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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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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
Regularity of the Donaldson Geometric Flow 唐纳森几何流的规律性
IF 0.5
Acta Mathematica Vietnamica Pub Date : 2021-10-02 DOI: 10.1007/s40306-021-00454-x
Robin S. Krom
{"title":"Regularity of the Donaldson Geometric Flow","authors":"Robin S. Krom","doi":"10.1007/s40306-021-00454-x","DOIUrl":"10.1007/s40306-021-00454-x","url":null,"abstract":"<div><p>We prove a regularity theorem for the solutions of the Donaldson geometric flow equation on the space of symplectic forms on a closed smooth four-manifold, representing a fixed cohomology class. The minimal initial conditions lay in the Besov space <span>(B^{1,p}_{2}(M, {varLambda }^{2}))</span> for <i>p</i> &gt; 4. The Donaldson geometric flow was introduced by Simon Donaldson in Donaldson (<i>Asian J. Math.</i> <b>3</b>, 1–16 1999). For a detailed exposition see Krom and Salamon (<i>J. Symplectic Geom.</i> <b>17</b>, 381–417 2019).</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40306-021-00454-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41322234","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
Graded Betti Numbers of Balanced Simplicial Complexes 平衡简单配合物的分级Betti数
IF 0.5
Acta Mathematica Vietnamica Pub Date : 2021-10-01 DOI: 10.1007/s40306-021-00449-8
Martina Juhnke-Kubitzke, Lorenzo Venturello
{"title":"Graded Betti Numbers of Balanced Simplicial Complexes","authors":"Martina Juhnke-Kubitzke,&nbsp;Lorenzo Venturello","doi":"10.1007/s40306-021-00449-8","DOIUrl":"10.1007/s40306-021-00449-8","url":null,"abstract":"<div><p>We prove upper bounds for the graded Betti numbers of Stanley-Reisner rings of balanced simplicial complexes. Along the way we show bounds for Cohen-Macaulay graded rings <i>S</i>/<i>I</i>, where <i>S</i> is a polynomial ring and <span>(Isubseteq S)</span> is a homogeneous ideal containing a certain number of generators in degree 2, including the squares of the variables. Using similar techniques we provide upper bounds for the number of linear syzygies for Stanley-Reisner rings of balanced normal pseudomanifolds. Moreover, we compute explicitly the graded Betti numbers of cross-polytopal stacked spheres, and show that they only depend on the dimension and the number of vertices, rather than also the combinatorial type.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40306-021-00449-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41925827","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
Some Results on Pure Ideals and Trace Ideals of Projective Modules 关于投射模的纯理想和迹理想的一些结果
IF 0.5
Acta Mathematica Vietnamica Pub Date : 2021-09-30 DOI: 10.1007/s40306-021-00451-0
Abolfazl Tarizadeh
{"title":"Some Results on Pure Ideals and Trace Ideals of Projective Modules","authors":"Abolfazl Tarizadeh","doi":"10.1007/s40306-021-00451-0","DOIUrl":"10.1007/s40306-021-00451-0","url":null,"abstract":"<div><p>Let <i>R</i> be a commutative ring with the unit element. It is shown that an ideal <i>I</i> in <i>R</i> is pure if and only if Ann(<i>f</i>) + <i>I</i> = <i>R</i> for all <i>f</i> ∈ <i>I</i>. If <i>J</i> is the trace of a projective <i>R</i>-module <i>M</i>, we prove that <i>J</i> is generated by the “coordinates” of <i>M</i> and <i>J</i><i>M</i> = <i>M</i>. These lead to a few new results and alternative proofs for some known results.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40306-021-00451-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48708078","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: 8
Schmidt’s Subspace Theorem for Moving Hypersurface Targets in Subgeneral Position in Projective Varieties 投影变体中超曲面目标在亚一般位置移动的Schmidt子空间定理
IF 0.5
Acta Mathematica Vietnamica Pub Date : 2021-09-29 DOI: 10.1007/s40306-021-00455-w
Giang Le
{"title":"Schmidt’s Subspace Theorem for Moving Hypersurface Targets in Subgeneral Position in Projective Varieties","authors":"Giang Le","doi":"10.1007/s40306-021-00455-w","DOIUrl":"10.1007/s40306-021-00455-w","url":null,"abstract":"<div><p>Our goal is to give Schmidt’s subspace theorem for moving hypersurface targets in subgeneral position in projective varieties.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50524671","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
Maximal Subgroups of Almost Subnormal Subgroups in Division Rings 除法环中概亚正规子群的极大子群
IF 0.5
Acta Mathematica Vietnamica Pub Date : 2021-09-27 DOI: 10.1007/s40306-021-00456-9
Bui Xuan Hai
{"title":"Maximal Subgroups of Almost Subnormal Subgroups in Division Rings","authors":"Bui Xuan Hai","doi":"10.1007/s40306-021-00456-9","DOIUrl":"10.1007/s40306-021-00456-9","url":null,"abstract":"<div><p>In this paper, we investigate maximal subgroups of an almost subnormal subgroup <i>G</i> in a division ring <i>D</i> whose center is infinite. Among results, we prove that if <i>M</i> is such a maximal subgroup, then <i>M</i> is abelian provided <i>M</i> is either locally finite or <i>FC</i>-group, and <i>D</i> is weakly locally finite. Also, we prove a theorem on the existence of non-cyclic free subgroups of a maximal subgroup <i>M</i> in such a <i>G</i>.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40306-021-00456-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50519171","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
Mixed Commuting Varieties over Nilpotent Matrices 幂零矩阵上的混合可交换变量
IF 0.5
Acta Mathematica Vietnamica Pub Date : 2021-09-22 DOI: 10.1007/s40306-021-00457-8
Jerry Magana, Nham V. Ngo
{"title":"Mixed Commuting Varieties over Nilpotent Matrices","authors":"Jerry Magana,&nbsp;Nham V. Ngo","doi":"10.1007/s40306-021-00457-8","DOIUrl":"10.1007/s40306-021-00457-8","url":null,"abstract":"<div><p>We give an explicit description of all irreducible components and their dimensions of mixed commuting varieties over nilpotent 3 × 3 matrices, hence describing the varieties of 3-dimensional modules for certain quotients of polynomial algebras over an algebraically closed field. Our results also provide insights on support varieties of simple modules over Frobenius kernels of <i>S</i><i>L</i><sub>3</sub>.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40306-021-00457-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45121025","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
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