数学最新文献

{"title":"Nakayama's lemma for Z-graded vertex algebras and its applications","authors":"Hao Wang ,&nbsp;Wei Wang","doi":"10.1016/j.aim.2025.110503","DOIUrl":"10.1016/j.aim.2025.110503","url":null,"abstract":"<div><div>This is the first paper in a series of studies on <span><math><mi>Z</mi></math></span>-graded vertex algebras arising from Lie algebras with triangular decomposition (referred to as triangulated Lie algebras for simplicity). In this paper, we establish the Jacobson radical theory for <span><math><mi>Z</mi></math></span>-graded vertex algebras and prove Nakayama's lemma. As an application, we investigate a specific triangulated Lie algebra: <span><math><mi>g</mi><mo>=</mo><mi>C</mi><mi>f</mi><mo>⊕</mo><mi>C</mi><mi>h</mi><mo>⊕</mo><mi>C</mi><mi>e</mi></math></span> with Lie brackets <span><math><mo>[</mo><mi>h</mi><mo>,</mo><mi>e</mi><mo>]</mo><mo>=</mo><mn>2</mn><mi>e</mi><mo>,</mo><mspace></mspace><mo>[</mo><mi>h</mi><mo>,</mo><mi>f</mi><mo>]</mo><mo>=</mo><mo>−</mo><mn>2</mn><mi>f</mi><mo>,</mo><mspace></mspace><mo>[</mo><mi>e</mi><mo>,</mo><mi>f</mi><mo>]</mo><mo>=</mo><mn>0</mn></math></span>. Denote the <span><math><mi>Z</mi></math></span>-graded vertex algebra constructed from <span><math><mi>g</mi></math></span> by <span><math><msub><mrow><mi>V</mi></mrow><mrow><mi>g</mi></mrow></msub><mo>(</mo><mi>l</mi><mo>,</mo><mn>0</mn><mo>)</mo></math></span>. Using Nakayama's lemma, we classify all the irreducible admissible <span><math><msub><mrow><mi>V</mi></mrow><mrow><mi>g</mi></mrow></msub><mo>(</mo><mi>l</mi><mo>,</mo><mn>0</mn><mo>)</mo></math></span>-modules. Finally, we construct a class of indecomposable admissible <span><math><msub><mrow><mi>V</mi></mrow><mrow><mi>g</mi></mrow></msub><mo>(</mo><mi>l</mi><mo>,</mo><mn>0</mn><mo>)</mo></math></span>-modules.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"480 ","pages":"Article 110503"},"PeriodicalIF":1.5,"publicationDate":"2025-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144996258","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Nonlinear dynamics of a quasizero energy harvester forced by flow and kinematic excitations","authors":"Jerzy Margielewicz ,&nbsp;Damian Gąska ,&nbsp;Sławomir Bucki ,&nbsp;Daniil Yurchenko ,&nbsp;Grzegorz Litak","doi":"10.1016/j.chaos.2025.117148","DOIUrl":"10.1016/j.chaos.2025.117148","url":null,"abstract":"<div><div>The paper proposes a novel design of a high-efficiency nonlinear energy harvester that benefits from the synergy between a quasi-zero stiffness system and flow-induced excitations. We demonstrate that this innovative approach enables improved adaptability and energy output. The harvester consists of a cantilever beam in a flag-like configuration subjected to both air-flow and kinematic excitations. In the wake galloping scenario, the variable lift force generated behind a fixed bluff body interacts with the tail-like cantilever beam. Using finite element modeling, we identified the lift force across a wide spectrum of air velocities and incorporated it as an excitation in a dimensionless mathematical model. Subsequently, vibrations of the cantilever beam, leading to the generation of electromotive force in an attached piezoelectric element. The system's displacement and voltage output responses were analyzed using nonlinear dynamics tools. An important advantage of this design is its tunability – by adjusting the elastic elements, the potential function can be configured for optimal performance. Key findings also concern the behavior of the system in chaotic and periodic motion zones and their impact on efficiency. We used tools such as the Lyapunov exponent, bifurcation diagrams, and Poincare sections to analyze nonlinear dynamics. We also identified transient chaos and periodic, chaotic, and quasi-periodic solutions to determine their impact on the performance of the system. The study further explores coexisting solutions and evaluates the effectiveness of the system under different types of excitation, both individually and together. The results demonstrate that the harvester maintains high efficiency even at low excitation levels, highlighting its potential for practical applications.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"200 ","pages":"Article 117148"},"PeriodicalIF":5.6,"publicationDate":"2025-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144996350","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Affine Deligne–Lusztig varieties via the double Bruhat graph, I : Semi-infinite orbits","authors":"Felix Schremmer","doi":"10.2140/ant.2025.19.1973","DOIUrl":"https://doi.org/10.2140/ant.2025.19.1973","url":null,"abstract":"<p>We introduce a new language to describe the geometry of affine Deligne–Lusztig varieties in affine flag varieties. This first part of a two-paper series develops the definition and fundamental properties of the double Bruhat graph by studying semi-infinite orbits. This double Bruhat graph was originally introduced by Naito and Watanabe to study periodic <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>R</mi></math>-polynomials. We use it to describe the geometry of many affine Deligne–Lusztig varieties, overcoming a previously ubiquitous regularity condition. </p>","PeriodicalId":50828,"journal":{"name":"Algebra & Number Theory","volume":"1 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145002869","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Universally Optimal Designs for Symmetric Models in Order-of-Addition Experiments","authors":"Ze Liu, Yongdao Zhou, Min-Qian Liu","doi":"10.1080/01621459.2025.2552515","DOIUrl":"https://doi.org/10.1080/01621459.2025.2552515","url":null,"abstract":"","PeriodicalId":17227,"journal":{"name":"Journal of the American Statistical Association","volume":"39 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2025-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145002903","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Foliations raised by quadratic-like polynomial submersions on the real plane and a sharp result on the real Jacobian conjecture","authors":"Francisco Braun ,&nbsp;Filipe Fernandes ,&nbsp;Ingrid S. Meza-Sarmiento","doi":"10.1016/j.jde.2025.113742","DOIUrl":"10.1016/j.jde.2025.113742","url":null,"abstract":"<div><div>We study the planar foliations whose leaves are the connected components of the fibers of polynomial submersion functions having degree 2 in one of the variables. As an application of this geometric study, we prove the following result on the so called real Jacobian conjecture in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>: it is true if one of the coordinate functions has degree 2 in one of the variables. This is sharp because of an existing counterexample with one of the coordinate functions having degree 3 in one of the variables.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"449 ","pages":"Article 113742"},"PeriodicalIF":2.3,"publicationDate":"2025-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144996929","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Efficiency of QMLE for dynamic panel data models with interactive effects","authors":"Jushan Bai","doi":"10.1080/01621459.2025.2552452","DOIUrl":"https://doi.org/10.1080/01621459.2025.2552452","url":null,"abstract":"","PeriodicalId":17227,"journal":{"name":"Journal of the American Statistical Association","volume":"16 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2025-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145002904","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Frobenius structure and p-adic zeta values","authors":"Frits Beukers ,&nbsp;Masha Vlasenko","doi":"10.1016/j.aim.2025.110512","DOIUrl":"10.1016/j.aim.2025.110512","url":null,"abstract":"<div><div>For differential operators of Calabi-Yau type, Candelas, De la Ossa and van Straten conjecture the appearance of <em>p</em>-adic zeta values in the matrix entries of their <em>p</em>-adic Frobenius structure expressed in the standard basis of solutions near a point of maximal unipotent local monodromy. We prove that this phenomenon holds for simplicial and hyperoctahedral families of Calabi-Yau hypersurfaces in <em>n</em> dimensions, in which case the limits of the Frobenius matrix entries are rational linear combinations of products of <span><math><msub><mrow><mi>ζ</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>(</mo><mi>k</mi><mo>)</mo></math></span> with <span><math><mn>1</mn><mo>&lt;</mo><mi>k</mi><mo>&lt;</mo><mi>n</mi></math></span>.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"480 ","pages":"Article 110512"},"PeriodicalIF":1.5,"publicationDate":"2025-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144996257","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Mechanisms of semantic communication of information and dynamics of complex systems. Application to financial markets","authors":"Inga Ivanova ,&nbsp;Grzegorz Rzadkowski","doi":"10.1016/j.chaos.2025.117131","DOIUrl":"10.1016/j.chaos.2025.117131","url":null,"abstract":"<div><div>The analysis of complex systems from an information theoretical perspective requires a more complex framework than that entertained in Shannon's mathematical theory of communication. Extending this theory from engineering to semantic communications allows us to move from the static to dynamic aspects of information communication. While in engineering communications information is only measurable, in semantic communications information is the driving force for the emergent properties of a complex system that determine its dynamics. The paper discusses how information is communicated in a complex system such as a financial market, how market prices change in response to information processing by market participants, and how non-linear information dynamics affect the movement of market prices. We analyze historical data of the SP 500 market for the period 1950–2025 using the logistic Continuous Wavelet Transformation method. This approach allows us to identify various patterns in system dynamics. These patterns are conceptualized using a theory of reflexive communication of information in a system consisting of heterogeneous agents who assign meaning to information from different perspectives. This allows us to describe the dynamics of the market and make forecasts of its development using the most general mechanisms of information circulation within the content-free information approach.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"200 ","pages":"Article 117131"},"PeriodicalIF":5.6,"publicationDate":"2025-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144996351","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Trapezoid and trapezoidal prism for the maximum relative drawdown: Probability, crash options pricing, and risk","authors":"Jia-Hao Syu,&nbsp;Yuh-Dauh Lyuu","doi":"10.1016/j.amc.2025.129708","DOIUrl":"10.1016/j.amc.2025.129708","url":null,"abstract":"<div><div>Maximum drawdown (MDD) and maximum relative drawdown (MrDD) are well-known in portfolio management and performance evaluations. They can also form the basis of a stop-loss strategy. But there is no closed-form formula for the probability that the MrDD (MDD) ever reaches some positive threshold over a period of time. This paper focuses on MrDD and employs a random walk to approximate the underlying geometric Brownian motion (GBM) for the price, taking care to match the threshold for faster convergence. Let <span><math><mi>n</mi></math></span> be the number of time steps. This paper proposes an <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msup><mi>n</mi><mrow><mn>1.5</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span>-sized trapezoid to calculate the above-mentioned probability. The trapezoid can price the crash option with a digital payoff accurately. This paper further proposes an <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msup><mi>n</mi><mrow><mn>2.5</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span>-sized trapezoidal prism to price the crash option with a resetting payoff accurately and calculate the expected return rate and common risk measures of an MrDD-based stop-loss strategy.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"510 ","pages":"Article 129708"},"PeriodicalIF":3.4,"publicationDate":"2025-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144996175","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Minimum bisections of graphs without even cycles","authors":"Mengjiao Rao ,&nbsp;Qinghou Zeng","doi":"10.1016/j.disc.2025.114768","DOIUrl":"10.1016/j.disc.2025.114768","url":null,"abstract":"<div><div>A bisection of a graph <em>G</em> is a partition of <span><math><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> into two parts <span><math><msub><mrow><mi>V</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>V</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> satisfying <span><math><mo>|</mo><mo>|</mo><msub><mrow><mi>V</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>|</mo><mo>−</mo><mo>|</mo><msub><mrow><mi>V</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>|</mo><mo>|</mo><mo>≤</mo><mn>1</mn></math></span>, and its size is the number of edges that go across the two parts. The minimum bisection problem asks for a bisection in a given graph minimizing the size which is defined as the bisection width. We present some upper bounds on the bisection width for graphs with a perfect matching and without short even cycles. Let <em>G</em> be an <em>n</em>-vertex <span><math><mo>{</mo><msub><mrow><mi>C</mi></mrow><mrow><mn>4</mn></mrow></msub><mo>,</mo><msub><mrow><mi>C</mi></mrow><mrow><mn>6</mn></mrow></msub><mo>}</mo></math></span>-free graph with <em>m</em> edges and a perfect matching. We first show that <em>G</em> has a bisection of size at most <span><math><mi>m</mi><mo>/</mo><mn>2</mn><mo>−</mo><mo>(</mo><mi>n</mi><mo>−</mo><mn>6</mn><mo>)</mo><mo>/</mo><mn>8</mn></math></span>. Together with probabilistic techniques, we show that there is a constant <span><math><mi>ζ</mi><mo>&gt;</mo><mn>0</mn></math></span> such that <em>G</em> has bisection of size at most <span><math><mi>m</mi><mo>/</mo><mn>2</mn><mo>−</mo><mi>ζ</mi><mspace></mspace><msubsup><mrow><mo>∑</mo></mrow><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>n</mi></mrow></msubsup><msqrt><mrow><msub><mrow><mi>d</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msqrt></math></span> if <span><math><mi>n</mi><mo>≥</mo><mn>8</mn></math></span>, and this is tight up to the value of <em>ζ</em>. Furthermore, if <em>G</em> is <span><math><msub><mrow><mi>C</mi></mrow><mrow><mn>2</mn><mi>k</mi></mrow></msub></math></span>-free for some fixed integer <span><math><mi>k</mi><mo>≥</mo><mn>3</mn></math></span> and <span><math><mi>n</mi><mo>≥</mo><mn>8</mn></math></span>, then there is a constant <span><math><mi>c</mi><mo>(</mo><mi>k</mi><mo>)</mo><mo>&gt;</mo><mn>0</mn></math></span> such that <em>G</em> has a bisection of size at most <span><math><mi>m</mi><mo>/</mo><mn>2</mn><mo>−</mo><mi>c</mi><mo>(</mo><mi>k</mi><mo>)</mo><msup><mrow><mi>m</mi></mrow><mrow><mo>(</mo><mn>2</mn><mi>k</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>/</mo><mo>(</mo><mn>2</mn><mi>k</mi><mo>+</mo><mn>2</mn><mo>)</mo></mrow></msup></math></span>. This is tight up to the value of <span><math><mi>c</mi><mo>(</mo><mi>k</mi><mo>)</mo></math></span> for <span><math><mn>2</mn><mi>k</mi><mo>∈</mo><mo>{</mo><mn>6</mn><mo>,</mo><mn>10</mn><mo>}</mo></math></span>.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"349 2","pages":"Article 114768"},"PeriodicalIF":0.7,"publicationDate":"2025-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144996898","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}