Pub Date : 2020-03-28DOI: 10.52737/18291163-2020.12.1-1-11
M. Alaeiyan, M. K. Hosseinipoor, M. Akbarizadeh
A $s$-arc in a graph is an ordered $(s+1)$-tuple $(v_{0}, v_{1}, cdots, v_{s-1}, v_{s})$ of vertices such that $v_{i-1}$ is adjacent to $v_{i}$ for $1leq i leq s$ and $v_{i-1}neq v_{i+1}$ for $1leq i < s$. A graph $X$ is called $s$-regular if its automorphism group acts regularly on the set of its $s$-arcs. In this paper, we classify all connected cubic $s$-regular graphs of order $18p^2$ for each $sgeq1$ and each prime $p$.
{"title":"Classifying cubic symmetric graphs of order $18 p^2$","authors":"M. Alaeiyan, M. K. Hosseinipoor, M. Akbarizadeh","doi":"10.52737/18291163-2020.12.1-1-11","DOIUrl":"https://doi.org/10.52737/18291163-2020.12.1-1-11","url":null,"abstract":"A $s$-arc in a graph is an ordered $(s+1)$-tuple $(v_{0}, v_{1}, cdots, v_{s-1}, v_{s})$ of vertices such that $v_{i-1}$ is adjacent to $v_{i}$ for $1leq i leq s$ and $v_{i-1}neq v_{i+1}$ for $1leq i < s$. A graph $X$ is called $s$-regular if its automorphism group acts regularly on the set of its $s$-arcs. In this paper, we classify all connected cubic $s$-regular graphs of order $18p^2$ for each $sgeq1$ and each prime $p$.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2020-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47121591","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 : 2019-12-13DOI: 10.52737/18291163-2019.11.12-1-12
T. Srichan, Pinthira Tangsupphathawat
Let $k$ and $r$ be fixed integers with $11$ be a real number. In this paper an asymptotic formula for the number of $(k,r)$-integers which are primitive roots modulo $p$ and do not exceed $x$ is obtained.
{"title":"On the distribution of primitive roots that are (k,r)-integers","authors":"T. Srichan, Pinthira Tangsupphathawat","doi":"10.52737/18291163-2019.11.12-1-12","DOIUrl":"https://doi.org/10.52737/18291163-2019.11.12-1-12","url":null,"abstract":"Let $k$ and $r$ be fixed integers with $1<r<k$. A positive integer is called $r$-free if it is not divisible by the $r^{th}$ power of any prime. A positive integer $n$ is called a $(k,r)$-integer if $n$ is written in the form $a^kb$ where $b$ is an $r$-free integer. Let $p$ be an odd prime and let $x>1$ be a real number.\u0000\u0000In this paper an asymptotic formula for the number of $(k,r)$-integers which are primitive roots modulo $p$ and do not exceed $x$ is obtained.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2019-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47909270","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 : 2019-11-15DOI: 10.52737/18291163-2019.11.11-1-19
A. Tomar, Ritu Sharma
The aim of this article is to introduce the notion of almost $alpha$-Hardy-Rogers-$F$-contractions in the partial metric space and utilize it to establish the existence of a unique fixed point. Some examples are given to demonstrate the validity of our main result. Our results generalize classical and newer results in the literature. As an application, we solve the initial value problem of damped harmonic oscillator and a nonlinear fractional differential equation satisfying periodic boundary conditions, which demonstrates the importance of our contraction and provides motivation for such investigations.
{"title":"Almost $alpha$-Hardy-Rogers-$F$-contractions and their applications","authors":"A. Tomar, Ritu Sharma","doi":"10.52737/18291163-2019.11.11-1-19","DOIUrl":"https://doi.org/10.52737/18291163-2019.11.11-1-19","url":null,"abstract":"The aim of this article is to introduce the notion of almost $alpha$-Hardy-Rogers-$F$-contractions in the partial metric space and utilize it to establish the existence of a unique fixed point. Some examples are given to demonstrate the validity of our main result. Our results generalize classical and newer results in the literature. As an application, we solve the initial value problem of damped harmonic oscillator and a nonlinear fractional differential equation satisfying periodic boundary conditions, which demonstrates the importance of our contraction and provides motivation for such investigations.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2019-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43287869","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 : 2019-09-17DOI: 10.52737/18291163-2019.11.10-1-17
M. Rahmane, M. Remili, Linda D. Oudjedi
The purpose of this paper is to establish a new result, which guarantees the asymptotic stability and boundedness of the zero solution and the square integrability of solutions and their derivatives to neutral type nonlinear differential equations of fourth-order. We illustrate our results by an example at the end of the paper.
{"title":"Stability, Boundedness, and Square Integrability of Solutions of Neutral Fourth-Order Differential Equations","authors":"M. Rahmane, M. Remili, Linda D. Oudjedi","doi":"10.52737/18291163-2019.11.10-1-17","DOIUrl":"https://doi.org/10.52737/18291163-2019.11.10-1-17","url":null,"abstract":"The purpose of this paper is to establish a new result, which guarantees the asymptotic stability and boundedness of the zero solution and the square integrability of solutions and their derivatives to neutral type nonlinear differential equations of fourth-order. We illustrate our results by an example at the end of the paper.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2019-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49379156","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 : 2019-06-11DOI: 10.52737/18291163-2019.11.9-1-27
A. Krapez, V. Shcherbacov
We investigate {left, right, middle} units of quasigroups and families of identities which might imply their existence. A prominent role is played by the newly introduced notion of derivative operation, generalizing Belousov's notions of left/right derivative operations for quasigroups. Partial solutions of the Belousov's Problem # 18 and its generalizations are obtained. Several related problems remain open.
{"title":"Quasigroups, Units and Belousov's Problem # 18","authors":"A. Krapez, V. Shcherbacov","doi":"10.52737/18291163-2019.11.9-1-27","DOIUrl":"https://doi.org/10.52737/18291163-2019.11.9-1-27","url":null,"abstract":"We investigate {left, right, middle} units of quasigroups and families of identities which might imply their existence. A prominent role is played by the newly introduced notion of derivative operation, generalizing Belousov's notions of left/right derivative operations for quasigroups. Partial solutions of the Belousov's Problem # 18 and its generalizations are obtained. Several related problems remain open.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2019-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43232196","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 : 2019-06-07DOI: 10.52737/18291163-2019.11.8-1-6
N. Srapionyan
In this paper, we estimate the democratic constant for the democratic subsystems of the $d$-dimensional Haar system in $L_1[0,1]^d$.
本文估计了$L_1[0,1]^d$中$d$维Haar系统的民主子系统的民主常数。
{"title":"On the democratic constant of Haar subsystems in $L_1 [0,1]^d$","authors":"N. Srapionyan","doi":"10.52737/18291163-2019.11.8-1-6","DOIUrl":"https://doi.org/10.52737/18291163-2019.11.8-1-6","url":null,"abstract":"In this paper, we estimate the democratic constant for the democratic subsystems of the $d$-dimensional Haar system in $L_1[0,1]^d$.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2019-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42197946","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 : 2019-05-24DOI: 10.52737/18291163-2019.11.7-1-14
H. M. Hayrapetyan, S. Aghekyan
The paper considers the Riemann boundary value problem in the half-plane in the class of functions that are $C(rho)$-continuous with respect to the weight $rho(x)$, when the weight function has infinite number of zeros. Necessary and sufficient conditions for solvability of the problem are established. If the problem is solvable, solutions are represented in an explicit form.
{"title":"On a Riemann boundary value problem for weighted spaces in the half-plane","authors":"H. M. Hayrapetyan, S. Aghekyan","doi":"10.52737/18291163-2019.11.7-1-14","DOIUrl":"https://doi.org/10.52737/18291163-2019.11.7-1-14","url":null,"abstract":"The paper considers the Riemann boundary value problem in the half-plane in the class of functions that are $C(rho)$-continuous with respect to the weight $rho(x)$, when the weight function has infinite number of zeros. Necessary and sufficient conditions for solvability of the problem are established. If the problem is solvable, solutions are represented in an explicit form.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2019-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48179784","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 : 2019-05-08DOI: 10.52737/18291163-2019.11.6-1-6
H. T. Aslanyan, A. Gevorgyan, H. Grigoryan
It is proved that all finite subgroups of the free groups of the infinitely based varieties of S.I. Adian are cyclic. The set of all non-isomorphic free groups of rank $m$ in this varieties is of continuum cardinality for every finite rank $m > 1$.
{"title":"Finite subgroups of the free groups of the infinitely based varieties of S.I. Adian","authors":"H. T. Aslanyan, A. Gevorgyan, H. Grigoryan","doi":"10.52737/18291163-2019.11.6-1-6","DOIUrl":"https://doi.org/10.52737/18291163-2019.11.6-1-6","url":null,"abstract":"It is proved that all finite subgroups of the free groups of the infinitely based varieties of S.I. Adian are cyclic. The set of all non-isomorphic free groups of rank $m$ in this varieties is of continuum cardinality for every finite rank $m > 1$.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2019-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48160129","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 : 2019-04-26DOI: 10.52737/18291163-2019.11.5-1-13
Elhadji Ousseynouu Accrachi, Cherif Ahmat Tidiane Aidara, A. S. Dabye
We consider the problem of parameter estimation by the observations of inhomogeneous Poisson processes. The intensity function of the process is supposed to be a smooth function with respect to the unknown parameter. We propose a Chi-square statistic on the base of agregated observations and we define a Minimum Chi-square Estimator with the help of this statistics. We show this that estimator is consistent and asymptotically normal. We discuss possible generalizations of the obtained results.
{"title":"On Parameter Estimation by Aggregated Poisson Observations","authors":"Elhadji Ousseynouu Accrachi, Cherif Ahmat Tidiane Aidara, A. S. Dabye","doi":"10.52737/18291163-2019.11.5-1-13","DOIUrl":"https://doi.org/10.52737/18291163-2019.11.5-1-13","url":null,"abstract":"We consider the problem of parameter estimation by the observations of inhomogeneous Poisson processes. The intensity function of the process is supposed to be a smooth function with respect to the unknown parameter. We propose a Chi-square statistic on the base of agregated observations and we define a Minimum Chi-square Estimator with the help of this statistics. We show this that estimator is consistent and asymptotically normal. We discuss possible generalizations of the obtained results.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2019-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43864789","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 : 2019-04-17DOI: 10.52737/18291163-2019.11.4-1-9
M. S. Martirosyan, D. Martirosyan
Ultimately aiming to estimate Dirichlet polynomials, a representation problem for special biorthogonal systems of exponentials is explored in $L^2(0,a)$. If $a=+infty$, a method of construction of such systems through suitable Blaschke products is known, but the method ceases to operate when $a$ is finite. It turns out that the Blaschke product cannot be even adjusted to maintain the old method for the new situation. The biorthogonal system is then represented by a single determinant of a modified Gram matrix of the original system. Bernstein-type inequalities for Dirichlet polynomials and their higher order derivatives are established. The best constants and extremal polynomials are obtained in terms of the Gram matrix.
{"title":"On Biorthogonalization of a Dirichlet System Over a Finite Interval","authors":"M. S. Martirosyan, D. Martirosyan","doi":"10.52737/18291163-2019.11.4-1-9","DOIUrl":"https://doi.org/10.52737/18291163-2019.11.4-1-9","url":null,"abstract":"Ultimately aiming to estimate Dirichlet polynomials, a representation problem for special biorthogonal systems of exponentials is explored in $L^2(0,a)$. If $a=+infty$, a method of construction of such systems through suitable Blaschke products is known, but the method ceases to operate when $a$ is finite.\u0000\u0000It turns out that the Blaschke product cannot be even adjusted to maintain the old method for the new situation. The biorthogonal system is then represented by a single determinant of a modified Gram matrix of the original system. Bernstein-type inequalities for Dirichlet polynomials and their higher order derivatives are established. The best constants and extremal polynomials are obtained in terms of the Gram matrix.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2019-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41769758","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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