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Armenian Journal of Mathematics最新文献

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Optimality of the Least Sum of Logarithms in the Problem of Matching Map Recovery in the Presence of Noise and Outliers 有噪声和异常情况下匹配图恢复问题中最小对数和的最优性
IF 0.4
Armenian Journal of Mathematics Pub Date : 2023-03-30 DOI: 10.52737/18291163-2023.15.5-1-9
T. Galstyan, A. Minasyan
{"title":"Optimality of the Least Sum of Logarithms in the Problem of Matching Map Recovery in the Presence of Noise and Outliers","authors":"T. Galstyan, A. Minasyan","doi":"10.52737/18291163-2023.15.5-1-9","DOIUrl":"https://doi.org/10.52737/18291163-2023.15.5-1-9","url":null,"abstract":"We consider the problem of estimating the matching map between two sets of feature-vectors observed in a noisy environment and contaminated by outliers. It was already known in the literature that in the outlier-free setting, the least sum of squares (LSS) and the least sum of logarithms (LSL) are both minimax-rate-optimal. It has been recently proved that the optimality properties of the LSS continue to hold in the case the data sets contain outliers. In this work, we show that the same is true for the LSL as well. Therefore, LSL has the same desirable properties as the LSS, and, in addition, it is minimax-rate-optimal in the outlier-free setting with heteroscedastic noise.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47585131","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}
引用次数: 0
Nonlocal Solvability of the Cauchy Problem for a System with Negative Functions of the Variable $t$ 变量$t为负函数系统Cauchy问题的非局部可解性$
IF 0.4
Armenian Journal of Mathematics Pub Date : 2023-03-22 DOI: 10.52737/18291163-2023.15.4-1-10
M. Dontsova
{"title":"Nonlocal Solvability of the Cauchy Problem for a System with Negative Functions of the Variable $t$","authors":"M. Dontsova","doi":"10.52737/18291163-2023.15.4-1-10","DOIUrl":"https://doi.org/10.52737/18291163-2023.15.4-1-10","url":null,"abstract":"We obtain sufficient conditions for the existence and uniqueness of a local solution of the Cauchy problem for a quasilinear system with negative functions of the variable $t$ and show that the solution has the same $x$-smoothness as the initial function. We also obtain sufficient conditions for the existence and uniqueness of a nonlocal solution of the Cauchy problem for a quasilinear system with negative functions of the variable $t$.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49620976","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}
引用次数: 0
Weak Type Estimate of Singular Integral Operators on Variable Weak Herz-Type Hardy Spaces 变弱herz型Hardy空间上奇异积分算子的弱型估计
IF 0.4
Armenian Journal of Mathematics Pub Date : 2023-03-10 DOI: 10.52737/18291163-2023.15.3-1-33
Hamza Brahim Boulares, D. Drihem, Wafa Hebbache
{"title":"Weak Type Estimate of Singular Integral Operators on Variable Weak Herz-Type Hardy Spaces","authors":"Hamza Brahim Boulares, D. Drihem, Wafa Hebbache","doi":"10.52737/18291163-2023.15.3-1-33","DOIUrl":"https://doi.org/10.52737/18291163-2023.15.3-1-33","url":null,"abstract":"This paper is concerned with the boundedness properties of singular integral operators on variable weak Herz spaces and variable weak Herz-type Hardy spaces. Allowing our parameters to vary from point to point will raise extra difficulties, which, in general, are overcome by imposing regularity assumptions on these exponents, either at the origin or at infinity. Our results cover the classical results on weak Herz-type Hardy spaces with fixed exponents.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44705523","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}
引用次数: 0
On Non-Comaximal Graphs of Ideals of Commutative Rings 交换环理想的非共极大图
IF 0.4
Armenian Journal of Mathematics Pub Date : 2023-02-08 DOI: 10.52737/18291163-2023.15.2-1-8
Bikash Barman, Kukil Kalpa Rajkhowa
{"title":"On Non-Comaximal Graphs of Ideals of Commutative Rings","authors":"Bikash Barman, Kukil Kalpa Rajkhowa","doi":"10.52737/18291163-2023.15.2-1-8","DOIUrl":"https://doi.org/10.52737/18291163-2023.15.2-1-8","url":null,"abstract":"In this paper, we relate some properties of non-comaximal graph of ideals of a commutative ring with identity with the properties of the ring.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48971317","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}
引用次数: 0
On the Minimal Annulus of Triangles and Parallelograms 关于三角形和平行四边形的极小环
IF 0.4
Armenian Journal of Mathematics Pub Date : 2023-01-26 DOI: 10.52737/18291163-2023.15.1-1-15
S. Vassallo
{"title":"On the Minimal Annulus of Triangles and Parallelograms","authors":"S. Vassallo","doi":"10.52737/18291163-2023.15.1-1-15","DOIUrl":"https://doi.org/10.52737/18291163-2023.15.1-1-15","url":null,"abstract":"Sharp upper and lower bounds for the isoperimetric deficit of triangles or parallelograms with the minimal annulus of radii R and r are given.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47248030","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}
引用次数: 0
Existence of Solutions for a Fractional Boundary Value Problem at Resonance 一类共振处分数阶边值问题解的存在性
IF 0.4
Armenian Journal of Mathematics Pub Date : 2022-12-21 DOI: 10.52737/18291163-2022.14.15-1-16
A. S. Silva
{"title":"Existence of Solutions for a Fractional Boundary Value Problem at Resonance","authors":"A. S. Silva","doi":"10.52737/18291163-2022.14.15-1-16","DOIUrl":"https://doi.org/10.52737/18291163-2022.14.15-1-16","url":null,"abstract":"In this paper, we focus on the existence of solutions to a fractional boundary value problem at resonance. By constructing suitable operators, we establish an existence theorem upon the coincidence degree theory of Mawhin.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48530477","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}
引用次数: 1
Acceleration of Convergence of Fourier Series Using the Phenomenon of Over-Convergence 利用过收敛现象加速傅立叶级数的收敛
IF 0.4
Armenian Journal of Mathematics Pub Date : 2022-12-12 DOI: 10.52737/18291163-2022.14.14-1-31
A. Nersessian
{"title":"Acceleration of Convergence of Fourier Series Using the Phenomenon of Over-Convergence","authors":"A. Nersessian","doi":"10.52737/18291163-2022.14.14-1-31","DOIUrl":"https://doi.org/10.52737/18291163-2022.14.14-1-31","url":null,"abstract":"In recent publications of the author, the phenomenon of over-convergence was discovered, and a spectral method has been presented for accelerating the convergence of truncated Fourier series for smooth functions. On this basis, a certain parametric system that is biorthogonal to the corresponding segment of the Fourier system turned out to be unusually effective. This article reconsiders some approaches and makes some adjustments to previous publications. As a result, two improved schemes for the recovery of a function based on a finite set of its Fourier coefficients are proposed. Numerical experiments confirm a significant increase in the efficiency of corresponding algorithms in typical classes of smooth functions. In conclusion, some prospects for the development and generalization of the above approaches are discussed.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48232410","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}
引用次数: 1
Bifurcation Analysis of a Piecewise Smooth Map with Two Asymptotes 具有两条渐近线的分段光滑映射的分岔分析
IF 0.4
Armenian Journal of Mathematics Pub Date : 2022-10-02 DOI: 10.52737/18291163-2022.14.13-1-12
Roya Makrooni
{"title":"Bifurcation Analysis of a Piecewise Smooth Map with Two Asymptotes","authors":"Roya Makrooni","doi":"10.52737/18291163-2022.14.13-1-12","DOIUrl":"https://doi.org/10.52737/18291163-2022.14.13-1-12","url":null,"abstract":"In this paper, we consider a discontinuous piecewise smooth system involving four parameters and two asymptotes, recently introduced as a model in engineering sciences. We classify and investigate its bifurcation behaviour. A local bifurcation analysis of the system in the range of parameters which has not been studied so far is undertaken and then supported by numerical computations. This reveals the existence of a flip bifurcation depends on the power singularity. Moreover, we state that a set of positive measure of points with divergent dynamic behaviour exists.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49217590","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}
引用次数: 0
Hypergeometric connections between balancing polynomials and Chebyshev polynomials of first and second kinds 平衡多项式与第一类和第二类切比雪夫多项式的超几何联系
IF 0.4
Armenian Journal of Mathematics Pub Date : 2022-09-23 DOI: 10.52737/18291163-2022.14.12-1-20
A. Behera, P. Ray
{"title":"Hypergeometric connections between balancing polynomials and Chebyshev polynomials of first and second kinds","authors":"A. Behera, P. Ray","doi":"10.52737/18291163-2022.14.12-1-20","DOIUrl":"https://doi.org/10.52737/18291163-2022.14.12-1-20","url":null,"abstract":"In the present study, we find several connections between balancing polynomials and the Chebyshev polynomials of the first and second kinds. The Chebyshev polynomials of the first and second kinds are expressed as the sum of two terms of balancing polynomials with hypergeometric coefficients. As an inversion, the balancing polynomials are also expressed as the sum of two terms of the Chebyshev polynomials of the first kind and the Chebyshev polynomials of the second kind with hypergeometric coefficients.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44813588","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}
引用次数: 0
Geometry associated with the SL(3,R) action on homogeneous space using the Erlangen program 利用Erlangen程序与齐次空间上SL(3,R)作用相关的几何
IF 0.4
Armenian Journal of Mathematics Pub Date : 2022-08-16 DOI: 10.52737/18291163-2022.14.11-1-15
D. Biswas, Ipsita Rajwar
{"title":"Geometry associated with the SL(3,R) action on homogeneous space using the Erlangen program","authors":"D. Biswas, Ipsita Rajwar","doi":"10.52737/18291163-2022.14.11-1-15","DOIUrl":"https://doi.org/10.52737/18291163-2022.14.11-1-15","url":null,"abstract":"We investigate the action of the Lie group SL(3,R) on the two-dimensional homogeneous space. All the one-parameter subgroups (up to conjugacy) of SL(3,R) are considered. We discuss the orbits and curvatures of these one-parameter subgroups. We also classify these subgroups in terms of fixed points.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41313251","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}
引用次数: 0
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