Pub Date : 2020-01-01DOI: 10.33039/ami.2020.07.007
A. Fekete, Z. Porkoláb
Software comprehension is one of the most important among software development tasks since most developers do not start a brand new software every time they switch jobs or get transferred from one project to another but join long-running software projects. Every experienced and expert developer has their own established methods of understanding complex software systems. These methods might be different for everyone but they still have common aspects by which multiple well-defined code comprehension models can be constructed. Furthermore, the degree of understanding of a software can be categorized as well, according to the ability of the programmer to mod-ify or develop a certain part of the software system. This paper is intended to provide a review of the cognitive software comprehension models established by extensive research in this topic as well as describe the dimensions of understanding software. It also determines the editor support of cognition models by examining common editor functionalities and categorizing code editors based on the availability of functionalities of each cognition approach.
{"title":"A comprehensive review on software comprehension models","authors":"A. Fekete, Z. Porkoláb","doi":"10.33039/ami.2020.07.007","DOIUrl":"https://doi.org/10.33039/ami.2020.07.007","url":null,"abstract":"Software comprehension is one of the most important among software development tasks since most developers do not start a brand new software every time they switch jobs or get transferred from one project to another but join long-running software projects. Every experienced and expert developer has their own established methods of understanding complex software systems. These methods might be different for everyone but they still have common aspects by which multiple well-defined code comprehension models can be constructed. Furthermore, the degree of understanding of a software can be categorized as well, according to the ability of the programmer to mod-ify or develop a certain part of the software system. This paper is intended to provide a review of the cognitive software comprehension models established by extensive research in this topic as well as describe the dimensions of understanding software. It also determines the editor support of cognition models by examining common editor functionalities and categorizing code editors based on the availability of functionalities of each cognition approach.","PeriodicalId":43454,"journal":{"name":"Annales Mathematicae et Informaticae","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82618678","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 : 2020-01-01DOI: 10.33039/ami.2020.05.005
V. Baláž, Kálmán Liptai, János Tóth T., T. Visnyai
Let ℐ ⊆ 2 N be an admissible ideal, we say that a sequence ( 𝑥 𝑛 ) of real numbers ℐ− converges to a number 𝐿 , and write ℐ − lim 𝑥 𝑛 = 𝐿 , if for each 𝜀 > 0 the set 𝐴 𝜀 = { 𝑛 : | 𝑥 𝑛 − 𝐿 | ≥ 𝜀 } belongs to the ideal ℐ . In this paper we discuss the relation ship between convergence of positive series and the convergence properties of the summand sequence. Concretely, we study the ideals ℐ having the following property as well:
{"title":"Convergence of positive series and ideal convergence","authors":"V. Baláž, Kálmán Liptai, János Tóth T., T. Visnyai","doi":"10.33039/ami.2020.05.005","DOIUrl":"https://doi.org/10.33039/ami.2020.05.005","url":null,"abstract":"Let ℐ ⊆ 2 N be an admissible ideal, we say that a sequence ( 𝑥 𝑛 ) of real numbers ℐ− converges to a number 𝐿 , and write ℐ − lim 𝑥 𝑛 = 𝐿 , if for each 𝜀 > 0 the set 𝐴 𝜀 = { 𝑛 : | 𝑥 𝑛 − 𝐿 | ≥ 𝜀 } belongs to the ideal ℐ . In this paper we discuss the relation ship between convergence of positive series and the convergence properties of the summand sequence. Concretely, we study the ideals ℐ having the following property as well:","PeriodicalId":43454,"journal":{"name":"Annales Mathematicae et Informaticae","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89200539","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 : 2020-01-01DOI: 10.33039/ami.2020.08.001
L. Fel, T. Komatsu, A. I. Suriajaya
We show explicit expressions for an inverse power series over the gaps values of numerical semigroups generated by two and three integers. As an application, a set of identities of the Hurwitz zeta functions is derived.
{"title":"A sum of negative degrees of the gaps values in 2 and 3-generated numerical semigroups","authors":"L. Fel, T. Komatsu, A. I. Suriajaya","doi":"10.33039/ami.2020.08.001","DOIUrl":"https://doi.org/10.33039/ami.2020.08.001","url":null,"abstract":"We show explicit expressions for an inverse power series over the gaps values of numerical semigroups generated by two and three integers. As an application, a set of identities of the Hurwitz zeta functions is derived.","PeriodicalId":43454,"journal":{"name":"Annales Mathematicae et Informaticae","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77332767","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 : 2020-01-01DOI: 10.33039/ami.2020.10.001
T. Tajti
We propose an algorithm improvement for classifying machine learning algorithms with the fuzzification of training data binary class membership values. This method can possibly be used to correct the training data output values during the training. The proposed modification can be used for algorithms running individual learners and also as an ensemble method for multiple learners for better performance. For this purpose, we define the single and the ensemble variants of the algorithm. Our experiment was done using convolutional neural network (CNN) classifiers for the base of our proposed method, however, these techniques might be used for other machine learning classifiers as well, which produce fuzzy output values. This fuzzification starts with using the original binary class membership values given in the dataset. During training these values are modified with the current knowledge of the machine learning algorithm.
{"title":"Fuzzification of training data class membership binary values for neural network algorithms","authors":"T. Tajti","doi":"10.33039/ami.2020.10.001","DOIUrl":"https://doi.org/10.33039/ami.2020.10.001","url":null,"abstract":"We propose an algorithm improvement for classifying machine learning algorithms with the fuzzification of training data binary class membership values. This method can possibly be used to correct the training data output values during the training. The proposed modification can be used for algorithms running individual learners and also as an ensemble method for multiple learners for better performance. For this purpose, we define the single and the ensemble variants of the algorithm. Our experiment was done using convolutional neural network (CNN) classifiers for the base of our proposed method, however, these techniques might be used for other machine learning classifiers as well, which produce fuzzy output values. This fuzzification starts with using the original binary class membership values given in the dataset. During training these values are modified with the current knowledge of the machine learning algorithm.","PeriodicalId":43454,"journal":{"name":"Annales Mathematicae et Informaticae","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78699733","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 : 2020-01-01DOI: 10.33039/ami.2020.10.002
Frontczak Robert, Goy Taras
The aim of the paper is to use some identities involving binomial coefficients to derive new combinatorial identities for balancing and Lucasbalancing polynomials. Evaluating these identities at specific points, we can also establish some combinatorial expressions for Fibonacci and Lucas numbers.
{"title":"Combinatorial sums associated with balancing and Lucas-balancing polynomials","authors":"Frontczak Robert, Goy Taras","doi":"10.33039/ami.2020.10.002","DOIUrl":"https://doi.org/10.33039/ami.2020.10.002","url":null,"abstract":"The aim of the paper is to use some identities involving binomial coefficients to derive new combinatorial identities for balancing and Lucasbalancing polynomials. Evaluating these identities at specific points, we can also establish some combinatorial expressions for Fibonacci and Lucas numbers.","PeriodicalId":43454,"journal":{"name":"Annales Mathematicae et Informaticae","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77120957","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 : 2020-01-01DOI: 10.33039/ami.2020.07.002
Ádám Kaló, Zoltán Kincses, Laszlo Schaffer, Szilveszter Pletl
Indoor position estimation is an important part of any indoor application which contains object tracking or environment mapping. Many indoor localization techniques (Angle of Arrival – AoA, Time of Flight – ToF, Return Time of Flight – RToF, Received Signal Strength Indicator – RSSI) and technologies (WiFi, Ultra Wideband – UWB, Bluetooth, Radio Frequency Identification Device – RFID) exist which can be applied to the indoor localization problem. Based on the measured distances (with a chosen technique), the position of the object can be estimated using several mathematical methods. The precision of the estimated position crucially depends on the placement of the anchors, which makes the position estimate less reliable. In this paper a simulation framework is presented, which uses genetic algorithm and the multilateral method to determine an optimal anchor placement for a given pathway in an indoor environment. In order to make the simulation more realistic, the error characteristics of the DWM1001 UWB ranging module were measured and implemented in the simulation framework. Using the proposed framework, various measurements with an optimal and with a reference anchor placement were carried out. The results show that using an optimal anchor placement, a higher position estimation accuracy can be achieved.
{"title":"Indoor localization simulation framework for optimized sensor placement to increase the position estimation accuracy","authors":"Ádám Kaló, Zoltán Kincses, Laszlo Schaffer, Szilveszter Pletl","doi":"10.33039/ami.2020.07.002","DOIUrl":"https://doi.org/10.33039/ami.2020.07.002","url":null,"abstract":"Indoor position estimation is an important part of any indoor application which contains object tracking or environment mapping. Many indoor localization techniques (Angle of Arrival – AoA, Time of Flight – ToF, Return Time of Flight – RToF, Received Signal Strength Indicator – RSSI) and technologies (WiFi, Ultra Wideband – UWB, Bluetooth, Radio Frequency Identification Device – RFID) exist which can be applied to the indoor localization problem. Based on the measured distances (with a chosen technique), the position of the object can be estimated using several mathematical methods. The precision of the estimated position crucially depends on the placement of the anchors, which makes the position estimate less reliable. In this paper a simulation framework is presented, which uses genetic algorithm and the multilateral method to determine an optimal anchor placement for a given pathway in an indoor environment. In order to make the simulation more realistic, the error characteristics of the DWM1001 UWB ranging module were measured and implemented in the simulation framework. Using the proposed framework, various measurements with an optimal and with a reference anchor placement were carried out. The results show that using an optimal anchor placement, a higher position estimation accuracy can be achieved.","PeriodicalId":43454,"journal":{"name":"Annales Mathematicae et Informaticae","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88331071","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 : 2020-01-01DOI: 10.33039/ami.2020.02.003
J. Kok, S. Naduvath, E. Mphako-Banda
In this paper, the notions of rainbow neighbourhood and rainbow neighbourhood number of a graph are generalised and further to these generalisations, the notion of a proper 𝑘 -jump colouring of a graph is also introduced. The generalisations follow from the understanding that a closed 𝑘 neighbourhood of a vertex 𝑣 ∈ 𝑉 ( 𝐺 ) denoted, 𝑁 𝑘 [ 𝑣 ] is the set, 𝑁 𝑘 [ 𝑣 ] = { 𝑢 : 𝑑 ( 𝑣, 𝑢 ) ≤ 𝑘, 𝑘 ∈ N and 𝑘 ≤ 𝑑𝑖𝑎𝑚 ( 𝐺 ) } . If the closed 𝑘 -neighbourhood 𝑁 𝑘 [ 𝑣 ] contains at least one of each colour of the chromatic colour set, we say that 𝑣 yields a 𝑘 -rainbow neighbourhood.
{"title":"Generalisation of the rainbow neighbourhood number and 𝑘-jump colouring of a graph","authors":"J. Kok, S. Naduvath, E. Mphako-Banda","doi":"10.33039/ami.2020.02.003","DOIUrl":"https://doi.org/10.33039/ami.2020.02.003","url":null,"abstract":"In this paper, the notions of rainbow neighbourhood and rainbow neighbourhood number of a graph are generalised and further to these generalisations, the notion of a proper 𝑘 -jump colouring of a graph is also introduced. The generalisations follow from the understanding that a closed 𝑘 neighbourhood of a vertex 𝑣 ∈ 𝑉 ( 𝐺 ) denoted, 𝑁 𝑘 [ 𝑣 ] is the set, 𝑁 𝑘 [ 𝑣 ] = { 𝑢 : 𝑑 ( 𝑣, 𝑢 ) ≤ 𝑘, 𝑘 ∈ N and 𝑘 ≤ 𝑑𝑖𝑎𝑚 ( 𝐺 ) } . If the closed 𝑘 -neighbourhood 𝑁 𝑘 [ 𝑣 ] contains at least one of each colour of the chromatic colour set, we say that 𝑣 yields a 𝑘 -rainbow neighbourhood.","PeriodicalId":43454,"journal":{"name":"Annales Mathematicae et Informaticae","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87835339","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 : 2019-06-26DOI: 10.33039/AMI.2019.06.001
F. Erduvan, R. Keskin
The Fibonacci sequence (Fn) is defined by F0 = 0, F1 = 1 and Fn = Fn−1 + Fn−2 for n ≥ 2. The balancing number sequence (Bn) is defined by B0 = 0, B1 = 1 and Bn = 6Bn−1 − Bn−2 for n ≥ 2. In this paper, we find all Fibonacci numbers which are products of two balancing numbers. Also we found all balancing numbers which are products of two Fibonacci numbers. More generally, taking k,m,m as positive integers, it is proved that Fk = BmBn implies that (k,m, n) = (1, 1, 1), (2, 1, 1) and Bk = FmFn implies that (k,m, n) = (1, 1, 1), (1, 1, 2), (1, 2, 2), (2, 3, 4).
{"title":"Fibonacci numbers which are products of two balancing numbers","authors":"F. Erduvan, R. Keskin","doi":"10.33039/AMI.2019.06.001","DOIUrl":"https://doi.org/10.33039/AMI.2019.06.001","url":null,"abstract":"The Fibonacci sequence (Fn) is defined by F0 = 0, F1 = 1 and Fn = Fn−1 + Fn−2 for n ≥ 2. The balancing number sequence (Bn) is defined by B0 = 0, B1 = 1 and Bn = 6Bn−1 − Bn−2 for n ≥ 2. In this paper, we find all Fibonacci numbers which are products of two balancing numbers. Also we found all balancing numbers which are products of two Fibonacci numbers. More generally, taking k,m,m as positive integers, it is proved that Fk = BmBn implies that (k,m, n) = (1, 1, 1), (2, 1, 1) and Bk = FmFn implies that (k,m, n) = (1, 1, 1), (1, 1, 2), (1, 2, 2), (2, 3, 4).","PeriodicalId":43454,"journal":{"name":"Annales Mathematicae et Informaticae","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2019-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75818742","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 : 2019-01-08DOI: 10.33039/ami.2019.03.003
J. Merikoski, P. Haukkanen, T. Tossavainen
We first introduce the arithmetic subderivative of a positive integer with respect to a non-empty set of primes. This notion generalizes the concepts of the arithmetic derivative and arithmetic partial derivative. More generally, we then define that an arithmetic function $f$ is Leibniz-additive if there is a nonzero-valued and completely multiplicative function $h_f$ satisfying $f(mn)=f(m)h_f(n)+f(n)h_f(m)$ for all positive integers $m$ and $n$. We study some basic properties of such functions. For example, we present conditions when an arithmetic function is Leibniz-additive and, generalizing well-known bounds for the arithmetic derivative, establish bounds for a Leibniz-additive function.
{"title":"Arithmetic subderivatives and Leibniz-additive functions","authors":"J. Merikoski, P. Haukkanen, T. Tossavainen","doi":"10.33039/ami.2019.03.003","DOIUrl":"https://doi.org/10.33039/ami.2019.03.003","url":null,"abstract":"We first introduce the arithmetic subderivative of a positive integer with respect to a non-empty set of primes. This notion generalizes the concepts of the arithmetic derivative and arithmetic partial derivative. More generally, we then define that an arithmetic function $f$ is Leibniz-additive if there is a nonzero-valued and completely multiplicative function $h_f$ satisfying $f(mn)=f(m)h_f(n)+f(n)h_f(m)$ for all positive integers $m$ and $n$. We study some basic properties of such functions. For example, we present conditions when an arithmetic function is Leibniz-additive and, generalizing well-known bounds for the arithmetic derivative, establish bounds for a Leibniz-additive function.","PeriodicalId":43454,"journal":{"name":"Annales Mathematicae et Informaticae","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2019-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78538700","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 : 2019-01-01DOI: 10.33039/ami.2019.01.001
L. Belarbi
In this work we study constant extrinsically Gaussian curvature translation surfaces in the 3-dimensional Heisenberg group which are invariant under the 1-parameter groups of isometries.
{"title":"Surfaces with constant extrinsically Gaussian curvature in the Heisenberg group","authors":"L. Belarbi","doi":"10.33039/ami.2019.01.001","DOIUrl":"https://doi.org/10.33039/ami.2019.01.001","url":null,"abstract":"In this work we study constant extrinsically Gaussian curvature translation surfaces in the 3-dimensional Heisenberg group which are invariant under the 1-parameter groups of isometries.","PeriodicalId":43454,"journal":{"name":"Annales Mathematicae et Informaticae","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85517680","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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