This research investigates the comparative efficacy of generating zero divisor graphs (ZDGs) of the ring of integers ℤ<sub>n</sub> modulo n using MAPLE algorithm. Zero divisor graphs, pivotal in the study ...This research investigates the comparative efficacy of generating zero divisor graphs (ZDGs) of the ring of integers ℤ<sub>n</sub> modulo n using MAPLE algorithm. Zero divisor graphs, pivotal in the study of ring theory, depict relationships between elements of a ring that multiply to zero. The paper explores the development and implementation of algorithms in MAPLE for constructing these ZDGs. The comparative study aims to discern the strengths, limitations, and computational efficiency of different MAPLE algorithms for creating zero divisor graphs offering insights for mathematicians, researchers, and computational enthusiasts involved in ring theory and mathematical computations.展开更多
The Time Fractional Burger equation was solved in this study using the Mabel software and the Variational Iteration approach. where a number of instances of the Time Fractional Burger Equation were handled using this ...The Time Fractional Burger equation was solved in this study using the Mabel software and the Variational Iteration approach. where a number of instances of the Time Fractional Burger Equation were handled using this technique. Tables and images were used to present the collected numerical results. The difference between the exact and numerical solutions demonstrates the effectiveness of the Mabel program’s solution, as well as the accuracy and closeness of the results this method produced. It also demonstrates the Mabel program’s ability to quickly and effectively produce the numerical solution.展开更多
BACKGROUND Maple syrup urine disease(MSUD)is an autosomal recessive genetic disorder caused by defects in the catabolism of the branched-chain amino acids(BCAAs).However,the clinical and metabolic screening is limited...BACKGROUND Maple syrup urine disease(MSUD)is an autosomal recessive genetic disorder caused by defects in the catabolism of the branched-chain amino acids(BCAAs).However,the clinical and metabolic screening is limited in identifying all MSUD patients,especially those patients with mild phenotypes or are asymptomatic.This study aims to share the diagnostic experience of an intermediate MSUD case who was missed by metabolic profiling but identified by genetic analysis.CASE SUMMARY This study reports the diagnostic process of a boy with intermediate MSUD.The proband presented with psychomotor retardation and cerebral lesions on magnetic resonance imaging scans at 8 mo of age.Preliminary clinical and metabolic profiling did not support a specific disease.However,whole exome sequencing and subsequent Sanger sequencing at 1 year and 7 mo of age identified bi-allelic pathogenic variants of the BCKDHB gene,confirming the proband as having MSUD with non-classic mild phenotypes.His clinical and laboratory data were retrospectively analyzed.According to his disease course,he was classified into an intermediate form of MSUD.His management was then changed to BCAAs restriction and metabolic monitoring conforming to MSUD.In addition,genetic counseling and prenatal diagnosis were provided to his parents.CONCLUSION Our work provides diagnostic experience of an intermediate MSUD case,suggesting that a genetic analysis is important for ambiguous cases,and alerts clinicians to avoid missing patients with non-classic mild phenotypes of MSUD.展开更多
This paper uses the Adomian Decomposition Method (ADM) to solve Boussinesq equations using Maple. The Boussinesq approximation for water waves is a weakly nonlinear and long-wave approximation in fluid dynamics. The a...This paper uses the Adomian Decomposition Method (ADM) to solve Boussinesq equations using Maple. The Boussinesq approximation for water waves is a weakly nonlinear and long-wave approximation in fluid dynamics. The approximation is named after Joseph Boussinesq, who developed it in response to John Scott Russell’s observation of a wave of translation (also known as solitary wave or soliton). Bossinesq’s article from 1872 introduced the equations that are now known as the Boussinesq equations. Numerical methods are commonly utilized to solve nonlinear equation systems. In this paper, we investigate a nonlinear singly perturbed advection-diffusion problem. Using the usual Adomian Decomposition Method, we formulate an approximate linear advection-diffusion problem and investigate several practical numerical approaches for solving it (ADM). The Adomian Decomposition Method (ADM) is a powerful tool for numerical simulations and approximation analytic solutions. The Adomian Decomposition Method (ADM) is used to solve nonlinear advection differential equations using Maple by illustrating numerous examples. The findings are presented in the form of tables and graphs for several examples. For various examples, the findings are presented in the form of tables and graphs. The difference between the precise and numerical solutions indicates the Maple program solution’s efficacy, as well as the ease and speed with which it was acquired.展开更多
In this paper, the Adomian decomposition method was used to solve the Time Fractional Burger equation using Mabel program. This method was applied to a number of examples of the Time Fractional Burger Equation. The ob...In this paper, the Adomian decomposition method was used to solve the Time Fractional Burger equation using Mabel program. This method was applied to a number of examples of the Time Fractional Burger Equation. The obtained numerical results were presented in the form of tables and graphics. The difference between the exact solutions and the numerical solutions shows us the effectiveness of the solution using the Mabel program and that this method gave accurate results and was close to the exact solution, in addition to its ability to obtain the numerical solution quickly and efficiently using the Mabel program.展开更多
The immense quest for proficient numerical schemes for the solution of mathematical models featuring nonlinear differential equations led to the realization of the Adomian decomposition method (ADM) in the 80<sup&g...The immense quest for proficient numerical schemes for the solution of mathematical models featuring nonlinear differential equations led to the realization of the Adomian decomposition method (ADM) in the 80<sup>th</sup>. Undoubtedly, the solution of nonlinear differential equations using ADM is presided over by the acquisition of Adomian polynomials, which are not always easy to find. Thus, the present study proposes easy-to-implement Maple programs for the computation of Adomian polynomials. In fact, the proposed algorithms performed remarkably on several test functions, consisting of one- and multi-variable nonlinearities. Moreover, the introduced programs are advantageous in terms of simplicity;coupled with the requirement of less computational time in comparison with what is known in the literature.展开更多
文摘This research investigates the comparative efficacy of generating zero divisor graphs (ZDGs) of the ring of integers ℤ<sub>n</sub> modulo n using MAPLE algorithm. Zero divisor graphs, pivotal in the study of ring theory, depict relationships between elements of a ring that multiply to zero. The paper explores the development and implementation of algorithms in MAPLE for constructing these ZDGs. The comparative study aims to discern the strengths, limitations, and computational efficiency of different MAPLE algorithms for creating zero divisor graphs offering insights for mathematicians, researchers, and computational enthusiasts involved in ring theory and mathematical computations.
文摘The Time Fractional Burger equation was solved in this study using the Mabel software and the Variational Iteration approach. where a number of instances of the Time Fractional Burger Equation were handled using this technique. Tables and images were used to present the collected numerical results. The difference between the exact and numerical solutions demonstrates the effectiveness of the Mabel program’s solution, as well as the accuracy and closeness of the results this method produced. It also demonstrates the Mabel program’s ability to quickly and effectively produce the numerical solution.
基金Supported by the Guangzhou Science Technology and Innovation Commission,No.202102020133。
文摘BACKGROUND Maple syrup urine disease(MSUD)is an autosomal recessive genetic disorder caused by defects in the catabolism of the branched-chain amino acids(BCAAs).However,the clinical and metabolic screening is limited in identifying all MSUD patients,especially those patients with mild phenotypes or are asymptomatic.This study aims to share the diagnostic experience of an intermediate MSUD case who was missed by metabolic profiling but identified by genetic analysis.CASE SUMMARY This study reports the diagnostic process of a boy with intermediate MSUD.The proband presented with psychomotor retardation and cerebral lesions on magnetic resonance imaging scans at 8 mo of age.Preliminary clinical and metabolic profiling did not support a specific disease.However,whole exome sequencing and subsequent Sanger sequencing at 1 year and 7 mo of age identified bi-allelic pathogenic variants of the BCKDHB gene,confirming the proband as having MSUD with non-classic mild phenotypes.His clinical and laboratory data were retrospectively analyzed.According to his disease course,he was classified into an intermediate form of MSUD.His management was then changed to BCAAs restriction and metabolic monitoring conforming to MSUD.In addition,genetic counseling and prenatal diagnosis were provided to his parents.CONCLUSION Our work provides diagnostic experience of an intermediate MSUD case,suggesting that a genetic analysis is important for ambiguous cases,and alerts clinicians to avoid missing patients with non-classic mild phenotypes of MSUD.
文摘This paper uses the Adomian Decomposition Method (ADM) to solve Boussinesq equations using Maple. The Boussinesq approximation for water waves is a weakly nonlinear and long-wave approximation in fluid dynamics. The approximation is named after Joseph Boussinesq, who developed it in response to John Scott Russell’s observation of a wave of translation (also known as solitary wave or soliton). Bossinesq’s article from 1872 introduced the equations that are now known as the Boussinesq equations. Numerical methods are commonly utilized to solve nonlinear equation systems. In this paper, we investigate a nonlinear singly perturbed advection-diffusion problem. Using the usual Adomian Decomposition Method, we formulate an approximate linear advection-diffusion problem and investigate several practical numerical approaches for solving it (ADM). The Adomian Decomposition Method (ADM) is a powerful tool for numerical simulations and approximation analytic solutions. The Adomian Decomposition Method (ADM) is used to solve nonlinear advection differential equations using Maple by illustrating numerous examples. The findings are presented in the form of tables and graphs for several examples. For various examples, the findings are presented in the form of tables and graphs. The difference between the precise and numerical solutions indicates the Maple program solution’s efficacy, as well as the ease and speed with which it was acquired.
文摘In this paper, the Adomian decomposition method was used to solve the Time Fractional Burger equation using Mabel program. This method was applied to a number of examples of the Time Fractional Burger Equation. The obtained numerical results were presented in the form of tables and graphics. The difference between the exact solutions and the numerical solutions shows us the effectiveness of the solution using the Mabel program and that this method gave accurate results and was close to the exact solution, in addition to its ability to obtain the numerical solution quickly and efficiently using the Mabel program.
文摘The immense quest for proficient numerical schemes for the solution of mathematical models featuring nonlinear differential equations led to the realization of the Adomian decomposition method (ADM) in the 80<sup>th</sup>. Undoubtedly, the solution of nonlinear differential equations using ADM is presided over by the acquisition of Adomian polynomials, which are not always easy to find. Thus, the present study proposes easy-to-implement Maple programs for the computation of Adomian polynomials. In fact, the proposed algorithms performed remarkably on several test functions, consisting of one- and multi-variable nonlinearities. Moreover, the introduced programs are advantageous in terms of simplicity;coupled with the requirement of less computational time in comparison with what is known in the literature.
