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Modified Proximal Point Methods Involving Quasi-pseudocontractive Mappings in Hadamard Spaces Hadamard空间中拟拟压缩映射的修正近点方法
IF 0.5
Acta Mathematica Vietnamica Pub Date : 2022-08-05 DOI: 10.1007/s40306-022-00480-3
G. N. Ogwo, H. A. Abass, C. Izuchukwu, O. T. Mewomo
{"title":"Modified Proximal Point Methods Involving Quasi-pseudocontractive Mappings in Hadamard Spaces","authors":"G. N. Ogwo,&nbsp;H. A. Abass,&nbsp;C. Izuchukwu,&nbsp;O. T. Mewomo","doi":"10.1007/s40306-022-00480-3","DOIUrl":"10.1007/s40306-022-00480-3","url":null,"abstract":"<div><p>In this paper, we propose two new proximal point methods involving quasi-pseudocontractive mappings in Hadamard spaces. We prove that the first method converges strongly to a common solution of a finite family of minimization problems and fixed point problem for a finite family of quasi-pseudocontractive mappings in an Hadamard space. We then extend this method to a more general method involving multivalued monotone operators to approximate the solution of monotone inclusion problem, which is an important optimization problem. We establish that this method converges strongly to a common zero of a finite family of multivalued monotone operators which is also a common fixed point of a finite family of quasi-pseudocontractive mappings in an Hadamard space. Furthermore, we provide various nontrivial numerical implementations of our method in Hadamard spaces (which are non-Hilbert) and compare them with some other recent methods in the literature.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"47 4","pages":"847 - 873"},"PeriodicalIF":0.5,"publicationDate":"2022-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40306-022-00480-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43975958","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: 1
On Monogenity of Certain Pure Number Fields Defined by x60 − m 关于x60−m定义的纯数域的单性
IF 0.5
Acta Mathematica Vietnamica Pub Date : 2022-07-04 DOI: 10.1007/s40306-022-00481-2
Lhoussain El Fadil, Hanan Choulli, Omar Kchit
{"title":"On Monogenity of Certain Pure Number Fields Defined by x60 − m","authors":"Lhoussain El Fadil,&nbsp;Hanan Choulli,&nbsp;Omar Kchit","doi":"10.1007/s40306-022-00481-2","DOIUrl":"10.1007/s40306-022-00481-2","url":null,"abstract":"<div><p>Let <i>K</i> be a pure number field generated by a complex root of a monic irreducible polynomial <span>(F(x)=x^{60}-min mathbb {Z}[x])</span>, with <i>m</i>≠ ± 1 a square free integer. In this paper, we study the monogenity of <i>K</i>. We prove that if <i>m</i>≢1 (mod 4), <i>m</i>≢ ± 1 (mod 9) and <span>(overline {m}not in {pm 1,pm 7} ~(textup {mod}~{25}))</span>, then <i>K</i> is monogenic. But if <i>m</i> ≡ 1 (mod 4), <i>m</i> ≡± 1 (mod 9), or <i>m</i> ≡± 1 (mod 25), then <i>K</i> is not monogenic. Our results are illustrated by examples.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"48 2","pages":"283 - 293"},"PeriodicalIF":0.5,"publicationDate":"2022-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47628037","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: 8
Measured Foliations and Hilbert 12th Problem 测叶与Hilbert第12问题
IF 0.5
Acta Mathematica Vietnamica Pub Date : 2022-06-09 DOI: 10.1007/s40306-022-00479-w
Igor V. Nikolaev
{"title":"Measured Foliations and Hilbert 12th Problem","authors":"Igor V. Nikolaev","doi":"10.1007/s40306-022-00479-w","DOIUrl":"10.1007/s40306-022-00479-w","url":null,"abstract":"<div><p>Yu. I. Manin conjectured that the maximal abelian extensions of the real quadratic number fields are generated by the pseudo-lattices with real multiplication. We prove this conjecture using theory of measured foliations on the modular curves.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"48 2","pages":"271 - 281"},"PeriodicalIF":0.5,"publicationDate":"2022-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40306-022-00479-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50466089","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
Discrete Fourier-Jacobi Transform and Generalized Lipschitz Classes 离散傅立叶-雅可比变换与广义Lipschitz类
IF 0.5
Acta Mathematica Vietnamica Pub Date : 2022-05-03 DOI: 10.1007/s40306-022-00478-x
El Mehdi Loualid, Abdelghani Elgargati, Radouan Daher
{"title":"Discrete Fourier-Jacobi Transform and Generalized Lipschitz Classes","authors":"El Mehdi Loualid,&nbsp;Abdelghani Elgargati,&nbsp;Radouan Daher","doi":"10.1007/s40306-022-00478-x","DOIUrl":"10.1007/s40306-022-00478-x","url":null,"abstract":"<div><p>In this paper, we use the methods of Fourier-Jacobi harmonic analysis to generalize Boas-type results. We give necessary and sufficient conditions in terms of the Fourier-Jacobi coefficients of a function <i>f</i> in order to ensure that it belongs either to one of the generalized Lipschitz classes <span>({H}_{alpha }^{m})</span> and <span>({h}_{alpha }^{m})</span> for <i>α</i> &gt; 0.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"48 2","pages":"259 - 269"},"PeriodicalIF":0.5,"publicationDate":"2022-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40306-022-00478-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42693595","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: 2
Problems About Torsors over Regular Rings 关于正则环上的Torsors问题
IF 0.5
Acta Mathematica Vietnamica Pub Date : 2022-04-04 DOI: 10.1007/s40306-022-00477-y
Kęstutis Česnavičius
{"title":"Problems About Torsors over Regular Rings","authors":"Kęstutis Česnavičius","doi":"10.1007/s40306-022-00477-y","DOIUrl":"10.1007/s40306-022-00477-y","url":null,"abstract":"<div><p>We overview a web of conjectures about torsors under reductive groups over regular rings and survey some techniques that have been used for making progress on such problems.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"47 1","pages":"39 - 107"},"PeriodicalIF":0.5,"publicationDate":"2022-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46190096","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: 10
Brill-Noether Conjecture on Cactus Graphs Cactus图的Brill-Noether猜想
IF 0.5
Acta Mathematica Vietnamica Pub Date : 2022-03-14 DOI: 10.1007/s40306-021-00475-6
Phan Thi Ha Duong
{"title":"Brill-Noether Conjecture on Cactus Graphs","authors":"Phan Thi Ha Duong","doi":"10.1007/s40306-021-00475-6","DOIUrl":"10.1007/s40306-021-00475-6","url":null,"abstract":"<div><p>We give a proof of the combinatorial Brill-Noether conjecture for cactus graphs. This conjecture was formulated by Baker in 2008 when studying the interaction between algebraic curves theory and graph theory. By analyzing the treelike structure of cactus graphs, we produce a construction proof that is based on the Chip Firing Game theory.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"47 4","pages":"833 - 845"},"PeriodicalIF":0.5,"publicationDate":"2022-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49061959","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
Formal Partial Derivatives and the Commutativity of Squaring Operations 形式偏导数与平方运算的交换性
IF 0.5
Acta Mathematica Vietnamica Pub Date : 2022-02-26 DOI: 10.1007/s40306-021-00473-8
Nguyễn Đ. Ngà, N. A. Tuấn
{"title":"Formal Partial Derivatives and the Commutativity of Squaring Operations","authors":"Nguyễn Đ. Ngà, N. A. Tuấn","doi":"10.1007/s40306-021-00473-8","DOIUrl":"https://doi.org/10.1007/s40306-021-00473-8","url":null,"abstract":"","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"47 1","pages":"269 - 277"},"PeriodicalIF":0.5,"publicationDate":"2022-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"52714304","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
Formal Partial Derivatives and the Commutativity of Squaring Operations 形式偏导数与平方运算的交换性
IF 0.5
Acta Mathematica Vietnamica Pub Date : 2022-02-26 DOI: 10.1007/s40306-021-00473-8
Nguyễn Đ. Ngà, Ngô A. Tuấn
{"title":"Formal Partial Derivatives and the Commutativity of Squaring Operations","authors":"Nguyễn Đ. Ngà,&nbsp;Ngô A. Tuấn","doi":"10.1007/s40306-021-00473-8","DOIUrl":"10.1007/s40306-021-00473-8","url":null,"abstract":"<div><p>We introduce the notion of (formal) partial derivative and develop an application of it to get a new proof for the commutativity of the classical squaring and the Kameko squaring.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"47 1","pages":"269 - 277"},"PeriodicalIF":0.5,"publicationDate":"2022-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50514507","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
The DG Products of Peeva and Srinivasan Coincide Peeva和Srinivasan的DG产品一致
IF 0.5
Acta Mathematica Vietnamica Pub Date : 2022-02-23 DOI: 10.1007/s40306-021-00474-7
Keller VandeBogert
{"title":"The DG Products of Peeva and Srinivasan Coincide","authors":"Keller VandeBogert","doi":"10.1007/s40306-021-00474-7","DOIUrl":"10.1007/s40306-021-00474-7","url":null,"abstract":"<div><p>Consider the ideal <span>((x_{1} , dotsc , x_{n})^{d} subseteq k[x_{1} , dotsc , x_{n}])</span>, where <i>k</i> is any field. This ideal can be resolved by both the <i>L</i>-complexes of Buchsbaum and Eisenbud, and the Eliahou-Kervaire resolution. Both of these complexes admit the structure of an associative DG algebra, and it is a question of Peeva as to whether these DG structures coincide in general. In this paper, we construct an isomorphism of complexes between the aforementioned complexes that is also an isomorphism of algebras with their respective products, thus giving an affirmative answer to Peeva’s question.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"47 4","pages":"817 - 832"},"PeriodicalIF":0.5,"publicationDate":"2022-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43622190","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
The First Hilbert Coefficient of Stretched Ideals 拉伸理想的第一希尔伯特系数
IF 0.5
Acta Mathematica Vietnamica Pub Date : 2022-02-12 DOI: 10.1007/s40306-021-00470-x
Kazuho Ozeki
{"title":"The First Hilbert Coefficient of Stretched Ideals","authors":"Kazuho Ozeki","doi":"10.1007/s40306-021-00470-x","DOIUrl":"10.1007/s40306-021-00470-x","url":null,"abstract":"<div><p>In this paper, we explore the almost Cohen-Macaulayness of the associated graded ring of stretched <span>({mathfrak m})</span>-primary ideals with small first Hilbert coefficient in a Cohen-Macaulay local ring <span>((A,{mathfrak m}))</span>. In particular, we explore the structure of stretched <span>({mathfrak m})</span>-primary ideals satisfying the equality e<sub>1</sub>(<i>I</i>) = e<sub>0</sub>(<i>I</i>) − <i>ℓ</i><sub><i>A</i></sub>(<i>A</i>/<i>I</i>) + 4, where e<sub>0</sub>(<i>I</i>) and e<sub>1</sub>(<i>I</i>) denote the multiplicity and the first Hilbert coefficient, respectively.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"47 1","pages":"251 - 267"},"PeriodicalIF":0.5,"publicationDate":"2022-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50473841","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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