In this research work, we present an exhaustive investigation of a numerical algorithm for the purpose of solving the partial differential equation (PDE) in an inhomogeneous form. The proposed approach utilizes a finite difference system to numerically solve the second-order partial differential equation inherent in the inhomogeneous PDE. The proposed finite difference method proves to be highly efficient in handling linear second-order PDEs of this nature. To confirm the usefulness of our technique, we compare the approximate solution obtained using the finite difference system with the analytic solution of inhomogeneous PDE. Remarkably, the approximate numerical solution aligns satisfactorily with the purely analytic solution, demonstrating the accuracy of our proposed approach. Furthermore, we delve into the numerical solutions generated by the finite difference scheme, varying the space step size and time step size. By presenting two illustrative examples, we ascertain the usefulness and efficiency of the finite difference procedure in solving the inhomogeneous partial differential equation. Our findings contribute to the field of advanced numerical analysis and provide a valuable tool for tackling similar types of PDEs.

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This study aims to investigate the influence of molar concentration and film thickness on the structural and optical properties of dip-coated copper oxide (CuO) thin films. The dip-coating technique, maintaining a constant withdrawal speed is employed to synthesize CuO films with varying molar concentrations. The molar concentration determines the film’s thickness. The structural, optical, and morphological properties are performed using X-ray diffraction (XRD) analysis, UV-Vis-NIR spectrophotometer, and scanning electron microscopy (SEM). The XRD analysis reveals that the molar concentration significantly impacts the structural properties, resulting in variations in the crystallinity and microstructural parameters of these films. The films exhibit varying optical absorbance, transmittance, and optical band gap depending on molar concentration. The SEM image of the films shows a porous, uniform surface morphology over a smooth background. The molar concentration along with film thickness plays a significant role in controlling the structural and optical properties of the dip-coated films, making them suitable for potential applications in optoelectronic devices and solar cell absorber layers.

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Paperboard is now being used to create a variety of functional products, including handicrafts that are easy to make and cost-effective. In this study, the effects of three types of fibers (Cotton, Polyester, and Okra) were used as reinforcement, and analyzed the mechanical properties such as tensile strength, ductility, and toughness of paperboard. The results showed that paperboard with Okra fiber reinforcement exhibited superior mechanical properties, including higher tensile strength, ductility, and toughness, compared to paperboard made with Cotton and Polyester fibers. This study revealed that Okra fiber could be a productive source of reinforcing fiber with superior mechanical qualities for the use of paperboard manufacturing.

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Identifying the sentence type and checking its validity in a semantic manner requires understanding the linguistic structure and meaning of Bangla sentences. It involves analysing the sentence's components, such as subject, verb, object, and other grammatical elements, to determine its type and then evaluating its semantic coherence. To check the validity of a sentence in a semantic manner, we need to consider the coherence and meaning of the sentence within the given context. Semantic validation involves analysing the sentence's components, their relationships, and their overall meaning. Semantic validation can include several checks, such as Grammatical correctness: Verify that the sentence follows the grammatical rules of Bangla and has proper subject-verb agreement, tense consistency, and word order. Meaningful vocabulary: Ensure that the words used in the sentence convey the intended meaning accurately and appropriately. Contextual relevance: Evaluate whether the sentence makes sense within the given context and aligns with the intended message or purpose. Logical consistency: Check if the sentence's components and their relationships are logically coherent and do not contradict each other. Semantic validation in Bangla sentences often requires a profound empathetic of the language and context. It involves analysing the sentence structure, word meanings, and syntactic relationships to ensure the sentence is both grammatically correct and conveys the intended meaning accurately. Now-a-days Bangla sentence type detection and check validation is a growing job. We use semantic feature for sentence type detection and validation check. Semantics is the branch of linguistics that deals with the study of meaning in language. It is concerned with understanding how words, phrases, sentences, and entire texts convey meaning. A word's meaning is not simply a collection of individual letters or sounds; it encompasses the various concepts, associations, and relationships that a word represents. For machine translation correlating words semantic features is useful. This is proficient by endeavouring to break language down into its essential parts. Phrasal categories include the noun phrase, verb phrase, and adjective phrase; lexical categories include noun, verb, adjective, adverb and many others. This paper presents methodology for pure Bangla sentence detection and validation check analysis in semantic manner. Context free grammar and top-down method have been used for the determination of producing interpreted parse tree. Model is tested for a simple sentence of Bangla and test result replicate the effective results for most of the test cases.

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This study focuses on the synthesis and characterization of hydroxyapatite (HAP) using the precipitation method, investigating the influence of reaction conditions and heat treatment on its properties. Firstly, X-ray diffraction (XRD) analysis was conducted on synthesized HAP-1, comparing its data to standard HAP. The superior performance of HAP-2 (pH 11) over HAP-1 (pH 10.26) made it the preferred choice for final composite production. The stability of the hexagonal-dipyramidal phase within HAP-2 was observed even at elevated temperatures up to 1200°C, implying exceptional thermal stability. Fourier-transform infrared (FTIR) analysis provided insights into the molecular composition of HAP-2. The results underscore the potential to tailor HAP properties for various applications by controlling synthesis conditions and heat treatment parameters.

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The escalating industrialization and urbanization in the northern part of Dhaka city have led to significant environmental degradation of the Turag River, manifesting through various forms of pollution. This study aims to delineate the adverse impacts of land use on the river's water quality, emphasizing the necessity of a comprehensive assessment to identify the pollution sources accurately. This study's primary goal is to evaluate the Water Quality Parameters and their potential influence on the Turag River's water's quality in terms of WQI. Ten parameters such as pH, TDS, TS, TSS, DO, BOD5, COD, Iron, Alkalinity and Arsenic were analyzed. The analyzed parameters values are pH 7.40 to 8.61: Total Dissolve Solids 121.5 mg/l to 201.3 mg/l; Total Solids 249.5 mg/l to 400.9 mg/l; Total Suspended Solids 105.8 mg/l to 213.5 mg/l; DO 0.55 mg/l to 0.87 mg/l; BOD5 1.41 mg/l to 1.51 mg/l; COD 25.4 mg/l to 78.7 mg/; Iron 0.10 mg/l; Alkalinity 84.4 mg/l to 150.7 mg/l and Arsenic 0 mg/l. The results of nearly each of the water quality parameters were higher above the ECR’23 standard limits and WHO but TDS, Iron and arsenic were within standards. Seasonal analysis indicated an alarming increase in pollutants from the wet to the dry season, underscoring the river's deteriorating condition. Consequently, the Water Quality Index (WQI) categorizes the river's water as unsafe for consumption, pointing towards an urgent need for targeted environmental management strategies.

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The Reinforced Concrete (RC) jacketing technique is a widely adopted method for retrofitting, strengthening, and rehabilitating structural elements of RC structures. It involves applying a new layer of concrete over an existing layer previously composed of broken brick and natural stone aggregate with similar properties. Achieving monolithic action necessitates a comprehensive understanding of the bond behaviour at the interface between aged and newly cast concrete. This study also underscores the significance of considering the type of aggregate used in concrete. It evaluates the bonding between stone aggregate and brick aggregate, crucial for practical scenarios where both combinations are prevalent. The research focuses on investigating the influence of surface roughness and pre-wetting on bond behaviour at the interface of brick aggregate concrete. These factors are examined to elucidate their impact on monolithic performance at the joint between old and new concrete. Pre-wetting and surface roughness, due to their similar textures and potential for promoting monolithic bond formation, are found to enhance bond strength. Notably, chipping the surface after 24 hours of pre-wetting led to a significant increase in bond strength, with the direct shear test showing a 105% improvement and the slant shear test reporting a 32.5% increase compared to normal circumstances.

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This study explores the influence of sewing thread count and speed on seam strength and efficiency in 100% cotton woven fabric. Utilizing samples with thread counts of 21 tex, 27 tex, and 40 tex, sewn at speeds of 3000 rpm, 4000 rpm, and 5000 rpm, a superimposed seam was applied. Results reveal that increasing thread count enhances both seam strength and efficiency. Higher thread counts (tex) contribute to stronger and more efficient seams. However, escalating sewing speeds (rpm) exhibit a mitigating effect on both strength and efficiency, compromising overall seam quality. The research provides crucial insights for garment manufacturers and designers, guiding the optimal selection of thread count and speed to achieve desired seam quality in 100% cotton woven fabric. This knowledge is instrumental in enhancing the quality and appearance of garment products, fostering greater customer satisfaction, and bolstering competitiveness in the dynamic fashion industry. Ultimately, the findings offer practical recommendations for industry professionals to fine-tune their manufacturing processes, ensuring superior seam performance and contributing to overall success in the market.

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In this article we have developed a method by which innumerable magic squares of order 3 can be constructed. We have cited several interesting examples for construction of such magic squares. The core idea is that if we assume an arbitrary source pack comprising of 9 distinct integers in the form of an arithmetic progression then by using this method, we can construct 8 different magic squares of order 3 for each source pack. The description of the method has been made elaborate only for reasons of clarity. We have stated and proved two conjectures which play vital roles in the development of the process.

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Bipedal robot is considered as more efficient, in terms of mobility and adaptation, than any other kind of robots. One of the most important problems in bipedal robot walking is the instability produced by the violent transition between the different dynamic phases of walking. In this research, a small size bipedal robot was designed and developed. A dynamic control algorithm for bipedal walking was also proposed and implemented. First, we designed mechanical, electrical and electronic aspects of the robot. Also, required firmware and software components were designed. Then we developed the full robotic system with hardware, firmware and software components. We tested the robot for walking and from experimental results we found that the robot could walk with certain degree of stability. In order to increase sophistication in the system further work is required. In particular, the dynamics of the system and trajectory patterns should be analysed based on the Augmented Model Predictive Control (AMPC) structure. Also, the Forward Kinematics (FK) and Inverse Kinematics (IK) of the bipedal system should be analysed with close attention. However, the output of this research will have the potentials in the field of education, research, and commercial uses.

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Heart disease is one of the widespread causes of human mortality, and it is important to regularly screen the condition of this organ. Electrocardiography is a popular tool to visualize heart activity, and this data can be used to differentiate a healthy versus a detrimental heart using machine learning techniques. This paper uses the Statlog heart dataset from the UCI repository to test the machine learning classification algorithms. The stacking ensemble classifier outperforms by giving 94.118% accuracy as the data is pre-processed using MinMax technique; while the algorithms KNN, GNB, LR, RF, SVM, DT, Bagging, AdaBoost, Gradient Boosting, and XGBoost are used as base learners and Random Forest is used as the meta classifier. It was cross-validated having almost similar accuracy. Also, different evaluation metrics as sensitivity, specificity, precision, logloss, coefficient of determination, root mean square error and computation time.

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The readymade garment sector of Bangladesh has been primarily dependent on the export of different knitwear. Knitted garments are made by the interloping of one set of yarns. Due to this reason, knitted garments have inherent extensibility and flexibility. Due to the laundering and several washing processes applied on the knitted garments for functional and beautification purposes, the garments come in contact with vigorous mechanical force, which significantly affects the dimensional stability commonly known as the shrinkage property of the garments. This has a significant impact on the final measurements of the garments. This research focuses on the impact of different garment washing techniques such as normal, detergent, bleach, and acid wash on the dimensional stability of single jersey and rib knitted t-shirts. The dimensions of the t-shirts were measured before washing and they were subjected to garments washing. After different washing, the garments showed a different level of changes in the dimensional stability that has been expressed as shrinkage percentage. Amongst the different washes, the acid wash has shown the highest amount of shrinkage due to the interaction with some strong washing conditions whereas normal wash with water showed the lowest amount of shrinkage as no chemicals have been used in this process. This research will be beneficial for garment manufacturers when patterns are being developed for fabric cutting, the expected shrinkage, known as residual shrinkage, needs to be considered to avoid unexpected changes in garment dimensions.

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