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Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences最新文献

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Simple Proof of the Risk Bound for Denoising by Exponential Weights for Asymmetric Noise Distributions 非对称噪声分布的指数加权去噪风险边界的简单证明
IF 0.3 4区 数学
Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences Pub Date : 2023-12-28 DOI: 10.3103/s106836232306002x
A. S. Dalalyan
{"title":"Simple Proof of the Risk Bound for Denoising by Exponential Weights for Asymmetric Noise Distributions","authors":"A. S. Dalalyan","doi":"10.3103/s106836232306002x","DOIUrl":"https://doi.org/10.3103/s106836232306002x","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this note, we consider the problem of aggregation of estimators in order to denoise a signal. The main contribution is a short proof of the fact that the exponentially weighted aggregate satisfies a sharp oracle inequality. While this result was already known for a wide class of symmetric noise distributions, the extension to asymmetric distributions presented in this note is new.</p>","PeriodicalId":54854,"journal":{"name":"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences","volume":"30 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139066425","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Entire Functions and Their High Order Difference Operators 全函数及其高阶差分算子
IF 0.3 4区 数学
Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences Pub Date : 2023-12-28 DOI: 10.3103/s1068362323060043
S. Majumder, N. Sarkar, D. Pramanik
{"title":"Entire Functions and Their High Order Difference Operators","authors":"S. Majumder, N. Sarkar, D. Pramanik","doi":"10.3103/s1068362323060043","DOIUrl":"https://doi.org/10.3103/s1068362323060043","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this paper, we prove that for a transcendental entire function <span>(f)</span> of finite order such that <span>(lambda(f-a)&lt;rho(f))</span>, where <span>(a)</span> is an entire function and satisfies <span>(rho(a)&lt;rho(f))</span>, <span>(ninmathbb{N})</span>, if <span>(Delta_{c}^{n}f)</span> and <span>(f)</span> share the entire function <span>(b)</span> satisfying <span>(rho(b)&lt;rho(f))</span> CM, where <span>(cinmathbb{C})</span> satisfies <span>(Delta_{c}^{n}fnotequiv 0)</span>, then <span>(f(z)=a(z)+de^{cz})</span>, where <span>(d,c)</span> are two nonzero constants. In particular, if <span>(a=b)</span>, then <span>(a)</span> reduces to a constant. This result improves and generalizes the recent results of Chen and Chen [3], Liao and Zhang [10] and Lü et al. [11] in a large scale. Also we exhibit some relevant examples to fortify our results.</p>","PeriodicalId":54854,"journal":{"name":"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences","volume":"44 4 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139066477","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Khinchin’s Theorem about the Special Role of the Gaussian Distribution 论欣钦关于高斯分布特殊作用的定理
IF 0.3 4区 数学
Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences Pub Date : 2023-12-28 DOI: 10.3103/s1068362323060031
L. A. Khachatryan
{"title":"On Khinchin’s Theorem about the Special Role of the Gaussian Distribution","authors":"L. A. Khachatryan","doi":"10.3103/s1068362323060031","DOIUrl":"https://doi.org/10.3103/s1068362323060031","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The purpose of this note is to recall one remarkable theorem of Khinchin about the special role of the Gaussian distribution. This theorem allows us to give a new interpretation of the Lindeberg condition: it guarantees the uniform integrability of the squares of normed sums of random variables and, thus, the passage to the limit under the expectation sign. The latter provides a simple proof of the central limit theorem for independent random variables.</p>","PeriodicalId":54854,"journal":{"name":"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences","volume":"95 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139066585","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Crossing Malmquist Systems with Certain Types 与某些类型的马尔奎斯特系统交叉
IF 0.3 4区 数学
Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences Pub Date : 2023-12-28 DOI: 10.3103/s1068362323060080
F. N. Wang, K. Liu
{"title":"Crossing Malmquist Systems with Certain Types","authors":"F. N. Wang, K. Liu","doi":"10.3103/s1068362323060080","DOIUrl":"https://doi.org/10.3103/s1068362323060080","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this paper, we will present the expression of meromorphic solutions on the crossing differential or difference Malmquist systems of certain types using Nevanlinna theory. For instance, we consider the admissible meromorphic solutions of the crossing differential Malmquist system</p><span>$$begin{cases}f^{prime}_{1}(z)=frac{a_{1}(z)f_{2}(z)+a_{0}(z)}{f_{2}(z)+d_{1}(z)}, f^{prime}_{2}(z)=frac{a_{2}(z)f_{1}(z)+b_{0}(z)}{f_{1}(z)+d_{2}(z)},end{cases}$$</span><p>where <span>(a_{1}(z)d_{1}(z)notequiv a_{0}(z))</span> and <span>(a_{2}(z)d_{2}(z)notequiv b_{0}(z))</span>.</p>","PeriodicalId":54854,"journal":{"name":"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences","volume":"20 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139066587","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Convergence of General Fourier Series of Differentiable Functions 可微分函数的一般傅里叶级数的收敛性
IF 0.3 4区 数学
Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences Pub Date : 2023-12-28 DOI: 10.3103/s1068362323060067
V. Tsagareishvili
{"title":"Convergence of General Fourier Series of Differentiable Functions","authors":"V. Tsagareishvili","doi":"10.3103/s1068362323060067","DOIUrl":"https://doi.org/10.3103/s1068362323060067","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Convergence of classical Fourier series (trigonometric, Haar, Walsh, <span>(dots)</span> systems) of differentiable functions are trivial problems and they are well known. But general Fourier series, as it is known, even for the function <span>(f(x)=1)</span> does not converge. In such a case, if we want differentiable functions with respect to the general orthonormal system (ONS) <span>((varphi_{n}))</span> to have convergent Fourier series, we must find the special conditions on the functions <span>(varphi_{n})</span> of system <span>((varphi_{n}))</span>. This problem is studied in the present paper. It is established that the resulting conditions are best possible. Subsystems of general orthonormal systems are considered.</p>","PeriodicalId":54854,"journal":{"name":"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences","volume":"54 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139066579","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Hardy–Littlewood Type Theorem for Harmonic Bergman–Orlicz Spaces and Applications 调和Bergman-Orlicz空间的Hardy-Littlewood型定理及其应用
4区 数学
Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences Pub Date : 2023-10-01 DOI: 10.3103/s1068362323050096
Xi Fu, Q. Shi#
{"title":"A Hardy–Littlewood Type Theorem for Harmonic Bergman–Orlicz Spaces and Applications","authors":"Xi Fu, Q. Shi#","doi":"10.3103/s1068362323050096","DOIUrl":"https://doi.org/10.3103/s1068362323050096","url":null,"abstract":"","PeriodicalId":54854,"journal":{"name":"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135963668","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Comparison of Polynomials and Weighted-Hyperbolic Operators 多项式与加权双曲算子的比较
4区 数学
Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences Pub Date : 2023-10-01 DOI: 10.3103/s1068362323050023
M. A. Khachaturyan, V. N. Margaryan
{"title":"Comparison of Polynomials and Weighted-Hyperbolic Operators","authors":"M. A. Khachaturyan, V. N. Margaryan","doi":"10.3103/s1068362323050023","DOIUrl":"https://doi.org/10.3103/s1068362323050023","url":null,"abstract":"","PeriodicalId":54854,"journal":{"name":"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135963494","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Operator Preserving Bernstein-Type Inequalities between Polynomials 多项式间保算子bernstein型不等式
4区 数学
Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences Pub Date : 2023-10-01 DOI: 10.3103/s1068362323050059
A. Mir, A. Hussain
{"title":"Operator Preserving Bernstein-Type Inequalities between Polynomials","authors":"A. Mir, A. Hussain","doi":"10.3103/s1068362323050059","DOIUrl":"https://doi.org/10.3103/s1068362323050059","url":null,"abstract":"","PeriodicalId":54854,"journal":{"name":"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences","volume":"121 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135963505","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On a Generalization of an Operator Preserving Turán-Type Inequality for Complex Polynomials 复多项式算子保持Turán-Type不等式的推广
4区 数学
Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences Pub Date : 2023-10-01 DOI: 10.3103/s1068362323050047
S. A. Malik, B. A. Zargar
{"title":"On a Generalization of an Operator Preserving Turán-Type Inequality for Complex Polynomials","authors":"S. A. Malik, B. A. Zargar","doi":"10.3103/s1068362323050047","DOIUrl":"https://doi.org/10.3103/s1068362323050047","url":null,"abstract":"Abstract Let $$W(zeta)=(a_{0}+a_{1}zeta+...+a_{n}zeta^{n})$$ be a polynomial of degree $$n$$ having all its zeros in $$mathbb{T}_{k}cupmathbb{E}^{-}_{k}$$ , $$kgeq 1$$ , then for every real or complex number $$alpha$$ with $$|alpha|geq 1+k+k^{n}$$ , Govil and McTume [7] showed that the following inequality holds $$maxlimits_{zetainmathbb{T}_{1}}|D_{alpha}W(zeta)|geq nleft(frac{|alpha|-k}{1+k^{n}}right)||W||+nleft(frac{|alpha|-(1+k+k^{n})}{1+k^{n}}right)minlimits_{zetainmathbb{T}_{k}}|W(zeta)|.$$ In this paper, we have obtained a generalization of this inequality involving sequence of operators known as polar derivatives. In addition, the problem for the limiting case is also considered.","PeriodicalId":54854,"journal":{"name":"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135963522","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Distribution of Zeros and Critical Points of a Polynomial, and Sendov’s Conjecture 多项式零点和临界点的分布及Sendov猜想
4区 数学
Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences Pub Date : 2023-10-01 DOI: 10.3103/s1068362323050084
G. M. Sofi, W. M. Shah
{"title":"Distribution of Zeros and Critical Points of a Polynomial, and Sendov’s Conjecture","authors":"G. M. Sofi, W. M. Shah","doi":"10.3103/s1068362323050084","DOIUrl":"https://doi.org/10.3103/s1068362323050084","url":null,"abstract":"Abstract According to the Gauss–Lucas theorem, the critical points of a complex polynomial $$p(z):=sum_{j=0}^{n}a_{j}z^{j}$$ where $$a_{j}inmathbb{C}$$ always lie in the convex hull of its zeros. In this paper, we prove certain relations between the distribution of zeros of a polynomial and its critical points. Using these relations, we prove the well-known Sendov’s conjecture for certain special cases.","PeriodicalId":54854,"journal":{"name":"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135963691","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","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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