Pub Date : 2019-01-01DOI: 10.33039/AMI.2019.08.001
Á. Figula, Kornélia Ficzere, A. Al-Abayechi
Using connected transversals we determine the six-dimensional indecomposable solvable Lie groups with five-dimensional nilradical and their subgroups which are the multiplication groups and the inner mapping groups of three-dimensional connected simply connected topological loops. Together with this result we obtain that every six-dimensional indecomposable solvable Lie group which is the multiplication group of a three-dimensional topological loop has one-dimensional centre and twoor three-dimensional commutator subgroup.
{"title":"Topological loops with six-dimensional solvable multiplication groups having five-dimensional nilradical","authors":"Á. Figula, Kornélia Ficzere, A. Al-Abayechi","doi":"10.33039/AMI.2019.08.001","DOIUrl":"https://doi.org/10.33039/AMI.2019.08.001","url":null,"abstract":"Using connected transversals we determine the six-dimensional indecomposable solvable Lie groups with five-dimensional nilradical and their subgroups which are the multiplication groups and the inner mapping groups of three-dimensional connected simply connected topological loops. Together with this result we obtain that every six-dimensional indecomposable solvable Lie group which is the multiplication group of a three-dimensional topological loop has one-dimensional centre and twoor three-dimensional commutator subgroup.","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":"83363782","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":"Pillai’s problem with the Fibonacci andPadovan sequences","authors":"Ana Cecilia García Lomelí, S. Hernández, F. Luca","doi":"10.33039/ami.2019.09.001","DOIUrl":"https://doi.org/10.33039/ami.2019.09.001","url":null,"abstract":"Let ( 𝐹 𝑚 ) 𝑚 > 0 and ( 𝑃 𝑛 ) 𝑛 > 0 be the Fibonacci and Padovan sequences given by the initial conditions 𝐹 0 = 0 , 𝐹 1 = 1 , 𝑃 0 = 0 , 𝑃 1 = 𝑃 2 = 1 and the recurrence formulas 𝐹 𝑚 +2 = 𝐹 𝑚 +1 + 𝐹 𝑚 , 𝑃 𝑛 +3 = 𝑃 𝑛 +1 + 𝑃 𝑛 for all 𝑚, 𝑛 > 0 , respectively. In this note we study and completely solve the Diophantine","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":"76751260","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.2019.03.002
Dániel Fülöp, Carolin Hannusch
We introduce an algorithm for the generation of complement-free sets of binary 𝑚 -tuples, where 𝑚 is even. We also provide an implementation for this algorithm for 𝑚 = 12 . Such complement-free sets are needed for the generation of a new class of error-correcting codes, which were introduced by Hannusch and Lakatos. These codes build the fundamental improvement in the cryptographic system of Dömösi, Hannusch and Horváth. Therefore the generation of complement-free sets will be important for cryptographic applications. In the end of the paper we give some interesting facts about complement-free sets as combinatorial objects.
{"title":"Algorithm for the generation of complement-free sets","authors":"Dániel Fülöp, Carolin Hannusch","doi":"10.33039/ami.2019.03.002","DOIUrl":"https://doi.org/10.33039/ami.2019.03.002","url":null,"abstract":"We introduce an algorithm for the generation of complement-free sets of binary 𝑚 -tuples, where 𝑚 is even. We also provide an implementation for this algorithm for 𝑚 = 12 . Such complement-free sets are needed for the generation of a new class of error-correcting codes, which were introduced by Hannusch and Lakatos. These codes build the fundamental improvement in the cryptographic system of Dömösi, Hannusch and Horváth. Therefore the generation of complement-free sets will be important for cryptographic applications. In the end of the paper we give some interesting facts about complement-free sets as combinatorial objects.","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":"83285363","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.2019.02.002
A. Lovas, R. Nagy, P. Sótonyi, B. Szilágyi
We present a new algorithm to reconstruct the volumetric flux in the aorta. We study a simple 1D blood flow model without viscosity term and sophisticated material model. Using the continuity law, we could reduce the original inverse problem related to a system of PDEs to a parameter iden-tification problem involving a Riccati-type ODE with periodic coefficients. We implemented a block-based optimization algorithm to recover the model parameters. We tested our method on real data obtained using CG-gated CT angiography imaging of the aorta. Local flow rate was calculated in 10 cm long aorta segments which are located 1 cm below the heart. The reconstructed volumetric flux shows a realistic wave-like behavior, where reflections from arteria iliaca can also be observed. Our approach is suitable for estimating the main characteristics of pulsatile flow in the aorta and thereby contributing to a more accurate description of several cardiovascular lesions.
{"title":"Volumetric flow rate reconstructionin great vessels","authors":"A. Lovas, R. Nagy, P. Sótonyi, B. Szilágyi","doi":"10.33039/AMI.2019.02.002","DOIUrl":"https://doi.org/10.33039/AMI.2019.02.002","url":null,"abstract":"We present a new algorithm to reconstruct the volumetric flux in the aorta. We study a simple 1D blood flow model without viscosity term and sophisticated material model. Using the continuity law, we could reduce the original inverse problem related to a system of PDEs to a parameter iden-tification problem involving a Riccati-type ODE with periodic coefficients. We implemented a block-based optimization algorithm to recover the model parameters. We tested our method on real data obtained using CG-gated CT angiography imaging of the aorta. Local flow rate was calculated in 10 cm long aorta segments which are located 1 cm below the heart. The reconstructed volumetric flux shows a realistic wave-like behavior, where reflections from arteria iliaca can also be observed. Our approach is suitable for estimating the main characteristics of pulsatile flow in the aorta and thereby contributing to a more accurate description of several cardiovascular lesions.","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":"85248620","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.2019.11.002
Armand Noubissie, A. Togbé
{"title":"A note on the exponential Diophantineequation(𝑎𝑛−1)(𝑏𝑛−1) =𝑥2","authors":"Armand Noubissie, A. Togbé","doi":"10.33039/ami.2019.11.002","DOIUrl":"https://doi.org/10.33039/ami.2019.11.002","url":null,"abstract":"","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":"86543635","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.2019.12.001
T. Tómács
In this paper a Marcinkiewicz–Zygmund type strong law of large numbers is proved for non-negative random variables with multidimensional indices, furthermore we give its an application for multi-index sequence of nonnegative random variables with finite variances.
{"title":"A Marcinkiewicz–Zygmund type strong law of large numbers for non-negative random variables with multidimensional indices","authors":"T. Tómács","doi":"10.33039/ami.2019.12.001","DOIUrl":"https://doi.org/10.33039/ami.2019.12.001","url":null,"abstract":"In this paper a Marcinkiewicz–Zygmund type strong law of large numbers is proved for non-negative random variables with multidimensional indices, furthermore we give its an application for multi-index sequence of nonnegative random variables with finite variances.","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":"79064517","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.2018.09.002
C. Biró, Gábor Kusper
Node localization and ranking is an essential issue in wireless sensor networks (WSNs). We model WSNs by communication graphs. In our inter-pretation a communication graph can be directed, in case of heterogeneous sensor nodes, or undirected, in case of homogeneous sensor nodes, and must be strongly connected. There are many metrics to characterize networks, most of them are either global ones or local ones. The local ones consider only the immediate neighbors of the observed nodes. We are not aware of a metric which considers a subgraph, i.e., which is between global and local ones. So our main goal was to construct metrics that interpret the local properties of the nodes in a wider environment. For example, how dense the environment of the given node, or in which extent it can be relieved within its environment. In this article we introduce several novel 𝑘 -hop based density and redundancy metrics: Weighted Communication Graph Density ( 𝒲𝒞𝒢𝒟 ), Relative Communication Graph Density ( ℛ𝒞𝒢𝒟 ), Weighted Relative Communication Graph Density ( 𝒲ℛ𝒞𝒢𝒟 ), Communication Graph Redundancy ( 𝒞𝒢ℛ ), Weighted Communication Graph Redundancy ( 𝒲𝒞𝒢ℛ ). We compare them to known graph metrics, and show that they can be used for node ranking.
{"title":"Somek-hop based graph metrics and noderanking in wireless sensor networks","authors":"C. Biró, Gábor Kusper","doi":"10.33039/ami.2018.09.002","DOIUrl":"https://doi.org/10.33039/ami.2018.09.002","url":null,"abstract":"Node localization and ranking is an essential issue in wireless sensor networks (WSNs). We model WSNs by communication graphs. In our inter-pretation a communication graph can be directed, in case of heterogeneous sensor nodes, or undirected, in case of homogeneous sensor nodes, and must be strongly connected. There are many metrics to characterize networks, most of them are either global ones or local ones. The local ones consider only the immediate neighbors of the observed nodes. We are not aware of a metric which considers a subgraph, i.e., which is between global and local ones. So our main goal was to construct metrics that interpret the local properties of the nodes in a wider environment. For example, how dense the environment of the given node, or in which extent it can be relieved within its environment. In this article we introduce several novel 𝑘 -hop based density and redundancy metrics: Weighted Communication Graph Density ( 𝒲𝒞𝒢𝒟 ), Relative Communication Graph Density ( ℛ𝒞𝒢𝒟 ), Weighted Relative Communication Graph Density ( 𝒲ℛ𝒞𝒢𝒟 ), Communication Graph Redundancy ( 𝒞𝒢ℛ ), Weighted Communication Graph Redundancy ( 𝒲𝒞𝒢ℛ ). We compare them to known graph metrics, and show that they can be used for node ranking.","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":"89400833","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.2019.03.004
Aubrey Blecher, Charlotte Brennan, Arnold Knopfmacher, Mark Shattuck
{"title":"Capacity of permutations Annales Mathematicae et Informaticae","authors":"Aubrey Blecher, Charlotte Brennan, Arnold Knopfmacher, Mark Shattuck","doi":"10.33039/AMI.2019.03.004","DOIUrl":"https://doi.org/10.33039/AMI.2019.03.004","url":null,"abstract":"","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":"88460788","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.2019.11.003
Á. Győry, E. Kónya
We examined the evolution of the van Hiele level of some study groups specialized in mathematics from 2015 to 2018, then selected two of these groups and measured the students’ proof skills by Zalman Usiskin’s proof test. We examined whether students were able to read from the text of the statement the given fact and the fact to be proved, whether they were able to draw a figure and, using the labels, whether they were able to perform a simple proof requiring 2-3 steps.
{"title":"Proving skills in geometry of secondary grammar school leavers specialized in mathematics","authors":"Á. Győry, E. Kónya","doi":"10.33039/ami.2019.11.003","DOIUrl":"https://doi.org/10.33039/ami.2019.11.003","url":null,"abstract":"We examined the evolution of the van Hiele level of some study groups specialized in mathematics from 2015 to 2018, then selected two of these groups and measured the students’ proof skills by Zalman Usiskin’s proof test. We examined whether students were able to read from the text of the statement the given fact and the fact to be proved, whether they were able to draw a figure and, using the labels, whether they were able to perform a simple proof requiring 2-3 steps.","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":"79481824","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.2019.01.002
Ádám Tóth, Ramin Karimi
Unexpected growth of high-throughput sequencing platforms in recent years impacted virtually all areas of modern biology. However, the ability to produce data continues to outpace the ability to analyze them. Therefore, continuous efforts are also needed to improve bioinformatics applications for a better use of these research opportunities. Due to the complexity and diver-sity of metagenomics data, it has been a major challenging field of bioinformatics. Sequence-based identification methods such as using DNA signature (unique k-mer) are the most recent popular methods of real-time analysis of raw sequencing data. DNA signature discovery is compute-intensive and time-consuming.Hadoop,the application of parallel and distributed computing is one of the popular applications for the analysis of large scale data in bioinformatics. Optimization of the time-consumption and computational resource usages such as CPU consumption and memory usage are the main goals of this paper, along with the management of the Hadoop cluster nodes.
{"title":"Optimization of hadoop cluster foranalyzing large-scale sequence data inbioinformatics","authors":"Ádám Tóth, Ramin Karimi","doi":"10.33039/AMI.2019.01.002","DOIUrl":"https://doi.org/10.33039/AMI.2019.01.002","url":null,"abstract":"Unexpected growth of high-throughput sequencing platforms in recent years impacted virtually all areas of modern biology. However, the ability to produce data continues to outpace the ability to analyze them. Therefore, continuous efforts are also needed to improve bioinformatics applications for a better use of these research opportunities. Due to the complexity and diver-sity of metagenomics data, it has been a major challenging field of bioinformatics. Sequence-based identification methods such as using DNA signature (unique k-mer) are the most recent popular methods of real-time analysis of raw sequencing data. DNA signature discovery is compute-intensive and time-consuming.Hadoop,the application of parallel and distributed computing is one of the popular applications for the analysis of large scale data in bioinformatics. Optimization of the time-consumption and computational resource usages such as CPU consumption and memory usage are the main goals of this paper, along with the management of the Hadoop cluster nodes.","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":"76044160","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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