Let XX be a compact Riemann surface of genus g≥2gge 2, GG be a semisimple complex Lie group and ρ:G→GL(V)rho :Gto {rm{GL}}left(V) be a complex representation of GG. Given a principal GG-bundle EE over XX, a vector bundle
设X X是g≥2g的紧致黎曼曲面ge 2, g g是半简单复李群，ρ: g→GL (V) rho: g to{rm{GL}}left (V)是g g的复表示。给定一个主G G -束E E / X X，诱导出一个矢量束E (V) E left (V)，其典型纤维是V V的复制品。A (G， ρ) left (G, rho) -希格斯对是一对(E， φ) left (E, varphi)，其中E E是X X上的一个主G G -束，φ varphi是E (V)⊗L E left (V) otimes L的全纯全局截面，L L是X X上的一个固定线束。在这项工作中，考虑了G= Spin (8, C) G= {rm{Spin}}left (8, {mathbb{C}})和Spin (8, C) {rm{Spin}}left (8, {mathbb{C}})承认的三种不可约的八维复表示的这种希格斯对。特别地，给出了这些特定希格斯对的稳定性、半稳定性和多稳定性的简化概念，并证明了相应的模空间是同构的，并描述了与自旋(8,C) {rm{Spin}}left (8, {mathbb{C}})的三种表述之一相关的稳定和非简单希格斯对的精确表达式。
{"title":"Spin(8,C)-Higgs pairs over a compact Riemann surface","authors":"Álvaro Antón-Sancho","doi":"10.1515/math-2023-0153","DOIUrl":"https://doi.org/10.1515/math-2023-0153","url":null,"abstract":"Let <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0153_eq_001.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>X</m:mi> </m:math> <jats:tex-math>X</jats:tex-math> </jats:alternatives> </jats:inline-formula> be a compact Riemann surface of genus <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0153_eq_002.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>g</m:mi> <m:mo>≥</m:mo> <m:mn>2</m:mn> </m:math> <jats:tex-math>gge 2</jats:tex-math> </jats:alternatives> </jats:inline-formula>, <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0153_eq_003.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>G</m:mi> </m:math> <jats:tex-math>G</jats:tex-math> </jats:alternatives> </jats:inline-formula> be a semisimple complex Lie group and <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0153_eq_004.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>ρ</m:mi> <m:mo>:</m:mo> <m:mi>G</m:mi> <m:mo>→</m:mo> <m:mi mathvariant=\"normal\">GL</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>V</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> <jats:tex-math>rho :Gto {rm{GL}}left(V)</jats:tex-math> </jats:alternatives> </jats:inline-formula> be a complex representation of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0153_eq_005.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>G</m:mi> </m:math> <jats:tex-math>G</jats:tex-math> </jats:alternatives> </jats:inline-formula>. Given a principal <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0153_eq_006.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>G</m:mi> </m:math> <jats:tex-math>G</jats:tex-math> </jats:alternatives> </jats:inline-formula>-bundle <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0153_eq_007.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>E</m:mi> </m:math> <jats:tex-math>E</jats:tex-math> </jats:alternatives> </jats:inline-formula> over <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0153_eq_008.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>X</m:mi> </m:math> <jats:tex-math>X</jats:tex-math> </jats:alternatives> </jats:inline-formula>, a vector bundle <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" ","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138527116","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}
Pub Date : 2023-08-11DOI: 10.1142/s2811007223500086
Rajat Kaushik, Sandip Banerjee
{"title":"Predator-prey ecological system with group defense and anti-predator traits of the preys: Synergies between two important ecological actions","authors":"Rajat Kaushik, Sandip Banerjee","doi":"10.1142/s2811007223500086","DOIUrl":"https://doi.org/10.1142/s2811007223500086","url":null,"abstract":"","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81412238","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}
Pub Date : 2023-08-04DOI: 10.1142/s2811007223500074
Charles Wend-Waoga Tougma
{"title":"Polya fields and Kuroda/Kubota unit formula","authors":"Charles Wend-Waoga Tougma","doi":"10.1142/s2811007223500074","DOIUrl":"https://doi.org/10.1142/s2811007223500074","url":null,"abstract":"","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76873333","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}
Pub Date : 2023-07-28DOI: 10.1142/s2811007223500062
Pinghua Yang, Rongling Yang
{"title":"The explicit solution of a class of a higher order impulsive fractional differential equation involving Hadamard fractional derivative","authors":"Pinghua Yang, Rongling Yang","doi":"10.1142/s2811007223500062","DOIUrl":"https://doi.org/10.1142/s2811007223500062","url":null,"abstract":"","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89835659","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}
Pub Date : 2023-05-26DOI: 10.1142/s2811007223500037
Samara Fatima, Naseem Abbas, M. Munawar, S. M. Eldin
{"title":"Ion-acoustic wave dynamics and sensitivity study in a magnetized Auroral phase plasma","authors":"Samara Fatima, Naseem Abbas, M. Munawar, S. M. Eldin","doi":"10.1142/s2811007223500037","DOIUrl":"https://doi.org/10.1142/s2811007223500037","url":null,"abstract":"","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87415706","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}
Pub Date : 2023-02-10DOI: 10.1142/s2811007223500013
Ying Song
{"title":"Global existence and decay rates of solutions for Vlasov-Navier-Stokes-Fokker-Planck equations with magnetic field","authors":"Ying Song","doi":"10.1142/s2811007223500013","DOIUrl":"https://doi.org/10.1142/s2811007223500013","url":null,"abstract":"","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89876605","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}
Abstract Let G G be a π pi -separable group for some set π pi of primes, let χ ∈ B π ( G ) chi in {B}_{pi }left(G) and let N ◃ G Nhspace{0.33em}triangleleft hspace{0.33em}G . In this article, we explore how to construct a nucleus for an irreducible constituent of χ N {chi }_{N} via the given nucleus ( W , γ ) left(W,gamma ) for χ chi .
摘要设G G是质数集π pi的π pi -可分群，设χ∈B π (G) chiin B＿{}{pi}left (G)，设N≠G N hspace{0.33em}triangleleft G。在本文中，我们探讨了如何hspace{0.33em}通过给定的χ chi{的核}(W， γ) {}left (W, gamma)来构造χ N {chi} ＿N的不可约成分的核。
{"title":"The construction of nuclei for normal constituents of Bπ-characters","authors":"Jun Jin, Junwei Zhang","doi":"10.1515/math-2022-0587","DOIUrl":"https://doi.org/10.1515/math-2022-0587","url":null,"abstract":"Abstract Let G G be a π pi -separable group for some set π pi of primes, let χ ∈ B π ( G ) chi in {B}_{pi }left(G) and let N ◃ G Nhspace{0.33em}<mml:mpadded xmlns:ali=\"http://www.niso.org/schemas/ali/1.0/\" xmlns:xsi=\"http://www.w3.org/2001/XMLSchema-instance\">triangleleft </mml:mpadded>hspace{0.33em}G . In this article, we explore how to construct a nucleus for an irreducible constituent of χ N {chi }_{N} via the given nucleus ( W , γ ) left(W,gamma ) for χ chi .","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41287929","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}
Abstract In this article, we obtain some sufficient conditions for the boundedness of commutators of p p -adic Hardy-Littlewood operators with symbols in central bounded mean oscillation space and Lipschitz space on the p p -adic function spaces with variable exponents such as the p p -adic local central Morrey, p p -adic Morrey-Herz, and p p -adic local block spaces with variable exponents.
{"title":"Commutators of Hardy-Littlewood operators on p-adic function spaces with variable exponents","authors":"K. Dung, P. T. Thuy","doi":"10.1515/math-2022-0579","DOIUrl":"https://doi.org/10.1515/math-2022-0579","url":null,"abstract":"Abstract In this article, we obtain some sufficient conditions for the boundedness of commutators of p p -adic Hardy-Littlewood operators with symbols in central bounded mean oscillation space and Lipschitz space on the p p -adic function spaces with variable exponents such as the p p -adic local central Morrey, p p -adic Morrey-Herz, and p p -adic local block spaces with variable exponents.","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49274183","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}
Abstract In this article, the general Liénard system d x d t = ϕ ( y ) − F ( x ) , d y d t = − g ( x ) left{begin{array}{l}frac{{rm{d}}x}{{rm{d}}t}=phi (y)-Fleft(x), frac{{rm{d}}y}{{rm{d}}t}=-gleft(x)end{array}right. is studied. By using the Filippov transformation, combined with the careful estimation of divergence along the closed orbit, we prove the sufficient conditions for the uniqueness of limit cycles in this system. Our results extend almost all the related existing studies on the Liénard system.
摘要在这篇文章中，一般的Liénard系统d x d t=ξ（y）−F（x），d y d t=−g（x）left｛begin｛array｝｛l｝frac｛rm｛d｝｝x｝。进行了研究。利用Filippov变换，结合对闭合轨道发散的仔细估计，我们证明了该系统极限环唯一性的充分条件。我们的结果扩展了几乎所有现有的关于Liénard系统的相关研究。
{"title":"On the uniqueness of limit cycles for generalized Liénard systems","authors":"HuiPing Zhou, Yueding Yuan","doi":"10.1515/math-2022-0558","DOIUrl":"https://doi.org/10.1515/math-2022-0558","url":null,"abstract":"Abstract In this article, the general Liénard system d x d t = ϕ ( y ) − F ( x ) , d y d t = − g ( x ) left{begin{array}{l}frac{{rm{d}}x}{{rm{d}}t}=phi (y)-Fleft(x), frac{{rm{d}}y}{{rm{d}}t}=-gleft(x)end{array}right. is studied. By using the Filippov transformation, combined with the careful estimation of divergence along the closed orbit, we prove the sufficient conditions for the uniqueness of limit cycles in this system. Our results extend almost all the related existing studies on the Liénard system.","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49520987","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}
Abstract In this work, the authors study some convergence results including weak law of large numbers, strong law of large numbers, complete convergence, and complete moment convergence for weighted sums of coordinatewise asymptotically negatively associated random vectors in Hilbert spaces. These results improve or extend some corresponding ones in the literature.
{"title":"Convergence properties for coordinatewise asymptotically negatively associated random vectors in Hilbert space","authors":"Qihui He, Lin Pan","doi":"10.1515/math-2022-0556","DOIUrl":"https://doi.org/10.1515/math-2022-0556","url":null,"abstract":"Abstract In this work, the authors study some convergence results including weak law of large numbers, strong law of large numbers, complete convergence, and complete moment convergence for weighted sums of coordinatewise asymptotically negatively associated random vectors in Hilbert spaces. These results improve or extend some corresponding ones in the literature.","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45063946","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}
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