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Galerkin-Bernstein Approximations for the System of Third-Order Nonlinear Boundary Value Problems

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Journal of Applied mathematics and Physics 2024年第6期12卷 2083-2101页

作者： Snigdha Dhar Md. Shafiqul Islam Department of Applied mathematics University of Dhaka Dhaka Bangladesh

This paper is devoted to find the numerical solutions of one dimensional general nonlinear system of third-order boundary value problems (BVPs) for the pair of functions using Galerkin weighted residual method. We derive mathematical formulations in matrix form, in detail, by exploiting Bernstein polynomials as basis functions. A reasonable accuracy is found when the proposed method is used on few examples. At the end of the study, a comparison is made between the approximate and exact solutions, and also with the solutions of the existing methods. Our results converge monotonically to the exact solutions. In addition, we show that the derived formulations may be applicable by reducing higher order complicated BVP into a lower order system of BVPs, and the performance of the numerical solutions is satisfactory. .

关键词： System of Third-Order BVP Galerkin Method Bernstein Polynomials Nonlinear BVP Higher-Order BVP

An Efficient Approach for Transforming Unbalanced Transportation Problems into Balanced Problems in Order to Find Optimal Solutions

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American Journal of Operations Research 2024年第1期14卷 74-86页

作者： Abdur Rashid Md. Amirul Islam Department of mathematics Jahangirnagar University Dhaka Bangladesh Department of mathematics Uttara University Dhaka Bangladesh

In operations research, the transportation problem (TP) is among the earliest and most effective applications of the linear programming problem. Unbalanced transportation problems reflect the reality of supply chain and logistics situations where the available supply of goods may not precisely match the demand at different locations. To deal with an unbalanced transportation problem (UTP), it is essential first to convert it into a balanced transportation problem (BTP) to find an initial basic feasible solution (IBFS) and hence the optimal solution. The present paper is concerned with introducing a new approach to convert an unbalanced transportation problem into a balanced one and as a consequence to obtain optimum total transportation cost. Numerical examples are provided to demonstrate the suggested method.

关键词： Unbalanced Transportation Problem (UTP) Supply Demand Initial Solution Optimal Solution

Heat and Mass Transfer on Non-Newtonian Peristaltic Flow in a Channel in Presence of Magnetic Field: Analytical and Numerical Analysis

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Applied mathematics 2024年第8期15卷 568-583页

作者： Md. Maruf Hasan Md. Enamul Karim Md. Abdus Samad Department of mathematics Comilla University Comilla Bangladesh Department of Applied mathematics University of Dhaka Dhaka Bangladesh

A study has been arranged to investigate the flow of non-Newtonian fluid in a vertical asymmetrical channel using peristalsis. The porous medium allows the electrically conductive fluid to flow in the channel, while a uniform magnetic field is applied perpendicular to the flow direction. The analysis takes into account the combined influence of heat and mass transfer, including the effects of Soret and Dufour. The flow’s non-Newtonian behavior is characterized using a Casson rheological model. The fluid flow equations are examined within a wave frame of reference that has a wave velocity. The analytic solution is examined using long wavelengths and a small Reynolds number assumption. The stream function, temperature, concentration and heat transfer coefficient expressions are derived. The bvp4c function from MATLAB has been used to numerically solve the transformed equations. The flow characteristics have been analyzed using graphs to demonstrate the impacts of different parameters.

关键词： Stream Function Mass Transfer Vertical Channel Casson Fluid

Bayesian Optimized LightGBM model for predicting the fundamental vibrational period of masonry infilled RC frames

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Frontiers of Structural and Civil Engineering 2024年第7期18卷 1084-1102页

作者： Taimur RAHMAN Pengfei ZHENG Shamima SULTANA Department of Civil Engineering World University of BangladeshDhaka 1230Bangladesh School of Civil Engineering Zhengzhou UniversityZhengzhou 450001China Department of Computer Science&Engineering University of Asia PacificDhaka 1205Bangladesh

The precise prediction of the fundamental vibrational period for reinforced concrete(RC)buildings with infilled walls is essential for structural design,especially earthquake-resistant *** learning models from previous studies,while boasting commendable accuracy in predicting the fundamental period,exhibit vulnerabilities due to lengthy training times and inherent dependence on pre-trained models,especially when engaging with continually evolving data *** predicament emphasizes the necessity for a model that adeptly balances predictive accuracy with robust adaptability and swift data *** latter should include consistent re-training ability as demanded by realtime,continuously updated data *** research implements an optimized Light Gradient Boosting Machine(LightGBM)model,highlighting its augmented predictive capabilities,realized through the astute use of Bayesian Optimization for hyperparameter tuning on the FP4026 research data set,and illuminating its adaptability and efficiency in predictive *** results show that the R^(2) score of LightGBM model is 0.9995 and RMSE is 0.0178,while training speed is 23.2 times faster than that offered by XGBoost and 45.5 times faster than for Gradient ***,this study introduces a practical application through a streamlit-powered,web-based dashboard,enabling engineers to effortlessly utilize and augment the model,contributing data and ensuring precise fundamental period predictions,effectively bridging scholarly research and practical applications.

关键词： masonry-infilled RC frame fundamental period LightGBM FP4026 research dataset machine learning data-driven approach Bayesian Optimization

Characteristics of Multi-Objective Linear Programming Problem and Multi-Objective Linear Fractional Programming Problem Taking Maximum Value of Multi-Objective Functions

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Applied mathematics 2024年第1期15卷 22-32页

作者： Samsun Nahar Md. Asadujjaman Khadiza Begum Mahede-Ul-Hassan Md. Abdul Alim Department of Basic Sciences and Humanities University of Asia Pacific Dhaka Bangladesh Department of mathematics University of Dhaka Dhaka Bangladesh Computer Science and Engineering Department Prime University Dhaka Bangladesh Department of mathematics and Statistics Bangladesh University of Business and Technology Dhaka Bangladesh Department of mathematics Bangladesh University of Engineering and Technology Dhaka Bangladesh

In this paper, a new statistical averaging technique is proposed for finding an optimal solution to a multi-objective linear fractional programming problem (MOLFPP) and multi-objective linear programming problem (MOLPP) by using new arithmetic averaging method and new geometric averaging method. It is significantly noticeable same characteristics among all the technique while taking maximum or minimum among all optimized values for multi-objective functions using simplex algorithm. The characteristics provided from the problems are verified by the numerical examples.

关键词： MOLPP MOLFPP New Arithmetic Averaging Method New Geometric Averaging Method

Integrated Machine Learning and Deep Learning Models for Cardiovascular Disease Risk Prediction: A Comprehensive Comparative Study

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Journal of Intelligent Learning Systems and Applications 2024年第1期16卷 12-22页

作者： Shadman Mahmood Khan Pathan Sakan Binte Imran departmentof Electrical and Computer Engineering Old Dominion University Norfolk USA Sir Salimullah Medical College Dhaka Bangladesh

Cardiovascular Diseases (CVDs) pose a significant global health challenge, necessitating accurate risk prediction for effective preventive measures. This comprehensive comparative study explores the performance of traditional Machine Learning (ML) and Deep Learning (DL) models in predicting CVD risk, utilizing a meticulously curated dataset derived from health records. Rigorous preprocessing, including normalization and outlier removal, enhances model robustness. Diverse ML models (Logistic Regression, Random Forest, Support Vector Machine, K-Nearest Neighbor, Decision Tree, and Gradient Boosting) are compared with a Long Short-Term Memory (LSTM) neural network for DL. Evaluation metrics include accuracy, ROC AUC, computation time, and memory usage. Results identify the Gradient Boosting Classifier and LSTM as top performers, demonstrating high accuracy and ROC AUC scores. Comparative analyses highlight model strengths and limitations, contributing valuable insights for optimizing predictive strategies. This study advances predictive analytics for cardiovascular health, with implications for personalized medicine. The findings underscore the versatility of intelligent systems in addressing health challenges, emphasizing the broader applications of ML and DL in disease identification beyond cardiovascular health.

关键词： Cardiovascular Disease Machine Learning Deep Learning Predictive Modeling Risk Assessment Comparative Analysis Gradient Boosting LSTM

Turning Trash into Treasure: Developing an Intelligent Bin for Plastic Bottle Recycling

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Journal of Social Computing 2024年第1期5卷 1-14页

作者： Sirajam Munira Niloy Paul Md Ashraful Alam Md.Mahmudur Rahman M.Shamim Kaiser Institute of Information Technology Jahangirnagar UniversityDhaka 1342Bangladesh

Plastic pollution has emerged as a major global concern due to its enduring nature and limited recycling *** response to this critical challenge,this paper presents a novel approach utilizing a Detection-Based Reward System(DBRS)alongside an innovative business model to promote effective plastic waste management,reduce plastic waste accumulation in the nature,and uphold environmental *** the YOLOv5 algorithm for its exceptional accuracy,speed,and open-source availability,plastic bottle detection becomes a pivotal aspect of this *** seamlessly enroll in the system,triggering an automated detection process that computes reward points corresponding to their deposited plastic *** reward points are meticulously stored within a centralized *** its operational facets,this comprehensive system encompasses a robust business model,strategically poised to capture widespread engagement with waste disposal practices,thereby contributing to the realization of Sustainable Development Goals(SDGs)geared towards fostering a healthier ***,the DBRS attains cutting-edge performance in plastic bottle detection,boasting an impressive mean Average Precision(mAP)of 0.973,underscoring its efficacy in tackling plastic pollution.

关键词： smart environment reward system YOLOv5 deep learning business model

Computer vision-based six layered ConvNeural network to recognize sign language for both numeral and alphabet signs

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Biomimetic Intelligence & Robotics 2024年第1期4卷 45-58页

作者： Muhammad Aminur Rahaman Kabiratun Ummi Oyshe Prothoma Khan Chowdhury Tanoy Debnath Anichur Rahman Md.Saikat Islam Khan Department of Computer Science and Engineering Green University of BangladeshDhakaBangladesh Department of Computer Science and Engineering National Institute of Textile Engineering and Research(NITER)Constituent Institute of Dhaka UniversityDhakaBangladesh Department of Computer Science and Engineering Mawlana Bhashani Science and Technology UniversityTangailBangladesh

People who have trouble communicating verbally are often dependent on sign language,which can be difficult for most people to understand,making interaction with them a difficult *** Sign Language Recognition(SLR)system takes an input expression from a hearing or speaking-impaired person and outputs it in the form of text or voice to a normal *** existing study related to the Sign Language Recognition system has some drawbacks,such as a lack of large datasets and datasets with a range of backgrounds,skin tones,and *** research efficiently focuses on Sign Language Recognition to overcome previous *** importantly,we use our proposed Convolutional Neural Network(CNN)model,“ConvNeural”,in order to train our ***,we develop our own datasets,“BdSL_OPSA22_STATIC1”and“BdSL_OPSA22_STATIC2”,both of which have ambiguous backgrounds.“BdSL_OPSA22_STATIC1”and“BdSL_OPSA22_STATIC2”both include images of Bangla characters and numerals,a total of 24,615 and 8437 images,***“ConvNeural”model outperforms the pre-trained models with accuracy of 98.38%for“BdSL_OPSA22_STATIC1”and 92.78%for“BdSL_OPSA22_STATIC2”.For“BdSL_OPSA22_STATIC1”dataset,we get precision,recall,F1-score,sensitivity and specificity of 96%,95%,95%,99.31%,and 95.78%***,in case of“BdSL_OPSA22_STATIC2”dataset,we achieve precision,recall,F1-score,sensitivity and specificity of 90%,88%,88%,100%,and 100%respectively.

关键词： Conv NeuralSign language CNN Static Feature extraction Convolution2D Fully connected layer Dropout

Adequate Closed Form Wave Solutions to the Generalized KdV Equation in Mathematical Physics

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Journal of Applied mathematics and Physics 2024年第6期12卷 2069-2082页

作者： Md. Munnu Miah Md. Al Amin Meia Md. Matiur Rahman Sarker Ahammodullah Hasan Department of mathematics Islamic University Kushtia Bangladesh Department of mathematics Government Titumir College Dhaka Bangladesh Department of Pharmacy University of Asia Pacific Dhaka Bangladesh

In this paper, we consider the generalized Korteweg-de-Vries (KdV) equations which are remarkable models of the water waves mechanics, the shallow water waves, the quantum mechanics, the ion acoustic waves in plasma, the electro-hydro-dynamical model for local electric field, signal processing waves through optical fibers, etc. We determine the useful and further general exact traveling wave solutions of the above mentioned NLDEs by applying the exp(−τ(ξ))-expansion method by aid of traveling wave transformations. Furthermore, we explain the physical significance of the obtained solutions of its definite values of the involved parameters with graphic representations in order to know the physical phenomena. Finally, we show that the exp(−τ(ξ))-expansion method is convenient, powerful, straightforward and provide more general solutions and can be helping to examine vast amount of travelling wave solutions to the other different kinds of NLDEs.

关键词： The Generalized KdV Equation The exp(-τ(ξ)) -Expansion Method Travelling Wave Solitary Wave