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The Weak Lefschetz Property of Artinian Algebras Associated to Paths and Cycles 与路径和循环相关的阿尔丁代数的弱勒夫谢茨性质
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2024-08-14 DOI: 10.1007/s40306-024-00549-1
Hop D. Nguyen, Quang Hoa Tran
{"title":"The Weak Lefschetz Property of Artinian Algebras Associated to Paths and Cycles","authors":"Hop D. Nguyen,&nbsp;Quang Hoa Tran","doi":"10.1007/s40306-024-00549-1","DOIUrl":"10.1007/s40306-024-00549-1","url":null,"abstract":"<div><p>Given a base field <span>(Bbbk )</span> of characteristic zero, for each graph <i>G</i>, we associate the artinian algebra <i>A</i>(<i>G</i>) defined by the edge ideal of <i>G</i> and the squares of the variables. We study the weak Lefschetz property of <i>A</i>(<i>G</i>). We classify some classes of graphs with relatively few edges, including paths and cycles, such that its associated artinian ring has the weak Lefschetz property.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"49 3","pages":"523 - 544"},"PeriodicalIF":0.3,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714512","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
New Algorithms for Solving the Split Equality Problems in Hilbert Spaces 求解Hilbert空间中分裂等式问题的新算法
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2024-08-13 DOI: 10.1007/s40306-024-00552-6
Nguyen Song Ha, Truong Minh Tuyen
{"title":"New Algorithms for Solving the Split Equality Problems in Hilbert Spaces","authors":"Nguyen Song Ha,&nbsp;Truong Minh Tuyen","doi":"10.1007/s40306-024-00552-6","DOIUrl":"10.1007/s40306-024-00552-6","url":null,"abstract":"<div><p>We introduce a new approach by using unconstrained optimization to find a solution to the system of the split equality problems in real Hilbert spaces. Our new algorithms do not depend on the norm of the transfer mappings. We also give the relaxed iterative algorithms corresponding to the proposed algorithms. Finally, we present some numerical experiments to demonstrate the performance of the main results.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"49 4","pages":"667 - 689"},"PeriodicalIF":0.3,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142761949","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
Minimal Balanced Neighborly Polynomials 最小平衡邻接多项式
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2024-08-06 DOI: 10.1007/s40306-024-00547-3
Satoshi Murai, Nguyen Thi Thanh Tam
{"title":"Minimal Balanced Neighborly Polynomials","authors":"Satoshi Murai,&nbsp;Nguyen Thi Thanh Tam","doi":"10.1007/s40306-024-00547-3","DOIUrl":"10.1007/s40306-024-00547-3","url":null,"abstract":"<div><p>In this paper we introduce minimal balanced neighborly polynomials and show some methods to construct such polynomials. In particular, using this notion, we prove the existence of balanced neighborly polynomials of the following types: (i) type <span>((p,dots ,p))</span> for most prime numbers <i>p</i>, (ii) types <span>((d-1,d,d,d))</span>, <span>((d-1,d-1,d,d))</span> and <span>((d-1,d-1,d-1,d))</span> when <i>d</i> is odd or is divisible by 4. We also construct balanced neighborly simplicial spheres of type <span>((2,4k-1,4k-1,4k-1))</span>.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"49 3","pages":"459 - 484"},"PeriodicalIF":0.3,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714209","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
Vanishing and Non-negativity of the First Normal Hilbert Coefficient 第一正态希尔伯特系数的消失和非负性
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2024-08-06 DOI: 10.1007/s40306-024-00548-2
Linquan Ma, Pham Hung Quy
{"title":"Vanishing and Non-negativity of the First Normal Hilbert Coefficient","authors":"Linquan Ma,&nbsp;Pham Hung Quy","doi":"10.1007/s40306-024-00548-2","DOIUrl":"10.1007/s40306-024-00548-2","url":null,"abstract":"<div><p>Let <span>((R,mathfrak {m}))</span> be a Noetherian local ring such that <span>(widehat{R})</span> is reduced. We prove that, when <span>(widehat{R})</span> is <span>(S_2)</span>, if there exists a parameter ideal <span>(Qsubseteq R)</span> such that <span>(bar{e}_1(Q)=0)</span>, then <i>R</i> is regular and <span>(nu (mathfrak {m}/Q)le 1)</span>. This leads to an affirmative answer to a problem raised by Goto-Hong-Mandal [Goto, S., Hong, J., Mandal, M.: The positivity of the first coefficients of normal Hilbert polynomials. Proc. Amer. Math. Soc. <b>139</b>(7), 2399–2406 \u0000(2011)]. We also give an alternative proof (in fact a strengthening) of their main result. In particular, we show that if <span>(widehat{R})</span> is equidimensional, then <span>(bar{e}_1(Q)ge 0)</span> for all parameter ideals <span>(Qsubseteq R)</span>, and in characteristic <span>(p&gt;0)</span>, we actually have <span>(e_1^*(Q)ge 0)</span>. Our proofs rely on the existence of big Cohen-Macaulay algebras.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"49 3","pages":"311 - 325"},"PeriodicalIF":0.3,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714207","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
Refinements and Extensions of Some Strong Duality Theorems in Conic Linear Programming 圆锥线性规划中若干强对偶定理的完善与扩展
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2024-08-06 DOI: 10.1007/s40306-024-00543-7
Nguyen Ngoc Luan, Nguyen Dong Yen
{"title":"Refinements and Extensions of Some Strong Duality Theorems in Conic Linear Programming","authors":"Nguyen Ngoc Luan,&nbsp;Nguyen Dong Yen","doi":"10.1007/s40306-024-00543-7","DOIUrl":"10.1007/s40306-024-00543-7","url":null,"abstract":"<div><p>In this paper, we establish a series of new results on strong duality and solution existence for conic linear programs in locally convex Hausdorff topological vector spaces and finite-dimensional Euclidean spaces. Namely, under certain regularity conditions based on quasi-relative interiors of convex sets, we prove that if one problem in the dual pair consisting of a primal program and its dual has a solution, then the other problem also has a solution, and the optimal values of the problems are equal. In addition, we show that if the cones are generalized polyhedral convex, then the regularity conditions can be omitted. Moreover, if the spaces are finite-dimensional and the ordering cones are closed convex, then instead of the solution existence condition, it suffices to require the finiteness of the optimal value. The present paper complements our recent research work [Luan, N.N., Yen, N.D.: <i>Strong duality and solution existence under minimal assumptions in conic linear programming</i>. J. Optim. Theory Appl. (https://doi.org/10.1007/s10957-023-02318-w)].</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"49 3","pages":"545 - 561"},"PeriodicalIF":0.3,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714208","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
Betti Numbers of the Tangent Cones of Monomial Space Curves 单项式空间曲线切锥的贝蒂数
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2024-08-06 DOI: 10.1007/s40306-024-00546-4
Nguyen P. H. Lan, Nguyen Chanh Tu, Thanh Vu
{"title":"Betti Numbers of the Tangent Cones of Monomial Space Curves","authors":"Nguyen P. H. Lan,&nbsp;Nguyen Chanh Tu,&nbsp;Thanh Vu","doi":"10.1007/s40306-024-00546-4","DOIUrl":"10.1007/s40306-024-00546-4","url":null,"abstract":"<div><p>Let <span>(H = langle n_1, n_2,n_3rangle )</span> be a numerical semigroup. Let <span>(widetilde{H})</span> be the interval completion of <i>H</i>, namely the semigroup generated by the interval <span>(langle n_1,n_1+1, ldots , n_3rangle )</span>. Let <i>K</i> be a field and <i>K</i>[<i>H</i>] the semigroup ring generated by <i>H</i>. Let <span>(I_H^{*})</span> be the defining ideal of the tangent cone of <i>K</i>[<i>H</i>]. In this paper, we describe the defining equations of <span>(I_H^{*})</span>. From that, we prove the Herzog-Stamate conjecture for monomial space curves stating that <span>(beta _i(I_H^{*}) le beta _i(I_{widetilde{H}}^{*}))</span> for all <i>i</i>, where <span>(beta _i(I_H^{*}))</span> and <span>(beta _i(I_{widetilde{H}}^{*}))</span> are the <i>i</i>th Betti numbers of <span>(I_H^{*})</span> and <span>(I_{widetilde{H}}^{*})</span> respectively.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"49 3","pages":"347 - 365"},"PeriodicalIF":0.3,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714206","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 the Diagonal Subgroup of the Special Linear Group Over a Division Ring 论划分环上特殊线性群的对角线子群
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2024-08-02 DOI: 10.1007/s40306-024-00544-6
Bui Xuan Hai
{"title":"On the Diagonal Subgroup of the Special Linear Group Over a Division Ring","authors":"Bui Xuan Hai","doi":"10.1007/s40306-024-00544-6","DOIUrl":"10.1007/s40306-024-00544-6","url":null,"abstract":"<div><p>Let <i>K</i> be a division ring with center <i>Z</i>(<i>K</i>), and <i>n</i> a positive integer. Let <span>(textrm{SL}(n,K))</span> be the special linear group of degree <i>n</i> over <i>K</i> and <span>(textrm{SD}(n,K))</span> its subgroup consisting of all diagonal matrices whose Dieudonne’s determinant is <span>(overline{1})</span>. We prove that <span>(textrm{SD}(n,K))</span> is weakly pronormal, but not pronormal in <span>(textrm{SL}(n,K))</span> provided either <i>Z</i>(<i>K</i>) is an infinite field in case <span>(nge 3)</span> or <i>Z</i>(<i>K</i>) is a finite field containing at least seven elements in case <span>(nge 5)</span>.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"49 3","pages":"427 - 440"},"PeriodicalIF":0.3,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714385","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 the Index of Depth Stability of Symbolic Powers of Cover Ideals of Graphs 论图的盖顶点的符号幂的深度稳定性指数
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2024-07-31 DOI: 10.1007/s40306-024-00550-8
S. A. Seyed Fakhari, S. Yassemi
{"title":"On the Index of Depth Stability of Symbolic Powers of Cover Ideals of Graphs","authors":"S. A. Seyed Fakhari,&nbsp;S. Yassemi","doi":"10.1007/s40306-024-00550-8","DOIUrl":"10.1007/s40306-024-00550-8","url":null,"abstract":"<div><p>Let <i>G</i> be a graph with <i>n</i> vertices and let <span>(S=mathbb {K}[x_1,dots ,x_n])</span> be the polynomial ring in <i>n</i> variables over a field <span>(mathbb {K})</span>. Assume that <i>I</i>(<i>G</i>) and <i>J</i>(<i>G</i>) denote the edge ideal and the cover ideal of <i>G</i>, respectively. We provide a combinatorial upper bound for the index of depth stability of symbolic powers of <i>J</i>(<i>G</i>). As a consequence, we compute the depth of symbolic powers of cover ideals of fully clique-whiskered graphs. Meanwhile, we determine a class of graphs <i>G</i> with the property that the Castelnuovo–Mumford regularity of <i>S</i>/<i>I</i>(<i>G</i>) is equal to the induced matching number of <i>G</i>.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"49 3","pages":"367 - 376"},"PeriodicalIF":0.3,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714652","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
Bertini Type Results and Their Applications 贝尔蒂尼式结果及其应用
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2024-07-17 DOI: 10.1007/s40306-024-00542-8
Indranil Biswas, Manish Kumar, A. J. Parameswaran
{"title":"Bertini Type Results and Their Applications","authors":"Indranil Biswas,&nbsp;Manish Kumar,&nbsp;A. J. Parameswaran","doi":"10.1007/s40306-024-00542-8","DOIUrl":"10.1007/s40306-024-00542-8","url":null,"abstract":"<div><p>We prove Bertini type theorems and give some applications of them. The applications are in the context of Lefschetz theorem for Nori fundamental group for normal varieties as well as for geometric formal orbifolds. In another application, it is shown that a certain class of a smooth quasi-projective variety contains a smooth curve such that irreducible lisse <span>(ell )</span>–adic sheaves on the variety with “ramification bounded by a branch data” remains irreducible when restricted to the curve.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"49 4","pages":"649 - 665"},"PeriodicalIF":0.3,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141830113","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 v-Number of Binomial Edge Ideals 二项边理想的v数
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2024-07-04 DOI: 10.1007/s40306-024-00540-w
Siddhi Balu Ambhore, Kamalesh Saha, Indranath Sengupta
{"title":"The v-Number of Binomial Edge Ideals","authors":"Siddhi Balu Ambhore,&nbsp;Kamalesh Saha,&nbsp;Indranath Sengupta","doi":"10.1007/s40306-024-00540-w","DOIUrl":"10.1007/s40306-024-00540-w","url":null,"abstract":"<div><p>The invariant <span>(textrm{v})</span>-number was introduced very recently in the study of Reed-Muller-type codes. Jaramillo and Villarreal (J. Combin. Theory Ser. A 177:105310, 2021) initiated the study of the <span>(textrm{v})</span>-number of edge ideals. Inspired by their work, we take the initiation to study the <span>(textrm{v})</span>-number of binomial edge ideals in this paper. We discuss some properties and bounds of the <span>(textrm{v})</span>-number of binomial edge ideals. We explicitly find the <span>(textrm{v})</span>-number of binomial edge ideals locally at the associated prime corresponding to the cutset <span>(emptyset )</span>. We show that the <span>(textrm{v})</span>-number of Knutson binomial edge ideals is less than or equal to the <span>(textrm{v})</span>-number of their initial ideals. Also, we classify all binomial edge ideals whose <span>(textrm{v})</span>-number is 1. Moreover, we try to relate the <span>(textrm{v})</span>-number with the Castelnuvo-Mumford regularity of binomial edge ideals and give a conjecture in this direction.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"49 4","pages":"611 - 628"},"PeriodicalIF":0.3,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142761993","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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