Journal of Mathematics and Statistics Studies
Journal of Mathematics and Statistics Studies (ISSN: 2709-4200) is a double-blind peer-reviewed, open-access monthly journal published by Al-Kindi Center for Research and Development. The journal is led by expert international editorial board members who take an objective approach to peer review, ensuring each research paper is reviewed and evaluated on its own scholarly merits and research integrity. Publishing your work in the Journal of Mathematics and Statistics Studiesmeans you will receive prompt and reliable publishing and a global platform for your research to reach its full potential. The journal is published in both online and print versions.
Al-Kindi Center for Research and Development.
Time Series Analysis to Evaluate the Impact of Foreign Direct Investment on Economic Growth in Sudan
The study aimed to evaluate how foreign direct investment (FDI) impacts economic growth in Sudan. A standard model was designed to analyze the relationship between the study variables from 2000 to 2022. The primary problem of the study is whether Sudan can offer the required standards, incentives, and privileges to attract foreign investors. In the theoretical aspect, the study utilized a descriptive analytical approach, but in the practical aspect, it employed a statistical method grounded on econometric tools in the analysis, applying the Autoregressive Distributed Lag (ARDL) model. The relevant data were acquired from the Sudan Central Bureau of Statistics for the study period. The study hypothesized that there is a statistically significant correlation between FDI and economic growth in Sudan. The findings determined a statistically significant long-term association between FDI and economic growth. The study recommended enhancement of an environment favorable to both foreign and domestic investment.
Economic growth, foreign direct investment, capital formation, GDP, trade openness.
Copyright (c) 2025 https://creativecommons.org/licenses/by/4.0/
Mathematical Modeling and Control of Drone Swarm Coordination Using PD Approach
This research paper introduces a mathematical model and control framework for coordinating multiple drones (a swarm) using a Proportional–Derivative (PD) control approach grounded in graph theory. Each drone functions as an independent agent, communicating only with its nearby neighbors. This local interaction creates a decentralized and scalable system that eliminates the need for a central controller. The inter-drone connectivity and interactions are represented through the Laplacian matrix, while eigenvalue analysis helps in designing the control gains to ensure smooth and stable motion.The model is formulated using Newton’s equations of motion, expressed through differential equations that describe each drone’s dynamic behavior. The proposed approach is tested on a five-drone ring formation, demonstrating that the drones can maintain formation, avoid collisions, and reach the target position with stable convergence.
Mathematical Modeling; Control of Drone Swarm Coordination; PD Approach
Mathematical and AI-Blockchain Integrated Framework for Strengthening Cybersecurity in National Critical Infrastructure
This article examines the intersection between mathematical modeling, artificial intelligence (AI), and blockchain technology as a way of strengthening cybersecurity in national critical infrastructures (NCI). The increasing frequency and sophistication of cyber threats against vital infrastructures, such as electrical grids, healthcare information networks, and transportation infrastructures, creates the need to develop some innovative protective mechanisms. To solve these concerns, in the article the authors propose a hybrid framework that combines the AI-driven predictive analysis and the decentralized ledger capabilities of blockchain technology. Decentralized ledger technology (DLT) forms the backbone of secure and tamper-proof data management and machine learning algorithms are used to identify and predict emerging threats in real-time. By combining the immutability of the blockchain technology and the adaptive analytical capabilities of AI, this framework aims to improve the integrity of the data, maintain the privacy of it, and provide a fast-responding mechanism in the NCI environments. The paper outlines possible applications, lists the benefits that come with such applications, and addresses challenges inherent in the implementation of such an integrated system in order to provide a blueprint for future scholarly investigation and practical implementation.
AI, Blockchain, Cybersecurity, Critical Infrastructure, Mathematical Framework, Decentralized Ledger Technology, Machine Learning
Copyright (c) 2023 https://creativecommons.org/licenses/by/4.0/
A Comparative Statistical Analysis of Machine Learning Regression Models for Economic Indicator Forecasting
Accurate forecasting of economic indicators is essential for informed policy-making and strategic financial planning. This study presents a comprehensive comparative statistical analysis of multiple machine learning regression models—including linear regression, ridge regression, lasso regression, support vector regression, and random forest regression—for predicting key economic indicators such as GDP growth, unemployment rate, and inflation. Using a simulated dataset of 1000 samples with multiple economic features, each model’s performance was evaluated using mean squared error (MSE), mean absolute error (MAE), root mean squared error (RMSE), and coefficient of determination ($R^2$). Results indicate that ensemble methods such as random forest provide superior predictive accuracy, while regularized models outperform ordinary linear regression. Visualizations of predicted versus actual values, residual analyses, and statistical comparisons are provided to support the findings. Implications for model selection and economic forecasting are discussed.
Copyright (c) 2025 Journal of Mathematics and Statistics Studies
A Bazilevic function related to the class of meromorphic functions
The goal of this article is to further geometric function theory by focusing on meromorphic functions and relying on the Bazilevic function, which represents the interactions of analytic functions. It focuses on presenting and investigating a differential operator for meromorphic functions. Using this operator, create meromorphic Bazilevic functions, a new subclass in the punctured unit disk This text also greatly expands knowledge and understanding of the meromorphic function to fall into this new subclass.
Bazilevic functions, Meromorphic functions, Diﬀerential operator
Leveraging Artificial Intelligence to Recommend Personalized Learning Pathways: A Case Study on Secondary Education Students
This study aims to develop an explainable artificial intelligence (XAI)–based educational recommendation system tailored for secondary school students. The system integrates classification and regression models to suggest personalized learning paths while estimating the confidence level of each recommendation. The dataset used was obtained from EdNet, comprising data for over 50,000 students including academic performance, educational level, interests, and learning pathways. The study followed an applied quantitative methodology involving data preprocessing, feature encoding, TF-IDF for text processing, model building, and the development of a user interface using Gradio. Four classification algorithms were evaluated: Decision Tree, Random Forest, KNN, and XGBoost. XGBoost outperformed others with an accuracy of 89%. For regression, LightGBM achieved the highest performance (R² = 0.9997, MAE = 0.000008). SHAP was utilized to interpret model outputs and provide visual explanations of the recommendation logic. The results demonstrated that incorporating explainability into educational recommender systems significantly increases users’ trust and engagement. The study recommends enriching the input data with behavioral indicators, testing the model in diverse learning contexts, and deploying the system as an interactive platform aligned with Saudi Vision 2030’s digital education goals.
Recommender systems, Explainable AI, Machine Learning, Adaptive Learning, XGBoost, SHAP, EdNet
Impact of Academic Stress on The Performance of The Grade 9 Students in Mathematics
One of the most frequent stressors that students encounter is academic stress. The purpose of this study was to determine whether there is a significant relationship between the academic performance of grade 9 students at Campagao High School in Campagao, Bilar, Bohol, and their level of academic stress. The study employed the descriptive-correlational survey research design and the complete enumeration technique was used to obtain 63 respondents. The survey instrument was based on a standardized questionnaire and the data gathered were analyzed using the Pearson Product Moment Coefficient of Correlation at 0.05 alpha level. The major finding of the study indicated that there is a significant relationship between the level of academic stress and the level of mathematics performance. Furthermore, it was revealed that most of the respondents were 14 years old and were female. Majority of the respondents’ female parents were high school level while the highest educational attainment of the male parents was either high school level or elementary level with a combined family monthly income of P10 000 and below. Moreover, the level of academic stress experienced by the respondents in learning mathematics was moderate while the level of the students’ academic performance in math was developing. In line with the findings and conclusion of the study, the researcher recommends that the proposed math performance enhancement plan can be used and monitored.
Academic Stress, Mathematics Performance, High School Education, Stress and Learning
Relationship Between Academic Stress and Math Scores in Grade 9 Students
This study investigated the relationship between academic stress and math scores in Grade 9 students. Additionally, it sought to examine the relationship between students' academic stress and their academic performance in the subject of Mathematics. It utilized the descriptive correlational method of research with the use standardized questionnaire. There were 210 respondents in the study and it used a simple random sampling technique. The respondents were Grade 9 students from Jagobiao National High School, one of the public high schools in the city of Mandaue. There were four statistical treatments employed in this study, namely, frequency count, simple percentage, weighted mean, and Pearson’s r. It was revealed that most of the respondents were 14 years old and were female. The level of academic stress experienced by the respondents in learning mathematics was moderate while the level of the students’ academic performance in math was approaching proficiency. The study found no statistically significant correlation between academic stress and math performance. However, the researcher suggests that the recommended approach for improving math performance should be implemented and monitored.
Comparing three recently developed techniques and using them to address the non-Newtonian fluid flow and heat transfer issue on a turbine disk
This study is investigating three distinct semi-analytical methods (SAGPM, q-HALPM, and PYRDTM) to solve nonlinear equations in the context of turbine cooling during heat transfer and fluid flow. These methods include Shehu, Laplace, and Young transformations and are improved by Padé approximation. The analysis not only explores how these methods deal with the complicated problems of cooling turbine systems but also remove to test efficiency, accuracy, and convergence of each of them. A comprehensive comparison of approximate solution methods to identify the most effective approach for modeling nonlinear thermal systems is conducted. The findings provide critical insights in to efficient analytical estimations for applications of the above recent methods. Ultimately, the results contribute to the advancement of accurate and computationally efficient solutions for complicated fluid dynamics problems, with broad applicability to various flow-thermal challenges. Moreover, the results showed that the methods are effective and powerful and give an indication that q-HALPM has superior convergence and high accuracy compared to PYRDTM and SAGPM
Fluid dynamics, SAGPM, q-HALPM, PYRDTM, Nonlinear thermal systems, Padé approximations, Computational efficiency, convergence, accuracy
The Impact of Effective Teaching Practices and Student Engagement on Grade 10 Students’ Mathematics Performance
This study explored the connection between teaching effectiveness, student engagement, and the academic performance of Grade Ten students in Mathematics at Don Vicente Rama Memorial National High School during the school year twenty twenty-four to twenty twenty-five. A correlational research design was used to examine how these variables are related within actual classroom settings. Teaching effectiveness was assessed through indicators such as clarity of explanations, provision of feedback, use of interactive strategies, and the creation of a supportive learning environment. Student engagement was examined across behavioral, cognitive, and emotional aspects, while academic performance was evaluated based on the students’ Mathematics grades. Data were gathered using a structured survey and analyzed through descriptive and inferential statistics to identify patterns and relationships. Findings revealed that teaching effectiveness was perceived at an excellent level, showing that teachers consistently applied high-quality instructional practices. Student engagement was rated as high, with particularly strong responses in active participation, asking questions, and enjoying interactive lessons. The academic performance of the students was also commendable, with the majority reaching outstanding and very satisfactory levels. Results further indicated a moderate positive relationship between teaching effectiveness and academic performance and a weak but meaningful link between student engagement and academic performance. These outcomes highlight the importance of maintaining effective, student-centered teaching strategies and fostering engaging classroom experiences to enhance motivation, active participation, and achievement in Mathematics.
Teaching effectiveness, student engagement, academic performance, Mathematics education, instructional strategies
Investigating the Effectiveness of Gamification Teaching Method on Self-directed Learning in Mathematics among High School Students of Herat City
Math education faces an ongoing challenge - many students struggle with fundamental concepts and lack the confidence to direct their own learning. Traditional teacher-centered approaches often leave learners dependent on instructors, hesitant to tackle difficult problems. Yet fostering independent, curious students who take ownership of their math education remains a critical goal. This study explored how gamification - using game elements in teaching - could help high school students develop self-directed math skills like planning, self-monitoring, and problem-solving. The study conducted on 194 tenth-grade high school students of Herat City, dividing them into experimental (gamification) and control (traditional teaching) groups. Over eight lessons, the experimental group learned challenging math concepts through gamified activities, while the control group received conventional instruction. Using a validated self-assessment questionnaire (α = 0.89 overall), we measured four key skills: motivation, planning, self-monitoring, and communication. The results of the data analysis showed that teaching by gamification has an effect on promoting the independence and responsibility of students' learning in mathematics and on the three components of self-directed learning in mathematics. In other words, teaching by gamification had a positive effect on students' self-directed learning by creating a feeling of need to learn and accepting their role and responsibility in it. The study showed that teaching by gamification had a positive effect on the students’ mathematical performance by increasing the level of interactive learning and creating independence in students. Teachers, authors of textbooks, planners, and educational experts can benefit from the results of this research to improve and modify educational methods.
Teaching method, gamification, self-directed learning, Herat City.
Applications of pre-open & α-open sets in bitopological spaces
Using the concept of pre-open set & α-open set in bitopological spaces, we introduce and study topological properties of pre-limit points, pre-derived sets, pre-interior and pre-closure of a set, pre-interior points, α-limit points, α-derived sets, -interiαor and α-closure of a set and α-interior points in a bitopological space.
ij-p-limit points, ij-p-derived set, ij-p-interior, ij-p-closure, ij-α-limit point, ij-α-derived, ij-α-interior, ij-α-closure
Methods of Calculating and Reducing Sampling Error
Sampling error is a significant factor in research, denoting the variance between sample statistics and actual population values. This study examines techniques for quantifying and mitigating sampling error to improve the reliability and accuracy of research findings. Essential methods for determining sampling error, such as the standard error of the mean, confidence intervals, proportional error estimates, and bootstrapping, are examined comprehensively. Strategies to mitigate sampling error, including augmenting sample size, using stratified sampling, utilizing systematic sampling, implementing weighted adjustments, and enhancing sampling frames, are examined. The results underscore the significance of rigorous sampling techniques in reducing error, guaranteeing representativeness, and improving the validity of outcomes. The research emphasizes the significance of sophisticated statistical methodologies and pilot studies in mitigating constraints in sampling methods. This study offers pragmatic insights and methodological directives for academics, policymakers, and practitioners in several fields. It also delineates avenues for further investigation, including the use of sophisticated computational techniques and context-specific sampling methodologies, to further reduce sample error and enhance study quality.
sampling error, bootstrapping, actual population values, statistics, mean.
An Extended Set-Theoretic Relational Model for Multi-Valued Attributes
The classical relational model, as proposed by Codd, is based on a rigid set structure where each attribute takes an atomic value. However, current data modeling needs, especially in semi-structured systems, require the representation of multi-valued attributes. In this paper, we propose a rigorous mathematical model extending the relational model to allow for multivalued attributes, while maintaining set consistency. We define the formal structure of this model, illustrate its operation through examples, and discuss its advantages and possible integration with modern databases.
Extended relational model, Multi-valued attributes, Set theory, Relational schema, Normalization, Natural join, Database systems.
A Modified Chen Inverse Rayleigh Distribution, Estimation and Application to Survival Data
The difficulties of modeling failure rates that exhibit both monotonic and non-monotonic behavior, as well as appropriately capturing the bathtub curve in reliability engineering, remains a significant difficulty. In study, paper a Chen Inverse Raleigh (CIR) distribution within the context of the Chen-G family was developed, to eliminate the difficulty of modeling failure rates. The Probability Distribution (PDF), Cumulative Distribution Function (CDF) and the statistical properties of these CIR distributions like the survival function, hazard function, cumulative hazard function, reverse hazard function, quartile function, skewness, kurtosis, moments, linear representation and Maximum Likelihood Estimation (MLE) was also provided in the study. Our Proposed distribution provided a mild to moderate right-skewedness, while majority of the data reveals mild to moderate left-skewness, it also models leptokurtic data (heavy-tailed distributions), with kurtosis values indicating effectiveness and consistent tail behavior. A simulation study written in R provides a comparison for the CIRDs with different parameters of (β, λ, δ) and sample sizes (n) = 50, 100, 200, and 500 proved that our model converges successfully for all initial parameter settings across all sample sizes, which confirmed the robustness of the MLE optimization process. The consistency in convergence, even for smaller datasets, highlights the CIR model’s reliability and adaptability to different data conditions. The real-life data utilized to validate the efficiency of our proposed model was the survival times (in days) for patients diagnosed with head and neck cancer whose values range from 12.20 to 1776. Result showed that the CIR model demonstrates the best fit, with the lowest AIC and BIC values among the competing models. Additionally, the CIR model achieves higher p-values in goodness-of-fit tests indicating excellent agreement between the model and the observed data.
Chen Inverse Raleigh Distribution (CIRD), Chen-G family, Hazard Function, Cumulative Distribution Function (CDF), Probability Distribution Function (PDF)
Double Intuitionistic Separation Axioms in Double Intuitionistic Topological Spaces
Our goal in this paper is to give a comprehensive study of S. Bayhan and D. Coker [5] paper entitled "On separation axioms in intuitionistic topological spaces" I give generalizations to the Double intuitionistic separation axioms named Double intuitionistic –space, Double intuitionistic -space, Double intuitionistic -space, Double intuitionistic –space, Double intuitionistic -space, Double intuitionistic space, Double intuitionistic – space. Also, give an example for each type and work on presenting the characteristics and relationships between them through the given theorems, Finally, I studied the relations among several types of Double intuitionistic separation axioms in Double intuitionistic topological spaces (DITS) with some fundamental properties and examples of the opposite are not true for these relationships.
DIT_0-space,〖 DIT〗_1-space,〖 DIT〗_2-space,DIT_3-space,DIT_4-space,DIR-space, DIN-space.
A Study on the Relationships Between the Norms of Complex Polynomials of Degrees 2, 3, and 4 and Their Derivatives Belonging to a2
In this paper, relations between the norms of complex polynomials of degrees 2, 3, and 4 and their derivatives are studied. Using bound-preserving convolution operators and interpolation formulas, we derive inequalities governing these polynomial norms. Clement Frappier previously found a relation for , but for , a unique relation does not exist. We establish new bounds for these cases by employing determinant analysis and principal minor calculations. The theoretical framework is constructed using Hermitian matrices, semi-bilinear functions, and norm-preserving operators, leading to a refined approach for identifying the smallest positive roots of characteristic equations. The results provide a deeper understanding of polynomial inequalities and contribute to the broader study of functional analysis and complex function theory.
Partial Probability of Mohamedou DEBAGH: A New Mathematical Approac
The partial probability approach, proposed by Mohamedou Debagh, explores a new way of modeling events as probabilities, using a hierarchical and recursive decomposition. This approach allows for the consideration of information internal to each event, thus providing increased flexibility in contexts where events are complex or partially known. The article presents the underlying theoretical principles, the fundamental properties of the model, as well as potential applications in fields such as artificial intelligence, decision theory, and multi-agent systems.
Partial probability, Modeling, Complex systems, Decision, Artificial intelligence, Decision theory, Multi-agent systems
Nilpotent Covers of Small Symmetric and Alternating Groups
We compute the size of a minimal nilpotent cover for small alternating and symmetric groups, An and Sn. We give precise values for values of n up to 8. For n=9 we give upper and lower bounds for the size of a minimal nilpotent cover of A9.
Alternating group; nilpotent cover; symmetric group
Some Generalized Inequalities via (s, m) -Convexity and their Applications
The main objective of this study is to formulate novel inequalities of the trapezoidal, mid-point, and Simpson types in connection with an extension of the Bullen-type inequality using the concept of (s,m)-convexity. Additionally, the investigation includes the exploration of particular cases and the application of these derived inequalities to some special means.
Convex functions; (s,m)-convex functions; Bullen type inequality; Simpson type inequality.
Optimizing Computational Techniques for Cauchy and Integral Equations Through Advanced Polynomial Methods
This study introduces a numerical approach for solving Cauchy and integral equations using the Chebyshev pseudospectral method. The approach involves approximating the solution with an Nth-degree interpolating polynomial based on Chebyshev nodes, followed by problem discretization through a cell-averaging technique. The main properties of the Chebyshev pseudospectral method are discussed and explained to simplify the computation of Cauchy and integral equations into a system of algebraic equations. Several examples are presented to validate the method and to show how the method is computationally efficient, and to prove its effectiveness.
Predicting S&P 500 Closing Prices Using a Feedforward Neural Network: A Machine Learning Approach
The Standard and Poor’s 500 index is a crucial benchmark for investors, financial analysts, and policymakers to assess stock market performance and make informed investment decisions. Accurate S&P 500 closing price prediction is vital for efficient portfolio management and risk mitigation. This study explores the application of neural networks, specifically the Feedforward Neural Network, to predict the S&P 500 closing price. The author used a dataset from 1950 to 2024, including variables such as open, high, low, close, and volume as the initial step. Various training-testing ratios are tested to evaluate the models' performance. The results highlight that an eighty to twenty split yields the best predictive accuracy, with the lowest Mean Absolute Error and Mean Absolute Percentage Error. Additionally, this study compares the Feedforward Neural Network's predictions to polynomial regression models and investigates cluster-wise fitting techniques to enhance accuracy. The findings demonstrate that neural networks can significantly improve the predictive power of S&P 500 closing prices, particularly when combined with advanced regression techniques, providing valuable insights for academic research and practical financial decisions.
S&P 500 index, closing prices, Feedforward Neural Network, Machine Learning, New York, Testing Ratio
Healthy Predator Crowding on a Delayed Non-autonomous Eco-epidemic System
This article presents a delayed non-autonomous eco-epidemiological prey-predator model with predator infection. The author considered incubation delay of infection in predator over-crowding among healthy species. The article contains the system solution’s existence, boundedness, and uniform persistence under certain conditions. The numerical simulation confirms analytical findings. The analysis of autonomous and non-autonomous models for the same incubation delays shows that the autonomous system leads stability to bifurcation while crossing the threshold value to incubation delay. However, the non-autonomous model leads from stability to chaos while crossing threshold values. Finally, simulating the effect of healthy predator crowding shows that increasing healthy predator crowding helps to remove infection from the environment.
Incubation delay, Periodic solutions, Chaos, Crowding
Decompositions of Hypercube Graphs into Diametral Paths and Cycle Decompositions
One of the most well-known and well-studied issues in graph theory is graph decomposition. Graph decomposition has been studied in great detail by extensive research. There are two main types of decomposition problems such as edge decompositions and vertex decompositions. It entails meeting certain requirements in order to divide an input graph into smaller segments (subgraphs). In this paper, an investigation into decomposition in hypercube graphs using diametral routes is studied. Additionally, we study the finding of the diametral path decomposition number, index, and hypercube graph's cycle decomposition.
Quantum Computing Applications in the Fields of Cryptography, Material Science, and Machine Learning
Despite the significant scientific and engineering hurdles in advancing quantum computers, notable strides are being made toward utilizing this technology in commercial domains. Quantum computers are projected to exceed the computational power of classical computers within the next decade, potentially revolutionizing various industries. This study explores a range of fields that have already begun integrating quantum hardware. By presenting these as examples of combinatorial problems, we demonstrate their applications across three key sectors: cryptography, material science, and Machine Learning. Further, we will conduct a survey on various industries and companies to identify the broader usage of quantum computing in their manufacturing. The survey will analyze the diverse potential applications and current advantages of quantum hardware and algorithms. The results will help further researchers identify and segment the companies and understand the rapid application of quantum computing.
Quantum Computing, Cryptography, Machine Learning, Material science, Qubits
Copyright (c) 2020 https://creativecommons.org/licenses/by/4.0/
Collatz Conjecture (3x+1) or in some literature as 3N+1 is a problem because it works in the way that if you take any positive number, if it is an odd number you multiply it by three (3) then add one (1). On the other hand, if it is an even number, you divide it by two (2). Eventually, all positive numbers decrease to one (1). One (1) is odd, so multiply it by three (3) is three (3) and add one (1) is four (4). Four (4) is even, so divide it by two (2) is two (2). Two (2) is also even, so divide it by two (2) is one (1) again. All positive numbers end up in the loop (4-2-1). This loop is like a numerical lock. Therefore, the solution of this problem will have to be a numerical key results to all positive numbers.
Copyright (c) 2024 https://creativecommons.org/licenses/by/4.0/
On the Angular Singularities of a Smooth Function
The paper studies angular singularities of a real smooth function of the 4th degree using real analysis and catastrophe theory. After that, we apply an ordinary differential equation (ODE) with its boundary conditions. We show that the real smooth function equivalent to the key function associated with the ODE's function by applying the Lyapunov-Schmidt local technique. The angular singularities have been used to study the bifurcation analysis of the real smooth function. We have discovered the (caustic) bifurcation set's parametric equation and geometric interpretation. Moreover, the critical spots' bifurcated spread has been identified.
Copyright (c) 2024 Journal of Mathematics and Statistics Studies
Degenerate Sturm-Liouville Problem for Second-Order Differential Operators on Star-Graph
In this paper, we present a comprehensive study of second-order differential operators on a star-graph geometric graph considering a star graph with three edges and a common vertex. We investigate the Dirichlet problem for a Sturm-Liouville operator defined on this network-type manifold. The Sturm-Liouville problem is formulated as a system of ordinary differential equations (1) on the individual edges, subject to the boundary conditions (2) and (3) at the common vertex. We assume that the condition holds, ensure the non-degeneracy of the boundary conditions by using a synthetic approach. We fully describe and solve the Dirichlet problem for the given second-order differential operator on the star graph. The key results include the characterization of the spectral parameter the construction of the matrix A composed of the boundary condition coefficients, and the analysis of the minors of A. The findings of this work contribute to the understanding of second-order differential operators on network-type manifolds and provide a framework for addressing similar problems on more complex geometric graphs. The insights gained from this study have potential applications in various fields, such as: quantum mechanics, control theory, and network analysis.
Differential operators, Green's function Sturm-Liouville
Simulation-Based Study on Extreme Ranked Set Sampling from Rician Distribution
The RSS approach is a useful method of sampling that reduces the cost and improves the representativeness of the population. It provides more efficient estimators than the competitors based on SRS. However, using RSS could be a difficult task to observe all the ranks. Thus, using only the extreme ranks eases the task and reduces the error in ranking. Samawi et al. (1996) proposed the method of Extreme Ranked Set Sampling (ERSS) to reduce errors in ranking and showed that the method gives an unbiased estimate of the population mean in the case of symmetric populations and it provides a more efficient estimator than SRS. However, the estimator of this method is biased when the distribution is skewed. Many researchers have considered ERSS, investigated several estimators, and studied their properties. In this paper, we adopt the ERSS technique when the samples are drawn from the Rician distribution. Several estimators have been studied, including arithmetic mean, geometric mean, harmonic mean, quadratic mean, median, variance, mean deviation, skewness, and kurtosis. Computer simulations were used to check the properties of these estimators and compared with the corresponding estimators using SRS. Some estimators based on ERSS are more efficient than the corresponding estimators from SRS, but some others are not.
Some Inequalities for Differentiable Functions on a Generalization of Hermite-Hadamard Inequality with Applications
The main identity of midpoint type inequalities is generalized and using this identity some composite midpoint type inequalities are estimated. Moreover, applications to some special means and some error estimates for the composite midpoint formula are discussed.
Trapezoid inequality, Convex function, Hermite-Hadamard inequality, Midpoint inequalities