The main aim of this paper is to extend the concepts of the 1MP and MP1 inverses defined for rectangular complex matrices. We present the weighted 1MP and MP1 inverses for a bounded linear operator between two Hilbert spaces as two new kinds of generalized inverses. The notions of the weighted 1MP and MP1 inverses are new in the context of rectangular complex matrices too. We establish a number of characterizations and some representations of the weighted 1MP and MP1 inverses. Several operator equations are solved applying the weighted 1MP and MP1 inverses. A special case of one of these equations is the normal equation which is related with the least-squares solution. As consequences of our results, we obtain new properties of the 1MP and MP1 inverses.
{"title":"Weighted 1MP and MP1 inverses for operators","authors":"Dijana Mosić, Janko Marovt","doi":"10.1515/ms-2024-0033","DOIUrl":"https://doi.org/10.1515/ms-2024-0033","url":null,"abstract":"The main aim of this paper is to extend the concepts of the 1MP and MP1 inverses defined for rectangular complex matrices. We present the weighted 1MP and MP1 inverses for a bounded linear operator between two Hilbert spaces as two new kinds of generalized inverses. The notions of the weighted 1MP and MP1 inverses are new in the context of rectangular complex matrices too. We establish a number of characterizations and some representations of the weighted 1MP and MP1 inverses. Several operator equations are solved applying the weighted 1MP and MP1 inverses. A special case of one of these equations is the normal equation which is related with the least-squares solution. As consequences of our results, we obtain new properties of the 1MP and MP1 inverses.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"17 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141168637","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this study, a novel family of analytical functions connected to convex functions in the open unit is introduced and investigated. Additionally, relationships between this class and other subclasses of analytic functions are deduced. Further, different results for the mentioned class and several new interesting properties are obtained.
{"title":"Subordination properties and coefficient problems for a novel class of convex functions","authors":"Ebrahim Analouei Adegani, Mostafa Jafari, Teodor Bulboacă, Nak Eun Cho, Ahmad Motamednezhad","doi":"10.1515/ms-2024-0005","DOIUrl":"https://doi.org/10.1515/ms-2024-0005","url":null,"abstract":"In this study, a novel family of analytical functions connected to convex functions in the open unit is introduced and investigated. Additionally, relationships between this class and other subclasses of analytic functions are deduced. Further, different results for the mentioned class and several new interesting properties are obtained.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"133 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141168469","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The authors of the paper suggest a novel approach in order to examine an integral equality using conformable fractional operators. By using this identity, some Newton-type inequalities are proved for differentiable convex functions by taking the modulus of the newly established equality. Moreover, we prove some Newton-type inequalities by using the Hölder and power-mean inequality. Furthermore, some new results are presented by using special choices of obtained inequalities. Finally, we give some conformable fractional Newton-type inequalities for functions of bounded variation.
{"title":"A study on error bounds for Newton-type inequalities in conformable fractional integrals","authors":"Hüseyin Budak, Cihan Ünal, Fatih Hezenci","doi":"10.1515/ms-2024-0024","DOIUrl":"https://doi.org/10.1515/ms-2024-0024","url":null,"abstract":"The authors of the paper suggest a novel approach in order to examine an integral equality using conformable fractional operators. By using this identity, some Newton-type inequalities are proved for differentiable convex functions by taking the modulus of the newly established equality. Moreover, we prove some Newton-type inequalities by using the Hölder and power-mean inequality. Furthermore, some new results are presented by using special choices of obtained inequalities. Finally, we give some conformable fractional Newton-type inequalities for functions of bounded variation.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"18 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141168776","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Islam A. Husseiny, Haroon M. Barakat, Taher S. Taher, Metwally A. Alawady
The Fisher information matrix (FIM) relevant to order statistics (OSs) and their concomitants of the shape-parameters vector of the Cambanis bivariate distribution is investigated. Singly or multiply censored bivariate samples drawn from the Cambanis bivariate distribution are used to obtain the Fisher information (FI). In addition, the FI contained in the scale and shape parameters of generalized exponential distributions in the concomitants of OSs is obtained. The cumulative residual FI in the concomitant of OSs based on the Cambanis family is theoretically and numerically studied. Finally, a bivariate real-world data set has been analyzed for illustrative purposes, and the performance of the proposed method is quite satisfactory.
本文研究了与坎巴尼斯二元分布的形状参数向量的阶次统计（OS）及其相关因素有关的费舍尔信息矩阵（FIM）。从坎巴尼斯二元分布中抽取的单删减或多删减二元样本被用来获取费雪信息（FI）。此外，还获得了操作系统的伴随变量中广义指数分布的规模和形状参数所包含的费雪信息。对基于 Cambanis 族的操作系统同时体中的累积残差 FI 进行了理论和数值研究。最后，为了说明问题，分析了一个二元真实世界数据集，所提方法的性能相当令人满意。
{"title":"Fisher information in order statistics and their concomitants for Cambanis bivariate distribution","authors":"Islam A. Husseiny, Haroon M. Barakat, Taher S. Taher, Metwally A. Alawady","doi":"10.1515/ms-2024-0038","DOIUrl":"https://doi.org/10.1515/ms-2024-0038","url":null,"abstract":"The Fisher information matrix (FIM) relevant to order statistics (OSs) and their concomitants of the shape-parameters vector of the Cambanis bivariate distribution is investigated. Singly or multiply censored bivariate samples drawn from the Cambanis bivariate distribution are used to obtain the Fisher information (FI). In addition, the FI contained in the scale and shape parameters of generalized exponential distributions in the concomitants of OSs is obtained. The cumulative residual FI in the concomitant of OSs based on the Cambanis family is theoretically and numerically studied. Finally, a bivariate real-world data set has been analyzed for illustrative purposes, and the performance of the proposed method is quite satisfactory.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"61 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141168533","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We say that an idempotent term t is an exact-m-majority term if t evaluates to a, whenever the element a occurs exactly m times in the arguments of t, and all the other arguments are equal. If m < n and some variety 𝓥 has an n-ary exact-m-majority term, then 𝓥 is congruence modular. For certain values of n and m, for example, n = 5 and m = 3, the existence of an n-ary exact-m-majority term neither implies congruence distributivity, nor congruence permutability.
如果元素 a 在 t 的参数中恰好出现了 m 次，并且所有其他参数都相等，那么我们说一个幂项 t 是一个精确-m-多数项。如果 m <n，且某个综项𝓥 有一个 nary 精确-m-多数项，那么𝓥 是全等模态的。对于 n 和 m 的某些值，例如 n = 5 和 m = 3，n-一元精确-m-多数项的存在既不意味着全等可分配性，也不意味着全等可变性。
{"title":"Exact-m-majority terms","authors":"Paolo Lipparini","doi":"10.1515/ms-2024-0022","DOIUrl":"https://doi.org/10.1515/ms-2024-0022","url":null,"abstract":"We say that an idempotent term <jats:italic>t</jats:italic> is an <jats:italic>exact</jats:italic>-<jats:italic>m</jats:italic>-<jats:italic>majority term</jats:italic> if <jats:italic>t</jats:italic> evaluates to <jats:italic>a</jats:italic>, whenever the element <jats:italic>a</jats:italic> occurs exactly <jats:italic>m</jats:italic> times in the arguments of <jats:italic>t</jats:italic>, and all the other arguments are equal. If <jats:italic>m</jats:italic> < <jats:italic>n</jats:italic> and some variety 𝓥 has an <jats:italic>n</jats:italic>-ary exact-<jats:italic>m</jats:italic>-majority term, then 𝓥 is congruence modular. For certain values of <jats:italic>n</jats:italic> and <jats:italic>m</jats:italic>, for example, <jats:italic>n</jats:italic> = 5 and <jats:italic>m</jats:italic> = 3, the existence of an <jats:italic>n</jats:italic>-ary exact-<jats:italic>m</jats:italic>-majority term neither implies congruence distributivity, nor congruence permutability.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"48 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141168460","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we define some combinatorial principles to characterize spaces X whose hyperspace satisfies some variation of some classical star selection principle. Specifically, the variations characterized are the selective and absolute versions of the star selection principles for the Menger and Rothberger cases; also, the hyperspaces considered in these characterizations are CL(X), 𝕂(X), 𝔽(X) and ℂ𝕊(X) in both cases, endowed with either the Fell topology or the Vietoris topology.
{"title":"Variations of star selection principles on hyperspaces","authors":"Javier Casas-de la Rosa","doi":"10.1515/ms-2024-0013","DOIUrl":"https://doi.org/10.1515/ms-2024-0013","url":null,"abstract":"In this paper, we define some combinatorial principles to characterize spaces <jats:italic>X</jats:italic> whose hyperspace satisfies some variation of some classical star selection principle. Specifically, the variations characterized are the selective and absolute versions of the star selection principles for the Menger and Rothberger cases; also, the hyperspaces considered in these characterizations are <jats:italic>CL</jats:italic>(<jats:italic>X</jats:italic>), 𝕂(<jats:italic>X</jats:italic>), 𝔽(<jats:italic>X</jats:italic>) and ℂ𝕊(<jats:italic>X</jats:italic>) in both cases, endowed with either the Fell topology or the Vietoris topology.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"38 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141168462","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The classical density topology is an extension of the natural topology on the real line, as the interior of arbitrary Lebesgue measurable set A is contained in the set of density points of A. Also each density point of A belongs to the closure of A for arbitrary measurable set A. In this paper, we concentrate on lower density operators for which the inclusions mentioned above are not fulfilled. In the first part, examples of such lower density operators generated by measure-preserving bijections are given. There are introduced three conditions to investigate lower density operators for which only the second inclusion holds. In the second part, the concept of operator D introduced by K. Kuratowski is applied to the characterization of such operators.
经典密度拓扑学是实线上自然拓扑学的扩展，因为任意 Lebesgue 可测集 A 的内部包含在 A 的密度点集合中。在第一部分中，我们举例说明了由保度量双射产生的此类低密度算子。本文引入了三个条件来研究只有第二个包含成立的低密度算子。在第二部分中，K. Kuratowski 引入的算子 D 概念被应用于此类算子的表征。
{"title":"On lower density operators","authors":"Gertruda Ivanova, Elżbieta Wagner-Bojakowska","doi":"10.1515/ms-2024-0014","DOIUrl":"https://doi.org/10.1515/ms-2024-0014","url":null,"abstract":"The classical density topology is an extension of the natural topology on the real line, as the interior of arbitrary Lebesgue measurable set <jats:italic>A</jats:italic> is contained in the set of density points of <jats:italic>A</jats:italic>. Also each density point of <jats:italic>A</jats:italic> belongs to the closure of <jats:italic>A</jats:italic> for arbitrary measurable set <jats:italic>A</jats:italic>. In this paper, we concentrate on lower density operators for which the inclusions mentioned above are not fulfilled. In the first part, examples of such lower density operators generated by measure-preserving bijections are given. There are introduced three conditions to investigate lower density operators for which only the second inclusion holds. In the second part, the concept of operator <jats:italic>D</jats:italic> introduced by K. Kuratowski is applied to the characterization of such operators.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"59 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141168534","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we first give a topological representation of some algebraic lattices of ideals of C(X). Next, we apply these results and prove that a space X is normal if and only if the lattice of closed fixed ideals of C(X) is a sublattice of the lattice of ideals of C(X). It is proved that if two rings C(X) and C(Y) are isomorphic, then two lattices Z∘[X] and Z∘[Y] are isomorphic. We conclude that two rings C*(X) and C*(Y) are isomorphic if and only if two lattices Z[βX] and Z[βY] are isomorphic.
在本文中，我们首先给出了 C(X) 的一些理想代数网格的拓扑表示。接着，我们应用这些结果，证明当且仅当 C(X) 的封闭固定理想格是 C(X) 理想格的子格时，空间 X 是正态的。证明了如果两个环 C(X) 和 C(Y) 同构，那么两个网格 Z ∘[X] 和 Z ∘[Y] 同构。我们的结论是，当且仅当两个网格 Z[βX] 和 Z[βY] 同构时，两个环 C *(X) 和 C *(Y) 同构。
{"title":"Topological representation of some lattices","authors":"Ali Taherifar, Mohamad Reza Ahmadi Zand","doi":"10.1515/ms-2024-0021","DOIUrl":"https://doi.org/10.1515/ms-2024-0021","url":null,"abstract":"In this paper, we first give a topological representation of some algebraic lattices of ideals of <jats:italic>C</jats:italic>(<jats:italic>X</jats:italic>). Next, we apply these results and prove that a space <jats:italic>X</jats:italic> is normal if and only if the lattice of closed fixed ideals of <jats:italic>C</jats:italic>(<jats:italic>X</jats:italic>) is a sublattice of the lattice of ideals of <jats:italic>C</jats:italic>(<jats:italic>X</jats:italic>). It is proved that if two rings <jats:italic>C</jats:italic>(<jats:italic>X</jats:italic>) and <jats:italic>C</jats:italic>(<jats:italic>Y</jats:italic>) are isomorphic, then two lattices <jats:italic>Z</jats:italic> <jats:sup>∘</jats:sup>[<jats:italic>X</jats:italic>] and <jats:italic>Z</jats:italic> <jats:sup>∘</jats:sup>[<jats:italic>Y</jats:italic>] are isomorphic. We conclude that two rings <jats:italic>C</jats:italic> <jats:sup>*</jats:sup>(<jats:italic>X</jats:italic>) and <jats:italic>C</jats:italic> <jats:sup>*</jats:sup>(<jats:italic>Y</jats:italic>) are isomorphic if and only if two lattices <jats:italic>Z</jats:italic>[<jats:italic>βX</jats:italic>] and <jats:italic>Z</jats:italic>[<jats:italic>βY</jats:italic>] are isomorphic.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"10 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141170122","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Maryam Taha, Ali Akbar Estaji, Maryam Robat Sarpoushi
Let Rα := {r ∈ ℝ : coz(α − r) ≠ → p} for every α ∈ 𝓡(L). The ring 𝓒c (L) is introduced as a pointfree version of the subring 𝓒c(X) of C(X) by Rα. In this paper, we show that 𝓒c(X) is a z-good ring and every radical ideal in it is an absolutely convex ideal. Also, we study this result which for any frame L, there exists a zero-dimensional frame M, which is a continuous image of L and 𝓒c(L) ≅ 𝓒c(M).
让 R α := {r ∈ ℝ : coz(α - r) ≠ → p} 为每一个 α ∈ 𝓡(L) 的 R α :={r∈ℝ : coz(α - r) ≠ → p}。环 𝓒 c (L) 是作为 C(X) 的子环 𝓒 c (X) 的无点版本由 R α 引入的。在本文中，我们证明了𝓒 c (X) 是一个 z 好环，并且其中的每个根理想都是绝对凸理想。此外，我们还研究了这样一个结果，即对于任意框架 L，存在一个零维框架 M，它是 L 的连续映像，且 𝓒 c (L) ≅ 𝓒 c (M)。
{"title":"The pointfree version of 𝓒 c (X) via the ranges of functions","authors":"Maryam Taha, Ali Akbar Estaji, Maryam Robat Sarpoushi","doi":"10.1515/ms-2024-0003","DOIUrl":"https://doi.org/10.1515/ms-2024-0003","url":null,"abstract":"Let <jats:italic>R</jats:italic> <jats:sub> <jats:italic>α</jats:italic> </jats:sub> := {<jats:italic>r</jats:italic> ∈ ℝ : coz(<jats:italic>α</jats:italic> − <jats:italic>r</jats:italic>) ≠ → <jats:italic>p</jats:italic>} for every <jats:italic>α</jats:italic> ∈ 𝓡(<jats:italic>L</jats:italic>). The ring 𝓒<jats:sub> <jats:italic>c</jats:italic> </jats:sub> (<jats:italic>L</jats:italic>) is introduced as a pointfree version of the subring 𝓒<jats:sub> <jats:italic>c</jats:italic> </jats:sub>(<jats:italic>X</jats:italic>) of <jats:italic>C</jats:italic>(<jats:italic>X</jats:italic>) by <jats:italic>R</jats:italic> <jats:sub> <jats:italic>α</jats:italic> </jats:sub>. In this paper, we show that 𝓒<jats:sub> <jats:italic>c</jats:italic> </jats:sub>(<jats:italic>X</jats:italic>) is a <jats:italic>z</jats:italic>-good ring and every radical ideal in it is an absolutely convex ideal. Also, we study this result which for any frame <jats:italic>L</jats:italic>, there exists a zero-dimensional frame <jats:italic>M</jats:italic>, which is a continuous image of <jats:italic>L</jats:italic> and 𝓒<jats:sub> <jats:italic>c</jats:italic> </jats:sub>(<jats:italic>L</jats:italic>) ≅ 𝓒<jats:sub> <jats:italic>c</jats:italic> </jats:sub>(<jats:italic>M</jats:italic>).","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"39 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141168733","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In Geometric function theory, the Ma-Minda class of starlike functions has a unique place as it unifies various subclasses of starlike functions. There has been an vivid interplay between special functions and their geometric properties, like starlikeness. In this article, we establish certain special function’s radius of Ma-Minda starlikness. As an application, we obtain conditions on parameters for these special functions to be in the Ma-Minda class. Further, we focus on certain convolution properties for the Ma-Minda class that are not done so far, and study their applications in radius problem. Finally, we prove a variational problem of Goluzin, namely, the region of variability for the Ma-Minda class. Our results simplify and generalize the already-known ones.
{"title":"Certain radii problems for 𝓢∗(ψ) and special functions","authors":"Kamaljeet Gangania, S. Sivaprasad Kumar","doi":"10.1515/ms-2024-0006","DOIUrl":"https://doi.org/10.1515/ms-2024-0006","url":null,"abstract":"In Geometric function theory, the Ma-Minda class of starlike functions has a unique place as it unifies various subclasses of starlike functions. There has been an vivid interplay between special functions and their geometric properties, like starlikeness. In this article, we establish certain special function’s radius of Ma-Minda starlikness. As an application, we obtain conditions on parameters for these special functions to be in the Ma-Minda class. Further, we focus on certain convolution properties for the Ma-Minda class that are not done so far, and study their applications in radius problem. Finally, we prove a variational problem of Goluzin, namely, the region of variability for the Ma-Minda class. Our results simplify and generalize the already-known ones.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"48 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141168458","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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