Pub Date : 2023-10-13DOI: 10.1142/s0219199723500438
Zhiqi Chen, Saiyu Wang, Hui Zhang
We consider the moment map $m:mathbb{P}V_nrightarrow text{i}mathfrak{u}(n)$ for the action of $text{GL}(n)$ on $V_n=otimes^{2}(mathbb{C}^{n})^{*}otimesmathbb{C}^{n}$, and study the functional $F_n=|m|^{2}$ restricted to the projectivizations of the algebraic varieties of all $n$-dimensional Leibniz algebras $L_n$ and all $n$-dimensional symmetric Leibniz algebras $S_n$, respectively. Firstly, we give a description of the maxima and minima of the functional $F_n: L_n rightarrow mathbb{R}$, proving that they are actually attained at the symmetric Leibniz algebras. Then, for an arbitrary critical point $[mu]$ of $F_n: S_n rightarrow mathbb{R}$, we characterize the structure of $[mu]$ by virtue of the nonnegative rationality. Finally, we classify the critical points of $F_n: S_n rightarrow mathbb{R}$ for $n=2$, $3$, respectively.
{"title":"The moment map for the variety of Leibniz algebras","authors":"Zhiqi Chen, Saiyu Wang, Hui Zhang","doi":"10.1142/s0219199723500438","DOIUrl":"https://doi.org/10.1142/s0219199723500438","url":null,"abstract":"We consider the moment map $m:mathbb{P}V_nrightarrow text{i}mathfrak{u}(n)$ for the action of $text{GL}(n)$ on $V_n=otimes^{2}(mathbb{C}^{n})^{*}otimesmathbb{C}^{n}$, and study the functional $F_n=|m|^{2}$ restricted to the projectivizations of the algebraic varieties of all $n$-dimensional Leibniz algebras $L_n$ and all $n$-dimensional symmetric Leibniz algebras $S_n$, respectively. Firstly, we give a description of the maxima and minima of the functional $F_n: L_n rightarrow mathbb{R}$, proving that they are actually attained at the symmetric Leibniz algebras. Then, for an arbitrary critical point $[mu]$ of $F_n: S_n rightarrow mathbb{R}$, we characterize the structure of $[mu]$ by virtue of the nonnegative rationality. Finally, we classify the critical points of $F_n: S_n rightarrow mathbb{R}$ for $n=2$, $3$, respectively.","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135853420","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}
Pub Date : 2023-10-13DOI: 10.1142/s0219199723500414
Chenfeng Zhu, Dachun Yang, Wen Yuan
Let $gammainmathbb{R}setminus{0}$ and $X(mathbb{R}^n)$ be a ball Banach function space satisfying some extra mild assumptions. Assume that $Omega=mathbb{R}^n$ or $Omegasubsetmathbb{R}^n$ is an $(varepsilon,infty)$-domain for some $varepsilonin(0,1]$. In this article, the authors prove that a function $f$ belongs to the homogeneous ball Banach Sobolev space $dot{W}^{1,X}(Omega)$ if and only if $fin L_{mathrm{loc}}^1(Omega)$ and $$ sup_{lambdain(0,infty)}lambda left|left[int_{{yinOmega: |f(cdot)-f(y)|>lambda|cdot-y|^{1+frac{gamma}{p}}}} left|cdot-yright|^{gamma-n},dy right]^frac{1}{p}right|_{X(Omega)}
{"title":"Brezis–Seeger–Van Schaftingen–Yung-Type Characterization of Homogeneous Ball Banach Sobolev Spaces and Its Applications","authors":"Chenfeng Zhu, Dachun Yang, Wen Yuan","doi":"10.1142/s0219199723500414","DOIUrl":"https://doi.org/10.1142/s0219199723500414","url":null,"abstract":"Let $gammainmathbb{R}setminus{0}$ and $X(mathbb{R}^n)$ be a ball Banach function space satisfying some extra mild assumptions. Assume that $Omega=mathbb{R}^n$ or $Omegasubsetmathbb{R}^n$ is an $(varepsilon,infty)$-domain for some $varepsilonin(0,1]$. In this article, the authors prove that a function $f$ belongs to the homogeneous ball Banach Sobolev space $dot{W}^{1,X}(Omega)$ if and only if $fin L_{mathrm{loc}}^1(Omega)$ and $$ sup_{lambdain(0,infty)}lambda left|left[int_{{yinOmega: |f(cdot)-f(y)|>lambda|cdot-y|^{1+frac{gamma}{p}}}} left|cdot-yright|^{gamma-n},dy right]^frac{1}{p}right|_{X(Omega)}<infty, $$ where $pin[1,infty)$ is related to $X(mathbb{R}^n)$. This result is of wide generality and can be applied to various specific Sobolev-type function spaces, including Morrey [Bourgain--Morrey-type, weighted (or mixed-norm or variable) Lebesgue, local (or global) generalized Herz, Lorentz, and Orlicz (or Orlicz-slice)] Sobolev spaces, which is new even in all these special cases; in particular, it coincides with the well-known result of H. Brezis, A. Seeger, J. Van Schaftingen, and P.-L. Yung when $X(Omega):=L^q(mathbb{R}^n)$ with $1","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135853579","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}
Pub Date : 2023-10-13DOI: 10.1142/s021919972350044x
Jun Hu, Lei Shi
In this paper we give a closed formula for the graded dimension of the cyclotomic quiver Hecke algebra $R^Lambda(beta)$ associated to an {it arbitrary} symmetrizable Cartan matrix $A=(a_{ij})_{i,j}in I$, where $Lambdain P^+$ and $betain Q_n^+$. As applications, we obtain some {it necessary and sufficient conditions} for the KLR idempotent $e(nu)$ (for any $nuin I^beta$) to be nonzero in the cyclotomic quiver Hecke algebra $R^Lambda(beta)$. We prove several level reduction results which decomposes $dim R^Lambda(beta)$ into a sum of some products of $dim R^{Lambda^i}(beta_i)$ with $Lambda=sum_iLambda^i$ and $beta=sum_{i}beta_i$, where $Lambda^iin P^+, beta^iin Q^+$ for each $i$. We construct some explicit monomial bases for the subspaces $e(widetilde{nu})R^Lambda(beta)e(mu)$ and $e(widetilde{nu})R^Lambda(beta)e(mu)$ of $R^Lambda(beta)$, where $muin I^beta$ is {it arbitrary} and $widetilde{nu}in I^beta$ is a certain specific $n$-tuple (see Section 4).Finally, we use our graded dimension formulae to provide some examples which show that $R^Lambda(n)$ is in general not graded free over its natural embedded subalgebra $R^Lambda(m)$ with $m
{"title":"Graded dimensions and monomial bases for the cyclotomic quiver Hecke algebras","authors":"Jun Hu, Lei Shi","doi":"10.1142/s021919972350044x","DOIUrl":"https://doi.org/10.1142/s021919972350044x","url":null,"abstract":"In this paper we give a closed formula for the graded dimension of the cyclotomic quiver Hecke algebra $R^Lambda(beta)$ associated to an {it arbitrary} symmetrizable Cartan matrix $A=(a_{ij})_{i,j}in I$, where $Lambdain P^+$ and $betain Q_n^+$. As applications, we obtain some {it necessary and sufficient conditions} for the KLR idempotent $e(nu)$ (for any $nuin I^beta$) to be nonzero in the cyclotomic quiver Hecke algebra $R^Lambda(beta)$. We prove several level reduction results which decomposes $dim R^Lambda(beta)$ into a sum of some products of $dim R^{Lambda^i}(beta_i)$ with $Lambda=sum_iLambda^i$ and $beta=sum_{i}beta_i$, where $Lambda^iin P^+, beta^iin Q^+$ for each $i$. We construct some explicit monomial bases for the subspaces $e(widetilde{nu})R^Lambda(beta)e(mu)$ and $e(widetilde{nu})R^Lambda(beta)e(mu)$ of $R^Lambda(beta)$, where $muin I^beta$ is {it arbitrary} and $widetilde{nu}in I^beta$ is a certain specific $n$-tuple (see Section 4).Finally, we use our graded dimension formulae to provide some examples which show that $R^Lambda(n)$ is in general not graded free over its natural embedded subalgebra $R^Lambda(m)$ with $m","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135854595","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}
Pub Date : 2023-10-13DOI: 10.1142/s0219199723500463
Jan-Henrik Metsch
We study half-spheres with small radii sitting on the boundary of a smooth bounded domain while meeting it orthogonally. Even though it is known that there exist families of CMC and Willmore type half-spheres near a nondegenerate critical point p of the domains boundaries mean curvature, it is unknown in both cases whether these provide a foliation of any deleted neighborhood of p. We prove that this is not guaranteed and establish a criterion in terms of the boundaries geometry that ensures or prevents the respective surfaces from providing such a foliation. This perhaps surprising phenomenon of conditional foliations is absent in the closely related Riemannian setting, where a foliation is guaranteed. We show how this unconditional foliation arises from symmetry considerations and how these fail to apply to the 'domain-setting'.
{"title":"On the Conditional Existence of Foliations by CMC and Willmore Type Half-Spheres","authors":"Jan-Henrik Metsch","doi":"10.1142/s0219199723500463","DOIUrl":"https://doi.org/10.1142/s0219199723500463","url":null,"abstract":"We study half-spheres with small radii sitting on the boundary of a smooth bounded domain while meeting it orthogonally. Even though it is known that there exist families of CMC and Willmore type half-spheres near a nondegenerate critical point p of the domains boundaries mean curvature, it is unknown in both cases whether these provide a foliation of any deleted neighborhood of p. We prove that this is not guaranteed and establish a criterion in terms of the boundaries geometry that ensures or prevents the respective surfaces from providing such a foliation. This perhaps surprising phenomenon of conditional foliations is absent in the closely related Riemannian setting, where a foliation is guaranteed. We show how this unconditional foliation arises from symmetry considerations and how these fail to apply to the 'domain-setting'.","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135854922","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}
Pub Date : 2023-10-13DOI: 10.1142/s0219199723500451
Carmelo A. Finocchiaro, Sophie Frisch, Daniel Windisch
In this work we present descriptions of prime ideals and in particular of maximal ideals in products $R = prod D_lambda$ of families $(D_lambda)_{lambda in Lambda}$ of commutative rings. We show that every maximal ideal is induced by an ultrafilter on the Boolean algebra $prod mathcal{P}(max(D_lambda))$. If every $D_lambda$ is in a certain class of rings including finite character domains and one-dimensional domains, then this leads to a characterization of the maximal ideals of $R$. If every $D_lambda$ is a Prufer domain, we depict all prime ideals of $R$. Moreover, we give an example of a (optionally non-local or local) Prufer domain such that every non-zero prime ideal is of infinite height.
本文给出了交换环族$(D_lambda)_{lambda in Lambda}$积$R = prod D_lambda$中的素理想，特别是极大理想的描述。我们证明了在布尔代数$prod mathcal{P}(max(D_lambda))$上每一个极大理想都是由一个超滤波器诱导出来的。如果每个$D_lambda$都在包含有限特征域和一维域的某一类环中，那么这将导致$R$的最大理想的表征。如果每个$D_lambda$都是一个普鲁特域，我们描述了$R$的所有素数理想。此外，我们给出了一个(可选的非局部或局部)普鲁弗域的例子，使得每个非零素数理想都是无限高的。
{"title":"Prime ideals in infinite products of commutative rings","authors":"Carmelo A. Finocchiaro, Sophie Frisch, Daniel Windisch","doi":"10.1142/s0219199723500451","DOIUrl":"https://doi.org/10.1142/s0219199723500451","url":null,"abstract":"In this work we present descriptions of prime ideals and in particular of maximal ideals in products $R = prod D_lambda$ of families $(D_lambda)_{lambda in Lambda}$ of commutative rings. We show that every maximal ideal is induced by an ultrafilter on the Boolean algebra $prod mathcal{P}(max(D_lambda))$. If every $D_lambda$ is in a certain class of rings including finite character domains and one-dimensional domains, then this leads to a characterization of the maximal ideals of $R$. If every $D_lambda$ is a Prufer domain, we depict all prime ideals of $R$. Moreover, we give an example of a (optionally non-local or local) Prufer domain such that every non-zero prime ideal is of infinite height.","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135805168","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}
Pub Date : 2023-10-13DOI: 10.1142/s0219199723500475
Yang Liu, Xin Zhong
We study an initial-boundary value problem of three-dimensional (3D) compressible isentropic magneto-micropolar fluid equations with Coulomb force and slip boundary conditions in a bounded simply connected domain, whose boundary has a finite number of two-dimensional connected components. We derive the global existence and uniqueness of classical solutions provided that the initial total energy is suitably small. Our result generalizes the Cauchy problems of compressible Navier-Stokes equations with Coulomb force (J. Differential Equations 269: 8468--8508, 2020) and compressible MHD equations (SIAM J. Math. Anal. 45: 1356--1387, 2013) to the case of bounded domains although tackling many surface integrals caused by the slip boundary condition are complex. The main ingredient of this paper is to overcome the strong nonlinearity caused by Coulomb force, magnetic field, and rotation effect of micro-particles by applying piecewise-estimate method and delicate analysis based on the effective viscous fluxes involving velocity and micro-rotational velocity.
{"title":"Global classical solution for three-dimensional compressible isentropic magneto-micropolar fluid equations with Coulomb force and slip boundary conditions in bounded domains","authors":"Yang Liu, Xin Zhong","doi":"10.1142/s0219199723500475","DOIUrl":"https://doi.org/10.1142/s0219199723500475","url":null,"abstract":"We study an initial-boundary value problem of three-dimensional (3D) compressible isentropic magneto-micropolar fluid equations with Coulomb force and slip boundary conditions in a bounded simply connected domain, whose boundary has a finite number of two-dimensional connected components. We derive the global existence and uniqueness of classical solutions provided that the initial total energy is suitably small. Our result generalizes the Cauchy problems of compressible Navier-Stokes equations with Coulomb force (J. Differential Equations 269: 8468--8508, 2020) and compressible MHD equations (SIAM J. Math. Anal. 45: 1356--1387, 2013) to the case of bounded domains although tackling many surface integrals caused by the slip boundary condition are complex. The main ingredient of this paper is to overcome the strong nonlinearity caused by Coulomb force, magnetic field, and rotation effect of micro-particles by applying piecewise-estimate method and delicate analysis based on the effective viscous fluxes involving velocity and micro-rotational velocity.","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135853578","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}
Pub Date : 2023-10-13DOI: 10.1142/s0219199723500505
Guilai Liu, Chengming Bai
The approach for Poisson bialgebras characterized by Manin triples with respect to the invariant bilinear forms on both the commutative associative algebras and the Lie algebras is not available for giving a bialgebra theory for transposed Poisson algebras. Alternatively, we consider Manin triples with respect to the commutative 2-cocycles on the Lie algebras instead. Explicitly, we first introduce the notion of anti-pre-Lie bialgebras as the equivalent structure of Manin triples of Lie algebras with respect to the commutative 2-cocycles. Then we introduce the notion of anti-pre-Lie Poisson bialgebras, characterized by Manin triples of transposed Poisson algebras with respect to the bilinear forms which are invariant on the commutative associative algebras and commutative 2-cocycles on the Lie algebras, giving a bialgebra theory for transposed Poisson algebras. Finally the coboundary cases and the related structures such as analogues of the classical Yang-Baxter equation and $mathcal O$-operators are studied.
{"title":"A bialgebra theory for transposed Poisson algebras via anti-pre-Lie bialgebras and anti-pre-Lie-Poisson bialgebras","authors":"Guilai Liu, Chengming Bai","doi":"10.1142/s0219199723500505","DOIUrl":"https://doi.org/10.1142/s0219199723500505","url":null,"abstract":"The approach for Poisson bialgebras characterized by Manin triples with respect to the invariant bilinear forms on both the commutative associative algebras and the Lie algebras is not available for giving a bialgebra theory for transposed Poisson algebras. Alternatively, we consider Manin triples with respect to the commutative 2-cocycles on the Lie algebras instead. Explicitly, we first introduce the notion of anti-pre-Lie bialgebras as the equivalent structure of Manin triples of Lie algebras with respect to the commutative 2-cocycles. Then we introduce the notion of anti-pre-Lie Poisson bialgebras, characterized by Manin triples of transposed Poisson algebras with respect to the bilinear forms which are invariant on the commutative associative algebras and commutative 2-cocycles on the Lie algebras, giving a bialgebra theory for transposed Poisson algebras. Finally the coboundary cases and the related structures such as analogues of the classical Yang-Baxter equation and $mathcal O$-operators are studied.","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135853272","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}
Pub Date : 2023-09-01DOI: 10.1142/s0219199723990018
Communications in Contemporary MathematicsVol. 25, No. 10, 2399001 (2023) No AccessAuthor index Volume 25 (2023)https://doi.org/10.1142/S0219199723990018Cited by:0 Previous AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail Remember to check out the Most Cited Articles! Be inspired by these NEW Mathematics books for inspirations & latest information in your research area! FiguresReferencesRelatedDetails Recommended Vol. 25, No. 10 Metrics History PDF download
当代数学通讯卷。25，第10号，2399001(2023)没有访问作者索引卷25 (2023)https://doi.org/10.1142/S0219199723990018Cited by:0 Previous AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack citations推荐到图书馆分享分享在facebook上推特链接在redditemail记得检查最多被引用的文章!受到这些新的数学书籍的启发，在您的研究领域获得灵感和最新信息!FiguresReferencesRelatedDetails推荐Vol. 25, No. 10 Metrics History PDF下载
{"title":"Author index Volume 25 (2023)","authors":"","doi":"10.1142/s0219199723990018","DOIUrl":"https://doi.org/10.1142/s0219199723990018","url":null,"abstract":"Communications in Contemporary MathematicsVol. 25, No. 10, 2399001 (2023) No AccessAuthor index Volume 25 (2023)https://doi.org/10.1142/S0219199723990018Cited by:0 Previous AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail Remember to check out the Most Cited Articles! Be inspired by these NEW Mathematics books for inspirations & latest information in your research area! FiguresReferencesRelatedDetails Recommended Vol. 25, No. 10 Metrics History PDF download","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135389411","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}
Pub Date : 2023-08-11DOI: 10.1142/s0219199723500402
J. Hedicke
{"title":"A causal characterisation of Spell+(2n)","authors":"J. Hedicke","doi":"10.1142/s0219199723500402","DOIUrl":"https://doi.org/10.1142/s0219199723500402","url":null,"abstract":"","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44840143","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}
Pub Date : 2023-06-09DOI: 10.1142/s021919972350030x
Luccas Campos, Jason Murphy, T. Hoose
{"title":"Averaging for the 2d dispersion-managed NLS","authors":"Luccas Campos, Jason Murphy, T. Hoose","doi":"10.1142/s021919972350030x","DOIUrl":"https://doi.org/10.1142/s021919972350030x","url":null,"abstract":"","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43284954","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}
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