Pub Date : 2019-01-01DOI: 10.7546/giq-giq-20-2019-122-130
A. Dobrogowska, G. Jakimowicz, M. Szajewska, Karolina Wojciechowicz
The main goal of this paper is to present the possibility of application of some well known tools of Poisson geometry to classification of real low dimensional Lie algebras. MSC : 53D17, 37K10
{"title":"Deformation of the Poisson Structure Related to Algebroid Bracket of Differential Forms and Application to Real Low Dimentional Lie Algebras","authors":"A. Dobrogowska, G. Jakimowicz, M. Szajewska, Karolina Wojciechowicz","doi":"10.7546/giq-giq-20-2019-122-130","DOIUrl":"https://doi.org/10.7546/giq-giq-20-2019-122-130","url":null,"abstract":"The main goal of this paper is to present the possibility of application of some well known tools of Poisson geometry to classification of real low dimensional Lie algebras. MSC : 53D17, 37K10","PeriodicalId":53425,"journal":{"name":"Geometry, Integrability and Quantization","volume":"53 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75347252","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-01-01DOI: 10.7546/giq-20-2019-131-160
D. Ghisa
The concept of fundamental domain, as defined by Ahlfors, plays an important role in the study of different classes of analytic functions. For more than a century the Dirichlet functions have been intensely studied by mathematicians working in the field of number theory as well as by those interested in their analytic properties. The fundamental domains pertain to the last field, yet we found a lot of theoretic aspects which can be dealt with by knowing in detail those domains. We gathered together in this survey paper some recent advances in this field. Proofs are provided for some of the theorems, so that the reader can navigate easily through it. MSC : 30C35, 11M26
{"title":"Fundamental Domains of Dirichlet Functions","authors":"D. Ghisa","doi":"10.7546/giq-20-2019-131-160","DOIUrl":"https://doi.org/10.7546/giq-20-2019-131-160","url":null,"abstract":"The concept of fundamental domain, as defined by Ahlfors, plays an important role in the study of different classes of analytic functions. For more than a century the Dirichlet functions have been intensely studied by mathematicians working in the field of number theory as well as by those interested in their analytic properties. The fundamental domains pertain to the last field, yet we found a lot of theoretic aspects which can be dealt with by knowing in detail those domains. We gathered together in this survey paper some recent advances in this field. Proofs are provided for some of the theorems, so that the reader can navigate easily through it. MSC : 30C35, 11M26","PeriodicalId":53425,"journal":{"name":"Geometry, Integrability and Quantization","volume":"16 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80818621","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-01-01DOI: 10.7546/GIQ-20-2019-99-114
R. Campoamor-Stursberg
Some aspects of the simple Lie algebra sl(2,R) realized as a subalgebra of Noether point symmetries of Lagrangian systems and related inverse problems are discussed, specially in connection to Lagrangians of kinetic type and some geometric properties like sectional curvatures. MSC : 70F17, 70H03, 70H33
{"title":"The Lie Algebra sl(2,R) and Noether Point Symmetries of Lagrangian Systems","authors":"R. Campoamor-Stursberg","doi":"10.7546/GIQ-20-2019-99-114","DOIUrl":"https://doi.org/10.7546/GIQ-20-2019-99-114","url":null,"abstract":"Some aspects of the simple Lie algebra sl(2,R) realized as a subalgebra of Noether point symmetries of Lagrangian systems and related inverse problems are discussed, specially in connection to Lagrangians of kinetic type and some geometric properties like sectional curvatures. MSC : 70F17, 70H03, 70H33","PeriodicalId":53425,"journal":{"name":"Geometry, Integrability and Quantization","volume":"59 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80257205","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-01-01DOI: 10.7546/GIQ-20-2019-255-265
N. Turgay, Alev Kelleci, R. Şen, E. O. Canfes
In this paper, first we gave a summary of recent results on biconservative immersions. Then, we obtained a necessary and sufficient condition for the existence of biconservative quasi-minimal immersions into a four dimensional semi-Riemannian space form of index two with non-zero sectional curvatures. We also constructed an explicit example of biconservative quasiminimal surface. MSC : 53D12, 53C40, 53C42
{"title":"On Quasi-Minimal Isometric Immersions into Non-Flat Semi Riemannian Space Forms of Index Two","authors":"N. Turgay, Alev Kelleci, R. Şen, E. O. Canfes","doi":"10.7546/GIQ-20-2019-255-265","DOIUrl":"https://doi.org/10.7546/GIQ-20-2019-255-265","url":null,"abstract":"In this paper, first we gave a summary of recent results on biconservative immersions. Then, we obtained a necessary and sufficient condition for the existence of biconservative quasi-minimal immersions into a four dimensional semi-Riemannian space form of index two with non-zero sectional curvatures. We also constructed an explicit example of biconservative quasiminimal surface. MSC : 53D12, 53C40, 53C42","PeriodicalId":53425,"journal":{"name":"Geometry, Integrability and Quantization","volume":"211 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80711232","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-01-01DOI: 10.7546/GIQ-20-2019-184-207
T. Kanazawa, A. Yoshioka
{"title":"Quasi-Classical Calculation of Eigenvalues by Maslov Quantization Condition","authors":"T. Kanazawa, A. Yoshioka","doi":"10.7546/GIQ-20-2019-184-207","DOIUrl":"https://doi.org/10.7546/GIQ-20-2019-184-207","url":null,"abstract":"","PeriodicalId":53425,"journal":{"name":"Geometry, Integrability and Quantization","volume":"50 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80927354","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-01-01DOI: 10.7546/giq-20-2019-297-310
A. Yanovski
We consider the theory of the hierarchies of nonlinear evolution equations associated with two gauge-equivalent systems we denote by L± and GMV± (GMVsystem). They are obtained from the Generalized Zakharov-Shabat system on sl(3,C) in general position making a Z2 × Z2 reductions of Mikhailov type in canonical and in pole gauge respectively. Using the Recursion Operators approach and expansions over the adjoint solutions we study the symplectic structures of the hierarchies of the nonlinear evolution equations associated with L± and GMV± and calculate the relation between them.
{"title":"Hierarchies of Symplectic Structures for sl(3,C) Zakharov-Shabat Systems in Canonical and Pole Gauge with Z2×Z2 Reduction of Mikhailov Type","authors":"A. Yanovski","doi":"10.7546/giq-20-2019-297-310","DOIUrl":"https://doi.org/10.7546/giq-20-2019-297-310","url":null,"abstract":"We consider the theory of the hierarchies of nonlinear evolution equations associated with two gauge-equivalent systems we denote by L± and GMV± (GMVsystem). They are obtained from the Generalized Zakharov-Shabat system on sl(3,C) in general position making a Z2 × Z2 reductions of Mikhailov type in canonical and in pole gauge respectively. Using the Recursion Operators approach and expansions over the adjoint solutions we study the symplectic structures of the hierarchies of the nonlinear evolution equations associated with L± and GMV± and calculate the relation between them.","PeriodicalId":53425,"journal":{"name":"Geometry, Integrability and Quantization","volume":"44 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79952093","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-01-01DOI: 10.7546/GIQ-20-2019-285-296
T. Valchev, A. Yanovski
In this report we consider a vector generalization of Heisenberg ferromagnet equation. That completely integrable system is related to a spectral problem in pole gauge for the Lie algebra sl(n + 1,C). We construct special solutions over constant background using dressing technique. MSC : 35C05, 35C08, 35G50, 37K15, 37K35
{"title":"Solutions to a Vector Heisenberg Ferromagnet Equation Related to Symmetric Spaces","authors":"T. Valchev, A. Yanovski","doi":"10.7546/GIQ-20-2019-285-296","DOIUrl":"https://doi.org/10.7546/GIQ-20-2019-285-296","url":null,"abstract":"In this report we consider a vector generalization of Heisenberg ferromagnet equation. That completely integrable system is related to a spectral problem in pole gauge for the Lie algebra sl(n + 1,C). We construct special solutions over constant background using dressing technique. MSC : 35C05, 35C08, 35G50, 37K15, 37K35","PeriodicalId":53425,"journal":{"name":"Geometry, Integrability and Quantization","volume":"31 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72441742","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-01-01DOI: 10.7546/giq-20-2019-239-245
M. Petrov, T. Todorov
{"title":"Refinement Strategies for 4D Regular Domains","authors":"M. Petrov, T. Todorov","doi":"10.7546/giq-20-2019-239-245","DOIUrl":"https://doi.org/10.7546/giq-20-2019-239-245","url":null,"abstract":"","PeriodicalId":53425,"journal":{"name":"Geometry, Integrability and Quantization","volume":"25 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84626988","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-01-01DOI: 10.7546/GIQ-20-2019-115-121
V. L. Cartas
In the last decade topnotch experiments (LIGO and GP-B) have putted into evidence the viscoelastic nature of the space time. In the present work we have applied the viscoelastic constitutive equations for a spcetime model, based on the fractional Zener representation, which is the most general way of thinking about materials. Dispersion and dissipation are discussed in the frame of the spacetime, considered as a viscoelastic material
{"title":"The Fractional Zener Model of the Spacetime","authors":"V. L. Cartas","doi":"10.7546/GIQ-20-2019-115-121","DOIUrl":"https://doi.org/10.7546/GIQ-20-2019-115-121","url":null,"abstract":"In the last decade topnotch experiments (LIGO and GP-B) have putted into evidence the viscoelastic nature of the space time. In the present work we have applied the viscoelastic constitutive equations for a spcetime model, based on the fractional Zener representation, which is the most general way of thinking about materials. Dispersion and dissipation are discussed in the frame of the spacetime, considered as a viscoelastic material","PeriodicalId":53425,"journal":{"name":"Geometry, Integrability and Quantization","volume":"21 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91329604","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-01-01DOI: 10.7546/GIQ-20-2019-79-87
Kamel Al-khaled
This paper aims to introduce a comparison of variation iteration method and wavelet basis method for the numerical solution of the Kawahara equation. Test problem is used to compare between the two methods. The comparison shows that variation iteration method is efficient and easy to use. On the other hand, the wavelet method is more stable as time increases. MSC : 35Q53, 65M60, 65R20
{"title":"Wavelet-Based Numerical Scheme Compared with VIM for Solving Kawahara Equation","authors":"Kamel Al-khaled","doi":"10.7546/GIQ-20-2019-79-87","DOIUrl":"https://doi.org/10.7546/GIQ-20-2019-79-87","url":null,"abstract":"This paper aims to introduce a comparison of variation iteration method and wavelet basis method for the numerical solution of the Kawahara equation. Test problem is used to compare between the two methods. The comparison shows that variation iteration method is efficient and easy to use. On the other hand, the wavelet method is more stable as time increases. MSC : 35Q53, 65M60, 65R20","PeriodicalId":53425,"journal":{"name":"Geometry, Integrability and Quantization","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82445443","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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