数学最新文献

{"title":"Morse Predecomposition of an Invariant Set.","authors":"Michał Lipiński, Konstantin Mischaikow, Marian Mrozek","doi":"10.1007/s12346-024-01144-3","DOIUrl":"10.1007/s12346-024-01144-3","url":null,"abstract":"<p><p>Motivated by the study of recurrent orbits and dynamics within a Morse set of a Morse decomposition we introduce the concept of Morse predecomposition of an isolated invariant set within the setting of both combinatorial and classical dynamical systems. While Morse decomposition summarizes solely the gradient part of a dynamical system, the developed generalization extends to the recurrent component as well. In particular, a chain recurrent set, which is indecomposable in terms of Morse decomposition, can be represented more finely in the Morse predecomposition framework. This generalization is achieved by forgoing the poset structure inherent to Morse decomposition and relaxing the notion of connection between Morse sets (elements of Morse decomposition) in favor of what we term 'links'. We prove that a Morse decomposition is a special case of Morse predecomposition indexed by a poset. Additionally, we show how a Morse predecomposition may be condensed back to retrieve a Morse decomposition.</p>","PeriodicalId":48886,"journal":{"name":"Qualitative Theory of Dynamical Systems","volume":"24 1","pages":"5"},"PeriodicalIF":1.9,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11568017/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142648758","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Well-posedness of Keller-Segel systems on compact metric graphs.","authors":"Hewan Shemtaga, Wenxian Shen, Selim Sukhtaiev","doi":"10.1007/s00028-024-01033-x","DOIUrl":"https://doi.org/10.1007/s00028-024-01033-x","url":null,"abstract":"<p><p>Chemotaxis phenomena govern the directed movement of microorganisms in response to chemical stimuli. In this paper, we investigate two Keller-Segel systems of reaction-advection-diffusion equations modeling chemotaxis on thin networks. The distinction between two systems is driven by the rate of diffusion of the chemo-attractant. The intermediate rate of diffusion is modeled by a coupled pair of parabolic equations, while the rapid rate is described by a parabolic equation coupled with an elliptic one. Assuming the polynomial rate of growth of the chemotaxis sensitivity coefficient, we prove local well-posedness of both systems on compact metric graphs, and, in particular, prove existence of unique classical solutions. This is achieved by constructing sufficiently regular mild solutions via analytic semigroup methods and combinatorial description of the heat kernel on metric graphs. The regularity of mild solutions is shown by applying abstract semigroup results to semi-linear parabolic equations on compact graphs. In addition, for logistic-type Keller-Segel systems we prove global well-posedness and, in some special cases, global uniform boundedness of solutions.</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"25 1","pages":"7"},"PeriodicalIF":1.1,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11646970/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142848398","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Continuous Operators from Spaces of Lipschitz Functions.","authors":"Christian Bargetz, Jerzy Kąkol, Damian Sobota","doi":"10.1007/s00025-024-02323-z","DOIUrl":"10.1007/s00025-024-02323-z","url":null,"abstract":"<p><p>We study the existence of continuous (linear) operators from the Banach spaces <math> <mrow> <msub><mrow><mspace></mspace> <mtext>Lip</mtext> <mspace></mspace></mrow> <mn>0</mn></msub> <mrow><mo>(</mo> <mi>M</mi> <mo>)</mo></mrow> </mrow> </math> of Lipschitz functions on infinite metric spaces <i>M</i> vanishing at a distinguished point and from their predual spaces <math><mrow><mi>F</mi> <mo>(</mo> <mi>M</mi> <mo>)</mo></mrow> </math> onto certain Banach spaces, including <i>C</i>(<i>K</i>)-spaces and the spaces <math><msub><mi>c</mi> <mn>0</mn></msub> </math> and <math><msub><mi>ℓ</mi> <mn>1</mn></msub> </math> . For pairs of spaces <math> <mrow> <msub><mrow><mspace></mspace> <mtext>Lip</mtext> <mspace></mspace></mrow> <mn>0</mn></msub> <mrow><mo>(</mo> <mi>M</mi> <mo>)</mo></mrow> </mrow> </math> and <i>C</i>(<i>K</i>) we prove that if they are endowed with topologies weaker than the norm topology, then usually no continuous (linear or not) surjection exists between those spaces. It is also showed that if a metric space <i>M</i> contains a bilipschitz copy of the unit sphere <math><msub><mi>S</mi> <msub><mi>c</mi> <mn>0</mn></msub> </msub> </math> of the space <math><msub><mi>c</mi> <mn>0</mn></msub> </math> , then <math> <mrow> <msub><mrow><mspace></mspace> <mtext>Lip</mtext> <mspace></mspace></mrow> <mn>0</mn></msub> <mrow><mo>(</mo> <mi>M</mi> <mo>)</mo></mrow> </mrow> </math> admits a continuous operator onto <math><msub><mi>ℓ</mi> <mn>1</mn></msub> </math> and hence onto <math><msub><mi>c</mi> <mn>0</mn></msub> </math> . Using this, we provide several conditions for a space <i>M</i> implying that <math> <mrow> <msub><mrow><mspace></mspace> <mtext>Lip</mtext> <mspace></mspace></mrow> <mn>0</mn></msub> <mrow><mo>(</mo> <mi>M</mi> <mo>)</mo></mrow> </mrow> </math> is not a Grothendieck space. Finally, we obtain a new characterization of the Schur property for Lipschitz-free spaces: a space <math><mrow><mi>F</mi> <mo>(</mo> <mi>M</mi> <mo>)</mo></mrow> </math> has the Schur property if and only if for every complete discrete metric space <i>N</i> with cardinality <i>d</i>(<i>M</i>) the spaces <math><mrow><mi>F</mi> <mo>(</mo> <mi>M</mi> <mo>)</mo></mrow> </math> and <math><mrow><mi>F</mi> <mo>(</mo> <mi>N</mi> <mo>)</mo></mrow> </math> are weakly sequentially homeomorphic.</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":"80 1","pages":"5"},"PeriodicalIF":1.1,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11611977/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142781571","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A higher-order quadratic NLS equation on the half-line.","authors":"A Alexandrou Himonas, Fangchi Yan","doi":"10.1007/s00028-024-01034-w","DOIUrl":"https://doi.org/10.1007/s00028-024-01034-w","url":null,"abstract":"<p><p>The well-posedness of the initial-boundary value problem for higher-order quadratic nonlinear Schrödinger equations on the half-line is studied by utilizing the Fokas solution formula for the corresponding linear problem. Using this formula, linear estimates are derived in Bourgain spaces for initial data in spatial Sobolev spaces on the half-line and boundary data in temporal Sobolev spaces suggested by the time regularity of the linear initial value problem. Then, the needed bilinear estimates are derived and used for showing that the iteration map defined via the Fokas solution formula is a contraction in appropriate solution spaces. Finally, well-posedness is established for optimal Sobolev exponents in a way analogous to the case of the initial value problem on the whole line with solutions in classical Bourgain spaces.</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"25 1","pages":"8"},"PeriodicalIF":1.1,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11646971/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142848397","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"More Weakly Biharmonic Maps from the Ball to the Sphere.","authors":"Volker Branding","doi":"10.1007/s12220-024-01852-x","DOIUrl":"10.1007/s12220-024-01852-x","url":null,"abstract":"<p><p>In this note we prove the existence of two proper biharmonic maps between the Euclidean ball of dimension bigger than four and Euclidean spheres of appropriate dimensions. We will also show that, in low dimensions, both maps are unstable critical points of the bienergy.</p>","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"35 1","pages":"23"},"PeriodicalIF":1.2,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11584471/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142711340","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"funBIalign: a hierachical algorithm for functional motif discovery based on mean squared residue scores.","authors":"Jacopo Di Iorio, Marzia A Cremona, Francesca Chiaromonte","doi":"10.1007/s11222-024-10537-y","DOIUrl":"10.1007/s11222-024-10537-y","url":null,"abstract":"<p><p>Motif discovery is gaining increasing attention in the domain of functional data analysis. Functional motifs are typical \"shapes\" or \"patterns\" that recur multiple times in different portions of a single curve and/or in misaligned portions of multiple curves. In this paper, we define functional motifs using an additive model and we propose <i>funBIalign</i> for their discovery and evaluation. Inspired by clustering and biclustering techniques, <i>funBIalign</i> is a multi-step procedure which uses agglomerative hierarchical clustering with complete linkage and a functional distance based on mean squared residue scores to discover functional motifs, both in a single curve (e.g., time series) and in a set of curves. We assess its performance and compare it to other recent methods through extensive simulations. Moreover, we use <i>funBIalign</i> for discovering motifs in two real-data case studies; one on food price inflation and one on temperature changes.</p><p><strong>Supplementary information: </strong>The online version contains supplementary material available at 10.1007/s11222-024-10537-y.</p>","PeriodicalId":22058,"journal":{"name":"Statistics and Computing","volume":"35 1","pages":"11"},"PeriodicalIF":1.6,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11632007/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142819226","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Para-Sasakian (phi -)symmetric spaces","authors":"Eugenia Loiudice","doi":"10.1007/s10455-024-09980-x","DOIUrl":"10.1007/s10455-024-09980-x","url":null,"abstract":"<div><p>We study the Boothby–Wang fibration of para-Sasakian manifolds and introduce the class of para-Sasakian <span>(phi )</span>-symmetric spaces, canonically fibering over para-Hermitian symmetric spaces. We remark that in contrast to the Hermitian setting the center of the isotropy group of a simple para-Hermitian symmetric space <i>G</i>/<i>H</i> can be either one- or two-dimensional, and prove that the associated metric is not necessarily the <i>G</i>-invariant extension of the Killing form of <i>G</i>. Using the Boothby–Wang fibration and the classification of semisimple para-Hermitian symmetric spaces, we explicitly construct semisimple para-Sasakian <span>(phi )</span>-symmetric spaces fibering over semisimple para-Hermitian symmetric spaces. We provide moreover an example of non-semisimple para-Sasakian <span>(phi )</span>-symmetric space.\u0000</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"67 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-024-09980-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142875201","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A class of permutations on $${mathbb {Z}}_{p}$$ with differential uniformity at most 3","authors":"Prachi Gupta, P. R. Mishra, Atul Gaur","doi":"10.1007/s10623-024-01548-x","DOIUrl":"https://doi.org/10.1007/s10623-024-01548-x","url":null,"abstract":"<p>In this paper, we give a class of permutations on <span>({mathbb {Z}}_{p})</span> having differential uniformity at most 3, where prime <i>p</i> satisfies <span>(p equiv 1 pmod {4})</span>. Further, we present a sufficient condition for differential uniformity exactly 3 and identify a subclass achieving this value.</p>","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"1 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142869956","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":"Oscillations in Wave Map Systems and Homogenization of the Einstein Equations in Symmetry","authors":"André Guerra,&nbsp;Rita Teixeira da Costa","doi":"10.1007/s00205-024-02042-3","DOIUrl":"10.1007/s00205-024-02042-3","url":null,"abstract":"<div><p>In 1989, Burnett conjectured that, under appropriate assumptions, the limit of highly oscillatory solutions to the Einstein vacuum equations is a solution of the Einstein–massless Vlasov system. In a recent breakthrough, Huneau–Luk (Ann Sci l’ENS, 2024) gave a proof of the conjecture in <i>U</i>(1)-symmetry and elliptic gauge. They also require control on up to fourth order derivatives of the metric components. In this paper, we give a streamlined proof of a stronger result and, in the spirit of Burnett’s original conjecture, we remove the need for control on higher derivatives. Our methods also apply to general wave map equations.</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"249 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00205-024-02042-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142859603","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Guessing less and better: improved attacks on GIFT-64","authors":"Federico Canale, María Naya-Plasencia","doi":"10.1007/s10623-024-01527-2","DOIUrl":"https://doi.org/10.1007/s10623-024-01527-2","url":null,"abstract":"<p>GIFT-64 is a block cipher that has received a lot of attention from the community since its proposal in 2017. The attack on the highest number of rounds is a differential related-key attack on 26 rounds. We studied this attack, in particular with respect to some recent generic frameworks for improving key recovery, and we realised that this framework, combined with an efficient parallel key guessing of interesting subsets of the key and a consequent list merging applied to the partial solutions, can improve the complexity of the attack. We propose two different trade-offs, as a result of the improved key-recovery. We believe that the techniques are quite generic and that it is possible to apply them to improve other differential attacks.</p>","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"31 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142867061","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}