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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
Entire Solutions of a Certain Type of Nonlinear Differential-Difference Equations 一类非线性微分-差分方程的全解
IF 0.5
Acta Mathematica Vietnamica Pub Date : 2021-11-23 DOI: 10.1007/s40306-021-00464-9
Wen-Jie Hao, Jun-Fan Chen
{"title":"Entire Solutions of a Certain Type of Nonlinear Differential-Difference Equations","authors":"Wen-Jie Hao,&nbsp;Jun-Fan Chen","doi":"10.1007/s40306-021-00464-9","DOIUrl":"10.1007/s40306-021-00464-9","url":null,"abstract":"<div><p>The aim of the paper is to investigate all transcendental entire solutions of the following general nonlinear equation of the form <span>(f^{n}+P_{d}(z,f)=p_{1}e^{alpha _{1}z}+p_{2}e^{alpha _{2}z})</span>, where <i>P</i><sub><i>d</i></sub>(<i>z</i>,<i>f</i>) is a differential-difference polynomial in <i>f</i> of degree <i>d</i>. Our result is a generalization and complement of known results obtained by Liu-Mao, L<span>({ddot {mathrm {u}}})</span> et al. and the references therein.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"47 4","pages":"731 - 741"},"PeriodicalIF":0.5,"publicationDate":"2021-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45919051","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 Hyperbolicity Modulo a Closed Subset of Singular Complex Spaces 关于奇异复空间闭子集的双曲模
IF 0.5
Acta Mathematica Vietnamica Pub Date : 2021-11-17 DOI: 10.1007/s40306-021-00462-x
Pham Nguyen Thu Trang, Nguyen Van Trao
{"title":"On Hyperbolicity Modulo a Closed Subset of Singular Complex Spaces","authors":"Pham Nguyen Thu Trang,&nbsp;Nguyen Van Trao","doi":"10.1007/s40306-021-00462-x","DOIUrl":"10.1007/s40306-021-00462-x","url":null,"abstract":"<div><p>The purpose of this article is threefold. In 1971, H. L. Royden introduced the Kobayashi-Royden pseudometrics on (nonsingular) complex manifolds and gave a criterion for the Kobayashi hyperbolicity of (nonsingular) complex manifolds which plays an essentially important role in Hyperbolic Complex Geometry. Perhaps, since there are some unresolved technical problems, the above theorem of Royden is not yet completely cleared up for singular complex spaces. Thus, the first is to prove Royden’s theorem for singular complex spaces. The second is to give a criteria of the hyperbolicity modulo a closed subset of singular complex spaces from the viewpoint of comparing the Kobayashi <i>k</i>-differential pseudometrics on these spaces and the Landau property of the ones. The third is to investigate the hyperbolicity modulo a closed subset of domains in a singular complex space from the condition on localization at their boundary points.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"47 3","pages":"719 - 729"},"PeriodicalIF":0.5,"publicationDate":"2021-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40306-021-00462-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44103581","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
Extensions of Valuation Domains and Going-up 估值域的扩展与上升
IF 0.5
Acta Mathematica Vietnamica Pub Date : 2021-11-13 DOI: 10.1007/s40306-021-00461-y
Shai Sarussi
{"title":"Extensions of Valuation Domains and Going-up","authors":"Shai Sarussi","doi":"10.1007/s40306-021-00461-y","DOIUrl":"10.1007/s40306-021-00461-y","url":null,"abstract":"<div><p>Suppose <i>F</i> is a field with valuation <i>v</i> and valuation domain <i>O</i><sub><i>v</i></sub>, <i>E</i>/<i>F</i> is a finite-dimensional field extension, and <i>R</i> is an <i>O</i><sub><i>v</i></sub>-subalgebra of <i>E</i> such that <i>F</i> ⋅ <i>R</i> = <i>E</i> and <i>R</i> ∩ <i>F</i> = <i>O</i><sub><i>v</i></sub>. It is known that <i>R</i> satisfies LO, INC, GD and SGB over <i>O</i><sub><i>v</i></sub>; it is also known that under certain conditions <i>R</i> satisfies GU over <i>O</i><sub><i>v</i></sub>. In this paper, we present a necessary and sufficient condition for the existence of such <i>R</i> that does not satisfy GU over <i>O</i><sub><i>v</i></sub>. We also present an explicit example of such <i>R</i> that does not satisfy GU over <i>O</i><sub><i>v</i></sub>.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"47 3","pages":"683 - 687"},"PeriodicalIF":0.5,"publicationDate":"2021-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45049798","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
“Infinite” Properties of Certain Local Cohomology Modules of Determinantal Rings 行列式环的某些局部上同调模的“无限”性质
IF 0.5
Acta Mathematica Vietnamica Pub Date : 2021-11-03 DOI: 10.1007/s40306-021-00459-6
Peter Schenzel
{"title":"“Infinite” Properties of Certain Local Cohomology Modules of Determinantal Rings","authors":"Peter Schenzel","doi":"10.1007/s40306-021-00459-6","DOIUrl":"10.1007/s40306-021-00459-6","url":null,"abstract":"<div><p>For given integers <i>m</i>,<i>n</i> ≥ 2 there are examples of ideals <i>I</i> of complete determinantal local rings <span>((R,mathfrak {m}), dim R = m+n-1, text {grade}~I = n-1,)</span> with the canonical module <i>ω</i><sub><i>R</i></sub> and the property that the socle dimensions of <span>(H^{m+n-2}_{I}(omega _{R}))</span> and <span>(H^{m}_{mathfrak {m}}left (H^{n-1}_{I}(omega _{R})right ))</span> are not finite. In the case of <i>m</i> = <i>n</i>, i.e., a Gorenstein ring, the socle dimensions provide further information about the <i>τ</i>-numbers as studied in Mahmood and Schenzel (<i>J. Algebra</i><b>372</b>, 56–67, 10). Moreover, the endomorphism ring of <span>(H^{n-1}_{I}(omega _{R}))</span> is studied and shown to be an <i>R</i>-algebra of finite type but not finitely generated as <i>R</i>-module generalizing an example of Schenzel (<i>J. Algebra</i> <b>344</b>, 229–245, 15).</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"47 1","pages":"243 - 250"},"PeriodicalIF":0.5,"publicationDate":"2021-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50446045","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
Rates of Convergence in the Central Limit Theorem for Nonlinear Statistics Under Relaxed Moment Conditions 松弛矩条件下非线性统计中心极限定理的收敛速度
IF 0.5
Acta Mathematica Vietnamica Pub Date : 2021-10-29 DOI: 10.1007/s40306-021-00453-y
Nguyen Tien Dung
{"title":"Rates of Convergence in the Central Limit Theorem for Nonlinear Statistics Under Relaxed Moment Conditions","authors":"Nguyen Tien Dung","doi":"10.1007/s40306-021-00453-y","DOIUrl":"10.1007/s40306-021-00453-y","url":null,"abstract":"<div><p>This paper is concerned with normal approximation under relaxed moment conditions using Stein’s method. We obtain the explicit rates of convergence in the central limit theorem for (i) nonlinear statistics with finite absolute moment of order 2 + <i>δ</i> ∈ (2,3] and (ii) nonlinear statistics with vanishing third moment and finite absolute moment of order 3 + <i>δ</i> ∈ (3,4]. When applied to specific examples, these rates are of the optimal order <span>(Oleft (n^{-frac {delta }{2}}right ))</span> and <span>(Oleft (n^{-frac {1+delta }{2}}right ))</span>. Our proofs are based on the covariance identity formula and simple observations about the solution of Stein’s equation.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"47 3","pages":"635 - 660"},"PeriodicalIF":0.5,"publicationDate":"2021-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49538481","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
On the Cohen-Macaulayness of Bracket Powers of Generalized Mixed Product Ideals 广义混合积理想托架幂的Cohen-Macaulayness
IF 0.5
Acta Mathematica Vietnamica Pub Date : 2021-10-28 DOI: 10.1007/s40306-021-00460-z
Roya Moghimipor
{"title":"On the Cohen-Macaulayness of Bracket Powers of Generalized Mixed Product Ideals","authors":"Roya Moghimipor","doi":"10.1007/s40306-021-00460-z","DOIUrl":"10.1007/s40306-021-00460-z","url":null,"abstract":"<div><p>Let <i>L</i> be the generalized mixed product ideal induced by a monomial ideal <i>I</i>. For every integer <i>k</i> ≥ 1, we denote the <i>k</i> th bracket power of <i>L</i> by <i>L</i><sup>[<i>k</i>]</sup>. We study algebraic properties of <i>L</i><sup>[<i>k</i>]</sup>, and show that <i>L</i><sup>[<i>k</i>]</sup> is Cohen-Macaulay if <i>I</i> is Cohen-Macaulay.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"47 3","pages":"709 - 718"},"PeriodicalIF":0.5,"publicationDate":"2021-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44400291","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
Hilbert-Kirby Polynomials in Generalized Local Cohomology Modules 广义局部上同调模中的Hilbert-Kirby多项式
IF 0.5
Acta Mathematica Vietnamica Pub Date : 2021-10-22 DOI: 10.1007/s40306-021-00440-3
M. Shafiei, A. Khojali, A. Azari, N. Zamani
{"title":"Hilbert-Kirby Polynomials in Generalized Local Cohomology Modules","authors":"M. Shafiei,&nbsp;A. Khojali,&nbsp;A. Azari,&nbsp;N. Zamani","doi":"10.1007/s40306-021-00440-3","DOIUrl":"10.1007/s40306-021-00440-3","url":null,"abstract":"<div><p>Let <span>(R = oplus _{nin mathbb {N}_{0}}R_{n})</span> be a Noetherian homogeneous ring with irrelevant ideal <span>(R_{+} = oplus _{nin mathbb {N}} R_{n})</span> and with local base ring <span>((R_{0},mathfrak {m}_{0}))</span>. Let <i>M</i>, <i>N</i> be two finitely generated <span>(mathbb {Z})</span>-graded <i>R</i>-modules. We show that the lengths of the graded components of various graded submodules and quotients of the <i>i</i>-th generalized local cohomology <span>(H^{i}_{R_{+}}(M, N))</span> are anti-polynomial. Under some mild assumptions, the Artinianness of <span>(H^{i}_{R_{+}}(M, N))</span> and the asymptotic behavior of the <i>R</i><sub>0</sub>-modules <span>(H^{i}_{R_{+}}(M, N)_{n})</span> for <span>(nrightarrow -infty )</span> in the range <span>(ileq inf {iin mathbb {N}_{0} vert sharp {nvert ell _{R_{0}})</span> <span>((H^{i}_{ R_{+}}(M , N)_{n}) = infty }=infty })</span> will be studied. Moreover, it has been proved that, if <i>u</i> is the least integer <i>i</i> for which <span>(H^{i}_{R_{+}}(M,N))</span> is not Artinian and <span>(mathfrak {q}_{0})</span> is an <span>(mathfrak {m}_{0})</span>-primary ideal of <i>R</i><sub>0</sub>, then <span>(H^{u}_{R_{+}}(M,N)/mathfrak q_{0}H^{u}_{R_{+}}(M,)</span> <i>N</i>) is Artinian with Hilbert-Kirby polynomial of degree less than <i>u</i>. In particular, with <i>M</i> = <i>R</i>, we deduce the correspondent result for ordinary local cohomology module <span>(H^{i}_{R_{+}}(N))</span>.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"46 4","pages":"747 - 759"},"PeriodicalIF":0.5,"publicationDate":"2021-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40306-021-00440-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46598580","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
On Approximately σ-biflat Banach Algebras 关于近似σ-双平面Banach代数
IF 0.5
Acta Mathematica Vietnamica Pub Date : 2021-10-09 DOI: 10.1007/s40306-021-00458-7
Sanaz Haddad Sabzevar, Amin Mahmoodi
{"title":"On Approximately σ-biflat Banach Algebras","authors":"Sanaz Haddad Sabzevar,&nbsp;Amin Mahmoodi","doi":"10.1007/s40306-021-00458-7","DOIUrl":"10.1007/s40306-021-00458-7","url":null,"abstract":"<div><p>We define and study approximate versions of <i>σ</i>-biflatness and <i>σ</i>-biprojectivity of a Banach algebra <i>A</i> where <i>σ</i> ∈Hom(<i>A</i>). We generalize the concepts pseudo amenability and pseudo contractibility via homomorphisms. We investigate their relations.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"47 3","pages":"671 - 681"},"PeriodicalIF":0.5,"publicationDate":"2021-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46275437","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: 3
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