for Learning Style identification, the Decision Tree classifier algorithm performed with the best average accuracy with 93.5% for Input, 86% for Perception, 89.5 for Processing and 94% for Understanding dimension. For the grade prediction process the Decision Tree algorithm performed with a 96% accuracy level. The models were validated using the K-fold Cross-validation and Standard Deviation values. Mean Squared Error, Bias and Variance values were considered the evaluation of the underfitting or overfitting context of the model. For parameter optimization, the Grid Search Methodology was applied to find the best combination of criterion for the model. Finally, an application was developed for Identifying the Learning Style of the Students and performance prediction using the designed Machine learning model. The Consistency of the ML Model based on the Decision Tree classifier algorithm were evaluated using the results generated through the developed application and the results suggested that consistency for taught machine learning algorithms is often between 85% to 95%, which is an acceptable range. For the grade prediction, the consistency of the models ranged nearly 89%. The results generated by the application for identification of the learning style suggested the combination of learning style for particular students sample as Global-Mild, Visual- Strong, Sensing- Moderate and Reflective-Strong. Identification of these combinations of learning styles assists teachers by giving an insight into which components of the learning content should be improved in the course designing process. One of the limitations is that though how much we encourage the students, some of them do not like to engage in the course works in the online learning environment. These behaviors may lead to difficulties in conducting the data collection process in a precise manner. Providing a mechanism to identify and analyze the factors that impact to increase in the attractiveness of students when reading the course materials or presentation will be one of the main future directions of this teaching and learning research paradigm.

The study of the stability of solutions to differential equations is a fundamental and ongoing area of research in mathematics and applied sciences with numerous applications, and it provides a framework for analysing the behaviour of dynamical systems and predicting their long-term behaviour. For a numerical solution to be useful it must be both consistent and stable, and such a solution can be said to be stable if small errors in the initial data or in the numerical approximation do not grow unbounded as the computations progresses. In this paper, the stability of finite difference methods for time-dependent Schrodinger equation with Dirichlet boundary conditions on a staggered mesh was considered with explicit and implicit discretization. It is demonstrated that the solution is conditionally stable for the explicit finite difference technique and unconditionally stable for the implicit finite difference methods using the numerical algorithm's matrix representation. We will utilize a 1D harmonic oscillator problem to demonstrate this behaviour.