A New Trapezoidal-Simpson 3/8 Method for Solving Systems of Nonlinear Equations
Azure Isaac,
Twum Boakye Stephen,
Baba Seidu
Issue:
Volume 6, Issue 1, March 2021
Pages:
1-8
Received:
18 December 2020
Accepted:
4 January 2021
Published:
15 January 2021
Abstract: Since its introduction, the Broyden method has been used as the foundation to develop several other Broyden-like methods (or hybrid Broyden methods) which in many cases have turned out to be improved forms of the original method. The modified classical Broyden methods developed by many authors to solve system of nonlinear equations have been effective in overcoming the deficiency of the classical Newton Raphson method, however there are new trends of methods proposed by authors, which have proven to be more efficient than some already existing ones. This work introduces two Broyden-like method developed from a weighted combination of quadrature rules, namely the Trapizoidal, Simpson 3/8 and Simpson 1/3 quadrature rules. Hence the new Broyden-like methods named by the authors as TS-3/8 and TS – 1/3 methods have been developed from these rules. After subjecting the proposed methods together with some other existing Broyden-like methods to solve four bench-mark problems, the results of numerical test confirm that the TS-3/8 method is promising (in terms of speed and in most cases accuracy) when compared with other proposed Broyden-like methods. Results gathered after the comparison of TS – 3/8 with the other methods revealed that TS – 3/8 method performed better than all the methods in terms of speed and the number of iterations needed to reach a solution. On the other hand, TS – 1/3 method yielded results for all the benchmark problems but with a relatively higher number of iterations compared with the other methods selected for comparison.
Abstract: Since its introduction, the Broyden method has been used as the foundation to develop several other Broyden-like methods (or hybrid Broyden methods) which in many cases have turned out to be improved forms of the original method. The modified classical Broyden methods developed by many authors to solve system of nonlinear equations have been effect...
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A Human Physiologically-based Bio-kinetic Model for Cadmium
Danjuma Dan-Adam Maza,
Stephen Friday Olukotun,
Grace Olubunmi Akinlade
Issue:
Volume 6, Issue 1, March 2021
Pages:
9-13
Received:
14 January 2021
Accepted:
22 January 2021
Published:
9 February 2021
Abstract: A physiologically-based bio-kinetic (PBBK) model, capable of simulating the absorption, distribution, and elimination of cadmium in humans has been developed. The formulation of this model was based on human data cleaned from literature. The liver, kidney, lung, artery, vein, stomach, small intestine and remainder of the body (other tissues not modelled explicitly) were modelled as compartments. While transfer rate coefficients were used to describe the kinetics of cadmium in the gastrointestinal track, the model used blood flow rates and partition coefficients rather than the traditional transfer rate coefficients to describe the distribution and accumulation of the chemical into critical organs such as liver, kidney and remainder of the body. A perfusion rate-limited kinetics model was assumed for these critical organs, where each of these tissues was regarded as a well-stirred compartment, without any concentration gradient within the compartment. The partition coefficients for critical organs modelled, along with transfer rate coefficients describing oral ingestion and inhalation were estimated by fitting the simulated concentration of cadmium in the liver, kidney and urine to observed concentrations found in literature. The model was capable of simulating, to a good degree of success, the results of empirical observations and other simulations found in literature. Simulations by the model also indicate that the partition coefficient of cadmium for the kidney, liver and other critical organs was higher in smokers.
Abstract: A physiologically-based bio-kinetic (PBBK) model, capable of simulating the absorption, distribution, and elimination of cadmium in humans has been developed. The formulation of this model was based on human data cleaned from literature. The liver, kidney, lung, artery, vein, stomach, small intestine and remainder of the body (other tissues not mod...
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Characterization of Associative PU-algebras by the Notion of Derivations
Mehmood Khan,
Dawood Khan,
Khalida Mir Aalm
Issue:
Volume 6, Issue 1, March 2021
Pages:
14-18
Received:
18 January 2021
Accepted:
2 February 2021
Published:
4 March 2021
Abstract: In this manuscript we insert the concept of derivations in associative PU-algebras and discuss some of its important results such that we prove that for a mapping being a (Left, Right) or (Right, Left)-derivation of an associative PU-algebra then such a mapping is one-one. If a mapping is regular then it is identity. If any element of an associative PU-algebra satisfying the criteria of identity function then such a map is identity. We also prove some useful properties for a mapping being (Left, Right)-regular derivation of an associative PU-algebra and (Right, Left)-regular derivation of an associative PU-algebra. Moreover we prove that if a mapping is regular (Left, Right)-derivation of an associative PU-algebra then its Kernel is a subalgebra. We have no doubt that the research along this line can be kept up, and indeed, some results in this manuscript have already made up a foundation for further exploration concerning the further progression of PU-algebras. These definitions and main results can be similarly extended to some other algebraic systems such as BCH-algebras, Hilbert algebras, BF-algebras, J-algebras, WS-algebras, CI-algebras, SU-algebras, BCL-algebras, BP-algebras and BO-algebras, Z- algebras and so forth. The main purpose of our future work is to investigate the fuzzy derivations ideals in PU-algebras, which may have a lot of applications in different branches of theoretical physics and computer science.
Abstract: In this manuscript we insert the concept of derivations in associative PU-algebras and discuss some of its important results such that we prove that for a mapping being a (Left, Right) or (Right, Left)-derivation of an associative PU-algebra then such a mapping is one-one. If a mapping is regular then it is identity. If any element of an associativ...
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