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Indian Journal of Advanced Mathematics最新文献

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Derivation And Implementation of a Fifth Stage Fourth Order Explicit Runge-Kutta Formula using 𝑓(𝑥,𝑦) Functional Derivatives 使用 𝑓(𝑥,𝑦) 函数导数的第五阶段四阶显式 Runge-Kutta 公式的推导与实现
Indian Journal of Advanced Mathematics Pub Date : 2023-12-30 DOI: 10.54105/ijam.a1144.043123
Esekhaigbe Aigbedion Christopher
{"title":"Derivation And Implementation of a Fifth Stage Fourth Order Explicit Runge-Kutta Formula using 𝑓(𝑥,𝑦) Functional Derivatives","authors":"Esekhaigbe Aigbedion Christopher","doi":"10.54105/ijam.a1144.043123","DOIUrl":"https://doi.org/10.54105/ijam.a1144.043123","url":null,"abstract":"This paper is aimed at using 𝒇(𝒙,𝒚) functional derivatives to derive a fifth stage fourth order Explicit Runge-Kutta formula for solving initial value problems in Ordinary Differential Equations. The 𝒇(𝒙,𝒚) functional derivatives from the general Runge-Kutta scheme will be compared with the 𝒇(𝒙,𝒚) functional derivatives from the Taylor series expansion to derive the method. The method will be implemented on some initial value problems, and results compared with results from the classical fourth order method. The results revealed that the method compared favorably well with the existing classical fourth order method.","PeriodicalId":366142,"journal":{"name":"Indian Journal of Advanced Mathematics","volume":" 19","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139139527","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
Ramanujan’s Tau-Function in Terms of Bell Polynomials 用贝尔多项式表示的拉马努金的tau函数
Indian Journal of Advanced Mathematics Pub Date : 2023-10-30 DOI: 10.54105/ijam.b1157.103223
Dr. R. Sivaraman, H. N. Núñez-Yépez, Prof. J. López-Bonilla
{"title":"Ramanujan’s Tau-Function in Terms of Bell Polynomials","authors":"Dr. R. Sivaraman, H. N. Núñez-Yépez, Prof. J. López-Bonilla","doi":"10.54105/ijam.b1157.103223","DOIUrl":"https://doi.org/10.54105/ijam.b1157.103223","url":null,"abstract":"We obtain a recurrence relation for the Ramanujan’s tau-function involving the sum of divisors function, and the solution of this recurrence gives a closed formula for 𝝉(𝒏) in terms of the complete Bell polynomials","PeriodicalId":366142,"journal":{"name":"Indian Journal of Advanced Mathematics","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136019522","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 the Polynomial Structure of 𝑟𝑘(𝑛) 论𝑟𝑘(𝑛) 的多项式结构
Indian Journal of Advanced Mathematics Pub Date : 2023-10-30 DOI: 10.54105/ijam.a1162.103223
Dr.R. Sivaraman, Prof. J. López-Bonilla, S. Vidal-Beltrán
{"title":"On the Polynomial Structure of 𝑟𝑘(𝑛)","authors":"Dr.R. Sivaraman, Prof. J. López-Bonilla, S. Vidal-Beltrán","doi":"10.54105/ijam.a1162.103223","DOIUrl":"https://doi.org/10.54105/ijam.a1162.103223","url":null,"abstract":"If 𝒓𝒌(𝒏) is the number of representations of a positive integer n as the sum of k squares, then 𝒓𝒌(𝒏) is a polynomial in k of degree n; here we exhibit expressions for certain coefficients through this polynomial.","PeriodicalId":366142,"journal":{"name":"Indian Journal of Advanced Mathematics","volume":"23 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139309769","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
Algebraizations of Propositional Logic and Monadic Logic 命题逻辑和一元逻辑的代数化
Indian Journal of Advanced Mathematics Pub Date : 2023-04-30 DOI: 10.54105/ijam.a1141.043123
A. M. Al-Odhari
{"title":"Algebraizations of Propositional Logic and Monadic Logic","authors":"A. M. Al-Odhari","doi":"10.54105/ijam.a1141.043123","DOIUrl":"https://doi.org/10.54105/ijam.a1141.043123","url":null,"abstract":"In this paper, we introduce the language systems of propositional logic (LSPL), which involves no variables, and monadic predicate logic (LSMPL), which consists of predicates applied to single variables. We review the validity and dedication related to (LSPL) and (LSMPL) with their properties. After that, we investigate the connection between Boolean algebras with (LSPL) and (LSMPL) to make algebraizations methods out of logic.","PeriodicalId":366142,"journal":{"name":"Indian Journal of Advanced Mathematics","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116860286","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
Pseudo Number 0.999... 伪数0.999…
Indian Journal of Advanced Mathematics Pub Date : 2023-04-30 DOI: 10.54105/ijam.a1148.043123
Sumit Gehlot
{"title":"Pseudo Number 0.999...","authors":"Sumit Gehlot","doi":"10.54105/ijam.a1148.043123","DOIUrl":"https://doi.org/10.54105/ijam.a1148.043123","url":null,"abstract":"As we know that the number 0.999... is a rational number and mathematicians, teachers and students of mathematics generally wonder whether the number 0.999... and the number 1 are really equal or not. This problem is one of the ancient problems of mathematics and is generally the most asked problem. While trying to solve the above problem, a new fact is found that the number 0.999... is not a real problem and with this a satisfactory solution of the above problem is obtained. In this paper, we do analysis about the existence of the number 0.999... on the real number line and prove that the number 0.999... is only a virtual number.","PeriodicalId":366142,"journal":{"name":"Indian Journal of Advanced Mathematics","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125433680","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
Proofs of Beal’s Conjecture, Fermat’s Conjecture, Collatz Conjecture and Goldbach Conjecture 比尔猜想、费马猜想、柯拉茨猜想和哥德巴赫猜想的证明
Indian Journal of Advanced Mathematics Pub Date : 2023-04-30 DOI: 10.54105/ijam.a1137.043123
Nishad T M, Dr. Mohamed M Azzedine
{"title":"Proofs of Beal’s Conjecture, Fermat’s Conjecture, Collatz Conjecture and Goldbach Conjecture","authors":"Nishad T M, Dr. Mohamed M Azzedine","doi":"10.54105/ijam.a1137.043123","DOIUrl":"https://doi.org/10.54105/ijam.a1137.043123","url":null,"abstract":"In this article the elementary mathematical methods are used to prove Beal’s Conjecture, Fermat’s Conjecture, Collatz Conjecture and Goldbach Conjecture.","PeriodicalId":366142,"journal":{"name":"Indian Journal of Advanced Mathematics","volume":"222 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135564026","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 the Results of Coffy and Moli 关于Coffy和Moli的结果
Indian Journal of Advanced Mathematics Pub Date : 2023-04-30 DOI: 10.54105/ijam.a1142.043123
A. Puranik
{"title":"On the Results of Coffy and Moli","authors":"A. Puranik","doi":"10.54105/ijam.a1142.043123","DOIUrl":"https://doi.org/10.54105/ijam.a1142.043123","url":null,"abstract":"The primary aim of this article is Generalization leading to search of integrals of the type∫ 𝒍𝒐𝒈𝑷 𝒍𝒐𝒈𝑸 𝒅𝒙 = ∫ 𝑭𝑮 𝒏𝒅𝒙 where both P, Q are functions of x only and also verification of results by using new trend. In this direction of verification, converting integrals into ordinary differential equations and finding the solutions, has significant trend and fresh impetus in the recent years. In this paper, along with the generalization of integrals, formation of ordinary differential equations and their solutions were also listed. Here in this article we obtained significant differential equations based on integrals of Russell [1], type. In the first part, generalizations of preliminary lemmas along with new integrals of logarithmic integrand were evaluated on the lines Mark Coffy [4]. Then first order linear differential equations were obtained for such integrals, to verify the truth of the solutions.","PeriodicalId":366142,"journal":{"name":"Indian Journal of Advanced Mathematics","volume":"119 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117294944","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
Partial Group Representations on Semialgebras 半代数上的部分群表示
Indian Journal of Advanced Mathematics Pub Date : 2023-03-20 DOI: 10.54105/ijam.A1147.043123
Dr. Meenakshi, Prof. R.P. Sharma
{"title":"Partial Group Representations on Semialgebras","authors":"Dr. Meenakshi, Prof. R.P. Sharma","doi":"10.54105/ijam.A1147.043123","DOIUrl":"https://doi.org/10.54105/ijam.A1147.043123","url":null,"abstract":"Let A bean additively cancellative semialgebra over an additively cancellative semifield K as defined in [9]. For a given partial action α of a group G on an algebra, the associativity of partial skew group ring together with the existence and uniqueness of enveloping (global) action were studied by M. Dokuchaev and R. Exel [2] which were extended for semialgebras with some restriction by Sharma et. al. using the ring of differences. In a similar way, we extend the results of [2,3] for semialgebras regarding partial representations.","PeriodicalId":366142,"journal":{"name":"Indian Journal of Advanced Mathematics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126982932","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
A Model for Combining Allegorical Mental Imagery with Intuitive Thinking in Understanding the Limit of a Function 隐喻心理意象与直觉思维相结合理解函数极限的模式
Indian Journal of Advanced Mathematics Pub Date : 2022-10-30 DOI: 10.54105/ijam.d1128.102222
Ahmad Hedayatpanah Shaldehi, Marziyeh Hedayatpanah Shaldehi, Badriyeh Hedayatpanah
{"title":"A Model for Combining Allegorical Mental Imagery with Intuitive Thinking in Understanding the Limit of a Function","authors":"Ahmad Hedayatpanah Shaldehi, Marziyeh Hedayatpanah Shaldehi, Badriyeh Hedayatpanah","doi":"10.54105/ijam.d1128.102222","DOIUrl":"https://doi.org/10.54105/ijam.d1128.102222","url":null,"abstract":"The main purpose of this article is to use a combination of mental imagery and puppet allegory to intuition the concept of limit for learners. Usually to start teaching, teaching the limit of functions, there are several methods, but most instructors use the Epsilon and Delta formula. Obviously, starting with teaching with formulas, it is not easy to explain the concept of limit. Because, learners achieve a deep understanding of the limit, when the concepts become intuitive for them. Intuition of the limit of functions, with proper mental imagery and allegory, can make understanding the limit easy and enjoyable. Obviously, following the optimal understanding of the limit, understanding, Neighborhood. Derivation and integrals, for learners It becomes easier. The use of a combination of mental imagery with puppet allegorical patterns to intuitive or sensory thinking that is the result of three decades of experience and teaching of the author, to be available to learners and educators. In this way, very soon, learners (especially non-mathematics learners), especially in high school classes, or the first years of university, they manage to have a deep understanding of the limit, Because one of the ways to teach mathematics is to use the properties of mental imagery to be objective or sensory through allegory, which has a high effectiveness and feedback in understanding the limit. In this article functions limit education is considered by combining mental and sensory imagery through allegory or simile with six puppet images. The experiences in this research can be used by teachers of teacher training centers, teachers and high schools and universities and designers of educational materials.","PeriodicalId":366142,"journal":{"name":"Indian Journal of Advanced Mathematics","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124735083","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 the Integer Solution of the Transcendental Equation 超越方程的整数解
Indian Journal of Advanced Mathematics Pub Date : 2022-04-30 DOI: 10.54105/ijam.c1120.041322
S. S, Veeramallan P
{"title":"On the Integer Solution of the Transcendental Equation","authors":"S. S, Veeramallan P","doi":"10.54105/ijam.c1120.041322","DOIUrl":"https://doi.org/10.54105/ijam.c1120.041322","url":null,"abstract":"Let C be a positive non-square integer. In this paper, we look at the complete solutions of the Transcendental equation √𝟐𝒛−𝟒=√𝒙+√𝑪𝒚± √𝒙−√𝑪𝒚 , where 𝒙𝟐−𝑪𝒚𝟐=𝜶𝟐 or 𝟐𝟐𝒕. In addition, we find repeated relationships in the solutions to this figure.","PeriodicalId":366142,"journal":{"name":"Indian Journal of Advanced Mathematics","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117048867","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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