Pub Date : 2023-01-01DOI: 10.33039/ami.2023.08.006
Dániel Kolozsvári, Norbert Pataki
. Programming languages evolve in the long term, new standards are specified in which new constructs appear, old elements may become dep-recated. Standard library of programming languages also changes time by time. The standard of the C++ programming language defines the elements of the C++ Standard Template Library (STL) that provides containers, algorithms, and iterators. According to the STL’s generic programming approach, these sets can be extended in a convenient way. The std::iterator class template had been in the C++ since beginning and has been deprecated in the C++17 standard. This class template’s purpose was to specify the traits of an iterator. Typically, it was a base class of many standard and non-standard iterator class to provide the necessary traits. However, the usage of iterator is straightforward and fits into the object-oriented programming paradigm. Many non-standard containers offer custom iterators because of the STL compatibility. Using this base class does not cause any weird effect, therefore usage of iterator can be found in code legacy. In this paper, we present a static analysis approach to assist the development of iterator classes in a modern way in which the iterator class template is not taken advantage of. We utilize the Clang compiler infrastructure to look for how the deprecated iterator classes can be found in legacy code and present an approach how to modernize them.
{"title":"A static analysis approach for modern iterator development","authors":"Dániel Kolozsvári, Norbert Pataki","doi":"10.33039/ami.2023.08.006","DOIUrl":"https://doi.org/10.33039/ami.2023.08.006","url":null,"abstract":". Programming languages evolve in the long term, new standards are specified in which new constructs appear, old elements may become dep-recated. Standard library of programming languages also changes time by time. The standard of the C++ programming language defines the elements of the C++ Standard Template Library (STL) that provides containers, algorithms, and iterators. According to the STL’s generic programming approach, these sets can be extended in a convenient way. The std::iterator class template had been in the C++ since beginning and has been deprecated in the C++17 standard. This class template’s purpose was to specify the traits of an iterator. Typically, it was a base class of many standard and non-standard iterator class to provide the necessary traits. However, the usage of iterator is straightforward and fits into the object-oriented programming paradigm. Many non-standard containers offer custom iterators because of the STL compatibility. Using this base class does not cause any weird effect, therefore usage of iterator can be found in code legacy. In this paper, we present a static analysis approach to assist the development of iterator classes in a modern way in which the iterator class template is not taken advantage of. We utilize the Clang compiler infrastructure to look for how the deprecated iterator classes can be found in legacy code and present an approach how to modernize them.","PeriodicalId":43454,"journal":{"name":"Annales Mathematicae et Informaticae","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86620780","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 : 2023-01-01DOI: 10.33039/ami.2023.03.003
Gergely Szmerka, Ö. Vancsó
. In the didactics of mathematics, a lot of such research appeared in the past twenty-thirty years that consider both mathematics and mathematics education as a cultural activity [20]. In this approach, didactical texts and social space are carriers of beliefs created about mathematics education. Similarly, the investigation of beliefs has strengthened in the past two decades [33]. In our paper, we examine what relationship appears between the beliefs of the Hungarian didactic tradition existing in written texts or personal contacts, and those of Hungarian mathematics teachers. To carry it out, we use means of cultural history and a questionnaire.
{"title":"The role of creation in the didactical traditions in Hungary","authors":"Gergely Szmerka, Ö. Vancsó","doi":"10.33039/ami.2023.03.003","DOIUrl":"https://doi.org/10.33039/ami.2023.03.003","url":null,"abstract":". In the didactics of mathematics, a lot of such research appeared in the past twenty-thirty years that consider both mathematics and mathematics education as a cultural activity [20]. In this approach, didactical texts and social space are carriers of beliefs created about mathematics education. Similarly, the investigation of beliefs has strengthened in the past two decades [33]. In our paper, we examine what relationship appears between the beliefs of the Hungarian didactic tradition existing in written texts or personal contacts, and those of Hungarian mathematics teachers. To carry it out, we use means of cultural history and a questionnaire.","PeriodicalId":43454,"journal":{"name":"Annales Mathematicae et Informaticae","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83552066","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 : 2022-12-21DOI: 10.33039/ami.2022.12.009
Csilla Bereczky-Zámbó, C. Szabó, Anna Muzsnay, J. Szeibert
. It is a common assumption that taking a mathematics course and passing the exam means that one has mastered the course requirements and gained a sufficiently deep understanding of the course material. According to the communication part of the Van Hiele Theory, if someone does not reach the expected entry-level, they won’t be able to develop during the course. In our research, we investigated this contradiction in the field of geometry. We examined this phenomenon with mathematics major and pre-service mathematics teacher students during their first geometry course.
{"title":"Passing the exam and not mastering the material in geometry","authors":"Csilla Bereczky-Zámbó, C. Szabó, Anna Muzsnay, J. Szeibert","doi":"10.33039/ami.2022.12.009","DOIUrl":"https://doi.org/10.33039/ami.2022.12.009","url":null,"abstract":". It is a common assumption that taking a mathematics course and passing the exam means that one has mastered the course requirements and gained a sufficiently deep understanding of the course material. According to the communication part of the Van Hiele Theory, if someone does not reach the expected entry-level, they won’t be able to develop during the course. In our research, we investigated this contradiction in the field of geometry. We examined this phenomenon with mathematics major and pre-service mathematics teacher students during their first geometry course.","PeriodicalId":43454,"journal":{"name":"Annales Mathematicae et Informaticae","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90588593","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 : 2022-01-01DOI: 10.33039/ami.2022.05.002
Azizul Hoque
Generalized Mersenne numbers are defined as 𝑀 𝑝,𝑛 = 𝑝 𝑛 − 𝑝 +1 , where 𝑝 is a prime and 𝑛 is a positive integer. Here, we prove that for each pair ( 𝑐, 𝑝 ) with 𝑐 ≥ 1 an integer, there is at most one 𝑀 𝑝,𝑛 of the form 𝑐𝑥 2 with a few exceptions.
{"title":"Generalized Mersenne numbers of the form cx²","authors":"Azizul Hoque","doi":"10.33039/ami.2022.05.002","DOIUrl":"https://doi.org/10.33039/ami.2022.05.002","url":null,"abstract":"Generalized Mersenne numbers are defined as 𝑀 𝑝,𝑛 = 𝑝 𝑛 − 𝑝 +1 , where 𝑝 is a prime and 𝑛 is a positive integer. Here, we prove that for each pair ( 𝑐, 𝑝 ) with 𝑐 ≥ 1 an integer, there is at most one 𝑀 𝑝,𝑛 of the form 𝑐𝑥 2 with a few exceptions.","PeriodicalId":43454,"journal":{"name":"Annales Mathematicae et Informaticae","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81488986","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 : 2022-01-01DOI: 10.33039/ami.2022.05.001
Aida Chefrour
The main objective of this study is the clustering of meteorological parameters and forecasting weather in the region of Annaba (Algeria) using clustering techniques. The proposed two-stage clustering approach is based on the first stage, on the proposition of ANN-DBSCAN, a combination of the DBSCAN algorithm and an Artificial Neural Network (ANN) for grouping the clusters. Internal indices of validation were used to compare and verify the correctness and efficiency of the results. Our experiments identified five groups, each of which was associated with the area’s usual weather parameters. Our proposed incremental DBSCAN is employed in the second stage to determine the data pattern that can predict the future atmosphere. The natural molecules of the measured pollutants (nitrogen dioxide (NO2), ozone (O3), carbon dioxide (CO2), and sulfur dioxide (SO2)) are directly dependent on weather forecasting. The focus of this research is on a section of the Samasafia database. The proposed algorithm is used to determine the weather trend in that database. Advanced numerical analysis was applied to a few prediction tasks.
{"title":"Weather forecasting using DBSCAN clustering algorithm","authors":"Aida Chefrour","doi":"10.33039/ami.2022.05.001","DOIUrl":"https://doi.org/10.33039/ami.2022.05.001","url":null,"abstract":"The main objective of this study is the clustering of meteorological parameters and forecasting weather in the region of Annaba (Algeria) using clustering techniques. The proposed two-stage clustering approach is based on the first stage, on the proposition of ANN-DBSCAN, a combination of the DBSCAN algorithm and an Artificial Neural Network (ANN) for grouping the clusters. Internal indices of validation were used to compare and verify the correctness and efficiency of the results. Our experiments identified five groups, each of which was associated with the area’s usual weather parameters. Our proposed incremental DBSCAN is employed in the second stage to determine the data pattern that can predict the future atmosphere. The natural molecules of the measured pollutants (nitrogen dioxide (NO2), ozone (O3), carbon dioxide (CO2), and sulfur dioxide (SO2)) are directly dependent on weather forecasting. The focus of this research is on a section of the Samasafia database. The proposed algorithm is used to determine the weather trend in that database. Advanced numerical analysis was applied to a few prediction tasks.","PeriodicalId":43454,"journal":{"name":"Annales Mathematicae et Informaticae","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86329826","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 : 2022-01-01DOI: 10.33039/ami.2022.02.002
V. Ďuriš, Veronika Bojdová, T. Šumný
The Chinese remainder theorem provides the solvability conditions for the system of linear congruences. In section 2 we present the construction of the solution of such a system. Focusing on the Chinese remainder theorem usage in the field of number theory, we looked for some problems. The main contribution is in section 3, consisting of Problems 3.1, 3.2 and 3.3 from number theory leading to the Chinese remainder theorem. Finally, we present a different view of the solution of the system of linear congruences by its geometric interpretation, applying lattice points.
{"title":"Solving selected problems on the Chinese remainder theorem","authors":"V. Ďuriš, Veronika Bojdová, T. Šumný","doi":"10.33039/ami.2022.02.002","DOIUrl":"https://doi.org/10.33039/ami.2022.02.002","url":null,"abstract":"The Chinese remainder theorem provides the solvability conditions for the system of linear congruences. In section 2 we present the construction of the solution of such a system. Focusing on the Chinese remainder theorem usage in the field of number theory, we looked for some problems. The main contribution is in section 3, consisting of Problems 3.1, 3.2 and 3.3 from number theory leading to the Chinese remainder theorem. Finally, we present a different view of the solution of the system of linear congruences by its geometric interpretation, applying lattice points.","PeriodicalId":43454,"journal":{"name":"Annales Mathematicae et Informaticae","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78268673","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 : 2022-01-01DOI: 10.33039/ami.2022.11.003
P. Walsh
. An explicit description of the trace of Frobenius is given for any elliptic curve over Q of the form 𝑦 2 = 𝑥 3 + 𝑑𝑥 . This description leads to an algorithm which computes the trace at a cost of one modular exponentiation.
{"title":"A note on the trace of Frobenius for curves of the form y² = x³ + dx","authors":"P. Walsh","doi":"10.33039/ami.2022.11.003","DOIUrl":"https://doi.org/10.33039/ami.2022.11.003","url":null,"abstract":". An explicit description of the trace of Frobenius is given for any elliptic curve over Q of the form 𝑦 2 = 𝑥 3 + 𝑑𝑥 . This description leads to an algorithm which computes the trace at a cost of one modular exponentiation.","PeriodicalId":43454,"journal":{"name":"Annales Mathematicae et Informaticae","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83302937","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 : 2022-01-01DOI: 10.33039/ami.2022.10.002
Nadhir Bendrici, Malika Boumedien-Zidani
. In this paper, we present a new method to evaluate the moving Frenet frame along the intersection curves of two parametric surfaces in the tangential intersection situations. To resolve such situation, we have combined a perturbation method with a classical method that works in transversal intersection situation. Unlike the existent methods, our method works even if the order contact of the point is more than one.
{"title":"Differential geometry properties by using the perturbation methods","authors":"Nadhir Bendrici, Malika Boumedien-Zidani","doi":"10.33039/ami.2022.10.002","DOIUrl":"https://doi.org/10.33039/ami.2022.10.002","url":null,"abstract":". In this paper, we present a new method to evaluate the moving Frenet frame along the intersection curves of two parametric surfaces in the tangential intersection situations. To resolve such situation, we have combined a perturbation method with a classical method that works in transversal intersection situation. Unlike the existent methods, our method works even if the order contact of the point is more than one.","PeriodicalId":43454,"journal":{"name":"Annales Mathematicae et Informaticae","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77596177","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 : 2022-01-01DOI: 10.33039/ami.2022.05.003
Rezwan Ul Shaban, B. Rather, S. Pirzada, A. Somasundaram
{"title":"On distance signless Laplacian spectral radius of power graphs of cyclic and dihedral groups","authors":"Rezwan Ul Shaban, B. Rather, S. Pirzada, A. Somasundaram","doi":"10.33039/ami.2022.05.003","DOIUrl":"https://doi.org/10.33039/ami.2022.05.003","url":null,"abstract":"","PeriodicalId":43454,"journal":{"name":"Annales Mathematicae et Informaticae","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72598068","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 : 2022-01-01DOI: 10.33039/ami.2022.02.001
Ronaldo Garcia, D. Reznik
This is a continuation of our simulation-based investigation of N -periodic trajectories in the elliptic billiard. With a special focus on self-intersected trajectories we (i) describe new properties of N = 4 family, (ii) derive expressions for quantities recently shown to be conserved, and to support further experimentation, we (iii) derive explicit expressions for vertices and caustic semi-axes for several families. Finally, (iv) we include links to several animations of the phenomena.
{"title":"Exploring self-intersected N-periodics in the elliptic billiard","authors":"Ronaldo Garcia, D. Reznik","doi":"10.33039/ami.2022.02.001","DOIUrl":"https://doi.org/10.33039/ami.2022.02.001","url":null,"abstract":"This is a continuation of our simulation-based investigation of N -periodic trajectories in the elliptic billiard. With a special focus on self-intersected trajectories we (i) describe new properties of N = 4 family, (ii) derive expressions for quantities recently shown to be conserved, and to support further experimentation, we (iii) derive explicit expressions for vertices and caustic semi-axes for several families. Finally, (iv) we include links to several animations of the phenomena.","PeriodicalId":43454,"journal":{"name":"Annales Mathematicae et Informaticae","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72506716","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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