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":null,"pages":null},"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":null,"pages":null},"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}
Pub Date : 2019-03-01DOI: 10.52737/18291163-2019.11.2-1-2
A. Nersessian
{"title":"A correction to the article \"On an Over-Convergence Phenomenon for Fourier Series. Basic Approach\"","authors":"A. Nersessian","doi":"10.52737/18291163-2019.11.2-1-2","DOIUrl":"https://doi.org/10.52737/18291163-2019.11.2-1-2","url":null,"abstract":"","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43832618","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 : 2019-03-01DOI: 10.52737/18291163-2019.11.1-1-14
Panwang Wang, Zongguang Liu
In this paper, we study the boundedness of the fractional maximal operator and fractional integral operator on the variable exponent Morrey spaces defined over spaces (X,d,μ) of homogeneous type.
{"title":"Fractional maximal and integral operators in variable exponent Morrey spaces","authors":"Panwang Wang, Zongguang Liu","doi":"10.52737/18291163-2019.11.1-1-14","DOIUrl":"https://doi.org/10.52737/18291163-2019.11.1-1-14","url":null,"abstract":"In this paper, we study the boundedness of the fractional maximal operator and fractional integral operator on the variable exponent Morrey spaces defined over spaces (X,d,μ) of homogeneous type.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45047024","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 : 2018-12-10DOI: 10.52737/18291163-2018.10.10-1-15
M. Norouzi, A. Asadi, Y. Jun
The notion of a subnexus based on ${mathcal{N}}$-function (briefly, ${mathcal{N}}$-subnexus) is introduced, and related properties are investigated. Also, the notions of ${mathcal{N}}$-subnexus of type $(alpha, beta)$, where $(alpha, beta)$ is $(in, in)$, $(in, q)$, $(in, in! vee , {q})$, $(q, in)$, $(q,q)$, $(q, in! vee , {q})$, $(overline{in}, overline{in})$ and $(overline{in}, overline{in} vee overline{q})$, are introduced, and their basic properties are investigated. Conditions for an ${mathcal{N}}$-structure to be an ${mathcal{N}}$-subnexus of type $(q, in! vee , {q})$ are given, and characterizations of ${mathcal{N}}$-subnexus of type $(in, in! vee , {q})$ and $(overline{in}, overline{in} vee overline{q})$ are provided. Homomorphic image and preimage of ${mathcal{N}}$-subnexus are discussed.
{"title":"Subnexuses Based on N-structures","authors":"M. Norouzi, A. Asadi, Y. Jun","doi":"10.52737/18291163-2018.10.10-1-15","DOIUrl":"https://doi.org/10.52737/18291163-2018.10.10-1-15","url":null,"abstract":"The notion of a subnexus based on ${mathcal{N}}$-function (briefly, ${mathcal{N}}$-subnexus) is introduced, and related properties are investigated. Also, the notions of ${mathcal{N}}$-subnexus of type $(alpha, beta)$, where $(alpha, beta)$ is $(in, in)$, $(in, q)$, $(in, in! vee , {q})$, $(q, in)$, $(q,q)$, $(q, in! vee , {q})$, $(overline{in}, overline{in})$ and $(overline{in}, overline{in} vee overline{q})$, are introduced, and their basic properties are investigated. Conditions for an ${mathcal{N}}$-structure to be an ${mathcal{N}}$-subnexus of type $(q, in! vee , {q})$ are given, and characterizations of ${mathcal{N}}$-subnexus of type $(in, in! vee , {q})$ and $(overline{in}, overline{in} vee overline{q})$ are provided. Homomorphic image and preimage of ${mathcal{N}}$-subnexus are discussed.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2018-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48595893","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 : 2018-12-10DOI: 10.52737/18291163-2018.10.11-1-15
K. Noor, Nasir Abbas Khan, Q. Z. Ahmad, N. Khan, Y. L. Chung
In the present investigation, a new general subclass $M_{alpha ,beta }left( phi right) $ of analytic functions is defined. Some subordination relations, inclusion relations, integral preserving properties, convolution properties and some other interesting properties are studied.
{"title":"On Certain Subclass of Analytic Functions","authors":"K. Noor, Nasir Abbas Khan, Q. Z. Ahmad, N. Khan, Y. L. Chung","doi":"10.52737/18291163-2018.10.11-1-15","DOIUrl":"https://doi.org/10.52737/18291163-2018.10.11-1-15","url":null,"abstract":"In the present investigation, a new general subclass $M_{alpha ,beta }left( phi right) $ of analytic functions is defined. Some subordination relations, inclusion relations, integral preserving properties, convolution properties and some other interesting properties are studied.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2018-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46214331","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 : 2018-07-09DOI: 10.52737/18291163-2018.10.6-1-15
K. Navasardyan
In this paper we discuss the uniqueness property of a summation method for multiple series with respect to Vilenkin and generalized Haar systems. It is proved that if the multiple series with respect to these systems is a.e. summable by that method to an integrable function on $[0,1)^d$ and satisfies an extra condition, then it is the Fourier series of this function.
{"title":"Uniqueness Theorems for Multiple Series by Vilenkin and Generalized Haar Systems","authors":"K. Navasardyan","doi":"10.52737/18291163-2018.10.6-1-15","DOIUrl":"https://doi.org/10.52737/18291163-2018.10.6-1-15","url":null,"abstract":"In this paper we discuss the uniqueness property of a summation method for multiple series with respect to Vilenkin and generalized Haar systems. It is proved that if the multiple series with respect to these systems is a.e. summable by that method to an integrable function on $[0,1)^d$ and satisfies an extra condition, then it is the Fourier series of this function.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2018-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45257415","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 : 2018-06-19DOI: 10.52737/18291163-2018.10.5-1-20
L. Khachatryan, B. Nahapetian
We introduce sufficiently wide classes of non--linear functionals preserving normal (Gaussian) distribution and establish various conditions under which a sequence of such functionals is asymptotically normal. As one of a consequence we obtain a generalization and sharpening of known results on the central limit theorem for weighted sums (linear functionals) of independent random variables.
{"title":"Non-linear Functionals Preserving Normal Distribution and Their Asymptotic Normality","authors":"L. Khachatryan, B. Nahapetian","doi":"10.52737/18291163-2018.10.5-1-20","DOIUrl":"https://doi.org/10.52737/18291163-2018.10.5-1-20","url":null,"abstract":"We introduce sufficiently wide classes of non--linear functionals preserving normal (Gaussian) distribution and establish various conditions under which a sequence of such functionals is asymptotically normal. As one of a consequence we obtain a generalization and sharpening of known results on the central limit theorem for weighted sums (linear functionals) of independent random variables.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2018-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49360415","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 : 2018-06-19DOI: 10.52737/18291163-2018.10.4-1-85
Yu. M. Movsisyan
This survey article illustrates many important current trends and perspectives for the field including classification of hyperidentities, characterizations of algebras with hyperidentities, functional representations of free algebras, structure results for bilattices, categorical questions and applications. However, the paper contains new results and open problems, too.
{"title":"Hyperidentities and Related Concepts, II","authors":"Yu. M. Movsisyan","doi":"10.52737/18291163-2018.10.4-1-85","DOIUrl":"https://doi.org/10.52737/18291163-2018.10.4-1-85","url":null,"abstract":"This survey article illustrates many important current trends and perspectives for the field including classification of hyperidentities, characterizations of algebras with hyperidentities, functional representations of free algebras, structure results for bilattices, categorical questions and applications. However, the paper contains new results and open problems, too.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2018-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49427163","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 : 2018-06-01DOI: 10.52737/18291163-2018.10.1-1-14
M. Beheshti, M. Azhini
In this paper, by using generalized viscosity mappings, we prove two strong convergence theorems for finding fixed points of a nonexpansive mapping which is also a unique solution of the variational inequality. Our results extend and improve the recent ones announced by some authors.
{"title":"Generalized Viscosity Approximation Methods of Ishikawa Type for Nonexpansive Mappings in Hilbert Spaces","authors":"M. Beheshti, M. Azhini","doi":"10.52737/18291163-2018.10.1-1-14","DOIUrl":"https://doi.org/10.52737/18291163-2018.10.1-1-14","url":null,"abstract":"In this paper, by using generalized viscosity mappings, we prove two strong convergence theorems for finding fixed points of a nonexpansive mapping which is also a unique solution of the variational inequality. Our results extend and improve the recent ones announced by some authors.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46981841","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：