Mathematical Physics, Analysis and Geometry最新文献_第9页

Kasteleyn Theorem, Geometric Signatures and KP-II Divisors on Planar Bipartite Networks in the Disk 盘上平面二部网络的Kasteleyn定理、几何特征和KP-II除数

IF 1 3区数学

Mathematical Physics, Analysis and Geometry Pub Date : 2021-10-13 DOI: 10.1007/s11040-021-09405-2

Simonetta Abenda

{"title":"Kasteleyn Theorem, Geometric Signatures and KP-II Divisors on Planar Bipartite Networks in the Disk","authors":"Simonetta Abenda","doi":"10.1007/s11040-021-09405-2","DOIUrl":"10.1007/s11040-021-09405-2","url":null,"abstract":"<div>Maximal minors of Kasteleyn sign matrices on planar bipartite graphs in the disk count dimer configurations with prescribed boundary conditions, and the weighted version of such matrices provides a natural parametrization of the totally non–negative part of real Grassmannians (Postnikov et al. J. Algebr. Combin. 30(2), 173–191, 2009; Lam J. Lond. Math. Soc. (2) 92(3), 633–656, 2015; Lam 2016; Speyer 2016; Affolter et al. 2019). In this paper we provide a geometric interpretation of such variant of Kasteleyn theorem: a signature is Kasteleyn if and only if it is geometric in the sense of Abenda and Grinevich (2019). We apply this geometric characterization to explicitly solve the associated system of relations and provide a new proof that the parametrization of positroid cells induced by Kasteleyn weighted matrices coincides with that of Postnikov boundary measurement map. Finally we use Kasteleyn system of relations to associate algebraic geometric data to KP multi-soliton solutions. Indeed the KP wave function solves such system of relations at the nodes of the spectral curve if the dual graph of the latter represents the soliton data. Therefore the construction of the divisor is automatically invariant, and finally it coincides with that in Abenda and Grinevich (Sel. Math. New Ser. 25(3), 43, 2019; Abenda and Grinevich 2020) for the present class of graphs.</div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-021-09405-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4556725","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}

引用次数: 6

Sums of Two-Parameter Deformations of Multiple Polylogarithms 多个多对数的双参数变形和

IF 1 3区数学

Mathematical Physics, Analysis and Geometry Pub Date : 2021-10-08 DOI: 10.1007/s11040-021-09407-0

Masaki Kato

引用次数: 1

From Auto-Bäcklund Transformations to Auto-Bäcklund Transformations, and Torqued ABS Equations 从Auto-Bäcklund变换到Auto-Bäcklund变换，以及扭力ABS方程

IF 1 3区数学

Mathematical Physics, Analysis and Geometry Pub Date : 2021-09-23 DOI: 10.1007/s11040-021-09406-1

Dan-da Zhang, Da-jun Zhang, Peter H. van der Kamp

引用次数: 4

Solitons for the Modified Camassa-Holm Equation and their Interactions Via Dressing Method 修正Camassa-Holm方程的孤子及其通过修饰法的相互作用

IF 1 3区数学

Mathematical Physics, Analysis and Geometry Pub Date : 2021-09-21 DOI: 10.1007/s11040-021-09395-1

Hui Mao, Yonghui Kuang

引用次数: 2

New Condition on Uniqueness of Gibbs Measure for Models with Uncountable Set of Spin Values on a Cayley Tree Cayley树上不可数自旋值集模型Gibbs测度唯一性的新条件

IF 1 3区数学

Mathematical Physics, Analysis and Geometry Pub Date : 2021-09-20 DOI: 10.1007/s11040-021-09404-3

F. H. Haydarov

引用次数: 1

Density of States and Lifshitz Tails for Discrete 1D Random Dirac Operators 离散1D随机Dirac算子的态密度和Lifshitz尾

IF 1 3区数学

Mathematical Physics, Analysis and Geometry Pub Date : 2021-09-14 DOI: 10.1007/s11040-021-09403-4

Roberto A. Prado, César R. de Oliveira, Edmundo C. de Oliveira

引用次数: 4

Solution of the System of Two Coupled First-Order ODEs with Second-Degree Polynomial Right-Hand Sides 右手边为二次多项式的两个耦合一阶ode系统的解

IF 1 3区数学

Mathematical Physics, Analysis and Geometry Pub Date : 2021-08-17 DOI: 10.1007/s11040-021-09400-7

Francesco Calogero, Farrin Payandeh

{"title":"Solution of the System of Two Coupled First-Order ODEs with Second-Degree Polynomial Right-Hand Sides","authors":"Francesco Calogero, Farrin Payandeh","doi":"10.1007/s11040-021-09400-7","DOIUrl":"10.1007/s11040-021-09400-7","url":null,"abstract":"<div>The explicit solution (x_{n}left (tright ) ,) n = 1,2, of the initial-values problem is exhibited of a subclass of the autonomous system of 2 coupled first-order ODEs with second-degree polynomial right-hand sides, hence featuring 12 a priori arbitrary (time-independent) coefficients: \u0000<div><div>$$ dot{x}_{n}=c_{n1}left( x_{1}right)^{2}+c_{n2}x_{1}x_{2}+c_{n3}left( x_{2}right)^{2}+c_{n4}x_{1}+c_{n5}x_{2}+c_{n6}~,~~~n=1,2~. $$</div></div> The solution is explicitly provided if the 12 coefficients cnj (n = 1,2; j = 1,2,3,4,5,6) are expressed by explicitly provided formulas in terms of 10 a priori arbitrary parameters; the inverse problem to express these 10 parameters in terms of the 12 coefficients cnj is also explicitly solved, but it is found to imply—as it were, a posteriori—that the 12 coefficients cnj must then satisfy 4 algebraic constraints, which are explicitly exhibited. Special subcases are also identified the general solutions of which are completely periodic with a period independent of the initial data (“isochrony”), or are characterized by additional restrictions on the coefficients cnj which identify particularly interesting models.</div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s11040-021-09400-7","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4668589","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}

引用次数: 3

Fundamental solutions and Hadamard states for a scalar field with arbitrary boundary conditions on an asymptotically AdS spacetimes 渐近ad时空上具有任意边界条件的标量场的基本解和Hadamard态

IF 1 3区数学

Mathematical Physics, Analysis and Geometry Pub Date : 2021-08-12 DOI: 10.1007/s11040-021-09402-5

Claudio Dappiaggi, Alessio Marta

{"title":"Fundamental solutions and Hadamard states for a scalar field with arbitrary boundary conditions on an asymptotically AdS spacetimes","authors":"Claudio Dappiaggi, Alessio Marta","doi":"10.1007/s11040-021-09402-5","DOIUrl":"10.1007/s11040-021-09402-5","url":null,"abstract":"<div>We consider the Klein-Gordon operator on an n-dimensional asymptotically anti-de Sitter spacetime (M,g) together with arbitrary boundary conditions encoded by a self-adjoint pseudodifferential operator on ∂M of order up to 2. Using techniques from b-calculus and a propagation of singularities theorem, we prove that there exist advanced and retarded fundamental solutions, characterizing in addition their structural and microlocal properties. We apply this result to the problem of constructing Hadamard two-point distributions. These are bi-distributions which are weak bi-solutions of the underlying equations of motion with a prescribed form of their wavefront set and whose anti-symmetric part is proportional to the difference between the advanced and the retarded fundamental solutions. In particular, under a suitable restriction of the class of admissible boundary conditions and setting to zero the mass, we prove their existence extending to the case under scrutiny a deformation argument which is typically used on globally hyperbolic spacetimes with empty boundary.</div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s11040-021-09402-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4484318","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}

引用次数: 9

Bilinear Equation and Additional Symmetries for an Extension of the Kadomtsev–Petviashvili Hierarchy Kadomtsev-Petviashvili层次扩展的双线性方程和附加对称性

IF 1 3区数学

Mathematical Physics, Analysis and Geometry Pub Date : 2021-08-06 DOI: 10.1007/s11040-021-09401-6

Jiaping Lu, Chao-Zhong Wu

引用次数: 7

Kahan Discretizations of Skew-Symmetric Lotka-Volterra Systems and Poisson Maps 斜对称Lotka-Volterra系统和泊松映射的Kahan离散化

IF 1 3区数学

Mathematical Physics, Analysis and Geometry Pub Date : 2021-07-30 DOI: 10.1007/s11040-021-09399-x

C. A. Evripidou, P. Kassotakis, P. Vanhaecke

引用次数: 1