This paper introduces and studies a novel method for approximating functions using the ideas of Padé (or rational function) approximations based on the Fourier-Bessel series representation of the function, where both the numerator and denominator are the truncated parts of the Fourier-Bessel series. The approximation using Fourier-Bessel series partial sums works well for smooth functions; however, it converges slowly and exhibits Gibbs phenomena near discontinuities. The coefficients appeared in this method are determined by enforcing orthogonality of the residual with respect to the weighted Fourier-Bessel basis (Galerkin method). The proposed method is illustrated by several functions, such as step, piecewise linear, and quadratic-linear functions. The obtained results show that this approach mitigates Gibbs phenomena near discontinuities, and reduces oscillations which are present in partial sums, improves accuracy in both the weighted L2 error and the maximum error at points away from the discontinuity. The method is also applied to the solution of an initial, boundary value problem for the radially symmetric wave equation, in the context of the vibrating circular membrane problem. The convergence results show faster error decay, and stability is maintained by keeping the denominator strictly positive. Overall, the proposed approximation method offers an effective and reliable alternative for approximating functions, especially when the functions are not smooth.
Nonwovens are one of the fastest growing textile sectors with diverse applications. These applications have an extensive list, ranging from baby diapers to high performance geotextiles. Geotextiles are widely used with soil structures and are effective tools in the hands of the civil engineer that have proved to solve a myriad of geotechnical problems. Present chapter discusses the nonwoven manufacturing processes, performance characteristics of nonwoven geotextiles, geotechnical functions, civil and environmental applications of nonwoven geotextiles, key design properties and testing standards and global market outlook.
The poor water stability of metal halide perovskites poses a significant challenge to use them as a fluorescent probes in aqueous medium. To adress this problem α-cyclodextrin (α-CD) was employed as an encapsulating agent for the preparation of cesium lead bromide perovskite quantum dots (CsPbBr3@α-CD PQDs). To the best of our knowledge, this is the first report to demonstrate α-CD as a ligand to impart water stability of CsPbBr3 PQDs while preserving their fluorescence properties. The as-prepared water-stable green fluorescent CsPbBr3@α-CD PQDs acted as a fluorescent probe for the detection of propiconazole (PCZ) fungicide via a fluorescence “turn-off” mechanism. The present study illustrates the strong affinity of CsPbBr3@α-CD PQDs toward PCZ, favoring to achieve a good linear range of 0.05–50 μM with a limit of detection of 17.11 nM. The proposed method demonstrated excellent accuracy, achieving recoveries of 99.40 − 99.76
The major challenges in the stir casting process for achieving sound castings include particle agglomeration, gravitational settling, and porosity formation. These issues primarily arise due to insufficient control over melt hydrodynamics and vortex stability during mechanical stirring. The present work examined the impact of two innovative blade designs, U-shaped and paraboloid-shaped, on the mechanical properties and microstructure of ADC12/silicon carbide (SiC) AMCs. These AMCs are produced through the bottom pouring process of stir casting. The two innovative blades were tested at various rotational speeds as a means of analyzing their effects on vortex formation, particle distribution, and composite properties. The reinforcement material, SiC, was selected due to its high strength, greater wear resistance, and widespread use in the commercial composites industry. The selected SiC has a weight percentage of 8
Produced water, a major by-product of oil and gas extraction, presents serious environmental challenges due to its high turbidity, oil and grease content, and potential for contaminant bioaccumulation. This study reports the synthesis, optimization, and performance evaluation of a novel organic–inorganic composite coagulant. Polyaluminium ferric chloride (PAFC) was synthesized, and then composite coagulant was prepared by grafting high-viscosity polyamine (HVP) onto PAFC. The coagulant composition was optimized at an Al/Fe ratio of 7, basicity (OH/(Al + Fe)) of 2.0, and 10
