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Indian Journal of Advanced Mathematics最新文献

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The Triple Product Rule is Incorrect 三重积法则不正确
Indian Journal of Advanced Mathematics Pub Date : 2021-10-10 DOI: 10.35940/IJAM.B1102.101221
I. Stepanov
{"title":"The Triple Product Rule is Incorrect","authors":"I. Stepanov","doi":"10.35940/IJAM.B1102.101221","DOIUrl":"https://doi.org/10.35940/IJAM.B1102.101221","url":null,"abstract":"The triple product rule, also known as the cyclic chain rule, cyclic relation, cyclical rule or Euler’s chain rule, relates the partial derivatives of three interdependent variables, and often finds application in thermodynamics. It is shown here that its derivation is wrong, and that this rule is not correct; hence, the Mayer’s relation and the heat capacity ratio, which describe the difference between isobaric and isochoric heat capacities, are also untrue. Also, the relationship linking thermal expansion and isothermal compressibility is wrong. These results are confirmed by many experiments and by the previous theoretical findings of the author.","PeriodicalId":366142,"journal":{"name":"Indian Journal of Advanced Mathematics","volume":"190 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123191370","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}
引用次数: 0
Special Diophantine Triples InvolvingSquare Pyramidal Numbers 涉及方形金字塔数的特殊丢番图三元组
Indian Journal of Advanced Mathematics Pub Date : 2021-10-10 DOI: 10.54105/ijam.b1108.101221
C. Saranya, B. Achya
{"title":"Special Diophantine Triples InvolvingSquare Pyramidal Numbers","authors":"C. Saranya, B. Achya","doi":"10.54105/ijam.b1108.101221","DOIUrl":"https://doi.org/10.54105/ijam.b1108.101221","url":null,"abstract":"In this communication, we accomplish special Diophantine triples comprising of square pyramidal numbers such that the product of any two members of the set added by their sum and increased by a polynomial with integer coefficient is a perfect square.","PeriodicalId":366142,"journal":{"name":"Indian Journal of Advanced Mathematics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116151798","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}
引用次数: 0
Adam-Bash forth-Multan Predictor Corrector Method for Solving First Order Initial value problem and Its Error Analysis 解决一阶初值问题的 Adam-Bash forth-Multan Predictor Corrector 方法及其误差分析
Indian Journal of Advanced Mathematics Pub Date : 2021-10-10 DOI: 10.54105/ijam.b1112.101221
Kedir Aliyi Koroche, Geleta Kinkino Mayu
{"title":"Adam-Bash forth-Multan Predictor Corrector Method for Solving First Order Initial value problem and Its Error Analysis","authors":"Kedir Aliyi Koroche, Geleta Kinkino Mayu","doi":"10.54105/ijam.b1112.101221","DOIUrl":"https://doi.org/10.54105/ijam.b1112.101221","url":null,"abstract":"This paper presents fourth order Adams predictor corrector numerical scheme for solving initial value problem. First, the solution domain is discretized. Then the derivatives in the given initial value problem are replaced by finite difference approximations and the numerical scheme that provides algebraic systems of difference equations is developed. The starting points are obtained by using fourth order Runge-Kutta method and then applying the present method to finding the solution of Initial value problem. To validate the applicability of the method, two model examples are solved for different values of mesh size. The stability and convergence of the present method have been investigated. The numerical results are presented by tables and graphs. The present method helps us to get good results of the solution for small value of mesh size h. The proposed method approximates the exact solution very well. Moreover, the present method improves the findings of some existing numerical methods reported in the literature.","PeriodicalId":366142,"journal":{"name":"Indian Journal of Advanced Mathematics","volume":" 35","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120828815","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}
引用次数: 0
On Symmetric Riemann-Derivatives 关于对称黎曼导数
Indian Journal of Advanced Mathematics Pub Date : 2021-10-10 DOI: 10.35940/IJAM.B1114.101221
S. Deb
{"title":"On Symmetric Riemann-Derivatives","authors":"S. Deb","doi":"10.35940/IJAM.B1114.101221","DOIUrl":"https://doi.org/10.35940/IJAM.B1114.101221","url":null,"abstract":"The basic properties like monotoni city, Darboux property, mean value property of symmetric Riemann-derivatives of order n of a real valued function f at a point x of its domain (a closed interval) is studied. In some cases, function is considered to be continuous or semi-continuous.","PeriodicalId":366142,"journal":{"name":"Indian Journal of Advanced Mathematics","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123749881","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}
引用次数: 0
Weighted Average Based Differential Quadrature Method for One-Dimensional Homogeneous First Order Nonlinear Parabolic Partial Differential Equation 一维齐次一阶非线性抛物型偏微分方程的加权平均微分求积分法
Indian Journal of Advanced Mathematics Pub Date : 2021-04-10 DOI: 10.35940/IJAM.B1104.041121
Kedir Aliyi Koroche
{"title":"Weighted Average Based Differential Quadrature Method for One-Dimensional Homogeneous First Order Nonlinear Parabolic Partial Differential Equation","authors":"Kedir Aliyi Koroche","doi":"10.35940/IJAM.B1104.041121","DOIUrl":"https://doi.org/10.35940/IJAM.B1104.041121","url":null,"abstract":"In this paper, the weighted average-based differential quadrature method is presented for solving one-dimensional homogeneous first-order non-linear parabolic partial differential equation. First, the given solution domain is discretized by using uniform discretization grid point. Next, by using Taylor series expansion we obtain central finite difference discretization of the partial differential equation involving with temporal variable associated with weighted average of partial derivative concerning spatial variable. From this, we obtain the system of nonlinear ordinary differential equations and it is linearized by using the quasilinearization method. Then by using the polynomial-based differential quadrature method for approximating derivative involving with spatial variable at specified grid point, we obtain the system of linear equation. Then they obtained linear system equation is solved by using the LU matrix decomposition method. To validate the applicability of the proposed method, two model examples are considered and solved at each specific grid point on its solution domain. The stability and convergent analysis of the present method is worked by supported the theoretical and mathematical statements and the accuracy of the solution is obtained. The accuracy of the present method has been shown in the sense of root mean square error norm and maximum absolute error norm and the local behavior of the solution is captured exactly. Numerical versus exact solutions and behavior of maximum absolute error between them have been presented in terms of graphs and the corresponding root mean square error norm and maximum absolute error norm presented in tables. The present method approximates the exact solution very well and it is quite efficient and practically well suited for solving the non-linear parabolic equation. The numerical result presented in tables and graphs indicates that the approximate solution is in good agreement with the exact solution.","PeriodicalId":366142,"journal":{"name":"Indian Journal of Advanced Mathematics","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128389603","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}
引用次数: 2
Modified Moments and Maximum Likelihood Estimators for Parameters of Erlang Truncated Exponential Distribution Erlang截断指数分布参数的修正矩和极大似然估计
Indian Journal of Advanced Mathematics Pub Date : 2021-04-10 DOI: 10.35940/IJAM.B1106.041121
Kannan Karuppaiah, Vinoth Raman
{"title":"Modified Moments and Maximum Likelihood Estimators for Parameters of Erlang Truncated Exponential Distribution","authors":"Kannan Karuppaiah, Vinoth Raman","doi":"10.35940/IJAM.B1106.041121","DOIUrl":"https://doi.org/10.35940/IJAM.B1106.041121","url":null,"abstract":"This study derives the parameter estimation in truncated form of a continuous distribution which is comparable to Erlang truncated exponential distribution. The shape and scale parameter will predict the whole distributions properties. Approximation will be useful in making the mathematical calculation an easy understand for non-mathematician or statistician. An explicit mathematical derivation is seen for some properties of, Method of Moments, Skewness, Kurtosis, Mean and Variance, Maximum Likelihood Function and Reliability Analysis. We compared ratio and regression estimators empirically based on bias and coefficient of variation.","PeriodicalId":366142,"journal":{"name":"Indian Journal of Advanced Mathematics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130634803","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}
引用次数: 0
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