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Monatshefte fur Mathematik最新文献

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On asymptotic stability of solitons for 2D Maxwell-Lorentz equations with spinning particle. 带自旋粒子的二维Maxwell-Lorentz方程孤子的渐近稳定性。
IF 0.8 4区 数学
Monatshefte fur Mathematik Pub Date : 2025-01-01 Epub Date: 2025-03-17 DOI: 10.1007/s00605-025-02064-3
E Kopylova
{"title":"On asymptotic stability of solitons for 2D Maxwell-Lorentz equations with spinning particle.","authors":"E Kopylova","doi":"10.1007/s00605-025-02064-3","DOIUrl":"https://doi.org/10.1007/s00605-025-02064-3","url":null,"abstract":"<p><p>We consider 2D Maxwell-Lorentz equations with an extended charged rotating particle. The system admits solitons which are solutions corresponding to a particle moving with constant velocity and rotating with constant angular velocity. Our main result is asymptotic stability of moving solitons with zero angular velocity.</p>","PeriodicalId":54737,"journal":{"name":"Monatshefte fur Mathematik","volume":"207 1","pages":"59-82"},"PeriodicalIF":0.8,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12021738/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144053452","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Almost automorphic and bijective factors of substitution shifts. 替代移位的几乎自同构和客观因素。
IF 0.8 4区 数学
Monatshefte fur Mathematik Pub Date : 2025-01-01 Epub Date: 2025-01-16 DOI: 10.1007/s00605-024-02053-y
Alvaro Bustos-Gajardo, Johannes Kellendonk, Reem Yassawi
{"title":"Almost automorphic and bijective factors of substitution shifts.","authors":"Alvaro Bustos-Gajardo, Johannes Kellendonk, Reem Yassawi","doi":"10.1007/s00605-024-02053-y","DOIUrl":"https://doi.org/10.1007/s00605-024-02053-y","url":null,"abstract":"<p><p>In this article we completely characterise constant length substitution shifts which have a proper almost automorphic factor, or which have a bijective substitution factor such that the factor map is injective on at least one point. Our approach is algebraic: we characterise these dynamical properties in terms of a finite semigroup defined by the substitution. We characterise the existence of almost automorphic factors in terms of Green's <math><mi>R</mi></math> -relation and the existence of bijective factors in terms of Green's <math><mi>L</mi></math> -relation. Our results are constructive.</p>","PeriodicalId":54737,"journal":{"name":"Monatshefte fur Mathematik","volume":"206 3","pages":"507-549"},"PeriodicalIF":0.8,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11872789/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143558623","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","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 new approach to weighted Sobolev spaces. 加权Sobolev空间的一种新方法。
IF 0.8 4区 数学
Monatshefte fur Mathematik Pub Date : 2025-01-01 Epub Date: 2025-01-09 DOI: 10.1007/s00605-024-02044-z
Djameleddine Kebiche
{"title":"A new approach to weighted Sobolev spaces.","authors":"Djameleddine Kebiche","doi":"10.1007/s00605-024-02044-z","DOIUrl":"https://doi.org/10.1007/s00605-024-02044-z","url":null,"abstract":"<p><p>We present in this paper a new way to define weighted Sobolev spaces when the weight functions are arbitrary small. This new approach can replace the old one consisting in modifying the domain by removing the set of points where at least one of the weight functions is very small. The basic idea is to replace the distributional derivative with a new notion of weak derivative. In this way, non-locally integrable functions can be considered in these spaces. Indeed, assumptions under which a degenerate elliptic partial differential equation has a unique non-locally integrable solution are given. Tools like a Poincaré inequality and a trace operator are developed, and density results of smooth functions are established.</p>","PeriodicalId":54737,"journal":{"name":"Monatshefte fur Mathematik","volume":"206 4","pages":"893-920"},"PeriodicalIF":0.8,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11909071/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143651951","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","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 note on Weyl's equidistribution theorem. 关于Weyl等分布定理的注解。
IF 0.8 4区 数学
Monatshefte fur Mathematik Pub Date : 2025-01-01 Epub Date: 2025-02-14 DOI: 10.1007/s00605-025-02057-2
Yuval Yifrach
{"title":"A note on Weyl's equidistribution theorem.","authors":"Yuval Yifrach","doi":"10.1007/s00605-025-02057-2","DOIUrl":"https://doi.org/10.1007/s00605-025-02057-2","url":null,"abstract":"<p><p>H. Weyl proved in Weyl (Eins Math Ann 77(3):313-352, 1916) that integer evaluations of polynomials are equidistributed mod 1 whenever at least one of the non-free coefficients (namely a coefficient of a monomial of degree at least 1) is irrational. We use Weyl's result to prove a higher dimensional analogue of this fact. Namely, we prove that evaluations of polynomials on lattice points are equidistributed mod 1 whenever at least one of the non-free coefficients is irrational. This result improves the main result of Arhipov et al. (Mat Zametki 25(1):3-14, 157, 1979). We prove this analogue as a corollary of a theorem that guarantees equidistribution of grid evaluations mod 1 for all functions which satisfy some restraints on their derivatives. Another corollary we prove is that for <math><mrow><mi>p</mi> <mo>∈</mo> <mo>(</mo> <mn>1</mn> <mo>,</mo> <mi>∞</mi> <mo>)</mo></mrow> </math> the <math><msup><mi>ℓ</mi> <mi>p</mi></msup> </math> norms of integer vectors are equidistributed mod 1.</p>","PeriodicalId":54737,"journal":{"name":"Monatshefte fur Mathematik","volume":"206 3","pages":"771-780"},"PeriodicalIF":0.8,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11872991/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143558619","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The AGM of Gauss, Ramanujan's corresponding theory, and spectral bounds of self-adjoint operators. 高斯的AGM， Ramanujan的相应理论，和自伴随算子的谱界。
IF 0.8 4区 数学
Monatshefte fur Mathematik Pub Date : 2025-01-01 Epub Date: 2025-01-22 DOI: 10.1007/s00605-024-02051-0
Markus Faulhuber, Anupam Gumber, Irina Shafkulovska
{"title":"The AGM of Gauss, Ramanujan's corresponding theory, and spectral bounds of self-adjoint operators.","authors":"Markus Faulhuber, Anupam Gumber, Irina Shafkulovska","doi":"10.1007/s00605-024-02051-0","DOIUrl":"10.1007/s00605-024-02051-0","url":null,"abstract":"<p><p>We study the spectral bounds of self-adjoint operators on the Hilbert space of square-integrable functions, arising from the representation theory of the Heisenberg group. Interestingly, starting either with the von Neumann lattice or the hexagonal lattice of density 2, the spectral bounds obey well-known arithmetic-geometric mean iterations. This follows from connections to Jacobi theta functions and Ramanujan's corresponding theories. As a consequence, we rediscover that these operators resemble the identity operator as the density of the lattice grows. We also prove that the conjectural value of Landau's constant is obtained as half the cubic arithmetic-geometric mean of <math><mroot><mn>2</mn> <mn>3</mn></mroot> </math> and 1, which we believe to be a new result.</p>","PeriodicalId":54737,"journal":{"name":"Monatshefte fur Mathematik","volume":"206 3","pages":"551-582"},"PeriodicalIF":0.8,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11872773/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143558627","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","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 generic convergence of successive approximations of mappings with convex and compact point images. 关于具有凸和紧点映象的映射的逐次逼近的一般收敛性。
IF 0.9 4区 数学
Monatshefte fur Mathematik Pub Date : 2023-01-01 Epub Date: 2022-12-22 DOI: 10.1007/s00605-022-01813-y
Christian Bargetz, Emir Medjic, Katriin Pirk
{"title":"On generic convergence of successive approximations of mappings with convex and compact point images.","authors":"Christian Bargetz,&nbsp;Emir Medjic,&nbsp;Katriin Pirk","doi":"10.1007/s00605-022-01813-y","DOIUrl":"10.1007/s00605-022-01813-y","url":null,"abstract":"<p><p>We study the generic behavior of the method of successive approximations for set-valued mappings in separable Banach spaces. We consider the case of nonexpansive mappings with convex and compact point images and show that for the typical such mapping and typical points of its domain the sequence of successive approximations is unique and converges to a fixed point of the mapping.</p>","PeriodicalId":54737,"journal":{"name":"Monatshefte fur Mathematik","volume":"202 4","pages":"659-683"},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10576736/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41240931","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","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 azimuthally propagating equatorial atmospheric waves. 关于方位角传播的赤道大气波。
IF 0.9 4区 数学
Monatshefte fur Mathematik Pub Date : 2023-01-01 Epub Date: 2022-07-08 DOI: 10.1007/s00605-022-01741-x
Calin I Martin
{"title":"On azimuthally propagating equatorial atmospheric waves.","authors":"Calin I Martin","doi":"10.1007/s00605-022-01741-x","DOIUrl":"10.1007/s00605-022-01741-x","url":null,"abstract":"<p><p>We investigate the existence of solutions to a recent model for large-scale equatorial waves, derived recently by an asymptotic method driven by the thin-shell approximation of the Earth's atmosphere in rotating spherical coordinates.</p>","PeriodicalId":54737,"journal":{"name":"Monatshefte fur Mathematik","volume":"201 4","pages":"1185-1195"},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10261202/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9657294","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The approximate functional equation of some Diophantine series. 一类丢番图级数的近似函数方程。
IF 0.9 4区 数学
Monatshefte fur Mathematik Pub Date : 2023-01-01 Epub Date: 2023-05-05 DOI: 10.1007/s00605-023-01859-6
Fernando Chamizo, Bruno Martin
{"title":"The approximate functional equation of some Diophantine series.","authors":"Fernando Chamizo,&nbsp;Bruno Martin","doi":"10.1007/s00605-023-01859-6","DOIUrl":"10.1007/s00605-023-01859-6","url":null,"abstract":"<p><p>We prove that a family of Diophantine series satisfies an approximate functional equation. It generalizes a result by Rivoal and Roques and proves an extended version of a conjecture posed in their paper. We also characterize the convergence points.</p>","PeriodicalId":54737,"journal":{"name":"Monatshefte fur Mathematik","volume":"202 1","pages":"41-52"},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10363075/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9920046","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Integer-valued polynomials on valuation rings of global fields with prescribed lengths of factorizations. 具有指定因子分解长度的全局域的赋值环上的整值多项式。
IF 0.9 4区 数学
Monatshefte fur Mathematik Pub Date : 2023-01-01 Epub Date: 2023-09-04 DOI: 10.1007/s00605-023-01895-2
Victor Fadinger-Held, Sophie Frisch, Daniel Windisch
{"title":"Integer-valued polynomials on valuation rings of global fields with prescribed lengths of factorizations.","authors":"Victor Fadinger-Held,&nbsp;Sophie Frisch,&nbsp;Daniel Windisch","doi":"10.1007/s00605-023-01895-2","DOIUrl":"10.1007/s00605-023-01895-2","url":null,"abstract":"<p><p>Let <i>V</i> be a valuation ring of a global field <i>K</i>. We show that for all positive integers <i>k</i> and <math><mrow><mn>1</mn><mo><</mo><msub><mi>n</mi><mn>1</mn></msub><mo>≤</mo><mo>⋯</mo><mo>≤</mo><msub><mi>n</mi><mi>k</mi></msub></mrow></math> there exists an integer-valued polynomial on <i>V</i>, that is, an element of <math><mrow><mrow><mspace></mspace><mtext>Int</mtext><mspace></mspace></mrow><mo>(</mo><mi>V</mi><mo>)</mo><mo>=</mo><mo>{</mo><mi>f</mi><mo>∈</mo><mi>K</mi><mo>[</mo><mi>X</mi><mo>]</mo><mo>∣</mo><mi>f</mi><mo>(</mo><mi>V</mi><mo>)</mo><mo>⊆</mo><mi>V</mi><mo>}</mo></mrow></math>, which has precisely <i>k</i> essentially different factorizations into irreducible elements of <math><mrow><mrow><mspace></mspace><mtext>Int</mtext><mspace></mspace></mrow><mo>(</mo><mi>V</mi><mo>)</mo></mrow></math> whose lengths are exactly <math><mrow><msub><mi>n</mi><mn>1</mn></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mi>n</mi><mi>k</mi></msub></mrow></math>. In fact, we show more, namely that the same result holds true for every discrete valuation domain <i>V</i> with finite residue field such that the quotient field of <i>V</i> admits a valuation ring independent of <i>V</i> whose maximal ideal is principal or whose residue field is finite. If the quotient field of <i>V</i> is a purely transcendental extension of an arbitrary field, this property is satisfied. This solves an open problem proposed by Cahen, Fontana, Frisch and Glaz in these cases.</p>","PeriodicalId":54737,"journal":{"name":"Monatshefte fur Mathematik","volume":"202 4","pages":"773-789"},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10576700/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41240930","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Expansion of eigenvalues of the perturbed discrete bilaplacian 扰动离散双placian特征值的展开式
IF 0.9 4区 数学
Monatshefte fur Mathematik Pub Date : 2022-02-05 DOI: 10.1007/s00605-022-01678-1
S. Kholmatov, Ahmad Khalkhuzhaev, Mardon Pardabaev
{"title":"Expansion of eigenvalues of the perturbed discrete bilaplacian","authors":"S. Kholmatov, Ahmad Khalkhuzhaev, Mardon Pardabaev","doi":"10.1007/s00605-022-01678-1","DOIUrl":"https://doi.org/10.1007/s00605-022-01678-1","url":null,"abstract":"","PeriodicalId":54737,"journal":{"name":"Monatshefte fur Mathematik","volume":"16 1","pages":"607 - 633"},"PeriodicalIF":0.9,"publicationDate":"2022-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77103075","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","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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