Pub Date : 2024-04-23DOI: 10.9734/jamcs/2024/v39i51892
Hao Yang, Jiawen Li, Suiju Jia
The main purpose of this paper is to select 15 primary school mathematics textbooks from China, the United States, Singapore, Japan, South Korea and Germany, take "fraction division" as an example, and clarify the characteristics and similarities and differences of its operational meaning model and revelation methods of arithmetic reasoning in Fraction Division through literature method, content analysis method and comparative research method. The results show that there are great differences in these two aspects between different versions of teaching materials. Therefore, combining the national conditions of various countries, seeking common ground while reserving differences, provides a teaching path of fraction division based on national conditions and absorbing the advantages of different countries, and provides theoretical support for the better implementation of curriculum standards and textbooks.
{"title":"Comparative Study of Elementary School Mathematics Textbooks in China, Japan, South Korea, Singapore, America, Germany: A Case Study on \"Fraction Division\"","authors":"Hao Yang, Jiawen Li, Suiju Jia","doi":"10.9734/jamcs/2024/v39i51892","DOIUrl":"https://doi.org/10.9734/jamcs/2024/v39i51892","url":null,"abstract":"The main purpose of this paper is to select 15 primary school mathematics textbooks from China, the United States, Singapore, Japan, South Korea and Germany, take \"fraction division\" as an example, and clarify the characteristics and similarities and differences of its operational meaning model and revelation methods of arithmetic reasoning in Fraction Division through literature method, content analysis method and comparative research method. The results show that there are great differences in these two aspects between different versions of teaching materials. Therefore, combining the national conditions of various countries, seeking common ground while reserving differences, provides a teaching path of fraction division based on national conditions and absorbing the advantages of different countries, and provides theoretical support for the better implementation of curriculum standards and textbooks.","PeriodicalId":503149,"journal":{"name":"Journal of Advances in Mathematics and Computer Science","volume":"107 17","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140669938","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}
Pub Date : 2024-04-18DOI: 10.9734/jamcs/2024/v39i51891
Olutimo Al, Williams Fa, Adeyemi Mo, Akewushola Jr
.
.
{"title":"Mathematical Modeling of Diarrhea with Vaccination and Treatment Factors","authors":"Olutimo Al, Williams Fa, Adeyemi Mo, Akewushola Jr","doi":"10.9734/jamcs/2024/v39i51891","DOIUrl":"https://doi.org/10.9734/jamcs/2024/v39i51891","url":null,"abstract":"<jats:p>.</jats:p>","PeriodicalId":503149,"journal":{"name":"Journal of Advances in Mathematics and Computer Science","volume":" 7","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140686802","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}
Pub Date : 2024-04-15DOI: 10.9734/jamcs/2024/v39i51890
Shaoyang Gao
This study mainly investigates the dynamical analysis of the FitzHugh-Nagumo (FHN) neuron model. Firstly, it analyzes the equilibrium stability of the system in the absence of network diffusion. Then, it considers two types of network topologies: random networks and higher-order networks. The paper analyzes the Turing instability phenomenon in the presence of network diffusion, identifies the critical diffusion coefficient in the FHN model that leads to Turing instability, and plots the eigenvalue distribution diagram, known as the Turing pattern. The research findings indicate that networks with higher-order connections, as opposed to random networks, display a more intricate interplay among neurons. This heightened interconnection intensifies the Turing instability phenomenon, amplifying its significance within the system. The stability of the dynamical system can be associated with the onset of neurological disorders such as epilepsy, caused by abnormal neuronal firing. This analogy facilitates the transfer of content related to the instability of control systems to the regulation of neurological disorders.
{"title":"Analysis of Turing Instability of the Fitzhugh-Nagumo Model in Diffusive Network","authors":"Shaoyang Gao","doi":"10.9734/jamcs/2024/v39i51890","DOIUrl":"https://doi.org/10.9734/jamcs/2024/v39i51890","url":null,"abstract":"This study mainly investigates the dynamical analysis of the FitzHugh-Nagumo (FHN) neuron model. Firstly, it analyzes the equilibrium stability of the system in the absence of network diffusion. Then, it considers two types of network topologies: random networks and higher-order networks. The paper analyzes the Turing instability phenomenon in the presence of network diffusion, identifies the critical diffusion coefficient in the FHN model that leads to Turing instability, and plots the eigenvalue distribution diagram, known as the Turing pattern. The research findings indicate that networks with higher-order connections, as opposed to random networks, display a more intricate interplay among neurons. This heightened interconnection intensifies the Turing instability phenomenon, amplifying its significance within the system. The stability of the dynamical system can be associated with the onset of neurological disorders such as epilepsy, caused by abnormal neuronal firing. This analogy facilitates the transfer of content related to the instability of control systems to the regulation of neurological disorders.","PeriodicalId":503149,"journal":{"name":"Journal of Advances in Mathematics and Computer Science","volume":"39 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140699559","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}
Pub Date : 2024-04-12DOI: 10.9734/jamcs/2024/v39i51889
Rohit Kumar Verma, M. B. Laxmi
Shannon entropy and Kolmogorov complexity are two conceptually distinct information metrics since the latter is based on probability distributions while the former is based on program size. All recursive probability distributions, however, are known to have an expected Up to a constant that solely depends on the distribution, the Kolmogorov complexity value is equal to its Shannon entropy. We investigate if a comparable correlation exists between Renyi and Havrda- Charvat Entropy entropies order α, indicating that it is consistent solely with Renyi and Havrda- Charvat entropies of order 1. Kolmogorov noted that the characteristics of Shannon entropy and algorithmic complexity are comparable. We examine a single facet of this resemblance. Specifically, linear inequalities that hold true for Shannon entropy and for Kolmogorov complexity. As it happens, the following are true: (1) all linear inequalities that hold true for Shannon entropy and vice versa for Kolmogorov complexity; (2) all linear inequalities that hold true for ranks of finite subsets of linear spaces for Shannon entropy; and (3) the reverse is untrue.
{"title":"Uniform Estimates on Length of Programs and Computing Algorithmic Complexities for Quantitative Information Measures","authors":"Rohit Kumar Verma, M. B. Laxmi","doi":"10.9734/jamcs/2024/v39i51889","DOIUrl":"https://doi.org/10.9734/jamcs/2024/v39i51889","url":null,"abstract":"Shannon entropy and Kolmogorov complexity are two conceptually distinct information metrics since the latter is based on probability distributions while the former is based on program size. All recursive probability distributions, however, are known to have an expected Up to a constant that solely depends on the distribution, the Kolmogorov complexity value is equal to its Shannon entropy. We investigate if a comparable correlation exists between Renyi and Havrda- Charvat Entropy entropies order α, indicating that it is consistent solely with Renyi and Havrda- Charvat entropies of order 1.\u0000Kolmogorov noted that the characteristics of Shannon entropy and algorithmic complexity are comparable. We examine a single facet of this resemblance. Specifically, linear inequalities that hold true for Shannon entropy and for Kolmogorov complexity. As it happens, the following are true: (1) all linear inequalities that hold true for Shannon entropy and vice versa for Kolmogorov complexity; (2) all linear inequalities that hold true for ranks of finite subsets of linear spaces for Shannon entropy; and (3) the reverse is untrue.","PeriodicalId":503149,"journal":{"name":"Journal of Advances in Mathematics and Computer Science","volume":"68 S11","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140709881","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 establish some common fixed-point theorems in supermetric space for Dass-Gupta Rational Contraction, E-contraction, generalized E-contraction and rational Dass-Gupta E-contraction. Additionally, these theorems expand and generalize several intriguing findings from metric fixed-point theory to the supermetric setting. Furthermore, an example is provided to support our results.
{"title":"Common Fixed Points of Dass-Gupta Rational Contraction and E-Contraction","authors":"Deepak Singh, Manoj Ughade, Sheetal Yadav, Alok Kumar, Manoj Kumar Shukla","doi":"10.9734/jamcs/2024/v39i51888","DOIUrl":"https://doi.org/10.9734/jamcs/2024/v39i51888","url":null,"abstract":"In this paper, we establish some common fixed-point theorems in supermetric space for Dass-Gupta Rational Contraction, E-contraction, generalized E-contraction and rational Dass-Gupta E-contraction. Additionally, these theorems expand and generalize several intriguing findings from metric fixed-point theory to the supermetric setting. Furthermore, an example is provided to support our results.","PeriodicalId":503149,"journal":{"name":"Journal of Advances in Mathematics and Computer Science","volume":"40 10","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140735327","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}
Pub Date : 2024-04-03DOI: 10.9734/jamcs/2024/v39i51887
V. James, B. Sivakumar
In this paper, we examine a family of recursively defined polynomials with four-variables on a fourth order recurrence relation and build their generating function. These generating functions enable us to derive several properties of the four-variable polynomials. Finally, we deduce new identities for the new class of polynomials with four-variables and also, we define the Q-matrix.
{"title":"Generating Functions For a New Class of Recursive Polynomials","authors":"V. James, B. Sivakumar","doi":"10.9734/jamcs/2024/v39i51887","DOIUrl":"https://doi.org/10.9734/jamcs/2024/v39i51887","url":null,"abstract":"In this paper, we examine a family of recursively defined polynomials with four-variables on a fourth order recurrence relation and build their generating function. These generating functions enable us to derive several properties of the four-variable polynomials. Finally, we deduce new identities for the new class of polynomials with four-variables and also, we define the Q-matrix.","PeriodicalId":503149,"journal":{"name":"Journal of Advances in Mathematics and Computer Science","volume":"477 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140749470","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}
Pub Date : 2024-04-03DOI: 10.9734/jamcs/2024/v39i51886
J. M. Mouanda
We show that the matrix exponential Diophantine equation (Xn - Iqxn)(Yn - Iqxn) = Z2; admits at least 4 x n2 different construction structures of matrix solutions. We also prove that the matrix exponential Diophantine equation (Xn - Inxm)(Ym - Inxm) = Z2; admits at least 4 x n x m different construction structures of matrix solutions in Mnxm((mathbb{N})) for every pair (n,m) of positive integers such that n (neq) m. We show the connection between the construction structures of matrix solutions of an exponential Diophantine equation and Integer factorization. We show that the matrix Diophantine equation Xn +Ym = Zq , n, m, q (varepsilon) (mathbb{N}); admits at least 8 x n x m x q different construction structures of matrix solutions in Mnxmxq((mathbb{N})).
我们证明矩阵指数二叉方程 (Xn - Iqxn)(Yn - Iqxn) = Z2; 至少有 4 x n2 种不同的矩阵解构造结构。我们还证明了矩阵指数二叉方程 (Xn - Inxm)(Ym - Inxm) = Z2; 在 Mnxm((mathbb{N})) 中，对于每一对（n,m）正整数，使得 n(neq) m，都允许至少 4 x n x m 不同的矩阵解构造结构。我们证明了矩阵 Diophantine 方程 Xn +Ym = Zq , n, m, q (varepsilon) (mathbb{N})；在 Mnxmxq((mathbb{N}))中允许至少 8 x n x m x q 不同的矩阵解构造结构。
{"title":"On Construction Structures of Matrix Solutions of Exponential Diophantine Equations","authors":"J. M. Mouanda","doi":"10.9734/jamcs/2024/v39i51886","DOIUrl":"https://doi.org/10.9734/jamcs/2024/v39i51886","url":null,"abstract":"We show that the matrix exponential Diophantine equation (Xn - Iqxn)(Yn - Iqxn) = Z2; admits at least 4 x n2 different construction structures of matrix solutions. We also prove that the matrix exponential Diophantine equation (Xn - Inxm)(Ym - Inxm) = Z2; admits at least 4 x n x m different construction structures of matrix solutions in Mnxm((mathbb{N})) for every pair (n,m) of positive integers such that n (neq) m. We show the connection between the construction structures of matrix solutions of an exponential Diophantine equation and Integer factorization. We show that the matrix Diophantine equation Xn +Ym = Zq , n, m, q (varepsilon) (mathbb{N}); admits at least 8 x n x m x q different construction structures of matrix solutions in Mnxmxq((mathbb{N})).","PeriodicalId":503149,"journal":{"name":"Journal of Advances in Mathematics and Computer Science","volume":"948 ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140748990","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}
Pub Date : 2024-04-02DOI: 10.9734/jamcs/2024/v39i41885
Sergio Da Silva
This research proposes a new approach to the Riemann Hypothesis, focusing on the interplay between prime gaps and the non-trivial zeros of the Riemann Zeta function. Utilizing various statistical models and experimental analysis techniques, three important insights are uncovered: 1) Granger causality tests reveal a predictive relationship in which past non-trivial zeros may predict future prime gaps; 2) Complex, nonlinear interactions between prime gaps and non-trivial zeros are identified, challenging simple linear correlations; and 3) Causal network analysis reveals intricate feedback-loop relationships. These findings contribute to a better understanding of prime number distribution and the Zeta function, opening up novel possibilities for further mathematical research. The study aims to motivate mathematicians towards a proof or disproof of the Riemann Hypothesis.
{"title":"The Riemann Hypothesis: A Fresh and Experimental Exploration","authors":"Sergio Da Silva","doi":"10.9734/jamcs/2024/v39i41885","DOIUrl":"https://doi.org/10.9734/jamcs/2024/v39i41885","url":null,"abstract":"This research proposes a new approach to the Riemann Hypothesis, focusing on the interplay between prime gaps and the non-trivial zeros of the Riemann Zeta function. Utilizing various statistical models and experimental analysis techniques, three important insights are uncovered: 1) Granger causality tests reveal a predictive relationship in which past non-trivial zeros may predict future prime gaps; 2) Complex, nonlinear interactions between prime gaps and non-trivial zeros are identified, challenging simple linear correlations; and 3) Causal network analysis reveals intricate feedback-loop relationships. These findings contribute to a better understanding of prime number distribution and the Zeta function, opening up novel possibilities for further mathematical research. The study aims to motivate mathematicians towards a proof or disproof of the Riemann Hypothesis.","PeriodicalId":503149,"journal":{"name":"Journal of Advances in Mathematics and Computer Science","volume":"17 8","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140754849","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}
Pub Date : 2024-03-23DOI: 10.9734/jamcs/2024/v39i41881
Bahadır Yılmaz, Y. Soykan
In this research, the generalized dual hyperbolic Guglielmo numbers are introduced. Various special cases are explored (including dual hyperbolic triangular numbers, dual hyperbolic triangular-Lucas numbers, dual hyperbolic oblong numbers, and dual hyperbolic pentagonal numbers). Binet.s formulas, generating functions and summation formulas for these numbers are presented. Moreover, Catalan.s and Cassini.s identities are provided, along with matrices associated with these sequences.
{"title":"On Dual Hyperbolic Guglielmo Numbers","authors":"Bahadır Yılmaz, Y. Soykan","doi":"10.9734/jamcs/2024/v39i41881","DOIUrl":"https://doi.org/10.9734/jamcs/2024/v39i41881","url":null,"abstract":"In this research, the generalized dual hyperbolic Guglielmo numbers are introduced. Various special cases are explored (including dual hyperbolic triangular numbers, dual hyperbolic triangular-Lucas numbers, dual hyperbolic oblong numbers, and dual hyperbolic pentagonal numbers). Binet.s formulas, generating functions and summation formulas for these numbers are presented. Moreover, Catalan.s and Cassini.s identities are provided, along with matrices associated with these sequences.","PeriodicalId":503149,"journal":{"name":"Journal of Advances in Mathematics and Computer Science","volume":" 7","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140210563","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}
Pub Date : 2024-03-23DOI: 10.9734/jamcs/2024/v39i41880
Khaled Moftah
Blocks are unit convergence between two consecutive odd numbers formed according to the three x plus one conjecture rules. The left odd number is the left hook, L, and the right odd number is the right hook, R. They include even numbers between their boundaries. They are divided into families (F1 = 5, 11, 17, … & F2 = 1, 7, 11, … & F3 = 3, 9, 15, …) and groups based on their group length (The number of the middle-even numbers between the two hooks). Blocks are taken individually and placed beside each other, similar to the domino tiles play, which, by their formulation, satisfies the conjecture rules. Formed chains reach number one in the convergence mode or continue generating odd positive numbers infinitely according to the generation mode. The final convergence to number one is reached because these blocks have all the positive integers included as left hooks (L1, L2, L3), and all the F1 and F2 odd positive numbers are included as right hooks (R1 and R2). Block rules mandate that a single left hook produces only one right hook. Accordingly, no looping or entanglement (Joining and consequent splitting) between chain branches would occur. Statistics show that R cannot increase infinitely. Repeated oscillation up and down without reaching number one would also violate the statistics. Statistics reveal that blocks of various lengths have a strict occurrence and repetition sequence along the positive integer series. Block lengths can extend infinitely, and each block length repeats its occurrence infinitely. In the generation mode, blocks are attached in reverse order to the conjecture/convergence rules. According to the rules, all positive integers can be generated starting from number one. Multiple sequences and clusters of specific block lengths occur according to specific rules and cannot continue infinitely.
{"title":"Block Format Solves the Collatz Conjecture","authors":"Khaled Moftah","doi":"10.9734/jamcs/2024/v39i41880","DOIUrl":"https://doi.org/10.9734/jamcs/2024/v39i41880","url":null,"abstract":"Blocks are unit convergence between two consecutive odd numbers formed according to the three x plus one conjecture rules. The left odd number is the left hook, L, and the right odd number is the right hook, R. They include even numbers between their boundaries. They are divided into families (F1 = 5, 11, 17, … & F2 = 1, 7, 11, … & F3 = 3, 9, 15, …) and groups based on their group length (The number of the middle-even numbers between the two hooks). Blocks are taken individually and placed beside each other, similar to the domino tiles play, which, by their formulation, satisfies the conjecture rules. Formed chains reach number one in the convergence mode or continue generating odd positive numbers infinitely according to the generation mode. The final convergence to number one is reached because these blocks have all the positive integers included as left hooks (L1, L2, L3), and all the F1 and F2 odd positive numbers are included as right hooks (R1 and R2). Block rules mandate that a single left hook produces only one right hook. Accordingly, no looping or entanglement (Joining and consequent splitting) between chain branches would occur. Statistics show that R cannot increase infinitely. Repeated oscillation up and down without reaching number one would also violate the statistics. Statistics reveal that blocks of various lengths have a strict occurrence and repetition sequence along the positive integer series. Block lengths can extend infinitely, and each block length repeats its occurrence infinitely. In the generation mode, blocks are attached in reverse order to the conjecture/convergence rules. According to the rules, all positive integers can be generated starting from number one. Multiple sequences and clusters of specific block lengths occur according to specific rules and cannot continue infinitely.","PeriodicalId":503149,"journal":{"name":"Journal of Advances in Mathematics and Computer Science","volume":" 32","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140211073","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：