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Article Citation - WoS: 79Citation - Scopus: 82The (2+1)-Dimensional Heisenberg Ferromagnetic Spin Chain Equation: Its Solitons and Jacobi Elliptic Function Solutions(Springer Heidelberg, 2021) Salahshour, Soheil; Mirzazadeh, Mohammad; Ahmadian, Ali; Baleanu, Dumitru; Khoshrang, Arian; Hosseini, Kamyar; 56389The search for exact solutions of nonlinear evolution models with different wave structures has achieved significant attention in recent decades. The present paper studies a nonlinear (2+1)-dimensional evolution model describing the propagation of nonlinear waves in Heisenberg ferromagnetic spin chain system. The intended aim is carried out by considering a specific transformation and adopting a modified version of the Jacobi elliptic expansion method. As a result, a number of solitons and Jacobi elliptic function solutions to the Heisenberg ferromagnetic spin chain equation are formally derived. Several three-dimensional plots are presented to demonstrate the dynamical features of the bright and dark soliton solutions.Article A 6-Point Subdivision Scheme and Its Applications for the Solution of 2nd Order Nonlinear Singularly Perturbed Boundary Value Problems(Amer inst Mathematical Sciences-aims, 2020) Baleanu, Dumitru; Ejaz, Syeda Tehmina; Anju, Kaweeta; Ahmadian, Ali; Salahshour, Soheil; Ferrara, Massimiliano; Mustafa, Ghulam; 56389In this paper, we first present a 6-point binary interpolating subdivision scheme (BISS) which produces a C-2 continuous curve and 4th order of approximation. Then as an application of the scheme, we develop an iterative algorithm for the solution of 2nd order nonlinear singularly perturbed boundary value problems (NSPBVP). The convergence of an iterative algorithm has also been presented. The 2nd order NSPBVP arising from combustion, chemical reactor theory, nuclear engineering, control theory, elasticity, and fluid mechanics can be solved by an iterative algorithm with 4th order of approximation.Article Citation - WoS: 1Citation - Scopus: 2Abstract Random Differential Equations With State-Dependent Delay Using Measures of Noncompactness(Vilnius Univ, inst Mathematics & informatics, 2024) Heris, Amel; Bouteffal, Zohra; Salim, Abdelkrim; Benchohra, Mouffak; Karapinar, ErdalThis paper is devoted to the existence of random mild solutions for a general class of second-order abstract random differential equations with state-dependent delay. The technique used is a generalization of the classical Darbo fixed point theorem for Frechet spaces associated with the concept of measures of noncompactness. An application related to partial random differential equations with state-dependent delay is presented.Article Citation - WoS: 30Citation - Scopus: 33Abundant New Solutions of the Transmission of Nerve Impulses of an Excitable System(Springer Heidelberg, 2020) Attia, Raghda A. M.; Baleanu, Dumitru; Khater, Mostafa M. A.; 56389This research investigates the dynamical behavior of the transmission of nerve impulses of a nervous system (the neuron) by studying the computational solutions of the FitzHugh-Nagumo equation that is used as a model of the transmission of nerve impulses. For achieving our goal, we employ two recent computational schemes (the extended simplest equation method and Sinh-Cosh expansion method) to evaluate some novel computational solutions of these models. Moreover, we study the stability property of the obtained solutions to show the applicability of them in life. For more explanation of this transmission, some sketches are given for the analytical obtained solutions. A comparison between our results and that obtained in previous work is also represented and discussed in detail to show the novelty for our solutions. The performance of the two used methods shows power, practical and their ability to apply to other nonlinear partial differential equations.Article Citation - WoS: 23Citation - Scopus: 23Abundant Optical Solitons To the (2+1)-Dimensional Kundu-Mukherjee Equation in Fiber Communication Systems(Springer, 2023) Baleanu, Dumitru; Ghanbari, Behzad; 56389The Kundu-Mukherjee-Naskar equation holds significant relevance as a nonlinear model for investigating intricate wave phenomena in fluid and optical systems. This study uncovers new optical soliton solutions for the KMN equation by employing analytical techniques that utilize combined elliptic Jacobian functions. The solutions exhibit mixtures of distinct Jacobian elliptic functions, offering novel insights not explored in prior KMN equation research. Visual representations in the form of 2D ContourPlots elucidate the physical behaviors and properties of these newly discovered solution forms. The utilization of symbolic computations facilitated the analytical derivation of these solutions, offering a deeper understanding of the nonlinear wave dynamics governed by the KMN equation. These employed techniques showcase the potential for future analytical advancements in unraveling the complex soliton landscape of the multifaceted KMN model. The findings provide valuable insights into the intricacies of soliton behavior within this nonlinear system, offering new perspectives for analysis and exploration in areas such as fiber optic communications, ocean waves, and fluid mechanics. Maple symbolic packages have enabled us to derive analytical results.Article Citation - WoS: 14Citation - Scopus: 16An Accurate Approximate-Analytical Technique for Solving Time-Fractional Partial Differential Equations(Wiley-hindawi, 2017) Salahshour, S.; Ahmadian, A.; Ismail, F.; Baleanu, D.; Bishehniasar, M.; 56389The demand of many scientific areas for the usage of fractional partial differential equations (FPDEs) to explain their real-world systems has been broadly identified. The solutions may portray dynamical behaviors of various particles such as chemicals and cells. The desire of obtaining approximate solutions to treat these equations aims to overcome the mathematical complexity of modeling the relevant phenomena in nature. This research proposes a promising approximate-analytical scheme that is an accurate technique for solving a variety of noninteger partial differential equations (PDEs). The proposed strategy is based on approximating the derivative of fractional-order and reducing the problem to the corresponding partial differential equation (PDE). Afterwards, the approximating PDE is solved by using a separation-variables technique. The method can be simply applied to nonhomogeneous problems and is proficient to diminish the span of computational cost as well as achieving an approximate-analytical solution that is in excellent concurrence with the exact solution of the original problem. In addition and to demonstrate the efficiency of the method, it compares with two finite difference methods including a nonstandard finite difference (NSFD) method and standard finite difference (SFD) technique, which are popular in the literature for solving engineering problems.Article Citation - WoS: 110Citation - Scopus: 112Active Laser Radar Systems With Stochastic Electromagnetic Beams in Turbulent Atmosphere(Optica Publishing Group, 2008) Cai, Yangjian; Korotkova, Olga; Eyyuboglu, Halil T.; Baykal, Yahya; 7688; 7812Propagation of stochastic electromagnetic beams through paraxial ABCD optical systems operating through turbulent atmosphere is investigated with the help of the ABCD matrices and the generalized Huygens-Fresnel integral. In particular, the analytic formula is derived for the cross-spectral density matrix of an electromagnetic Gaussian Schell-model (EGSM) beam. We applied our analysis for the ABCD system with a single lens located on the propagation path, representing, in a particular case, the unfolded double-pass propagation scenario of active laser radar. Through a number of numerical examples we investigated the effect of local turbulence strength and lens' parameters on spectral, coherence and polarization properties of the EGSM beam. (C) 2008 Optical Society of AmericaArticle Citation - WoS: 34Adaptive Fractional-Order Blood Glucose Regulator Based on High-Order Sliding Mode Observer(inst Engineering Technology-iet, 2019) Heydarinejad, Hamid; Baleanu, Dumitru; Delavari, Hadi; 56389Type I diabetes is described by the destruction of the insulin-producing beta-cells in the pancreas. Hence, exogenous insulin administration is necessary for Type I diabetes patients. In this study, to estimate the states that are not directly available from the Bergman minimal model a high-order sliding mode observer is proposed. Then fractional calculus is combined with sliding mode control (SMC) for blood glucose regulation to create more robustness performance and make more degree of freedom and flexibility for the proposed method. Then an adaptive fractional-order SMC is proposed. The adaptive SMC protect controller against disturbance and uncertainties while the fractional calculus provides robust performance. Numerical simulation verifies that the proposed controllers have better performance in the presence of disturbance and uncertainties without chattering.Article Citation - WoS: 7Citation - Scopus: 6Adaptive Optics Correction of Beam Spread in Biological Tissues(Pergamon-elsevier Science Ltd, 2022) Baykal, YahyaBeam spread in turbulent biological tissues is examined when the tissue is excited with a collimated Gaussian laser beam. Adaptive optics correction is applied to the beam spread in the form of piston only (P Only), tilt only (T Only), piston + tilt (P + T), and the reduction in the beam spread is evaluated as com-pared to the no adaptive optics (No AO) corrected beam spread. No AO and adaptive optics corrected beam spread are expressed for various biological tissue types, against the variations in the strength co-efficient of the refractive-index fluctuations, source size, small length-scale factor of turbulence, tissue length, fractal dimension, characteristic lengths of heterogeneity and the wavelength. For the examined tissue types of liver parenchyma (mouse), intestinal epithelium (mouse), upper dermis (human) and deep dermis (mouse), No AO beam spread and the adaptive optics corrected beam spread are found to increase as the strength coefficient of the refractive-index fluctuations, tissue length, fractal dimension, the char-acteristic lengths of heterogeneity increase, and to decrease as the source size, small length-scale factor, wavelength increase. Reduction ratio of P + T correction is almost the same for all the evaluated cases which is 74%.(C) 2022 Elsevier Ltd. All rights reserved.Article Citation - WoS: 14Citation - Scopus: 16Adaptive Optics Effect on Performance of Bpsk-Sim Oceanic Optical Wireless Communication Systems With Aperture Averaging in Weak Turbulence(Pergamon-elsevier Science Ltd, 2020) Baykal, Yahya; Ata, Yalcin; Gokce, Muhsin Caner; 7812Turbulence-induced wavefront deformations cause the irradiance of an optical signal to fluctuate resulting a in serious degradation in the bit-error-rate (BER) performance of optical wireless communication (OWC) system. Adaptive optics is an effective technique to compensate for the wavefront aberrations to reduce the fluctuations in the received intensity. In this paper, we investigate how the adaptive optics technique affects the BER performance of an oceanic OWC (OOWC) system employing binary phase shift keying-subcarrier intensity modulation (BPSK-SIM) and aperture averaging. To evaluate BER performance in weak oceanic turbulence, the required entities such as the received optical power captured by a circular aperture and the aperture averaged scintillation index measuring the fluctuations in the received irradiance are derived. The effect of adaptive optics correction of various wavefront aberrations (i.e., tilt, defocus, astigmatism and the coma) on the BER performance is illustrated and the performance of the adaptive optics-OOWC system is compared to that of a non-adaptive optics OOWC system by the metric defined. (C) 2020 Elsevier Ltd. All rights reserved.Article Citation - WoS: 24Citation - Scopus: 31Advanced Exact Solutions To the Nano-Ionic Currents Equation Through Mts and the Soliton Equation Containing the Rlc Transmission Line(Springer Heidelberg, 2023) Miah, M. Mamun; Iqbal, M. Ashik; Alshehri, Hashim M.; Baleanu, Dumitru; Osman, M. S.; Chowdhury, M. Akher; 56389In this study, the double (G '/G, 1/G)-expansion method is utilized for illustrating the improved explicit integral solutions for the two of nonlinear evolution equations. To expose the importance and convenience of our assumed method, we herein presume two models, namely the nano-ionic currents equation and the soliton equation. The exact solutions are generated with the aid of our proposed method in such a manner that the solutions involve to the rational, trigonometric, and hyperbolic functions for the first presumed nonlinear equation as well as the trigonometric and hyperbolic functions for the second one with meaningful symbols that promote some unique periodic and solitary solutions. The method used here is an extension of the (G '/G)-expansion method to rediscover all known solutions. We offer 2D and 3D charts of the various recovery solutions to better highlight our findings. Finally, we compared our results with those of earlier solutions.Article Citation - WoS: 28Citation - Scopus: 31Advanced Fractional Calculus, Differential Equations and Neural Networks: Analysis, Modeling and Numerical Computations(Iop Publishing Ltd, 2023) Karaca, Yeliz; Vazquez, Luis; Macias-Diaz, Jorge E.; Baleanu, Dumitru; 56389Most physical systems in nature display inherently nonlinear and dynamical properties; hence, it would be difficult for nonlinear equations to be solved merely by analytical methods, which has given rise to the emerging of engrossing phenomena such as bifurcation and chaos. Conjointly, due to nonlinear systems' exhibiting more exotic behavior than harmonic distortion, it becomes compelling to test, classify and interpret the results in an accurate way. For this reason, avoiding preconceived ideas of the way the system is likely to respond is of pivotal importance since this facet would have effect on the type of testing run and processing techniques used in nonlinear systems. Paradigms of nonlinear science may suggest that it is 'the study of every single phenomenon' due to its interdisciplinary nature, which is another challenge encountered and needs to be addressed by generating and designing a systematic mathematical framework where the complexity of natural phenomena hints the requirement of identifying their commonalties and classifying their various manifestations in different nonlinear systems. Studying such common properties, concepts or paradigms can enable one to gain insight into nonlinear problems, their essence and consequences in a broad range of disciplines all forthwith. Fractional differential equations associated with non-local phenomena in physics have arisen as a powerful mathematical tool within a multidisciplinary research framework. Fractional differential equations, as one extension of the fractional calculus theory, can yield the evolution of various systems properly, which reinforces its position in mathematics and science while setting stage for the description of dynamic, complicated and nonlinear events. Through the reflection of the systems' actual properties, fractional calculus manifests unforeseeable and hidden variations, and thus, enables integration and differentiation, with the solutions to be approximated by numerical methods along with modeling and predicting the dynamics of multiphysics, multiscale and physical systems. Neural Networks (NNs), consisting of hidden layers with nonlinear functions that have vector inputs and outputs, are also considerably employed owing to their versatile and efficient characteristics in classification problems as well as their sophisticated neural network architectures, which make them capable of tackling complicated governing partial differential equation problems. Furthermore, partial differential equations are used to provide comprehensive and accurate models for many scientific phenomena owing to the advancements of data gathering and machine learning techniques which have raised opportunities for data-driven identification of governing equations derived from experimentally observed data. Given these considerations, while many problems are solvable and have been solved, efforts are still needed to be able to respond to the remaining open questions in the fields that have a broad range of spectrum ranging from mathematics, physics, biology, virology, epidemiology, chemistry, engineering, social sciences to applied sciences. With a view of different aspects of such questions, our special issue provides a collection of recent research focusing on the advances in the foundational theory, methodology and topical applications of fractals, fractional calculus, fractional differential equations, differential equations (PDEs, ODEs, to name some), delay differential equations (DDEs), chaos, bifurcation, stability, sensitivity, machine learning, quantum machine learning, and so forth in order to expound on advanced fractional calculus, differential equations and neural networks with detailed analyses, models, simulations, data-driven approaches as well as numerical computations.Article Citation - WoS: 2Citation - Scopus: 2Advanced Rheological Characterization of Asphalt Binders Modified With Eco-Friendly and Polymer-Based Additives Under Dynamic Loading(Multidisciplinary Digital Publishing Institute (MDPI), 2025) Almusawi, A.; Nasraldeen, S.T.N.This study explores the rheological performance of bitumen modified with a synthetic polymer (styrene–butadiene–styrene, SBS) and two environmentally sustainable additives—animal bone ash (AB) and waste cooking oil (WCO)—to enhance durability and deformation resistance under dynamic loading. Frequency sweep and linear amplitude sweep (LAS) tests were conducted to evaluate viscoelastic and fatigue behavior. SBS at 5% showed the highest elasticity and fatigue life, making it optimal for heavily trafficked pavements. Among bio-waste additives, 6% AB provided the highest stiffness and rutting resistance in laboratory tests; however, 5% AB offered a better balance between structural integrity and cracking resistance, making it more suitable for general pavement applications. WCO-modified binders demonstrated improved flexibility, with 4% WCO achieving the best balance between elasticity and softening, ideal for low-load or temperate environments. These results highlight the potential of combining synthetic and bio-based waste materials to tailor bitumen properties for sustainable and climate-responsive pavement design. © 2025 by the authors.Article Citation - WoS: 1Citation - Scopus: 1Advancing Nanomaterials Research: a Comprehensive Review of Artificial Intelligence Applications in Geotechnical Properties(Techno-Press, 2024) Cemiloglu, A.; Zhu, L.; Arslan, S.; Nanehkaran, Y.A.; Azarafza, M.; Derakhshani, R.This article explores the role of artificial intelligence (AI) in predicting nanomaterial properties, particularly its significance within geotechnical engineering. By analyzing multiple AI-based studies, the review concentrates on the forecasting of nanomaterial-altered soil characteristics and behaviors. Encouraging findings from these studies underscore AI’s ability to accurately predict the geotechnical properties of nanomaterials, though challenges remain, particularly in quantifying nanomaterial percentages and their implications across various applications. Future research should address these challenges to enhance the accuracy of AI-based prediction models in geotechnical engineering. Nonetheless, the growing adoption of AI for predicting nanomaterial properties demonstrates its potential to revolutionize geotechnical engineering. AI’s capacity to uncover intricate patterns and relationships beyond human capabilities enables more precise soil behavior predictions, fostering innovative solutions to geotechnical challenges. Its ability to process vast datasets, adapt to various scenarios, and continuously learn from new information makes AI an indispensable tool for understanding nanomaterial properties and their impact on soil behavior. In summary, the integration of AI and geotechnical engineering represents a pivotal advancement in comprehending nanomaterial properties and their practical applications. As research advances and AI technologies evolve, transformative progress in geotechnical engineering is expected. By harnessing AI’s capabilities, researchers can unlock groundbreaking insights, drive innovation, and shape a more resilient and sustainable future for the geotechnical engineering industry. © 2024 Techno-Press, Ltd.Article Citation - WoS: 10Citation - Scopus: 10Aggregation Operators for Interval-Valued Pythagorean Fuzzy Hypersoft Set With Their Application To Solve Mcdm Problem(Tech Science Press, 2023) Siddique, Imran; Ali, Rifaqat; Jarad, Fahd; Iampan, Aiyared; Zulqarnain, Rana Muhammad; 234808Experts use Pythagorean fuzzy hypersoft sets (PFHSS) in their investigations to resolve the indeterminate and imprecise information in the decision-making process. Aggregation operators (AOs) perform a leading role in perceptivity among two circulations of prospect and pull out concerns from that perception. In this paper, we extend the concept of PFHSS to interval-valued PFHSS (IVPFHSS), which is the generalized form of interval -valued intuitionistic fuzzy soft set. The IVPFHSS competently deals with uncertain and ambagious information compared to the existing interval-valued Pythagorean fuzzy soft set. It is the most potent method for amplifying fuzzy data in the decision-making (DM) practice. Some operational laws for IVPFHSS have been proposed. Based on offered operational laws, two inventive AOs have been established: interval-valued Pythagorean fuzzy hypersoft weighted average (IVPFHSWA) and interval-valued Pythagorean fuzzy hypersoft weighted geometric (IVPFHSWG) operators with their essential properties. Multi-criteria group decision-making (MCGDM) shows an active part in contracts with the difficulties in industrial enterprise for material selection. But, the prevalent MCGDM approaches consistently carry irreconcilable consequences. Based on the anticipated AOs, a robust MCGDM technique is deliberate for material selection in industrial enterprises to accommodate this shortcoming. A real-world application of the projected MCGDM method for material selection (MS) of cryogenic storing vessels is presented. The impacts show that the intended model is more effective and reliable in handling imprecise data based on IVPFHSS.Article Citation - WoS: 32Citation - Scopus: 37Aggregation Operators for Interval-Valued Pythagorean Fuzzy Soft Set With Their Application To Solve Multi-Attribute Group Decision Making Problem(Tech Science Press, 2022) Zulqarnain, Rana Muhammad; Siddique, Imran; Iampan, Aiyared; Baleanu, DumitruInterval-valued Pythagorean fuzzy soft set (IVPFSS) is a generalization of the interval-valued intuitionistic fuzzy soft set (IVIFSS) and interval-valued Pythagorean fuzzy set (IVPFS). The IVPFSS handled more uncertainty comparative to IVIFSS; it is the most significant technique for explaining fuzzy information in the decision-making process. In this work, some novel operational laws for IVPFSS have been proposed. Based on presented operational laws, two innovative aggregation operators (AOs) have been developed such as interval-valued Pythagorean fuzzy soft weighted average (IVPFSWA) and interval-valued Pythagorean fuzzy soft weighted geometric (IVPFSWG) operators with their fundamental properties. A multi-attribute group decision-making (MAGDM) approach has been established utilizing our developed operators. A numerical example has been presented to ensure the validity of the proposed MAGDM technique. Finally, comparative studies have been given between the proposed approach and some existing studies. The obtained results through comparative studies show that the proposed technique is more credible and reliable than existing approaches.Article Citation - WoS: 1Citation - Scopus: 1Agribusiness Resilience During the Covid-19 Pandemic: the Role of Credit Constraints(Czech Academy Agricultural Sciences, 2024) Ozsuca, Ekin ayseThis paper investigates the effect of pre-COVID credit constraints and the moderating role of government support on agribusiness resilience following the outbreak of COVID-19. Using a dataset covering 42 countries, we provide empirical evidence on how firm characteristics and credit constraints affect agribusinesses' likelihood of survival and performance during the pandemic. On the enterprise level, size, foreign ownership and gender of the manager are found to display a statistically significant relationship with closure and sales performance. The findings reveal that pre-existing credit constraints tended to magnify the negative impacts of the pandemic. Specifically, agribusinesses with better access to finance were less likely to experience a decline in sales and exit from the market and, hence, were in a better position to withstand pandemic-induced shock. The results further highlighted the positive role of government support on agribusiness resilience, whereas obtaining government aid was found to have no significant effect on moderating the link between financial conditions and resilience. Finally, the results showed that financially constrained agribusinesses are more likely to suffer from liquidity/cash flow problems and experience overdue financial obligations during the pandemic. In coping with their liquidity shortfalls, these agribusinesses were less likely to access formal credit and more likely to delay payments to suppliers/workers.Article Citation - WoS: 1Citation - Scopus: 1Airy-Type Relativistic Matter Wave(Elsevier Gmbh, 2021) Umul, Yusuf Ziya; 4269A new relativistic Airy-type matter wave is introduced as a solution of the kinetic energy based wave equation. The parametric solution of the related differential equation is obtained. The total energy and momentum of the relativistic particle are derived by using a Bohmian type of decomposition of the kinetic energy based equation. The acceleration of the particle is also evaluated. The behavior of the matter wave is investigated numerically.Article Citation - WoS: 4Citation - Scopus: 5Almost Autonomous Training of Mixtures of Principal Component Analyzers(Elsevier Science Bv, 2004) Musa, MEM; de Ridder, D; Duin, RPW; Atalay, VIn recent years, a number of mixtures of local PCA models have been proposed. Most of these models require the user to set the number of submodels (local models) in the mixture and the dimensionality of the submodels (i.e., number of PC's) as well. To make the model free of these parameters, we propose a greedy expectation-maximization algorithm to find a suboptimal number of submodels. For a given retained variance ratio, the proposed algorithm estimates for each submodel the dimensionality that retains this given variability ratio. We test the proposed method on two different classification problems: handwritten digit recognition and 2-class ionosphere data classification. The results show that the proposed method has a good performance. (C) 2004 Elsevier B.V. All rights reserved.Article Citation - WoS: 203Citation - Scopus: 231Ammonia Removal From Anaerobically Digested Dairy Manure by Struvite Precipitation(Elsevier Sci Ltd, 2005) Uludag-Demirer, S; Demirer, GN; Chen, SAmmonia is one of the most important contaminants impairing the quality of water resources. When this is considered along with the fact that the global demand for nitrogenous fertilizers is in constant rise, the need for recovery as well as removal of nitrogen is well justified. Crystallization of N and P in the form of struvite (MgNH4PO4 center dot 6H(2)O), which is a slow releasing and valuable fertilizer, is one possible technique for this purpose. This study investigated the removal of NR4+ through struvite precipitation from the effluents of one- (R1) and two-phase (R2) anaerobic reactors digesting dairy manure. To force the formation of struvite in the anaerobic reactor effluents, Ma(2+) ion was added by using both Mg(OH)(2) and MgCl2 center dot 6H(2)O. To prevent the effect of different total phosphorus (TP) concentration in the effluents of RI and R2, as well as to not limit the formation of struvite, an excess amount Of PO43- (0.14 M) was added in the form of NaHPO4. Different stoichiometric Mg2+:NH4+:PO43- ratios were tested to determine the required Mg2+ concentrations for maximum NH4+ removal by keeping NH4+:PO43- ratio constant for the effluents of reactors RI and R2. The results revealed that very high NH4+ removal efficiencies (above 95%) were possible by adding Mg 21 ions higher than 0.06 M concentration in the effluents from reactors RI and R2. It was also observed that the initial pH adjustment to 8.50 using NaOH did not result in any significant increase in the removal of NH4+ and the removal of NH4+ in the reactors treated with MgCl2 center dot 6H(2)O was higher than those treated with Mg(OH)(2) for the same Mg2+ concentration. (c) 2005 Published by Elsevier Ltd.
