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Acta Mathematica Vietnamica最新文献

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Gromov’s Oka Principle, Fiber Bundles and the Conformal Module Gromov的Oka原理、光纤束和保形模
IF 0.5
Acta Mathematica Vietnamica Pub Date : 2022-01-31 DOI: 10.1007/s40306-021-00452-z
Burglind Jöricke
{"title":"Gromov’s Oka Principle, Fiber Bundles and the Conformal Module","authors":"Burglind Jöricke","doi":"10.1007/s40306-021-00452-z","DOIUrl":"10.1007/s40306-021-00452-z","url":null,"abstract":"<div><p>The conformal module of conjugacy classes of braids is an invariant that appeared earlier than the entropy of conjugacy classes of braids, and is inversely proportional to the entropy. Using the relation between the two invariants, we give a short conceptional proof of an earlier result on the conformal module. Mainly, we consider situations, when the conformal module of conjugacy classes of braids serves as obstruction for the existence of homotopies (or isotopies) of smooth objects involving braids to the respective holomorphic objects, and present theorems on the restricted validity of Gromov’s Oka principle in these situations.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"47 2","pages":"375 - 440"},"PeriodicalIF":0.5,"publicationDate":"2022-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47749406","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
Hybrid Inertial Contraction Algorithms for Solving Variational Inequalities with Fixed Point Constraints in Hilbert Spaces 求解Hilbert空间中不动点约束变分不等式的混合惯性收缩算法
IF 0.5
Acta Mathematica Vietnamica Pub Date : 2022-01-28 DOI: 10.1007/s40306-021-00467-6
Pham Ngoc Anh
{"title":"Hybrid Inertial Contraction Algorithms for Solving Variational Inequalities with Fixed Point Constraints in Hilbert Spaces","authors":"Pham Ngoc Anh","doi":"10.1007/s40306-021-00467-6","DOIUrl":"10.1007/s40306-021-00467-6","url":null,"abstract":"<div><p>In this paper, basing on the forward-backward method and inertial techniques, we introduce a new algorithm for solving a variational inequality problem over the fixed point set of a nonexpansive mapping. The strong convergence of the algorithm is established under strongly monotone and Lipschitz continuous assumptions imposed on the cost mapping. As an application, we also apply and analyze our algorithm to solve a convex minimization problem of the sum of two convex functions.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"47 4","pages":"743 - 753"},"PeriodicalIF":0.5,"publicationDate":"2022-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45827527","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
Skew Polynomial Rings: the Schreier Technique 斜多项式环：Schreier技术
IF 0.5
Acta Mathematica Vietnamica Pub Date : 2022-01-22 DOI: 10.1007/s40306-021-00466-7
Phạm Ngọc Ánh
{"title":"Skew Polynomial Rings: the Schreier Technique","authors":"Phạm Ngọc Ánh","doi":"10.1007/s40306-021-00466-7","DOIUrl":"10.1007/s40306-021-00466-7","url":null,"abstract":"<div><p>Schreier bases are introduced and used to show that skew polynomial rings are free ideal rings, i.e., rings whose one-sided ideals are free of unique rank, as well as to compute a rank of one-sided ideals together with a description of corresponding bases. The latter fact, a so-called Schreier-Lewin formula (Lewin <i>Trans. Am. Math. Soc.</i> <b>145</b>, 455–465 1969), is a basic tool determining a module type of perfect localizations which reveal a close connection between classical Leavitt algebras, skew polynomial rings, and free associative algebras.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"47 1","pages":"5 - 17"},"PeriodicalIF":0.5,"publicationDate":"2022-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40306-021-00466-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50504925","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The First Syzygy of Hibi Rings Associated with Planar Distributive Lattices 平面分布格相关Hibi环的第一次合性
IF 0.5
Acta Mathematica Vietnamica Pub Date : 2022-01-18 DOI: 10.1007/s40306-021-00463-w
Priya Das, Himadri Mukherjee
{"title":"The First Syzygy of Hibi Rings Associated with Planar Distributive Lattices","authors":"Priya Das,&nbsp;Himadri Mukherjee","doi":"10.1007/s40306-021-00463-w","DOIUrl":"10.1007/s40306-021-00463-w","url":null,"abstract":"<div><p>In this article, we give explicit minimal generators of the first syzygy of the Hibi ring for a planar distributive lattice in terms of sublattices. We also give a characterization when it is linearly related and derive an exact formula for the first Betti number of a planar distributive lattice.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"47 3","pages":"689 - 707"},"PeriodicalIF":0.5,"publicationDate":"2022-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40306-021-00463-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46115988","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Gröbner Bases of Toric Ideals Associated with Matroids 与拟阵相关的托里理想的Gröbner基
IF 0.5
Acta Mathematica Vietnamica Pub Date : 2022-01-15 DOI: 10.1007/s40306-021-00468-5
Ken-ichi Hayase, Takayuki Hibi, Koyo Katsuno, Kazuki Shibata
{"title":"Gröbner Bases of Toric Ideals Associated with Matroids","authors":"Ken-ichi Hayase,&nbsp;Takayuki Hibi,&nbsp;Koyo Katsuno,&nbsp;Kazuki Shibata","doi":"10.1007/s40306-021-00468-5","DOIUrl":"10.1007/s40306-021-00468-5","url":null,"abstract":"<div><p>In 1980, White conjectured that the toric ideal of a matroid is generated by quadratic binomials corresponding to a symmetric exchange. In this paper, we compute Gröbner bases of toric ideals associated with matroids and show that, for every matroid on ground sets of size at most seven except for two matroids, Gröbner bases of toric ideals consist of quadratic binomials corresponding to a symmetric exchange.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"47 4","pages":"775 - 779"},"PeriodicalIF":0.5,"publicationDate":"2022-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42379930","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
q-Analogue of a Kantorovitch Variant of an Operator Defined by Stancu 由Stancu定义的算子的Kantorovitch变体的q-模拟
IF 0.5
Acta Mathematica Vietnamica Pub Date : 2022-01-13 DOI: 10.1007/s40306-021-00472-9
P. N. Agrawal, Arun Kajla, Abhishek Kumar
{"title":"q-Analogue of a Kantorovitch Variant of an Operator Defined by Stancu","authors":"P. N. Agrawal,&nbsp;Arun Kajla,&nbsp;Abhishek Kumar","doi":"10.1007/s40306-021-00472-9","DOIUrl":"10.1007/s40306-021-00472-9","url":null,"abstract":"<div><p>The purpose of this paper is to introduce a new kind of <i>q</i> −Stancu-Kantorovich type operators and study its various approximation properties. We establish some local direct theorems, e.g., Voronovskaja type asymptotic theorem, global approximation and an estimate of error by means of the Lipschitz type maximal function and the Peetre K-functional. We also consider a <i>n</i> th-order generalization of these operators and study its approximation properties. Next, we define a bivariate case of these operators and investigate the order of convergence by means of moduli of continuity and the elements of Lipschitz class. Furthermore, we consider the associated Generalized Boolean Sum (GBS) operators and examine the approximation degree for functions in a Bögel space. Some numerical examples to illustrate the convergence of these operators to certain functions are also given.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"47 4","pages":"781 - 816"},"PeriodicalIF":0.5,"publicationDate":"2022-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43534999","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: 2
A Note on Generalized Derivations of Order 2 and Multilinear Polynomials in Prime Rings 关于素环中2阶广义导子和多线性多项式的一个注记
IF 0.5
Acta Mathematica Vietnamica Pub Date : 2022-01-10 DOI: 10.1007/s40306-021-00471-w
Basudeb Dhara, Sukhendu Kar, Swarup Kuila
{"title":"A Note on Generalized Derivations of Order 2 and Multilinear Polynomials in Prime Rings","authors":"Basudeb Dhara,&nbsp;Sukhendu Kar,&nbsp;Swarup Kuila","doi":"10.1007/s40306-021-00471-w","DOIUrl":"10.1007/s40306-021-00471-w","url":null,"abstract":"<div><p>Let <i>R</i> be a prime ring of char(<i>R</i>)≠ 2, <i>U</i> its Utumi ring of quotients and center <i>C</i> = <i>Z</i>(<i>U</i>) its extended centroid, <i>I</i> a both sided ideal of <i>R</i>, <i>f</i>(<i>x</i><sub>1</sub>,…,<i>x</i><sub><i>n</i></sub>) a multilinear polynomial over <i>C</i>, that is noncentral-valued on <i>R</i>, <i>F</i>, <i>G</i> be two generalized derivations of <i>R</i> and <i>d</i> be a derivation of <i>R</i>. Let <i>f</i>(<i>I</i>) be the set of all evaluations of the multilinear polynomial <i>f</i>(<i>x</i><sub>1</sub>,…,<i>x</i><sub><i>n</i></sub>) in <i>I</i>. If @@@ for all <i>u</i> ∈ <i>f</i>(<i>I</i>), then all possible forms of the maps are determined. As an application of this result, we also study the commutator identity [<i>F</i><sup>2</sup>(<i>u</i>)<i>u</i>,<i>G</i><sup>2</sup>(<i>v</i>)<i>v</i>] = 0 for all <i>u</i>,<i>v</i> ∈ <i>f</i>(<i>I</i>), where <i>F</i> and <i>G</i> are two generalized derivations of <i>R</i>.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"47 4","pages":"755 - 773"},"PeriodicalIF":0.5,"publicationDate":"2022-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45780664","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
Maximal Generating Degrees of Powers of Homogeneous Ideals 齐次理想的最大生成次幂
IF 0.5
Acta Mathematica Vietnamica Pub Date : 2022-01-08 DOI: 10.1007/s40306-021-00469-4
Le Tuan Hoa
{"title":"Maximal Generating Degrees of Powers of Homogeneous Ideals","authors":"Le Tuan Hoa","doi":"10.1007/s40306-021-00469-4","DOIUrl":"10.1007/s40306-021-00469-4","url":null,"abstract":"<div><p>The degree excess function <i>𝜖</i>(<i>I</i>; <i>n</i>) is the difference between the maximal generating degree <i>d</i>(<i>I</i><sup><i>n</i></sup>) of the n-th power of a homogeneous ideal <i>I</i> of a polynomial ring and <i>p</i>(<i>I</i>)<i>n</i>, where <i>p</i>(<i>I</i>) is the leading coefficient of the asymptotically linear function <i>d</i>(<i>I</i><sup><i>n</i></sup>). It is shown that any non-increasing numerical function can be realized as a degree excess function, and there is a monomial ideal <i>I</i> whose <i>𝜖</i>(<i>I</i>; <i>n</i>) has exactly a given number of local maxima. In the case of monomial ideals, an upper bound on <i>𝜖</i>(<i>I</i>; <i>n</i>) is provided. As an application, it is shown that in the worst case, the so-called stability index of the Castelnuovo-Mumford regularity of a monomial ideal <i>I</i> must be at least an exponential function of the number of variables.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"47 1","pages":"19 - 37"},"PeriodicalIF":0.5,"publicationDate":"2022-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46991186","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
Lelong Number and the Log Canonical Thresholds of Plurisubharmonic Functions on Analytic Subsets Lelong数与分析子集上复数正则函数的对数正则阈值
IF 0.5
Acta Mathematica Vietnamica Pub Date : 2022-01-05 DOI: 10.1007/s40306-021-00465-8
Le Mau Hai, Pham Hoang Hiep, Trinh Tung
{"title":"Lelong Number and the Log Canonical Thresholds of Plurisubharmonic Functions on Analytic Subsets","authors":"Le Mau Hai,&nbsp;Pham Hoang Hiep,&nbsp;Trinh Tung","doi":"10.1007/s40306-021-00465-8","DOIUrl":"10.1007/s40306-021-00465-8","url":null,"abstract":"<div><p>The aim of this paper is to introduce the notion of Lelong number and the log canonical thresholds of plurisubharmonic functions on analytic subsets <i>A</i> in an open subset Ω of <span>(mathbb {C}^{n})</span>. Next, we establish some results about the relationship between these quantities in the relation with the analyticity of <i>A</i>.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"47 1","pages":"223 - 241"},"PeriodicalIF":0.5,"publicationDate":"2022-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50452378","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
Lelong Number and the Log Canonical Thresholds of Plurisubharmonic Functions on Analytic Subsets 解析子集上多次调和函数的Lelong数与对数正则阈值
IF 0.5
Acta Mathematica Vietnamica Pub Date : 2022-01-05 DOI: 10.1007/s40306-021-00465-8
L. M. Hai, Phạm Hoàng Hiệp, Trinh Tung
{"title":"Lelong Number and the Log Canonical Thresholds of Plurisubharmonic Functions on Analytic Subsets","authors":"L. M. Hai, Phạm Hoàng Hiệp, Trinh Tung","doi":"10.1007/s40306-021-00465-8","DOIUrl":"https://doi.org/10.1007/s40306-021-00465-8","url":null,"abstract":"","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"47 1","pages":"223 - 241"},"PeriodicalIF":0.5,"publicationDate":"2022-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"52714281","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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