E. Donkoh, D. Otoo, Shaibu Osman, Maxwell Baafi, Martin Anokye, Ernest Yeboah Boateng
Dengue fever is one of the neglected tropical diseases around the globe and its ravaging effect over the period has been enormous in the affected areas. Globalisation, immigration and urbanization and poor urban planning have become the contributory factors in the spread of infectious diseases. In this paper, a model describing the dynamics of dengue fever incorporated with infection immigrants is formulated and analysed using ordinary differential equations with a constant immigration recruitment rate. The model was qualitatively and quantitatively analysed for its local stability, basic reproductive number and sensitivity of the model parameters values to the basic reproductive number to understand the impact of the parameters on the disease spread. In the analysis, it was found that in the presence of infectious immigrants, there cannot be a disease free state demonstrated by ∅ ≥ 0 where the model demonstrates a unique endemic equilibrium state if the fraction of infectious immigrants ∅ is positive. The unique endemic equilibrium for which there is a fraction of infectious immigrants is globally asymptotically stable. Numerical simulation was performed and the results displayed graphically and discussed. It was revealed that immigration of infected immigrants contributes significantly in the spread of dengue fever and that it can be controlled by preventing the influx of infected immigrants and reducing the mosquitoes and human contact rate.
{"title":"Mathematical modelling of transmission dynamics of Dengue Fever in the presence of infective immigrants","authors":"E. Donkoh, D. Otoo, Shaibu Osman, Maxwell Baafi, Martin Anokye, Ernest Yeboah Boateng","doi":"10.59400/jam.v2i3.160","DOIUrl":"https://doi.org/10.59400/jam.v2i3.160","url":null,"abstract":"Dengue fever is one of the neglected tropical diseases around the globe and its ravaging effect over the period has been enormous in the affected areas. Globalisation, immigration and urbanization and poor urban planning have become the contributory factors in the spread of infectious diseases. In this paper, a model describing the dynamics of dengue fever incorporated with infection immigrants is formulated and analysed using ordinary differential equations with a constant immigration recruitment rate. The model was qualitatively and quantitatively analysed for its local stability, basic reproductive number and sensitivity of the model parameters values to the basic reproductive number to understand the impact of the parameters on the disease spread. In the analysis, it was found that in the presence of infectious immigrants, there cannot be a disease free state demonstrated by ∅ ≥ 0 where the model demonstrates a unique endemic equilibrium state if the fraction of infectious immigrants ∅ is positive. The unique endemic equilibrium for which there is a fraction of infectious immigrants is globally asymptotically stable. Numerical simulation was performed and the results displayed graphically and discussed. It was revealed that immigration of infected immigrants contributes significantly in the spread of dengue fever and that it can be controlled by preventing the influx of infected immigrants and reducing the mosquitoes and human contact rate.","PeriodicalId":504292,"journal":{"name":"Journal of AppliedMath","volume":"15 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141926295","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}
A. Yalnaik, Mookanahallipatna Shivanna Ranganath, Veerabhadraiah Lokesha, Raju Basavaraju Jummannaver
The M-polynomial yields degree based topological indices that anticipate different physical and chemical properties of material being scrutinized. In this work, M- polynomial of linear chains of perylene and coronene are acquired. From M-polynomial, some degree based topological dicriptors are determined. Some topological indices of these compounds are compared by plotting graphs.
M-多项式产生基于度数的拓扑指数，可预测被研究材料的不同物理和化学特性。在这项工作中，获得了过烯烃和冠烯线性链的 M 多项式。根据 M 多项式，确定了一些基于度的拓扑二叉。通过绘制图表，对这些化合物的一些拓扑指数进行了比较。
{"title":"Computation of topological indices of linear chains of perylene and coronene using M-polynomial","authors":"A. Yalnaik, Mookanahallipatna Shivanna Ranganath, Veerabhadraiah Lokesha, Raju Basavaraju Jummannaver","doi":"10.59400/jam.v2i3.563","DOIUrl":"https://doi.org/10.59400/jam.v2i3.563","url":null,"abstract":"The M-polynomial yields degree based topological indices that anticipate different physical and chemical properties of material being scrutinized. In this work, M- polynomial of linear chains of perylene and coronene are acquired. From M-polynomial, some degree based topological dicriptors are determined. Some topological indices of these compounds are compared by plotting graphs.","PeriodicalId":504292,"journal":{"name":"Journal of AppliedMath","volume":"59 31","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141804717","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}
Elvis Kobina Donkor, Bismark Ansu, Shaibu Osman, D. Otoo, W. Onsongo, Ernest Yeboah Boateng
Syphilis is a sexually transmitted infection which when left untreated wouldlead to major health problems. Syphilis can easily be contracted by direct contact withSyphilis sore during vaginal, anal, or oral sex. Syphilis can also be passed on froman infected mother to her unborn child. In this paper, a nonlinear deterministic modelof Syphilis disease was constructed to determine the dynamics of Syphilis infections.The study deduced model’s equilibria and analyzed the local and global stability ofthese equilibria. The model was extended to optimal control problem by adding timedependent controls that helped characterize a range of possible controls that minimizedthe disease. The control system was solved qualitatively and numerically to evaluatethe effectiveness of the considered controls using Pontryagin’s Maximum Principle.The analysis indicated that strategies B and C are considered most effective as theysubstantially minimized the exposed, asymptomatic and symptomatic infectious. Werecommend that stakeholders should consider strategy B and C in their effort to mitigate the disease from the population as they all have the same effect of substantiallyminimizing the exposed, symptomatic and asymptomatic populations.
梅毒是一种性传播疾病，如果不及时治疗会导致严重的健康问题。通过阴道、肛门或口交直接接触梅毒疮很容易感染梅毒。梅毒还可以通过受感染的母亲传染给胎儿。本文构建了梅毒疾病的非线性确定性模型，以确定梅毒感染的动态变化。研究推导了模型的均衡点，并分析了这些均衡点的局部和全局稳定性。该研究推导出了模型的均衡点，并分析了这些均衡点的局部和全局稳定性。通过添加与时间相关的控制，该模型被扩展为最优控制问题，这有助于确定一系列可能的控制措施，从而最大限度地减少疾病的发生。分析表明，策略 B 和 C 被认为是最有效的，因为它们大大减少了暴露、无症状和有症状的传染性。我们建议利益相关者在努力减少人口中的疾病时应考虑策略 B 和 C，因为它们都有同样的效果，即大大减少暴露人群、无症状人群和无症状人群。
{"title":"Modelling the dynamics of syphilis infection with personal protection and treatment as optimal control strategies","authors":"Elvis Kobina Donkor, Bismark Ansu, Shaibu Osman, D. Otoo, W. Onsongo, Ernest Yeboah Boateng","doi":"10.59400/jam.v2i3.179","DOIUrl":"https://doi.org/10.59400/jam.v2i3.179","url":null,"abstract":"Syphilis is a sexually transmitted infection which when left untreated wouldlead to major health problems. Syphilis can easily be contracted by direct contact withSyphilis sore during vaginal, anal, or oral sex. Syphilis can also be passed on froman infected mother to her unborn child. In this paper, a nonlinear deterministic modelof Syphilis disease was constructed to determine the dynamics of Syphilis infections.The study deduced model’s equilibria and analyzed the local and global stability ofthese equilibria. The model was extended to optimal control problem by adding timedependent controls that helped characterize a range of possible controls that minimizedthe disease. The control system was solved qualitatively and numerically to evaluatethe effectiveness of the considered controls using Pontryagin’s Maximum Principle.The analysis indicated that strategies B and C are considered most effective as theysubstantially minimized the exposed, asymptomatic and symptomatic infectious. Werecommend that stakeholders should consider strategy B and C in their effort to mitigate the disease from the population as they all have the same effect of substantiallyminimizing the exposed, symptomatic and asymptomatic populations.","PeriodicalId":504292,"journal":{"name":"Journal of AppliedMath","volume":"44 19","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141809504","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}
Despite partial solutions by famous scientists during the early Industrial Revolution, gyroscope problems remained unsolvable until the beginning of the twentieth century when several fundamental physical laws were finally formulated to describe them. Today, the principles of classical mechanics enable the formulation and description of the physical processes involved in the rotation of any object. Gyroscopic devices are objects that rotate and exhibit oscillation, which has been a challenging problem in engineering mechanics. The oscillation of a gyroscope is caused by the interaction between external and inertial torques. This is different from other examples of oscillation, such as pendulums and springs, which have been well documented. The main difference in the physics of gyroscopic oscillation is that the spinning rotors of the gyroscopic devices are supported on one side, with their axes perpendicular to the axis of oscillation. The oscillation of gyroscopic devices is interrelated with the potential and kinetic energy of their components. However, the physics of oscillation of such objects has not been fully described in publications until recently. The theory of gyroscopic effects for rotating objects has now been published and provides a solution to this problem. According to this theory, gyroscopic inertial torques represent the potential energy of the external torque and kinetic energy of the spinning rotor. This paper demonstrates the distribution of inertial torques about the axes of Cartesian coordinates, which enables the computation of gyroscope motion and oscillation.
{"title":"Fundamental properties of the gyroscope oscillation","authors":"R. Usubamatov","doi":"10.59400/jam.v2i3.532","DOIUrl":"https://doi.org/10.59400/jam.v2i3.532","url":null,"abstract":"Despite partial solutions by famous scientists during the early Industrial Revolution, gyroscope problems remained unsolvable until the beginning of the twentieth century when several fundamental physical laws were finally formulated to describe them. Today, the principles of classical mechanics enable the formulation and description of the physical processes involved in the rotation of any object. Gyroscopic devices are objects that rotate and exhibit oscillation, which has been a challenging problem in engineering mechanics. The oscillation of a gyroscope is caused by the interaction between external and inertial torques. This is different from other examples of oscillation, such as pendulums and springs, which have been well documented. The main difference in the physics of gyroscopic oscillation is that the spinning rotors of the gyroscopic devices are supported on one side, with their axes perpendicular to the axis of oscillation. The oscillation of gyroscopic devices is interrelated with the potential and kinetic energy of their components. However, the physics of oscillation of such objects has not been fully described in publications until recently. The theory of gyroscopic effects for rotating objects has now been published and provides a solution to this problem. According to this theory, gyroscopic inertial torques represent the potential energy of the external torque and kinetic energy of the spinning rotor. This paper demonstrates the distribution of inertial torques about the axes of Cartesian coordinates, which enables the computation of gyroscope motion and oscillation.","PeriodicalId":504292,"journal":{"name":"Journal of AppliedMath","volume":" 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141828988","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 address the general case of a light clock in uniform translational motion parallel to itself and perpendicular to its uniform velocity v, as well as the case of the light clock in relativistic hyperbolic motion. Neither case has been previously addressed in the specialized literature, which typically restricts itself to canonical orientations where the light clock moves parallel to either the vertical or horizontal axis with uniform velocity, without acceleration. Therefore, it becomes interesting to study the more general case where the clock has an arbitrary orientation and/or is accelerated. Our paper is divided into two main sections. The first section deals with the light clock moving with constant velocity, oriented at an arbitrary angle with respect to the x-axis. We prove that the moving clock exhibits a standard time dilation, identical to that of a light clock moving in a canonical orientation. The second section deals with the light clock moving with constant acceleration, i.e., in hyperbolic motion. For the light clock in hyperbolic motion, we derive the period as measured from the perspective of an inertial frame and draw parallels with the case of uniform motion, outlining a term that is similar (but not identical) to the γ factor of uniform motion. We also point out that this factor depends not only on acceleration but also on the height of the light clock. This dependency on the dimension of the light clock distinguishes the accelerated case from the case of uniform motion. The first three sections deal with the theoretical aspects of light (optical) clocks, while the fourth section addresses the experimental implementations of optical clocks.
在本文中，我们讨论了光钟在平行于自身和垂直于其匀速 v 的匀速平移运动中的一般情况，以及光钟在相对论双曲运动中的情况。这两种情况以前在专业文献中都没有涉及过，因为专业文献通常局限于典型的方向，即光钟平行于垂直轴或水平轴匀速运动，没有加速度。因此，研究时钟具有任意方向和/或加速度的更一般情况就变得很有趣了。本文分为两个主要部分。第一部分涉及相对于 x 轴以任意角度匀速运动的光钟。我们证明了移动时钟表现出的标准时间膨胀，与以典型方向移动的光钟的时间膨胀相同。第二部分涉及以恒定加速度运动的光钟，即双曲运动的光钟。对于双曲线运动的光钟，我们推导出从惯性框架角度测量的周期，并将其与匀速运动的情况进行比较，勾勒出一个与匀速运动的 γ 因子相似（但不完全相同）的项。我们还指出，这个系数不仅取决于加速度，还取决于光钟的高度。这种对光钟尺寸的依赖性将加速运动与匀速运动区分开来。前三节涉及光（光学）钟的理论方面，第四节讨论光钟的实验实现。
{"title":"Relativistic light clocks: Arbitrary orientation in uniform motion and hyperbolic motion analysis","authors":"A. Sfarti","doi":"10.59400/jam.v2i2.405","DOIUrl":"https://doi.org/10.59400/jam.v2i2.405","url":null,"abstract":"In this paper, we address the general case of a light clock in uniform translational motion parallel to itself and perpendicular to its uniform velocity v, as well as the case of the light clock in relativistic hyperbolic motion. Neither case has been previously addressed in the specialized literature, which typically restricts itself to canonical orientations where the light clock moves parallel to either the vertical or horizontal axis with uniform velocity, without acceleration. Therefore, it becomes interesting to study the more general case where the clock has an arbitrary orientation and/or is accelerated. Our paper is divided into two main sections. The first section deals with the light clock moving with constant velocity, oriented at an arbitrary angle with respect to the x-axis. We prove that the moving clock exhibits a standard time dilation, identical to that of a light clock moving in a canonical orientation. The second section deals with the light clock moving with constant acceleration, i.e., in hyperbolic motion. For the light clock in hyperbolic motion, we derive the period as measured from the perspective of an inertial frame and draw parallels with the case of uniform motion, outlining a term that is similar (but not identical) to the γ factor of uniform motion. We also point out that this factor depends not only on acceleration but also on the height of the light clock. This dependency on the dimension of the light clock distinguishes the accelerated case from the case of uniform motion. The first three sections deal with the theoretical aspects of light (optical) clocks, while the fourth section addresses the experimental implementations of optical clocks.","PeriodicalId":504292,"journal":{"name":"Journal of AppliedMath","volume":"52 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141355216","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}
Numerous dark matter studies of galactic halo gravitation depend on models with core radius r0 and central density ρ0. Central surface density product ρ0r0 is found to be nearly a universal constant for a large range of galaxies. Standard variational field theory with Weyl conformal symmetry postulated for gravitation and the Higgs scalar field, without dark matter, implies nonclassical centripetal acceleration ∆a, for a = aN +∆a, where Newtonian acceleration aN is due to observable baryonic matter. Neglecting a halo cutoff at very large galactic radius, conformal ∆a is constant over the entire halo and a = aN + ∆a is a universal function, consistent with a recent study of galaxies, with independently measured mass, that constrains acceleration due to dark matter or to alternative theory. An equivalent dark matter source would be a pure cusp distribution with cutoff parameter determined by a halo boundary radius. This is shown to imply universal central surface density for any dark matter core model.
许多关于星系晕引力的暗物质研究都依赖于具有核心半径r0和中心密度ρ0的模型。研究发现，中心表面密度乘积ρ0r0对于大量星系来说几乎是一个普遍常数。在没有暗物质的情况下，假设引力和希格斯标量场具有韦尔保角对称性的标准变分场论意味着非经典的向心加速度Δa，为a = aN +Δa，其中牛顿加速度aN是由可观测到的重子物质引起的。如果不考虑星系半径非常大时的光晕截断，共形 ∆a 在整个光晕中是恒定的，而 a = aN + ∆a 是一个普遍函数，这与最近一项独立测量质量的星系研究是一致的，它限制了暗物质或替代理论引起的加速度。一个等效的暗物质源将是一个纯粹的尖顶分布，其截止参数由光环边界半径决定。这意味着任何暗物质核心模型都具有普遍的中心表面密度。
{"title":"Conformal theory of central surface density for galactic dark halos","authors":"R. K. Nesbet","doi":"10.59400/jam.v2i1.465","DOIUrl":"https://doi.org/10.59400/jam.v2i1.465","url":null,"abstract":"Numerous dark matter studies of galactic halo gravitation depend on models with core radius r0 \u0000and central density ρ0. Central surface density product ρ0r0 is found to be nearly a universal constant \u0000for a large range of galaxies. Standard variational field theory with Weyl conformal symmetry \u0000postulated for gravitation and the Higgs scalar field, without dark matter, implies nonclassical \u0000centripetal acceleration ∆a, for a = aN +∆a, where Newtonian acceleration aN is due to observable \u0000baryonic matter. Neglecting a halo cutoff at very large galactic radius, conformal ∆a is constant \u0000over the entire halo and a = aN + ∆a is a universal function, consistent with a recent study of \u0000galaxies, with independently measured mass, that constrains acceleration due to dark matter or to \u0000alternative theory. An equivalent dark matter source would be a pure cusp distribution with cutoff \u0000parameter determined by a halo boundary radius. This is shown to imply universal central surface \u0000density for any dark matter core model.","PeriodicalId":504292,"journal":{"name":"Journal of AppliedMath","volume":" 37","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140999267","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}
One of the most widespread interpretations of the mass-energy equivalence establishes that not only can mass be transformed into energy (e.g., through nuclear fission, fusion, or annihilation) but that every type of energy also has mass (via the mass-energy equivalence formula). Here, we show that this is not always the case. With the help a few thought experiments, we show that, for instance, the electric potential energy of a charged capacitor should not contribute to the capacitor’s gravitational rest mass (while still contributing to its linear momentum). That result is in agreement with the fact that light (ultimately, an electromagnetic phenomenon) has momentum but not rest mass.
{"title":"Mass-energy equivalence and the gravitational redshift: Does energy always have mass?","authors":"G. D’Abramo","doi":"10.59400/jam.v2i2.525","DOIUrl":"https://doi.org/10.59400/jam.v2i2.525","url":null,"abstract":"One of the most widespread interpretations of the mass-energy equivalence establishes that not only can mass be transformed into energy (e.g., through nuclear fission, fusion, or annihilation) but that every type of energy also has mass (via the mass-energy equivalence formula). Here, we show that this is not always the case. With the help a few thought experiments, we show that, for instance, the electric potential energy of a charged capacitor should not contribute to the capacitor’s gravitational rest mass (while still contributing to its linear momentum). That result is in agreement with the fact that light (ultimately, an electromagnetic phenomenon) has momentum but not rest mass.","PeriodicalId":504292,"journal":{"name":"Journal of AppliedMath","volume":" 39","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140691668","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 have considered normal paracontact metric space forms ad- mitting (α, β) −type almost η−Ricci-Yamabe solitons by means of some curvature ten- sors. Ricci pseudosymmetry concepts of normal paracontact metric space forms admit- ting (α, β) −type almost η−Ricci-Yamabe soliton have introduced according to choos- ing of some special curvature tensors such as Riemann, concircular, projective, W1 curvature tensor. After that, according to choosing of the curvature tensors, necessary conditions are given for normal paracontact metric space form admitting (α, β) −type almost η−Ricci-Yamabe soliton to be Ricci semisymmetric. Then some characteriza- tions are obtained and some classifications are made under the some conditions.
{"title":"Pseudosymmetric normal paracontact metric space forms admitting (α, β)− type almost η−Ricci-Yamabe solitons","authors":"Tuğba Mert, M. Atc̣eken","doi":"10.59400/jam.v2i2.231","DOIUrl":"https://doi.org/10.59400/jam.v2i2.231","url":null,"abstract":"In this paper, we have considered normal paracontact metric space forms ad- mitting (α, β) −type almost η−Ricci-Yamabe solitons by means of some curvature ten- sors. Ricci pseudosymmetry concepts of normal paracontact metric space forms admit- ting (α, β) −type almost η−Ricci-Yamabe soliton have introduced according to choos- ing of some special curvature tensors such as Riemann, concircular, projective, W1 curvature tensor. After that, according to choosing of the curvature tensors, necessary conditions are given for normal paracontact metric space form admitting (α, β) −type almost η−Ricci-Yamabe soliton to be Ricci semisymmetric. Then some characteriza- tions are obtained and some classifications are made under the some conditions.","PeriodicalId":504292,"journal":{"name":"Journal of AppliedMath","volume":"52 44","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140795970","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 aim of this paper is to propose a new iterative algorithm (scheme or method) for solving algebraic and transcendental equations considering fixed point and an initial guess value on the x-axis. The concepts of slope of a line and Taylor series are used in the derivation. The algorithm has second-order convergence and requires two function evaluations in each step, which shows that it is optimal with computational efficiency index 1.414 and informational efficiency 1. The validity of the algorithm is examined by solving some examples and their comparisons with the Newton’s method.
本文旨在提出一种新的迭代算法（方案或方法），用于求解代数方程和超越方程，并考虑 x 轴上的定点和初始猜测值。在推导过程中使用了直线斜率和泰勒级数的概念。该算法具有二阶收敛性，每一步需要两次函数求值，这表明该算法是最优的，计算效率指数为 1.414，信息效率为 1。通过求解一些例子及其与牛顿法的比较，检验了该算法的有效性。
{"title":"A new optimal iterative algorithm for solving nonlinear equations","authors":"Dhyan R. Gorashiya, Rajesh C. Shah","doi":"10.59400/jam.v2i1.477","DOIUrl":"https://doi.org/10.59400/jam.v2i1.477","url":null,"abstract":"The aim of this paper is to propose a new iterative algorithm (scheme or method) for solving algebraic and transcendental equations considering fixed point and an initial guess value on the x-axis. The concepts of slope of a line and Taylor series are used in the derivation. The algorithm has second-order convergence and requires two function evaluations in each step, which shows that it is optimal with computational efficiency index 1.414 and informational efficiency 1. The validity of the algorithm is examined by solving some examples and their comparisons with the Newton’s method.","PeriodicalId":504292,"journal":{"name":"Journal of AppliedMath","volume":"76 16","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140371433","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}
Sanjukta Pramanik, Krishna Pada Das, P. Karmakar, Seema Sarkar (Mondal)
This paper deals with the various definitions involved in the very old yet novel topic called fractional calculus. This survey intends to report some of the major works carried out in the arena of fractional calculus that took place since 2010. Fractional calculus is a prominent topic for research within the discipline of applied mathematics doe to its usefulness in solving problems in several different branches of science, engineering, medicine, finance, economics and the likes. With the various definitions involved in this field, we explore the various models taken into consideration to study the effect and impact of fractional calculus to understand how the dynamics of such models change.
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