发布求助
文献互助 智能选刊 最新文献

Arnold Mathematical Journal最新文献

筛选
英文 中文
Red Sizes of Quivers 红色大小的箭袋
Arnold Mathematical Journal Pub Date : 2023-03-06 DOI: 10.1007/s40598-023-00226-5
Eric Bucher, John Machacek
{"title":"Red Sizes of Quivers","authors":"Eric Bucher,&nbsp;John Machacek","doi":"10.1007/s40598-023-00226-5","DOIUrl":"10.1007/s40598-023-00226-5","url":null,"abstract":"<div><p>In this article, we will expand on the notions of maximal green and reddening sequences for quivers associated with cluster algebras. The existence of these sequences has been studied for a variety of applications related to Fomin and Zelevinsky’s cluster algebras. Ahmad and Li considered a numerical measure of how close a quiver is to admitting a maximal green sequence called a <i>red number</i>. In this paper, we generalized this notion to what we call <i>unrestricted red numbers</i> which are related to reddening sequences. In addition to establishing this more general framework, we completely determine the red numbers and unrestricted red numbers for all finite mutation type of quivers. Furthermore, we give conjectures on the possible values of red numbers and unrestricted red numbers in general.</p></div>","PeriodicalId":37546,"journal":{"name":"Arnold Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46327127","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
Sandpile Solitons in Higher Dimensions 高维中的沙堆孤子
Arnold Mathematical Journal Pub Date : 2023-01-30 DOI: 10.1007/s40598-023-00224-7
Nikita Kalinin
{"title":"Sandpile Solitons in Higher Dimensions","authors":"Nikita Kalinin","doi":"10.1007/s40598-023-00224-7","DOIUrl":"10.1007/s40598-023-00224-7","url":null,"abstract":"<div><p>Let <span>(pin {mathbb {Z}}^n)</span> be a primitive vector and <span>(Psi :{mathbb {Z}}^nrightarrow {mathbb {Z}}, zrightarrow min (pcdot z, 0))</span>. The theory of <i>husking</i> allows us to prove that there exists a pointwise minimal function among all integer-valued superharmonic functions equal to <span>(Psi )</span> “at infinity”. We apply this result to sandpile models on <span>({mathbb {Z}}^n)</span>. We prove existence of so-called <i>solitons</i> in a sandpile model, discovered in 2-dim setting by S. Caracciolo, G. Paoletti, and A. Sportiello and studied by the author and M. Shkolnikov in previous papers. We prove that, similarly to 2-dim case, sandpile states, defined using our husking procedure, move changeless when we apply the sandpile wave operator (that is why we call them solitons). We prove an analogous result for each lattice polytope <i>A</i> without lattice points except its vertices. Namely, for each function </p><div><div><span>$$begin{aligned} Psi :{mathbb {Z}}^nrightarrow {mathbb {Z}}, zrightarrow min _{pin Acap {mathbb {Z}}^n}(pcdot z+c_p), c_pin {mathbb {Z}}end{aligned}$$</span></div></div><p>there exists a pointwise minimal function among all integer-valued superharmonic functions coinciding with <span>(Psi )</span> “at infinity”. The Laplacian of the latter function corresponds to what we observe when solitons, corresponding to the edges of <i>A</i>, intersect (see Fig. 1).</p></div>","PeriodicalId":37546,"journal":{"name":"Arnold Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41268245","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
Solvability of Some Systems of Integro-differential Equations in Population Dynamics Depending on the Natality and Mortality Rates 基于出生率和死亡率的人口动力学中某些积分微分方程组的可解性
Arnold Mathematical Journal Pub Date : 2023-01-27 DOI: 10.1007/s40598-023-00225-6
Vitali Vougalter, Vitaly Volpert
{"title":"Solvability of Some Systems of Integro-differential Equations in Population Dynamics Depending on the Natality and Mortality Rates","authors":"Vitali Vougalter,&nbsp;Vitaly Volpert","doi":"10.1007/s40598-023-00225-6","DOIUrl":"10.1007/s40598-023-00225-6","url":null,"abstract":"<div><p>We establish the existence of stationary solutions for certain systems of reaction–diffusion-type equations in the corresponding <span>(H^{2})</span> spaces. Our method relies on the fixed point theorem when the elliptic problem contains second-order differential operators with and without the Fredholm property, which may depend on the outcome of the competition between the natality and the mortality rates involved in the equations of the systems.</p></div>","PeriodicalId":37546,"journal":{"name":"Arnold Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44453917","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
Classification of Schubert Galois Groups in (textit{Gr},(4,9)) Schubert-Galois群在（textit｛Gr｝，（4,9））中的分类
Arnold Mathematical Journal Pub Date : 2023-01-17 DOI: 10.1007/s40598-022-00221-2
Abraham Martín del Campo, Frank Sottile, Robert Lee Williams
{"title":"Classification of Schubert Galois Groups in (textit{Gr},(4,9))","authors":"Abraham Martín del Campo,&nbsp;Frank Sottile,&nbsp;Robert Lee Williams","doi":"10.1007/s40598-022-00221-2","DOIUrl":"10.1007/s40598-022-00221-2","url":null,"abstract":"<div><p>We classify Schubert problems in the Grassmannian of 4-planes in 9-dimensional space by their Galois groups. Of the 31,806 essential Schubert problems in this Grassmannian, there are only 149 whose Galois group does not contain the alternating group. We identify the Galois groups of these 149—each is an imprimitive permutation group. These 149 fall into two families according to their geometry. This study suggests a possible classification of Schubert problems whose Galois group is not the full symmetric group, and is a first step toward the inverse Galois problem for Schubert calculus.</p></div>","PeriodicalId":37546,"journal":{"name":"Arnold Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40598-022-00221-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50490033","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
Classification of Schubert Galois Groups in $$textit{Gr},(4,9)$$ Gr ( 4 , 9 ) $$textit｛Gr｝，（4,9）$$Gr（4，9）中Schubert-Galois群的分类
Arnold Mathematical Journal Pub Date : 2023-01-17 DOI: 10.1007/s40598-022-00221-2
Abraham Martín del Campo, F. Sottile, Robert Williams
{"title":"Classification of Schubert Galois Groups in \u0000 \u0000 \u0000 \u0000 $$textit{Gr},(4,9)$$\u0000 \u0000 \u0000 Gr\u0000 \u0000 (\u0000 4\u0000 ,\u0000 9\u0000 )\u0000 \u0000 ","authors":"Abraham Martín del Campo, F. Sottile, Robert Williams","doi":"10.1007/s40598-022-00221-2","DOIUrl":"https://doi.org/10.1007/s40598-022-00221-2","url":null,"abstract":"","PeriodicalId":37546,"journal":{"name":"Arnold Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45286327","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
Self-Similar Groups and Holomorphic Dynamics: Renormalization, Integrability, and Spectrum 自相似群与全纯动力学：重整化、可积性和谱
Arnold Mathematical Journal Pub Date : 2023-01-05 DOI: 10.1007/s40598-022-00223-0
N.-B. Dang, R. Grigorchuk, M. Lyubich
{"title":"Self-Similar Groups and Holomorphic Dynamics: Renormalization, Integrability, and Spectrum","authors":"N.-B. Dang,&nbsp;R. Grigorchuk,&nbsp;M. Lyubich","doi":"10.1007/s40598-022-00223-0","DOIUrl":"10.1007/s40598-022-00223-0","url":null,"abstract":"<div><p>In this paper, we explore the spectral measures of the Laplacian on Schreier graphs for several self-similar groups (the Grigorchuk, Lamplighter, and Hanoi groups) from the dynamical and algebro-geometric viewpoints. For these graphs, classical Schur renormalization transformations act on appropriate spectral parameters as rational maps in two variables. We show that the spectra in question can be interpreted as asymptotic distributions of slices by a line of iterated pullbacks of certain algebraic curves under the corresponding rational maps (leading us to a notion of a <i>spectral current</i>). We follow up with a dynamical criterion for discreteness of the spectrum. In case of atomic spectrum, the precise rate of convergence of finite-scale approximands to the limiting spectral measure is given. For the three groups under consideration, the corresponding rational maps happen to be fibered over polynomials in one variable. We reveal the algebro-geometric nature of this integrability phenomenon.</p></div>","PeriodicalId":37546,"journal":{"name":"Arnold Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41470153","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: 6
Planar Sections of a Surface Close to an Umbilic 靠近脐带的平面剖面
Arnold Mathematical Journal Pub Date : 2022-12-20 DOI: 10.1007/s40598-022-00222-1
Peter Giblin, Aleksandr Pukhlikov
{"title":"Planar Sections of a Surface Close to an Umbilic","authors":"Peter Giblin,&nbsp;Aleksandr Pukhlikov","doi":"10.1007/s40598-022-00222-1","DOIUrl":"10.1007/s40598-022-00222-1","url":null,"abstract":"<div><p>We study the intersection between a smooth algebraic surface with an umbilic point and a plane parallel and close to the tangent plane at the umbilic. The problem has its origin in the study of isophote (equal illumination) curves in a 2-dimensional image. In particular, we study the circles which have exceptional tangency to this intersection curve: ordinary tangency at one point and osculating at another; ordinary tangency at three points; and 4-point tangency at a vertex. The centres of circles having ordinary tangency at two points trace out a curve whose closure is the <i>symmetry set</i> of the intersection curve, and the exceptional circles above give respectively cusps, triple crossings and endpoints of this set. We analyse the curves traced out by the contact points and centres of the exceptional circles as the plane approaches the tangent plane at the umbilic. We also briefly discuss the global structure of the symmetry set by means of a typical example.</p></div>","PeriodicalId":37546,"journal":{"name":"Arnold Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40598-022-00222-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42119963","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
A Generalized Problem Associated to the Kummer–Vandiver Conjecture 与Kummer-Vandiver猜想有关的一个广义问题
Arnold Mathematical Journal Pub Date : 2022-11-07 DOI: 10.1007/s40598-022-00220-3
Hiroki Sumida-Takahashi
{"title":"A Generalized Problem Associated to the Kummer–Vandiver Conjecture","authors":"Hiroki Sumida-Takahashi","doi":"10.1007/s40598-022-00220-3","DOIUrl":"10.1007/s40598-022-00220-3","url":null,"abstract":"<div><p>To discuss the validity of the Kummer–Vandiver conjecture, we consider a generalized problem associated to the conjecture. Let <i>p</i> be an odd prime number and <span>(zeta _p)</span> a primitive <i>p</i>-th root of unity. Using new programs, we compute the Iwasawa invariants of <span>({textbf{Q}}(sqrt{d},zeta _p))</span> in the range <span>(|d|&lt;200)</span> and <span>(200&lt;p &lt;1{,}000{,}000)</span>. From our data, the actual numbers of exceptional cases seem to be near the expected numbers for <span>(p&lt;1{,}000{,}000)</span>. Moreover, we find a few rare exceptional cases for <span>(|d|&lt;10)</span> and <span>(p&gt;1{,}000{,}000)</span>. We give two partial reasons why it is difficult to find exceptional cases for <span>(d=1)</span> including counter-examples to the Kummer–Vandiver conjecture.</p></div>","PeriodicalId":37546,"journal":{"name":"Arnold Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42514584","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 Polyhedral Homotopy Algorithm for Real Zeros 实零点的多面体同胚算法
Arnold Mathematical Journal Pub Date : 2022-10-27 DOI: 10.1007/s40598-022-00219-w
Alperen A. Ergür, Timo de Wolff
{"title":"A Polyhedral Homotopy Algorithm for Real Zeros","authors":"Alperen A. Ergür,&nbsp;Timo de Wolff","doi":"10.1007/s40598-022-00219-w","DOIUrl":"10.1007/s40598-022-00219-w","url":null,"abstract":"<div><p>We design a homotopy continuation algorithm, that is based on Viro’s patchworking method, for finding real zeros of sparse polynomial systems. The algorithm is targeted for polynomial systems with coefficients that satisfy certain concavity conditions, it tracks optimal number of solution paths, and it operates entirely over the reals. In more technical terms, we design an algorithm that correctly counts and finds the real zeros of polynomial systems that are located in the unbounded components of the complement of the underlying A-discriminant amoeba. We provide a detailed exposition of connections between Viro’s patchworking method, convex geometry of A-discriminant amoeba complements, and computational real algebraic geometry.</p></div>","PeriodicalId":37546,"journal":{"name":"Arnold Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46281127","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
Jordan Types of Triangular Matrices over a Finite Field 有限域上三角矩阵的Jordan型
Arnold Mathematical Journal Pub Date : 2022-10-13 DOI: 10.1007/s40598-022-00214-1
Dmitry Fuchs, Alexandre Kirillov Sr.
{"title":"Jordan Types of Triangular Matrices over a Finite Field","authors":"Dmitry Fuchs,&nbsp;Alexandre Kirillov Sr.","doi":"10.1007/s40598-022-00214-1","DOIUrl":"10.1007/s40598-022-00214-1","url":null,"abstract":"<div><p>Let <span>(lambda )</span> be a partition of an integer <i>n</i> and <span>({mathbb F}_q)</span> be a finite field of order <i>q</i>. Let <span>(P_lambda (q))</span> be the number of strictly upper triangular <span>(ntimes n)</span> matrices of the Jordan type <span>(lambda )</span>. It is known that the polynomial <span>(P_lambda )</span> has a tendency to be divisible by high powers of <i>q</i> and <span>(Q=q-1)</span>, and we put <span>(P_lambda (q)=q^{d(lambda )}Q^{e(lambda )}R_lambda (q))</span>, where <span>(R_lambda (0)ne 0)</span> and <span>(R_lambda (1)ne 0)</span>. In this article, we study the polynomials <span>(P_lambda (q))</span> and <span>(R_lambda (q))</span>. Our main results: an explicit formula for <span>(d(lambda ))</span> (an explicit formula for <span>(e(lambda ))</span> is known, see Proposition 3.3 below), a recursive formula for <span>(R_lambda (q))</span> (a similar formula for <span>(P_lambda (q))</span> is known, see Proposition 3.1 below), the stabilization of <span>(R_lambda )</span> with respect to extending <span>(lambda )</span> by adding strings of 1’s, and an explicit formula for the limit series <span>(R_{lambda 1^infty })</span>. Our studies are motivated by projected applications to the orbit method in the representation theory of nilpotent algebraic groups over finite fields.</p></div>","PeriodicalId":37546,"journal":{"name":"Arnold Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40598-022-00214-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41782923","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
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信