Purpose of writing this paper is to provide a new dynamic geometric method and also a mechanical model based upon it, to solve quintic equations. A triangle ABC with base BC, perpendicular AB of length equal to unity, hypotenuse AC, right angle at point B, is constructed. Perpendiculars BD, EF, GH upon AC, perpendiculars DE, FG upon BC, are drawn. Value of angle C is adjusted so that difference in lengths of BD and GH equals constant term of quintic equation transformed to Bring-Jerrard normal form, then one real root of given quintic equation equals length of perpendicular BD. Presently, there are two geometric methods available to solve quintic equations, first by paper folding art, called Origami and second given by Australian engineer, Edward Lill. This paper presents third simple and unique geometric method. Notwithstanding this dynamic geometric method, a mathematical model, explaining its fabrication, operation, has also been devised to present a real life picture of solution to the equations.
{"title":"Solution of quintic equation by geometric method and based upon it: A mathematical model","authors":"Narinder Kumar Wadhawan","doi":"10.47974/jim-1538","DOIUrl":"https://doi.org/10.47974/jim-1538","url":null,"abstract":"Purpose of writing this paper is to provide a new dynamic geometric method and also a mechanical model based upon it, to solve quintic equations. A triangle ABC with base BC, perpendicular AB of length equal to unity, hypotenuse AC, right angle at point B, is constructed. Perpendiculars BD, EF, GH upon AC, perpendiculars DE, FG upon BC, are drawn. Value of angle C is adjusted so that difference in lengths of BD and GH equals constant term of quintic equation transformed to Bring-Jerrard normal form, then one real root of given quintic equation equals length of perpendicular BD. Presently, there are two geometric methods available to solve quintic equations, first by paper folding art, called Origami and second given by Australian engineer, Edward Lill. This paper presents third simple and unique geometric method. Notwithstanding this dynamic geometric method, a mathematical model, explaining its fabrication, operation, has also been devised to present a real life picture of solution to the equations.","PeriodicalId":46278,"journal":{"name":"JOURNAL OF INTERDISCIPLINARY MATHEMATICS","volume":"51 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70467781","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The numerical technique for 2D time dependent linear Schrodinger equation is the subject of this work. The approximations are produced using the weak Galerkin finite element technique with continous and discrete FEM, on relay , using the backward Euler method in time. Using the elliptic projection operator, we provide L2 error speculation for continues and discretely weak Galerkin finite element.
{"title":"Weak galerkin finite element method for the linear Schrodinger equation","authors":"Dalal Ismael Aziz, Ahmed J. Hussein","doi":"10.47974/jim-1529","DOIUrl":"https://doi.org/10.47974/jim-1529","url":null,"abstract":"The numerical technique for 2D time dependent linear Schrodinger equation is the subject of this work. The approximations are produced using the weak Galerkin finite element technique with continous and discrete FEM, on relay , using the backward Euler method in time. Using the elliptic projection operator, we provide L2 error speculation for continues and discretely weak Galerkin finite element.","PeriodicalId":46278,"journal":{"name":"JOURNAL OF INTERDISCIPLINARY MATHEMATICS","volume":"12 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70467799","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we apply Lie group theory to a Hamilton-Jacobi type equation, which is a nonlinear partial differential equation of the first order. We then employ the local inverse theorem to build the Lie invariance condition for this equation. The determining equations are then obtained by using this condition. We split and solve these obtained equations to obtain the symmetries of the equation under study. We obtain the largest solvable Lie algebra. We also obtain the symmetry algebra and make a group classification of this equation. Further, some exact solutions are deduced and represented graphically.
{"title":"Group analysis of a Hamilton–Jacobi type equation","authors":"Jervin Zen Lobo","doi":"10.47974/jim-1646","DOIUrl":"https://doi.org/10.47974/jim-1646","url":null,"abstract":"In this paper, we apply Lie group theory to a Hamilton-Jacobi type equation, which is a nonlinear partial differential equation of the first order. We then employ the local inverse theorem to build the Lie invariance condition for this equation. The determining equations are then obtained by using this condition. We split and solve these obtained equations to obtain the symmetries of the equation under study. We obtain the largest solvable Lie algebra. We also obtain the symmetry algebra and make a group classification of this equation. Further, some exact solutions are deduced and represented graphically.","PeriodicalId":46278,"journal":{"name":"JOURNAL OF INTERDISCIPLINARY MATHEMATICS","volume":"1 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70468456","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
O. Giri, P. B. Shahi, Janani Selvam, Sandeep Poddar, A. Bhaumik
Road safety has emerged as a global priority due to the multifaceted consequences of road traffic accidents (RTAs) in modern society. The study is focused on the development of an accident prediction model (APM) and identifying the influence of geometric factors on road safety. The study section of the highway was divided into 190 identical segments based on geometric characteristics. Eight models have been developed for establishing the relationship between crash numbers and respective parameters. The significance of the models has been validated by the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). The study unveils that the shoulder and lane width, numbers, and radius of the horizontal curve significantly influence RTAs. However, the gradient and shoulder type have less impact on road accident frequency. The research recommendations for the improvement of safety are increasing the radius of the curves, lane, and shoulder width. Similarly, the study suggests the reduction of the number of horizontal curves for the reduction of crash frequency.
{"title":"Effects of road geometric parameters on safety: A case study of Mugling-Narayanghat road in Nepal","authors":"O. Giri, P. B. Shahi, Janani Selvam, Sandeep Poddar, A. Bhaumik","doi":"10.47974/jim-1677","DOIUrl":"https://doi.org/10.47974/jim-1677","url":null,"abstract":"Road safety has emerged as a global priority due to the multifaceted consequences of road traffic accidents (RTAs) in modern society. The study is focused on the development of an accident prediction model (APM) and identifying the influence of geometric factors on road safety. The study section of the highway was divided into 190 identical segments based on geometric characteristics. Eight models have been developed for establishing the relationship between crash numbers and respective parameters. The significance of the models has been validated by the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). The study unveils that the shoulder and lane width, numbers, and radius of the horizontal curve significantly influence RTAs. However, the gradient and shoulder type have less impact on road accident frequency. The research recommendations for the improvement of safety are increasing the radius of the curves, lane, and shoulder width. Similarly, the study suggests the reduction of the number of horizontal curves for the reduction of crash frequency.","PeriodicalId":46278,"journal":{"name":"JOURNAL OF INTERDISCIPLINARY MATHEMATICS","volume":"1 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70469053","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this research, the fixed points of the functions in F = {fc(x) = c csc(x): c, x ∈ ℝ} are investigated. And also, the types of fixed points of the functions in F are investigated. In addition, the some important conditions for convergence of {fcn (x)} as n → ∞ are obtained.
本文研究了F = {fc(x) = c csc(x): c, x∈x}中函数的不动点。同时，研究了函数在F中的不动点的类型。此外，还得到了n→∞时{fcn (x)}收敛的一些重要条件。
{"title":"On fixed points of the transcendental meromorphic functions","authors":"Iman A. Hussain, Zeana Z. Jamil","doi":"10.47974/jim-1517","DOIUrl":"https://doi.org/10.47974/jim-1517","url":null,"abstract":"In this research, the fixed points of the functions in F = {fc(x) = c csc(x): c, x ∈ ℝ} are investigated. And also, the types of fixed points of the functions in F are investigated. In addition, the some important conditions for convergence of {fcn (x)} as n → ∞ are obtained.","PeriodicalId":46278,"journal":{"name":"JOURNAL OF INTERDISCIPLINARY MATHEMATICS","volume":"59 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70467259","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
N. Srimannarayana, F. Ayant, Y. Kumar, D. Kumar, B. Satyanarayana
Many authors have recently provided a number of expressions for a general Eulerian integrals about the multi-variable H-functions. Inspired by these works, we evaluated here a general class of multi-variable Eulerian integrals with modified multi-variable I-function (MMIF) with general arguments, which has been defined in this article. Some of the particular cases have been discussed. These results will help to deduce numerous useful integrals.
{"title":"Multiple eulerian integrals with modified multivariable I-function having general arguments","authors":"N. Srimannarayana, F. Ayant, Y. Kumar, D. Kumar, B. Satyanarayana","doi":"10.47974/jim-1649","DOIUrl":"https://doi.org/10.47974/jim-1649","url":null,"abstract":"Many authors have recently provided a number of expressions for a general Eulerian integrals about the multi-variable H-functions. Inspired by these works, we evaluated here a general class of multi-variable Eulerian integrals with modified multi-variable I-function (MMIF) with general arguments, which has been defined in this article. Some of the particular cases have been discussed. These results will help to deduce numerous useful integrals.","PeriodicalId":46278,"journal":{"name":"JOURNAL OF INTERDISCIPLINARY MATHEMATICS","volume":"1 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70468180","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we discussed about the geo chromatic number cgc (G) of sunlet graph, prism graph, book graph, banana graph, herschel graph, grotzsch graph and also for tree graph.
{"title":"Geo chromatic number of certain graphs","authors":"R. J. Paul, U. Mary","doi":"10.47974/jim-1643","DOIUrl":"https://doi.org/10.47974/jim-1643","url":null,"abstract":"In this paper, we discussed about the geo chromatic number cgc (G) of sunlet graph, prism graph, book graph, banana graph, herschel graph, grotzsch graph and also for tree graph.","PeriodicalId":46278,"journal":{"name":"JOURNAL OF INTERDISCIPLINARY MATHEMATICS","volume":"1 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70468211","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper focuses on the dynamics of the mathematical model by considering the effect of human conduct and the role of immunity on cholera contamination. Since, spreading of infection is commonly modeled with the help of classes of the SIR model, the model is formulated as a SIR model inaugurated with one more compartment B which showcases the concentration of bacteria in the polluted water. We have obtained the basic reproductive rate R0 and showcased local stability as well as global stability through geometrical approach. Without infection, equilibrium point (E0 ) is stable locally in conjunction with globally whenever 0 R <1. Similarly, the stability condition for endemic equilibrium E* is 0 R ≥ 1. Hence, our aim is basically to explore the outcome as to how the alertness of mankind can play an effective role in the dynamics of such infections.
本文通过考虑人类行为的影响和免疫对霍乱污染的作用，重点研究数学模型的动力学。由于感染的传播通常是在SIR模型的类别的帮助下建模的，因此该模型被制定为SIR模型，其中增加了一个隔间B，该隔间B显示了受污染水中细菌的浓度。我们得到了基本繁殖率R0，并通过几何方法展示了局部稳定性和全局稳定性。在没有感染的情况下，当0 R <1时，平衡点E0局部稳定，全局稳定。同样，地方性平衡E*的稳定条件为0 R≥1。因此，我们的目标基本上是探索人类的警觉性如何在这种感染的动态中发挥有效作用的结果。
{"title":"Dynamical analysis of effects of human behavior on cholera in context to specific strata’s","authors":"Chetan Swarup, Sudipa Chauhan, Amulya Chaudhary, Mamta Barik","doi":"10.47974/jim-1650","DOIUrl":"https://doi.org/10.47974/jim-1650","url":null,"abstract":"This paper focuses on the dynamics of the mathematical model by considering the effect of human conduct and the role of immunity on cholera contamination. Since, spreading of infection is commonly modeled with the help of classes of the SIR model, the model is formulated as a SIR model inaugurated with one more compartment B which showcases the concentration of bacteria in the polluted water. We have obtained the basic reproductive rate R0 and showcased local stability as well as global stability through geometrical approach. Without infection, equilibrium point (E0 ) is stable locally in conjunction with globally whenever 0 R <1. Similarly, the stability condition for endemic equilibrium E* is 0 R ≥ 1. Hence, our aim is basically to explore the outcome as to how the alertness of mankind can play an effective role in the dynamics of such infections.","PeriodicalId":46278,"journal":{"name":"JOURNAL OF INTERDISCIPLINARY MATHEMATICS","volume":"80 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70468269","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Max-plus algebra is one of many idempotent semi-rings. The max-plus algebraic structure is semi field while the conventional algebra is a field. Because of their similar structure, various properties and concepts in the conventional algebra such as characteristic equations have max plus algebraic equivalence. The characteristic equation has been proved in the max-plus algebra. The other semi-field is min-plus algebra. Because of the structure in the min-plus algebra is also similar to the conventional algebra, the characteristic equation also has a min-plus algebraic equivalent. In this paper, it is discussed how to prove the characteristic equation of the matrix over conventional algebra into the min-plus algebra. The results are almost the same. The addition and multiplication operations in the conventional algebra are replaced by min and plus operations in the min-plus algebra. In addition, because of the min-plus algebra does not define the subtraction operation, the formulation of the characteristic equation of the matrix over min-plus algebra is not equal to zero.
{"title":"The characteristic equation of the matrix over min-plus algebra","authors":"","doi":"10.47974/jim-1593","DOIUrl":"https://doi.org/10.47974/jim-1593","url":null,"abstract":"Max-plus algebra is one of many idempotent semi-rings. The max-plus algebraic structure is semi field while the conventional algebra is a field. Because of their similar structure, various properties and concepts in the conventional algebra such as characteristic equations have max plus algebraic equivalence. The characteristic equation has been proved in the max-plus algebra. The other semi-field is min-plus algebra. Because of the structure in the min-plus algebra is also similar to the conventional algebra, the characteristic equation also has a min-plus algebraic equivalent. In this paper, it is discussed how to prove the characteristic equation of the matrix over conventional algebra into the min-plus algebra. The results are almost the same. The addition and multiplication operations in the conventional algebra are replaced by min and plus operations in the min-plus algebra. In addition, because of the min-plus algebra does not define the subtraction operation, the formulation of the characteristic equation of the matrix over min-plus algebra is not equal to zero.","PeriodicalId":46278,"journal":{"name":"JOURNAL OF INTERDISCIPLINARY MATHEMATICS","volume":"1 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70468434","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Adel Almalki, Y. M. Alawaideh, B. M. Al-Khamiseh, Samer Alawaideh
A comparative analysis of the Hamiltonian and Lagrangian equations for the Maxwell field was conducted, and it was demonstrated that both methods are equivalent. Dirac’s and Euler’s techniques were employed to handle the Hamiltonian approach. Additionally, a novel fractional Hamilton formulation was developed for the Maxwell field using fractional derivatives. This formulation yielded a fractional Riemann-Liouville derivative operator and a fractional Hamilton function in terms of the variables Ai, Aj, and A0. The effectiveness of this approach was verified by employing it to examine Maxwell’s electrodynamic equation, and the results obtained were in perfect agreement, confirming the validity of the study
{"title":"Hamilton formulation for the electrodynamics of generalized maxwell using fractional derivatives","authors":"Adel Almalki, Y. M. Alawaideh, B. M. Al-Khamiseh, Samer Alawaideh","doi":"10.47974/jim-1594","DOIUrl":"https://doi.org/10.47974/jim-1594","url":null,"abstract":"A comparative analysis of the Hamiltonian and Lagrangian equations for the Maxwell field was conducted, and it was demonstrated that both methods are equivalent. Dirac’s and Euler’s techniques were employed to handle the Hamiltonian approach. Additionally, a novel fractional Hamilton formulation was developed for the Maxwell field using fractional derivatives. This formulation yielded a fractional Riemann-Liouville derivative operator and a fractional Hamilton function in terms of the variables Ai, Aj, and A0. The effectiveness of this approach was verified by employing it to examine Maxwell’s electrodynamic equation, and the results obtained were in perfect agreement, confirming the validity of the study","PeriodicalId":46278,"journal":{"name":"JOURNAL OF INTERDISCIPLINARY MATHEMATICS","volume":"1 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70468509","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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