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On Leavitt Path Algebras of Hopf Graphs 论霍普夫图的莱维特路径代数
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2023-09-19 DOI: 10.1007/s40306-023-00511-7
T. G. Nam, N. T. Phuc
{"title":"On Leavitt Path Algebras of Hopf Graphs","authors":"T. G. Nam,&nbsp;N. T. Phuc","doi":"10.1007/s40306-023-00511-7","DOIUrl":"10.1007/s40306-023-00511-7","url":null,"abstract":"<div><p>In this paper, we provide the structure of Hopf graphs associated to pairs <span>((G, mathfrak {r}))</span> consisting of groups <i>G</i> together with ramification datas <span>(mathfrak {r})</span> and their Leavitt path algebras. Consequently, we characterize the Gelfand-Kirillov dimension, the stable rank, the purely infinite simplicity and the existence of a nonzero finite dimensional representation of the Leavitt path algebra of a Hopf graph via properties of ramification data <span>(mathfrak {r})</span> and <i>G</i>.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"48 4","pages":"533 - 549"},"PeriodicalIF":0.3,"publicationDate":"2023-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135015875","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
Respondent-Driven Sampling on Sparse Erdös-Rényi Graphs 稀疏Erdös-Rényi图的响应驱动抽样
IF 0.5
Acta Mathematica Vietnamica Pub Date : 2023-09-12 DOI: 10.1007/s40306-023-00510-8
Anthony Cousien, Jean-Stéphane Dhersin, Viet Chi Tran, Thi Phuong Thuy Vo
{"title":"Respondent-Driven Sampling on Sparse Erdös-Rényi Graphs","authors":"Anthony Cousien,&nbsp;Jean-Stéphane Dhersin,&nbsp;Viet Chi Tran,&nbsp;Thi Phuong Thuy Vo","doi":"10.1007/s40306-023-00510-8","DOIUrl":"10.1007/s40306-023-00510-8","url":null,"abstract":"<div><p>We study the exploration of an Erdös-Rényi random graph by a respondent-driven sampling method, where discovered vertices reveal their neighbors. Some of them receive coupons to reveal in their turn their own neighborhood. This leads to the study of a Markov chain on the random graph that we study. For sparse Erdös-Rényi graphs of large sizes, this process correctly renormalized converges to the solution of a deterministic curve, solution of a system of ODEs absorbed on the abscissa axis. The associated fluctuation process is also studied, providing a functional central limit theorem, with a Gaussian limiting process. Simulations and numerical computation illustrate the study.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"48 3","pages":"479 - 513"},"PeriodicalIF":0.5,"publicationDate":"2023-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50476179","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
Cone of Maximal Subextensions of the Plurisubharmonic Functions 多次调和函数的极大子扩展锥
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2023-08-05 DOI: 10.1007/s40306-023-00509-1
Le Mau Hai, Pham Hoang Hiep, Trinh Tung
{"title":"Cone of Maximal Subextensions of the Plurisubharmonic Functions","authors":"Le Mau Hai,&nbsp;Pham Hoang Hiep,&nbsp;Trinh Tung","doi":"10.1007/s40306-023-00509-1","DOIUrl":"10.1007/s40306-023-00509-1","url":null,"abstract":"<div><p>In this note, we give some results on maximal subextensions of plurisubharmonic functions on hyperconvex domains in <span>(mathbb C^n)</span> and introduce the notion about cone of maximal subextensions of plurisubharmonic functions. Furthermore, we establish the invariant of this cone through proper holomorphic surjections.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"49 1","pages":"83 - 97"},"PeriodicalIF":0.3,"publicationDate":"2023-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47294605","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
A Note on Jacobian Problem Over (mathbb {Z}) 关于$$mathbb｛Z｝上Jacobian问题的一个注记$$
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2023-07-25 DOI: 10.1007/s40306-023-00504-6
Nguyen Van Chau
{"title":"A Note on Jacobian Problem Over (mathbb {Z})","authors":"Nguyen Van Chau","doi":"10.1007/s40306-023-00504-6","DOIUrl":"10.1007/s40306-023-00504-6","url":null,"abstract":"<div><p>Motivated by the Jacobian problem, this article is concerned with the density of the image set <span>(F( mathbb {Z}^n))</span> of polynomial maps <span>(Fin mathbb {Z}[X_1,dots ,X_n]^n)</span> with <span>(det DFequiv 1)</span>. It is shown that if such a map <i>F</i> is not invertible, its image set <span>(F( mathbb {Z}^n))</span> must be very thin in the lattice <span>( mathbb {Z}^n)</span>: (1) for almost all lines <i>l</i> in <span>( mathbb {Z}^n)</span> the numbers <span>(texttt {#}(F^{-1}(l) cap mathbb {Z}^n))</span> are uniformly bounded; (2) <span>(texttt {#}{ zin F( mathbb {Z}^n): vert z_ivert le B} ll B^{n-1})</span> as <span>(Brightarrow +infty )</span>, where the implicit constants depend on <i>F</i>.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"48 4","pages":"515 - 521"},"PeriodicalIF":0.3,"publicationDate":"2023-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41969905","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 Constraint Equations of the Einstein-Vlasov-Maxwell System in the Maximal-isotropic Coordinates Einstein-Vlasov-Maxwell系统在最大各向同性坐标系中的约束方程
IF 0.5
Acta Mathematica Vietnamica Pub Date : 2023-07-19 DOI: 10.1007/s40306-023-00507-3
Timothée Raoul Moutngui See, Pierre Noundjeu
{"title":"The Constraint Equations of the Einstein-Vlasov-Maxwell System in the Maximal-isotropic Coordinates","authors":"Timothée Raoul Moutngui See,&nbsp;Pierre Noundjeu","doi":"10.1007/s40306-023-00507-3","DOIUrl":"10.1007/s40306-023-00507-3","url":null,"abstract":"<div><p>In this paper we prove the existence of initial data satisfying the constraint equations corresponding to the 1+3 formulation of asymptotically flat spherically symmetric Einstein-Vlasov-Maxwell system, when the charge of the particles is either low or large, the initial distribution function is compactly supported, the shift vector is non-zero and the isotropic metric ansatz is not diagonal. This result extends the work (Rein and Rendall, Commun. Math. Phys. <b>150</b>(3), 561–583 1992) concerning the existence of solutions to the constraint equations for chargeless particles.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"48 3","pages":"445 - 458"},"PeriodicalIF":0.5,"publicationDate":"2023-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40306-023-00507-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47283373","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
Modified Subgradient Extragradient Methods for Solving Bilevel Split Variational Inequality Problems in Hilbert Spaces 求解Hilbert空间中双层分裂变分不等式问题的修正亚梯度外聚方法
IF 0.5
Acta Mathematica Vietnamica Pub Date : 2023-07-18 DOI: 10.1007/s40306-023-00508-2
Le Huynh My Van, Dang Le Thuy, Tran Viet Anh
{"title":"Modified Subgradient Extragradient Methods for Solving Bilevel Split Variational Inequality Problems in Hilbert Spaces","authors":"Le Huynh My Van,&nbsp;Dang Le Thuy,&nbsp;Tran Viet Anh","doi":"10.1007/s40306-023-00508-2","DOIUrl":"10.1007/s40306-023-00508-2","url":null,"abstract":"<div><p>In this work, we propose a new method for solving a bilevel split variational inequality problem (BSVIP) in Hilbert spaces. The proposed method is inspired by the subgradient extragradient method for solving a monotone variational inequality problem. A strong convergence theorem for an algorithm for solving such a BSVIP is proved without knowing any information of the Lipschitz and strongly monotone constants of the mappings. Moreover, we do not require any prior information regarding the norm of the given bounded linear operator. Special cases are considered. Two numerical examples are given to illustrate the performance of our algorithm.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"48 3","pages":"459 - 478"},"PeriodicalIF":0.5,"publicationDate":"2023-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48474134","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
Real Interpolation Between Strong Martingale Hardy Spaces 强鞅Hardy空间之间的实插值
IF 0.5
Acta Mathematica Vietnamica Pub Date : 2023-07-17 DOI: 10.1007/s40306-023-00505-5
Kaituo Liu, Jianzhong Lu, Lihua Peng
{"title":"Real Interpolation Between Strong Martingale Hardy Spaces","authors":"Kaituo Liu,&nbsp;Jianzhong Lu,&nbsp;Lihua Peng","doi":"10.1007/s40306-023-00505-5","DOIUrl":"10.1007/s40306-023-00505-5","url":null,"abstract":"<div><p>In this paper, we establish a decomposition theorem for strong martingale Hardy space <span>(sH_p^sigma )</span>, which is based on its atomic decomposition theorem. By using of this decomposition theorem, we investigate the real interpolation spaces between <span>(sH_p^sigma ;(0&lt;ple 1))</span> and <span>(sL_2)</span>. Furthermore, with the help of the decomposition theorem and the real interpolation method, a sufficient condition to ensure the boundedness of a sublinear operator defined on strong martingale Hardy-Lorentz spaces is given.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"48 3","pages":"423 - 443"},"PeriodicalIF":0.5,"publicationDate":"2023-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46630442","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
On Segre Products, F-regularity, and Finite Frobenius Representation Type 关于分段积、f正则性和有限Frobenius表示类型
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2023-07-11 DOI: 10.1007/s40306-023-00506-4
Anurag K. Singh, Kei-ichi Watanabe
{"title":"On Segre Products, F-regularity, and Finite Frobenius Representation Type","authors":"Anurag K. Singh,&nbsp;Kei-ichi Watanabe","doi":"10.1007/s40306-023-00506-4","DOIUrl":"10.1007/s40306-023-00506-4","url":null,"abstract":"<div><p>We study the behavior of various properties of commutative Noetherian rings under Segre products, with a special focus on properties in positive prime characteristic defined using the Frobenius endomorphism. Specifically, we construct normal graded rings of finite Frobenius representation type that are not Cohen-Macaulay.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"49 1","pages":"129 - 138"},"PeriodicalIF":0.3,"publicationDate":"2023-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45511127","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
Continuity of the Solution to a Stochastic Time-fractional Diffusion Equations in the Spatial Domain with Locally Lipschitz Sources 具有局部Lipschitz源的随机时间分数扩散方程在空间域中解的连续性
IF 0.5
Acta Mathematica Vietnamica Pub Date : 2023-04-24 DOI: 10.1007/s40306-023-00503-7
Dang Duc Trong, Nguyen Dang Minh, Nguyen Nhu Lan, Nguyen Thi Mong Ngoc
{"title":"Continuity of the Solution to a Stochastic Time-fractional Diffusion Equations in the Spatial Domain with Locally Lipschitz Sources","authors":"Dang Duc Trong,&nbsp;Nguyen Dang Minh,&nbsp;Nguyen Nhu Lan,&nbsp;Nguyen Thi Mong Ngoc","doi":"10.1007/s40306-023-00503-7","DOIUrl":"10.1007/s40306-023-00503-7","url":null,"abstract":"<div><p>We-24pt study the nonlinear stochastic time-fractional diffusion equation in the spatial domain <span>(mathbb {R})</span> driven by a locally Lipschitz source satisfying </p><div><div><span>$$begin{aligned} left( {~}_{t}D_{0^{+}}^{alpha } - frac{partial ^{2} }{partial x^{2}}right) u(t,x) = I_{t}^{gamma }left( F(t,x,u)right) , end{aligned}$$</span></div></div><p>where <span>(xin mathbb {R},alpha in (0,1],gamma ge 1-alpha )</span>, the source term is defined <span>(F(t,x,u) = f(t,x,u(t,x)))</span> <span>( + rho (t,x,u(t,x))dot{W}(t,x))</span> and <i>W</i> is the multiplicative space-time white noise. We investigate the existence, uniqueness of a maximal random field solution. Moreover, we prove the stability of the solution with respect to perturbed fractional orders <span>(alpha , gamma )</span> and the initial condition.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"48 1","pages":"237 - 257"},"PeriodicalIF":0.5,"publicationDate":"2023-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40306-023-00503-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48136681","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 Carleman Contraction Mapping Method for Quasilinear Elliptic Equations with Over-determined Boundary Data 边界数据过定的拟线性椭圆方程的Carleman收缩映射方法
IF 0.5
Acta Mathematica Vietnamica Pub Date : 2023-04-20 DOI: 10.1007/s40306-023-00500-w
Loc H. Nguyen
{"title":"The Carleman Contraction Mapping Method for Quasilinear Elliptic Equations with Over-determined Boundary Data","authors":"Loc H. Nguyen","doi":"10.1007/s40306-023-00500-w","DOIUrl":"10.1007/s40306-023-00500-w","url":null,"abstract":"<div><p>We propose a globally convergent numerical method to compute solutions to a general class of quasi-linear PDEs with both Neumann and Dirichlet boundary conditions. Combining the quasi-reversibility method and a suitable Carleman weight function, we define a map of which fixed point is the solution to the PDE under consideration. To find this fixed point, we define a recursive sequence with an arbitrary initial term using the same manner as in the proof of the contraction principle. Applying a Carleman estimate, we show that the sequence above converges to the desired solution. On the other hand, we also show that our method delivers reliable solutions even when the given data are noisy. Numerical examples are presented.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"48 3","pages":"401 - 422"},"PeriodicalIF":0.5,"publicationDate":"2023-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40306-023-00500-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43053841","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
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