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Unicity of Meromorphic Functions Concerning Differential-Difference Polynomials 关于微分-差分多项式的单调函数
IF 0.3 4区 数学
Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences Pub Date : 2024-04-09 DOI: 10.3103/s1068362324010072
M. L. Zeng, J. Y. Fan, M. L. Fang
{"title":"Unicity of Meromorphic Functions Concerning Differential-Difference Polynomials","authors":"M. L. Zeng, J. Y. Fan, M. L. Fang","doi":"10.3103/s1068362324010072","DOIUrl":"https://doi.org/10.3103/s1068362324010072","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this paper, we study unicity of meromorphic functions concerning differential-difference polynomials and mainly prove: Let <span>(k_{1},k_{2},cdots,k_{n})</span> be nonnegative integers and <span>(k=)</span> max<span>({k_{1},k_{2},cdots,k_{n}})</span>, let <span>(l)</span> be the number of distinct values of <span>({0,c_{1},c_{2},cdots,c_{n}})</span>, let <span>(s)</span> be the number of distinct values of <span>({c_{1},c_{2},cdots,c_{n}})</span>, let <span>(f(z))</span> be a nonconstant meromorphic function of finite order satisfying <span>(N(r,f)leqfrac{1}{8(lk+l+2s-1)+1}T(r,f))</span>, let <span>(m_{1}(z),m_{2}(z),cdots,m_{n}(z),)</span>\u0000<span>(a(z),b(z))</span> be small functions of <span>(f(z))</span> such that <span>(a(z)notequiv b(z))</span>, let <span>((c_{1},k_{1}),(c_{2},k_{2}),)</span>\u0000<span>(cdots,(c_{n},k_{n}))</span> be distinct and let <span>(F(z)=m_{1}(z)f^{(k_{1})}(z+c_{1})+m_{2}(z)f^{(k_{2})}(z+c_{2})+cdots+m_{n}(z)f^{(k_{n})}(z+c_{n}))</span>. If <span>(f(z))</span> and <span>(F(z))</span> share <span>(a(z),b(z))</span> CM, then <span>(f(z)equiv F(z))</span>. Our results improve and extend some results due to [1, 18, 20].</p>","PeriodicalId":54854,"journal":{"name":"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140571595","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
Simplified Whittle Estimators for Spectral Parameters of Stationary Linear Models with Tapered Data 具有锥形数据的静态线性模型频谱参数的简化惠特尔估计器
IF 0.3 4区 数学
Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences Pub Date : 2024-04-09 DOI: 10.3103/s1068362324010047
M. S. Ginovyan
{"title":"Simplified Whittle Estimators for Spectral Parameters of Stationary Linear Models with Tapered Data","authors":"M. S. Ginovyan","doi":"10.3103/s1068362324010047","DOIUrl":"https://doi.org/10.3103/s1068362324010047","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The paper is concerned with the statistical estimation of the spectral parameters of stationary models with tapered data. As estimators of the unknown parameters we consider the tapered Whittle estimator and the simplified tapered Whittle estimators. We show that under broad regularity conditions on the spectral density of the model these estimators are asymptotically statistically equivalent, in the sense that these estimators possess the same asymptotic properties. The processes considered will be discrete-time and continuous-time Gaussian, linear or Lévy-driven linear processes with memory.</p>","PeriodicalId":54854,"journal":{"name":"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140571629","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 the Euclidean Distance between Two Gaussian Points and the Normal Covariogram of $$boldsymbol{mathbb{R}}^{boldsymbol{d}}$$ 论两个高斯点与 $$boldsymbol{mathbb{R}}^{boldsymbol{d}}$ 的正态协方差图之间的欧氏距离
IF 0.3 4区 数学
Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences Pub Date : 2024-04-09 DOI: 10.3103/s1068362324010059
D. M. Martirosyan, V. K. Ohanyan
{"title":"On the Euclidean Distance between Two Gaussian Points and the Normal Covariogram of $$boldsymbol{mathbb{R}}^{boldsymbol{d}}$$","authors":"D. M. Martirosyan, V. K. Ohanyan","doi":"10.3103/s1068362324010059","DOIUrl":"https://doi.org/10.3103/s1068362324010059","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The concept of covariogram is extended from bounded convex bodies in <span>(mathbb{R}^{d})</span> to the entire space <span>(mathbb{R}^{d})</span> by obtaining integral representations for the distribution and probability density functions of the Euclidean distance between two <span>(d)</span>-dimensional Gaussian points that have correlated coordinates governed by a covariance matrix. When <span>(d=2)</span>, a closed-form expression for the density function is obtained. Precise bounds for the moments of the considered distance are found in terms of the extreme eigenvalues of the covariance matrix.</p>","PeriodicalId":54854,"journal":{"name":"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140571673","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Movability of Morphisms in an Enriched Pro-Category and in a $$boldsymbol{J}$$ -Shape Category 丰富的原类和 $$boldsymbol{J}$ 形类中形态的可动性
IF 0.3 4区 数学
Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences Pub Date : 2024-04-09 DOI: 10.3103/s1068362324010035
P. S. Gevorgyan, I. Pop
{"title":"Movability of Morphisms in an Enriched Pro-Category and in a $$boldsymbol{J}$$ -Shape Category","authors":"P. S. Gevorgyan, I. Pop","doi":"10.3103/s1068362324010035","DOIUrl":"https://doi.org/10.3103/s1068362324010035","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Various types of movability for abstract classical pro-morphisms or coherent mappings, and for abstract classical or strong shape morphisms was given by the same authors in some previous paper [10–12]. In the present paper we introduce and study the notions of (uniform) movability, and (uniform) co-movability for a new type of pro-morphisms and shape morphisms belonging to the so called enriched pro-category <span>(pro^{J})</span>-<span>(mathcal{C})</span> and to the corresponding shape category <span>(Sh^{J}_{(mathcal{C},mathcal{D})})</span>, which were introduced by Uglešić [27].</p>","PeriodicalId":54854,"journal":{"name":"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140571630","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 Benign Subgroups Constructed by Higman’s Sequence Building Operation 论通过希格曼序列构建操作构建的良性子群
IF 0.3 4区 数学
Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences Pub Date : 2024-04-09 DOI: 10.3103/s1068362324010023
V. S. Atabekyan, V. H. Mikaelian
{"title":"On Benign Subgroups Constructed by Higman’s Sequence Building Operation","authors":"V. S. Atabekyan, V. H. Mikaelian","doi":"10.3103/s1068362324010023","DOIUrl":"https://doi.org/10.3103/s1068362324010023","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>For Higman’s sequence building operation <span>(omega_{m})</span> and for any integer sequences set <span>({mathcal{B}})</span> the subgroup <span>(A_{omega_{m}{mathcal{B}}})</span> is benign in a free group <span>(G)</span> as soon as <span>(A_{mathcal{B}})</span> is benign in <span>(G)</span>. Higman used this property as a key step to prove that a finitely generated group is embeddable into a finitely presented group if and only if it is recursively presented. We build the explicit analog of this fact, i.e., we explicitly give a finitely presented overgroup <span>(K_{omega_{m}{mathcal{B}}})</span> of <span>(G)</span> and its finitely generated subgroup <span>(L_{omega_{m}{mathcal{B}}}leq K_{omega_{m}{mathcal{B}}})</span> such that <span>(Gcap L_{omega_{m}{mathcal{B}}}=A_{omega_{m}{mathcal{B}}})</span> holds. Our construction can be used in explicit embeddings of finitely generated groups into finitely presented groups, which are theoretically possible by Higman’s theorem. To build our construction we suggest some auxiliary ‘‘nested’’ free constructions based on free products with amalgamation and HNN-extensions.</p>","PeriodicalId":54854,"journal":{"name":"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140571340","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
Uniqueness of $$boldsymbol{L}$$ -Functions and General Meromorphic Functions in Light of Two Shared Sets 从两个共享集看$$boldsymbol{L}$-函数和一般同态函数的唯一性
IF 0.3 4区 数学
Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences Pub Date : 2024-04-09 DOI: 10.3103/s1068362324010060
R. Saha, S. Mallick
{"title":"Uniqueness of $$boldsymbol{L}$$ -Functions and General Meromorphic Functions in Light of Two Shared Sets","authors":"R. Saha, S. Mallick","doi":"10.3103/s1068362324010060","DOIUrl":"https://doi.org/10.3103/s1068362324010060","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this paper, we have dealt with the uniqueness problem of a general meromorphic function with <span>(mathcal{L})</span> function in terms of two shared sets. In our main theorem, we deal with general meromorphic functions instead of meromorphic functions having finitely many poles. As a corollary of our main theorem, we have shown that our result not only fills the gap of some theorems of [3] and [1] for <span>(m=n-1)</span> but also reduces the cardinality of the main range set and hence our result significantly improves all the results in this direction.</p>","PeriodicalId":54854,"journal":{"name":"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140571547","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
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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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
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