In this note we proved that if Ln ≥ Pn − n log n for n ≥ 1 then Ln → ∞ as n → ∞ using the prime number theorem and Rosser theorem, and Goldbach conjecture follows from the result, where Ln is the largest strong Goldbach number generated by the n-th prime Pn and denotes an even number such that every even number from 4 to Ln is the sum of two primes among the first n primes but Ln + 2 is not such a sum. It means Pn − n log n is the smallest possible value of Ln for n ≥ 1 to support Goldbach conjecture, therefore, Goldbach conjecture is true if it can be proven that Ln > Pn − n log n for n ≥ 1. Mathematics Subject Classification: 11A41
{"title":"A weak method to come close to solution of Goldbach conjecture","authors":"Pingyuan Zhou","doi":"10.12988/imf.2019.9938","DOIUrl":"https://doi.org/10.12988/imf.2019.9938","url":null,"abstract":"In this note we proved that if Ln ≥ Pn − n log n for n ≥ 1 then Ln → ∞ as n → ∞ using the prime number theorem and Rosser theorem, and Goldbach conjecture follows from the result, where Ln is the largest strong Goldbach number generated by the n-th prime Pn and denotes an even number such that every even number from 4 to Ln is the sum of two primes among the first n primes but Ln + 2 is not such a sum. It means Pn − n log n is the smallest possible value of Ln for n ≥ 1 to support Goldbach conjecture, therefore, Goldbach conjecture is true if it can be proven that Ln > Pn − n log n for n ≥ 1. Mathematics Subject Classification: 11A41","PeriodicalId":107214,"journal":{"name":"International Mathematical Forum","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116628312","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 : 1900-01-01DOI: 10.12988/imf.2023.912384
Ebru Aydoğan, E. Demir
In this study, we investigate uo-convergence of nets of positive continuous operators defined on the topological dual of a completely regular Hausdorff topological space. Firstly, we make the definition of uo-convergence on this class and then we present some characterizations of it
{"title":"On unbounded order convergence of operator nets","authors":"Ebru Aydoğan, E. Demir","doi":"10.12988/imf.2023.912384","DOIUrl":"https://doi.org/10.12988/imf.2023.912384","url":null,"abstract":"In this study, we investigate uo-convergence of nets of positive continuous operators defined on the topological dual of a completely regular Hausdorff topological space. Firstly, we make the definition of uo-convergence on this class and then we present some characterizations of it","PeriodicalId":107214,"journal":{"name":"International Mathematical Forum","volume":"269 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125822356","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}
Mushtaq K. Abd Al-Rahem, Zainab H. Abood, Sada Faydh Mohammad
Recently, the field of C − Algebra valued A − Metric space be more popular and mentioned in various articles. Concepts of C − Algebra valued A − Metric space introduced in this paper based on the concepts and properties of C − Algebra. Moreover, this work proved some of the fixed point theorems for self –map with contractive. Examples are given to illustrate the results.
{"title":"Generalizing on C*- algebra valued A - metric space","authors":"Mushtaq K. Abd Al-Rahem, Zainab H. Abood, Sada Faydh Mohammad","doi":"10.12988/IMF.2019.912","DOIUrl":"https://doi.org/10.12988/IMF.2019.912","url":null,"abstract":"Recently, the field of C − Algebra valued A − Metric space be more popular and mentioned in various articles. Concepts of C − Algebra valued A − Metric space introduced in this paper based on the concepts and properties of C − Algebra. Moreover, this work proved some of the fixed point theorems for self –map with contractive. Examples are given to illustrate the results.","PeriodicalId":107214,"journal":{"name":"International Mathematical Forum","volume":"115 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124691347","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 : 1900-01-01DOI: 10.12988/imf.2022.912319
Giovanni Campisi, S. Muzzioli
This paper develops an heterogeneous agents model with fundamentalists and chartists trading in two different speculative markets. It examines whether investors’ behaviour is related to the volatility and its dynamics. We find that investors’ heterogeneity in price trends and trading strategies can significantly explain asymmetry in semi-volatility transmission.
{"title":"Asymmetric semi-volatility spillover in a nonlinear model of interacting markets","authors":"Giovanni Campisi, S. Muzzioli","doi":"10.12988/imf.2022.912319","DOIUrl":"https://doi.org/10.12988/imf.2022.912319","url":null,"abstract":"This paper develops an heterogeneous agents model with fundamentalists and chartists trading in two different speculative markets. It examines whether investors’ behaviour is related to the volatility and its dynamics. We find that investors’ heterogeneity in price trends and trading strategies can significantly explain asymmetry in semi-volatility transmission.","PeriodicalId":107214,"journal":{"name":"International Mathematical Forum","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124027750","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 : 1900-01-01DOI: 10.12988/imf.2022.912321
M. Azarian
We discuss combinatorics of discrete relations, (total) functions, and partial functions. For two sets A and B , we present formulas for the calculations of the number of relations from A to B that are not: (i) functions, (ii) one-to-one functions, or (iii) onto functions. W e provide formulas to calculate the number of functions from A to B that are not: (i) one-to-one or (ii) onto. Also, we determine the number of partial and proper partial functions from A to B . Moreover, we state some conjectures and pose questions for the reader. This paper generates numerous integer sequences, some of which can be found in The On-Line Encyclopedia of Integer Sequences (OEIS) .
{"title":"Remarks and conjectures regarding combinatorics of discrete partial functions","authors":"M. Azarian","doi":"10.12988/imf.2022.912321","DOIUrl":"https://doi.org/10.12988/imf.2022.912321","url":null,"abstract":"We discuss combinatorics of discrete relations, (total) functions, and partial functions. For two sets A and B , we present formulas for the calculations of the number of relations from A to B that are not: (i) functions, (ii) one-to-one functions, or (iii) onto functions. W e provide formulas to calculate the number of functions from A to B that are not: (i) one-to-one or (ii) onto. Also, we determine the number of partial and proper partial functions from A to B . Moreover, we state some conjectures and pose questions for the reader. This paper generates numerous integer sequences, some of which can be found in The On-Line Encyclopedia of Integer Sequences (OEIS) .","PeriodicalId":107214,"journal":{"name":"International Mathematical Forum","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129414687","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 : 1900-01-01DOI: 10.12988/imf.2023.912353
Rita Vincenti
We construct linear codes from projective systems in a finite projective space, by considering the points of the lines of partial ruled sets. In two complementary subspaces we choose known varieties V and V (cid:48) , V ∼ = V (cid:48) via a projectivity, and study both the linear codes and the varieties arising by connecting corresponding points
在有限射影空间中，通过考虑部分规则集的直线点，从射影系统构造线性码。在两个互补的子空间中，我们通过投影选择已知的V和V (cid:48)， V ~ = V (cid:48)，并研究了线性码和由对应点连接产生的变体
{"title":"Varieties and codes from partial ruled sets","authors":"Rita Vincenti","doi":"10.12988/imf.2023.912353","DOIUrl":"https://doi.org/10.12988/imf.2023.912353","url":null,"abstract":"We construct linear codes from projective systems in a finite projective space, by considering the points of the lines of partial ruled sets. In two complementary subspaces we choose known varieties V and V (cid:48) , V ∼ = V (cid:48) via a projectivity, and study both the linear codes and the varieties arising by connecting corresponding points","PeriodicalId":107214,"journal":{"name":"International Mathematical Forum","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116307719","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 : 1900-01-01DOI: 10.12988/imf.2021.912251
O. Gok
In this paper, it is shown that tensor product of order ideals is an order ideal. Mathematics Subject Classification: 46A40, 46B28, 06B10, 15A69
本文证明了序理想张量积是一个序理想。数学学科分类:46A40、46B28、06B10、15A69
{"title":"Tensor product of order ideals","authors":"O. Gok","doi":"10.12988/imf.2021.912251","DOIUrl":"https://doi.org/10.12988/imf.2021.912251","url":null,"abstract":"In this paper, it is shown that tensor product of order ideals is an order ideal. Mathematics Subject Classification: 46A40, 46B28, 06B10, 15A69","PeriodicalId":107214,"journal":{"name":"International Mathematical Forum","volume":"63 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131891940","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}
{"title":"Dissociation number and vertex 3-path cover number of the join of graphs","authors":"Kenneth B. Larena, M. P. Baldado","doi":"10.12988/IMF.2019.914","DOIUrl":"https://doi.org/10.12988/IMF.2019.914","url":null,"abstract":"","PeriodicalId":107214,"journal":{"name":"International Mathematical Forum","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133466623","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 equation x2m+y2n = z2r is considered for positive integer values of m, n, and r. If m, n, and r are not pairwise relatively prime, then there are no solutions to this equation in nonzero integers. Formulas that generate infinitely many solutions to this equation are given when m, n, and r are pairwise relatively prime; the newly discovered formulas tend to yield non-primitive solutions. Along the way, it is shown that x2 + y2n = z2n (or equivalently, z2n − y2n = x2) has no solutions in nonzero integers when n > 1. Mathematics Subject Classification: 11D41
{"title":"Solutions to a generalized Fermat equation that has even exponents","authors":"R. F. Ryan","doi":"10.12988/imf.2019.9835","DOIUrl":"https://doi.org/10.12988/imf.2019.9835","url":null,"abstract":"The equation x2m+y2n = z2r is considered for positive integer values of m, n, and r. If m, n, and r are not pairwise relatively prime, then there are no solutions to this equation in nonzero integers. Formulas that generate infinitely many solutions to this equation are given when m, n, and r are pairwise relatively prime; the newly discovered formulas tend to yield non-primitive solutions. Along the way, it is shown that x2 + y2n = z2n (or equivalently, z2n − y2n = x2) has no solutions in nonzero integers when n > 1. Mathematics Subject Classification: 11D41","PeriodicalId":107214,"journal":{"name":"International Mathematical Forum","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133039234","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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