Pub Date : 2022-01-01DOI: 10.33039/ami.2022.10.001
T. Tómács
In the LATEX document preparation system (see [3]) it is possible to insert automatically the appropriate definite article for cross-references and other commands containing texts in Hungarian language documents. Thus, if these change, the definite articles will also change accordingly. Such a tool is the magyar.ldf, which sets the Hungarian typography and also handles the automatic definite articles. Another one is the nevelok package, created specifically for this task. Both packages work with numerous errors and have shortcomings. This motivated the author of this paper to develop a new package, that corrects these errors and fills the gaps in. The new package is called huaz.
{"title":"On a new LaTeX package for automatic Hungarian definite article","authors":"T. Tómács","doi":"10.33039/ami.2022.10.001","DOIUrl":"https://doi.org/10.33039/ami.2022.10.001","url":null,"abstract":"In the LATEX document preparation system (see [3]) it is possible to insert automatically the appropriate definite article for cross-references and other commands containing texts in Hungarian language documents. Thus, if these change, the definite articles will also change accordingly. Such a tool is the magyar.ldf, which sets the Hungarian typography and also handles the automatic definite articles. Another one is the nevelok package, created specifically for this task. Both packages work with numerous errors and have shortcomings. This motivated the author of this paper to develop a new package, that corrects these errors and fills the gaps in. The new package is called huaz.","PeriodicalId":43454,"journal":{"name":"Annales Mathematicae et Informaticae","volume":"43 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77837675","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.2021.12.002
S. Rihane, Bir Kafle, A. Togbé
{"title":"Padovan and Perrin numbers of the form xᵃ ± xᵇ + 1","authors":"S. Rihane, Bir Kafle, A. Togbé","doi":"10.33039/ami.2021.12.002","DOIUrl":"https://doi.org/10.33039/ami.2021.12.002","url":null,"abstract":"","PeriodicalId":43454,"journal":{"name":"Annales Mathematicae et Informaticae","volume":"72 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86267809","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.2022.07.001
Valdete Loku
. In this paper, we will show Tauberian conditions under which ordinary convergence of the sequence ( 𝑥 𝑛 ) in 2-normed space 𝑋 , follows from 𝑇 𝑝,𝑞𝑛 -summability. In fact we give a necessary and sufficient Tauberian condition for this method of summability. Also, we prove that Tauberian Theorems for these summability methods are valid with Schmidt-type slowly oscillating condition as well as with Hardy-type “big O” condition.
{"title":"Tauberian theorems via the generalized Nörlund mean for sequences in 2-normed spaces","authors":"Valdete Loku","doi":"10.33039/ami.2022.07.001","DOIUrl":"https://doi.org/10.33039/ami.2022.07.001","url":null,"abstract":". In this paper, we will show Tauberian conditions under which ordinary convergence of the sequence ( 𝑥 𝑛 ) in 2-normed space 𝑋 , follows from 𝑇 𝑝,𝑞𝑛 -summability. In fact we give a necessary and sufficient Tauberian condition for this method of summability. Also, we prove that Tauberian Theorems for these summability methods are valid with Schmidt-type slowly oscillating condition as well as with Hardy-type “big O” condition.","PeriodicalId":43454,"journal":{"name":"Annales Mathematicae et Informaticae","volume":"391 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78066612","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.2022.09.002
G. Pataki
. We introduce (generalized) proximities in the same way as (gen-eralized) uniformities in paper of Weil. We prove the equivalence of our new definitions with classical ones. Using these analog definitions, we compare the properties of (generalized) proximities and (generalized) uniformities. The main parts of this paper are examples of an ( 𝑋, ℛ ) relator space such that ℛ # is uniformly (and proximally) transitive, but neither ℛ nor ℛ Φ is proximally (or uniformly) transitive. For this, we summarize the essential properties of relators, using their theory from earlier works of Á. Száz.
{"title":"Two illustrating examples for comparison of uniform and proximal spaces using relators","authors":"G. Pataki","doi":"10.33039/ami.2022.09.002","DOIUrl":"https://doi.org/10.33039/ami.2022.09.002","url":null,"abstract":". We introduce (generalized) proximities in the same way as (gen-eralized) uniformities in paper of Weil. We prove the equivalence of our new definitions with classical ones. Using these analog definitions, we compare the properties of (generalized) proximities and (generalized) uniformities. The main parts of this paper are examples of an ( 𝑋, ℛ ) relator space such that ℛ # is uniformly (and proximally) transitive, but neither ℛ nor ℛ Φ is proximally (or uniformly) transitive. For this, we summarize the essential properties of relators, using their theory from earlier works of Á. Száz.","PeriodicalId":43454,"journal":{"name":"Annales Mathematicae et Informaticae","volume":"87 1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84025376","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.2022.01.002
R. Frontczak, T. Goy, M. Shattuck
In this paper, we prove several identities involving linear combinations of convolutions of the generalized Fibonacci and Lucas sequences. Our results apply more generally to broader classes of second-order linearly recurrent sequences with constant coefficients. As a consequence, we obtain as special cases many identities relating exactly four sequences amongst the Fibonacci, Lucas, Pell, Pell–Lucas, Jacobsthal, and Jacobsthal–Lucas number sequences. We make use of algebraic arguments to establish our results, frequently employing the Binet-like formulas and generating functions of the corresponding sequences. Finally, our identities above may be extended so that they include only terms whose subscripts belong to a given arithmetic progression of the non-negative integers.
{"title":"Fibonacci–Lucas–Pell–Jacobsthal relations","authors":"R. Frontczak, T. Goy, M. Shattuck","doi":"10.33039/ami.2022.01.002","DOIUrl":"https://doi.org/10.33039/ami.2022.01.002","url":null,"abstract":"In this paper, we prove several identities involving linear combinations of convolutions of the generalized Fibonacci and Lucas sequences. Our results apply more generally to broader classes of second-order linearly recurrent sequences with constant coefficients. As a consequence, we obtain as special cases many identities relating exactly four sequences amongst the Fibonacci, Lucas, Pell, Pell–Lucas, Jacobsthal, and Jacobsthal–Lucas number sequences. We make use of algebraic arguments to establish our results, frequently employing the Binet-like formulas and generating functions of the corresponding sequences. Finally, our identities above may be extended so that they include only terms whose subscripts belong to a given arithmetic progression of the non-negative integers.","PeriodicalId":43454,"journal":{"name":"Annales Mathematicae et Informaticae","volume":"20 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86033420","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.2021.12.001
T. He, A. Shannon, P. Shiue
In this paper, we present some identities of Gaussian binomial coefficients with respect to recursive sequences, Fibonomial coefficients, and complete functions by use of their relationships.
{"title":"Some identities of Gaussian binomial coefficients","authors":"T. He, A. Shannon, P. Shiue","doi":"10.33039/ami.2021.12.001","DOIUrl":"https://doi.org/10.33039/ami.2021.12.001","url":null,"abstract":"In this paper, we present some identities of Gaussian binomial coefficients with respect to recursive sequences, Fibonomial coefficients, and complete functions by use of their relationships.","PeriodicalId":43454,"journal":{"name":"Annales Mathematicae et Informaticae","volume":"11 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83821221","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.2022.01.001
T. Mansour, J. L. Ramírez
In this paper, we introduce the concept of a Fuss-skew path and then we study the distribution of the semi-perimeter, area, peaks, and corners statistics. We use generating functions to obtain our main results.
{"title":"Enumeration of Fuss-skew paths","authors":"T. Mansour, J. L. Ramírez","doi":"10.33039/ami.2022.01.001","DOIUrl":"https://doi.org/10.33039/ami.2022.01.001","url":null,"abstract":"In this paper, we introduce the concept of a Fuss-skew path and then we study the distribution of the semi-perimeter, area, peaks, and corners statistics. We use generating functions to obtain our main results.","PeriodicalId":43454,"journal":{"name":"Annales Mathematicae et Informaticae","volume":"117 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76687768","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 : 2021-06-28DOI: 10.33039/ami.2020.02.002
J. Cereceda
In this methodological paper, we first review the classic cubic Diophantine equation $a^3 + b^3 + c^3 = d^3$, and consider the specific class of solutions $q_1^3 + q_2^3 + q_3^3 = q_4^3$ with each $q_i$ being a binary quadratic form. Next we turn our attention to the familiar sums of powers of the first $n$ positive integers, $S_k = 1^k + 2^k + cdots + n^k$, and express the squares $S_k^2$, $S_m^2$, and the product $S_k S_m$ as a linear combination of power sums. These expressions, along with the above quadratic-form solution for the cubic equation, allows one to generate an infinite number of relations of the form $Q_1^3 + Q_2^3 + Q_3^3 = Q_4^3$, with each $Q_i$ being a linear combination of power sums. Also, we briefly consider the quadratic Diophantine equations $a^2 + b^2 + c^2 = d^2$ and $a^2 + b^2 = c^2$, and give a family of corresponding solutions $Q_1^2 + Q_2^2 + Q_3^2 = Q_4^2$ and $Q_1^2 + Q_2^2 = Q_3^2$ in terms of sums of powers of integers.
{"title":"Binary quadratic forms and sums of powersof integers","authors":"J. Cereceda","doi":"10.33039/ami.2020.02.002","DOIUrl":"https://doi.org/10.33039/ami.2020.02.002","url":null,"abstract":"In this methodological paper, we first review the classic cubic Diophantine equation $a^3 + b^3 + c^3 = d^3$, and consider the specific class of solutions $q_1^3 + q_2^3 + q_3^3 = q_4^3$ with each $q_i$ being a binary quadratic form. Next we turn our attention to the familiar sums of powers of the first $n$ positive integers, $S_k = 1^k + 2^k + cdots + n^k$, and express the squares $S_k^2$, $S_m^2$, and the product $S_k S_m$ as a linear combination of power sums. These expressions, along with the above quadratic-form solution for the cubic equation, allows one to generate an infinite number of relations of the form $Q_1^3 + Q_2^3 + Q_3^3 = Q_4^3$, with each $Q_i$ being a linear combination of power sums. Also, we briefly consider the quadratic Diophantine equations $a^2 + b^2 + c^2 = d^2$ and $a^2 + b^2 = c^2$, and give a family of corresponding solutions $Q_1^2 + Q_2^2 + Q_3^2 = Q_4^2$ and $Q_1^2 + Q_2^2 = Q_3^2$ in terms of sums of powers of integers.","PeriodicalId":43454,"journal":{"name":"Annales Mathematicae et Informaticae","volume":"15 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2021-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73468845","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 : 2021-06-04DOI: 10.33039/ami.2021.09.001
M. Sahai, S. F. Ansari
Let $D_{n}$ be the dihedral group of order $n$. The structure of the unit group $U(F(C_3 times D_{10}))$ of the group algebra $F(C_3 times D_{10})$ over a finite field $F$ of characteristic $3$ is given in cite{sh13}. In this article, the structure of $U(F(C_3 times D_{10}))$ is obtained over any finite field $F$ of characteristic $p neq 3$.
设$D_{n}$为顺序$n$的二面体组。在cite{sh13}中给出了特征为$3$的有限域$F$上群代数$F(C_3 times D_{10})$的单位群$U(F(C_3 times D_{10}))$的结构。本文在特征为$p neq 3$的任意有限域$F$上得到了$U(F(C_3 times D_{10}))$的结构。
{"title":"The structure of the unit group of the group algebra F(C₃ × D₁₀)","authors":"M. Sahai, S. F. Ansari","doi":"10.33039/ami.2021.09.001","DOIUrl":"https://doi.org/10.33039/ami.2021.09.001","url":null,"abstract":"Let $D_{n}$ be the dihedral group of order $n$. The structure of the unit group $U(F(C_3 times D_{10}))$ of the group algebra $F(C_3 times D_{10})$ over a finite field $F$ of characteristic $3$ is given in cite{sh13}. In this article, the structure of $U(F(C_3 times D_{10}))$ is obtained over any finite field $F$ of characteristic $p neq 3$.","PeriodicalId":43454,"journal":{"name":"Annales Mathematicae et Informaticae","volume":"76 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2021-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88972882","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：