Pub Date : 2021-01-01DOI: 10.33039/AMI.2021.03.016
R. Frontczak
In this note, we introduce a very simple approach to obtain Horadam identities with binomial coefficients including an additional parameter. Many known Fibonacci identities (as well as polynomial identities) will follow im-mediately as special cases.
{"title":"A short remark on Horadam identities with binomial coefficients","authors":"R. Frontczak","doi":"10.33039/AMI.2021.03.016","DOIUrl":"https://doi.org/10.33039/AMI.2021.03.016","url":null,"abstract":"In this note, we introduce a very simple approach to obtain Horadam identities with binomial coefficients including an additional parameter. Many known Fibonacci identities (as well as polynomial identities) will follow im-mediately as special cases.","PeriodicalId":43454,"journal":{"name":"Annales Mathematicae et Informaticae","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79365407","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 : 2021-01-01DOI: 10.33039/ami.2021.08.003
Zoltán Matos, E. Kónya
In the first decade after the turn of the millennium, previous doubts about the inclusion of the history of mathematics in education also received more attention. Several researchers point to the difficulties of teachers enthusiastic on the topic, to the research methodological difficulties of such studies, and the need to increase the number of empirical researches. In addition to increasing the amount of such empirical evidence, this paper seeks to contribute to the continuously developing answers to the basic questions (what and how?) of integrating the history of mathematics into public education in the recent decades by presenting a given topic, the teaching of numeral systems based on history, and the results of the related surveys. In the course of our research, we examined the question of whether the use of the history of mathematics as a tool, as opposed to teaching by focusing solely on routine tasks, helps to fix the curriculum into the long-term memory.
{"title":"Teaching numeral systems based on history in high school","authors":"Zoltán Matos, E. Kónya","doi":"10.33039/ami.2021.08.003","DOIUrl":"https://doi.org/10.33039/ami.2021.08.003","url":null,"abstract":"In the first decade after the turn of the millennium, previous doubts about the inclusion of the history of mathematics in education also received more attention. Several researchers point to the difficulties of teachers enthusiastic on the topic, to the research methodological difficulties of such studies, and the need to increase the number of empirical researches. In addition to increasing the amount of such empirical evidence, this paper seeks to contribute to the continuously developing answers to the basic questions (what and how?) of integrating the history of mathematics into public education in the recent decades by presenting a given topic, the teaching of numeral systems based on history, and the results of the related surveys. In the course of our research, we examined the question of whether the use of the history of mathematics as a tool, as opposed to teaching by focusing solely on routine tasks, helps to fix the curriculum into the long-term memory.","PeriodicalId":43454,"journal":{"name":"Annales Mathematicae et Informaticae","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73375576","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 : 2021-01-01DOI: 10.33039/ami.2021.10.003
M. Różański, Barbara Smolen-Duda, R. Witula, Marcin Jochlik, Adrian Smuda
The paper presents original methods of calculating integrals of selected trigonometric rational functions.
本文给出了计算三角有理函数积分的原始方法。
{"title":"On some methods of calculating the integrals of trigonometric rational functions","authors":"M. Różański, Barbara Smolen-Duda, R. Witula, Marcin Jochlik, Adrian Smuda","doi":"10.33039/ami.2021.10.003","DOIUrl":"https://doi.org/10.33039/ami.2021.10.003","url":null,"abstract":"The paper presents original methods of calculating integrals of selected trigonometric rational functions.","PeriodicalId":43454,"journal":{"name":"Annales Mathematicae et Informaticae","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88328203","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 : 2021-01-01DOI: 10.33039/ami.2021.09.002
Wanna Sriprad, Somnuk Srisawat, Peesiri Naklor
In this paper, we introduce a new type of the Vieta polynomial, which is Vieta–Fibonacci-like polynomial. After that, we establish the Binet formula, the generating function, the well-known identities, and the sum formula of this polynomial. Finally, we present the relationship between this polynomial and the previous well-known Vieta polynomials.
{"title":"Vieta–Fibonacci-like polynomials and some identities","authors":"Wanna Sriprad, Somnuk Srisawat, Peesiri Naklor","doi":"10.33039/ami.2021.09.002","DOIUrl":"https://doi.org/10.33039/ami.2021.09.002","url":null,"abstract":"In this paper, we introduce a new type of the Vieta polynomial, which is Vieta–Fibonacci-like polynomial. After that, we establish the Binet formula, the generating function, the well-known identities, and the sum formula of this polynomial. Finally, we present the relationship between this polynomial and the previous well-known Vieta polynomials.","PeriodicalId":43454,"journal":{"name":"Annales Mathematicae et Informaticae","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82410979","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 : 2021-01-01DOI: 10.33039/ami.2021.10.001
Szilárd Svitek, Miklós Vontszemű
Let 0 ≤ 𝑞 ≤ 1 and N denotes the set of all positive integers. In this paper we will be interested in the family 𝒰 ( 𝑥 𝑞 ) of all regularly distributed set 𝑋 ⊂ N whose ratio block sequence is asymptotically distributed with distribution function 𝑔 ( 𝑥 ) = 𝑥 𝑞 ; 𝑥 ∈ (0 , 1] , and we will study the structure of this family with respect to the union.
{"title":"On structure of the family of regularly distributed sets with respect to the union","authors":"Szilárd Svitek, Miklós Vontszemű","doi":"10.33039/ami.2021.10.001","DOIUrl":"https://doi.org/10.33039/ami.2021.10.001","url":null,"abstract":"Let 0 ≤ 𝑞 ≤ 1 and N denotes the set of all positive integers. In this paper we will be interested in the family 𝒰 ( 𝑥 𝑞 ) of all regularly distributed set 𝑋 ⊂ N whose ratio block sequence is asymptotically distributed with distribution function 𝑔 ( 𝑥 ) = 𝑥 𝑞 ; 𝑥 ∈ (0 , 1] , and we will study the structure of this family with respect to the union.","PeriodicalId":43454,"journal":{"name":"Annales Mathematicae et Informaticae","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86539940","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 : 2020-09-27DOI: 10.33039/AMI.2020.09.001
G. Lucca
The paper presents formulas and conditions relevant to the construction of chains of mutually tangent ellipses inscribed inside a parabola. Moreover, some connections with certain integer sequences and Pythagorean triplets are shown.
{"title":"Ellipse chains inscribed inside a parabola and integer sequences","authors":"G. Lucca","doi":"10.33039/AMI.2020.09.001","DOIUrl":"https://doi.org/10.33039/AMI.2020.09.001","url":null,"abstract":"The paper presents formulas and conditions relevant to the construction of chains of mutually tangent ellipses inscribed inside a parabola. Moreover, some connections with certain integer sequences and Pythagorean triplets are shown.","PeriodicalId":43454,"journal":{"name":"Annales Mathematicae et Informaticae","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2020-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79223283","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 : 2020-06-05DOI: 10.33039/ami.2020.06.001
C. A. Gómez, Jhonny C. Gómez, F. Luca
We find all triples (x, y, z) of k-Fibonacci numbers which satisfy the Markov equation x + y + z = 3xyz. This paper continues and extends previous work by Luca and Srinivasan [6].
我们找到k-Fibonacci数的所有三元组(x, y, z)，它们满足马尔可夫方程x + y + z = 3xyz。本文继续并扩展了Luca和Srinivasan[6]之前的工作。
{"title":"Markov triples with k-generalized Fibonacci components","authors":"C. A. Gómez, Jhonny C. Gómez, F. Luca","doi":"10.33039/ami.2020.06.001","DOIUrl":"https://doi.org/10.33039/ami.2020.06.001","url":null,"abstract":"We find all triples (x, y, z) of k-Fibonacci numbers which satisfy the Markov equation x + y + z = 3xyz. This paper continues and extends previous work by Luca and Srinivasan [6].","PeriodicalId":43454,"journal":{"name":"Annales Mathematicae et Informaticae","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2020-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85140423","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 : 2020-06-03DOI: 10.33039/ami.2020.05.004
V. Ďuriš, A. Tirpáková
The article deals with experimental comparison and verification of stochastic algorithms for global optimization while searching the global optimum in dimensions 3 and 4 of selected testing functions in Matlab computing environment. To draw a comparison, we took the algorithms Controlled Random Search, Differential Evolution that we created for this test and implemented in Matlab, and fminsearch function which is directly built in Matlab. The basic quantities to compare algorithms were time complexity while searching the considered area and reliability of finding the global optimum of the 1st De Jong function, Rosenbrock’s saddle, Ackley’s function and Griewangk’s function. The time complexity of the algorithms was determined by the number of test function evaluations during the global optimum search and we analysed the results of the experiment using the “Kruskal–Wallis test” non-parametric
{"title":"A survey on the global optimization problem using Kruskal–Wallis test","authors":"V. Ďuriš, A. Tirpáková","doi":"10.33039/ami.2020.05.004","DOIUrl":"https://doi.org/10.33039/ami.2020.05.004","url":null,"abstract":"The article deals with experimental comparison and verification of stochastic algorithms for global optimization while searching the global optimum in dimensions 3 and 4 of selected testing functions in Matlab computing environment. To draw a comparison, we took the algorithms Controlled Random Search, Differential Evolution that we created for this test and implemented in Matlab, and fminsearch function which is directly built in Matlab. The basic quantities to compare algorithms were time complexity while searching the considered area and reliability of finding the global optimum of the 1st De Jong function, Rosenbrock’s saddle, Ackley’s function and Griewangk’s function. The time complexity of the algorithms was determined by the number of test function evaluations during the global optimum search and we analysed the results of the experiment using the “Kruskal–Wallis test” non-parametric","PeriodicalId":43454,"journal":{"name":"Annales Mathematicae et Informaticae","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2020-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79854129","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 : 2020-05-01DOI: 10.33039/ami.2020.05.002
F. Nagy
The isoptic surface of a three-dimensional shape is defined in [1] as the generalization of isoptics of curves. The authors of the paper also presented an algorithm to determine isoptic surfaces of convex meshes. In [9] new searching algorithms are provided to find points of the isoptic surface of a triangulated model in E 3 . The new algorithms work for concave shapes as well.In this paper, we present a faster, simpler, and efficiently parallelised version of the algorithm of [9] that can be used to search for the points of the isoptic surface of a given closed polyhedral mesh, taking advantage of the computing capabilities of the high-performance graphics cards and using the benefits of nested parallelism. For the simultaneous computations, the NVIDIA’s Compute Unified Device Architecture (CUDA) was used. Our experiments show speedups up to 100 times using the new parallel algorithm.
{"title":"Efficiently parallelised algorithm to find isoptic surface of polyhedral meshes","authors":"F. Nagy","doi":"10.33039/ami.2020.05.002","DOIUrl":"https://doi.org/10.33039/ami.2020.05.002","url":null,"abstract":"The isoptic surface of a three-dimensional shape is defined in [1] as the generalization of isoptics of curves. The authors of the paper also presented an algorithm to determine isoptic surfaces of convex meshes. In [9] new searching algorithms are provided to find points of the isoptic surface of a triangulated model in E 3 . The new algorithms work for concave shapes as well.In this paper, we present a faster, simpler, and efficiently parallelised version of the algorithm of [9] that can be used to search for the points of the isoptic surface of a given closed polyhedral mesh, taking advantage of the computing capabilities of the high-performance graphics cards and using the benefits of nested parallelism. For the simultaneous computations, the NVIDIA’s Compute Unified Device Architecture (CUDA) was used. Our experiments show speedups up to 100 times using the new parallel algorithm.","PeriodicalId":43454,"journal":{"name":"Annales Mathematicae et Informaticae","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2020-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87642221","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 : 2020-01-09DOI: 10.33039/ami.2020.01.001
Pap Melinda, Király Sándor, Molják Sándor
Bioenergy plants are widely used as a form of renewable energy. It is important to monitor the vegetation and accurately estimate the yield before harvest in order to maximize the profit and reduce the costs of production. The automatic tracking of plant development by traditional methods is quite difficult and labor intensive. Nowadays, the application of Unmanned Aerial Vehicles (UAV) became more and more popular in precision agriculture. Detailed, precise, three-dimensional (3D) representations of energy forestry are required as a prior condition for an accurate assessment of crop growth. Using a small UAV equipped with a multispectral camera, we collected imagery of 1051 pictures of a study area in Kompolt, Hungary, then the Pix4D software was used to create a 3D model of the forest canopy. Remotely sensed data was processed with the aid of Pix4Dmapper to create the orthophotos and the digital surface model. The calculated Normalized Difference Vegetation Index (NDVI) values were also calculated. The aim of this case study was to do the first step towards yield estimation, and segment the created orthophoto, based on tree species. This is required, since different type of trees have different characteristics, thus, their yield calculations may differ. How-ever, the trees in the study area are versatile, there are also hybrids of the same species present. This paper presents the results of several segmentation algorithms, such as those that the widely used eCognition provides and other Matlab implementations of segmentation algorithms.
{"title":"Analysing the vegetation of energy plantsby processing UAV images","authors":"Pap Melinda, Király Sándor, Molják Sándor","doi":"10.33039/ami.2020.01.001","DOIUrl":"https://doi.org/10.33039/ami.2020.01.001","url":null,"abstract":"Bioenergy plants are widely used as a form of renewable energy. It is important to monitor the vegetation and accurately estimate the yield before harvest in order to maximize the profit and reduce the costs of production. The automatic tracking of plant development by traditional methods is quite difficult and labor intensive. Nowadays, the application of Unmanned Aerial Vehicles (UAV) became more and more popular in precision agriculture. Detailed, precise, three-dimensional (3D) representations of energy forestry are required as a prior condition for an accurate assessment of crop growth. Using a small UAV equipped with a multispectral camera, we collected imagery of 1051 pictures of a study area in Kompolt, Hungary, then the Pix4D software was used to create a 3D model of the forest canopy. Remotely sensed data was processed with the aid of Pix4Dmapper to create the orthophotos and the digital surface model. The calculated Normalized Difference Vegetation Index (NDVI) values were also calculated. The aim of this case study was to do the first step towards yield estimation, and segment the created orthophoto, based on tree species. This is required, since different type of trees have different characteristics, thus, their yield calculations may differ. How-ever, the trees in the study area are versatile, there are also hybrids of the same species present. This paper presents the results of several segmentation algorithms, such as those that the widely used eCognition provides and other Matlab implementations of segmentation algorithms.","PeriodicalId":43454,"journal":{"name":"Annales Mathematicae et Informaticae","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2020-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81914726","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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