Pub Date : 2023-03-30DOI: 10.7546/jgsp-65-2023-67-91
C. Mladenova, I. Mladenov
Despite the longstanding interest in the shapes of the eggs the available parametric descriptions in the modern literature are given only via purely empirical formulas without any clear relationships with their measurable parameters. Here we present geometrical models of the eggs based on Perseus spirics and Cassinian ovals which were known since the ancient time but their analytical parameterization was also absent in the meantime. Such ones have been found recently and the present work is based on the idea to use spirics or Cassinians as geometrical models of the eggs shapes. New explicit formulas for the volumes, surface areas and the curvatures of the avian eggs have been derived from the first principles and these have been compared with the available experimental data.
{"title":"Geometry of the Ovoids: Avian Eggs and Similar Asymmetric Forms","authors":"C. Mladenova, I. Mladenov","doi":"10.7546/jgsp-65-2023-67-91","DOIUrl":"https://doi.org/10.7546/jgsp-65-2023-67-91","url":null,"abstract":"Despite the longstanding interest in the shapes of the eggs the available parametric descriptions in the modern literature are given only via purely empirical formulas without any clear relationships with their measurable parameters. Here we present geometrical models of the eggs based on Perseus spirics and Cassinian ovals which were known since the ancient time but their analytical parameterization was also absent in the meantime. Such ones have been found recently and the present work is based on the idea to use spirics or Cassinians as geometrical models of the eggs shapes. New explicit formulas for the volumes, surface areas and the curvatures of the avian eggs have been derived from the first principles and these have been compared with the available experimental data.","PeriodicalId":43078,"journal":{"name":"Journal of Geometry and Symmetry in Physics","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49660503","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 : 2023-03-30DOI: 10.7546/jgsp-65-2023-41-65
V. Le, Tu T. C. Nguyen, T. Nguyen
We consider connected and simply connected seven-dimensional Lie groups whose Lie algebras have nilradical $g_{5,2}$ of Dixmier. First, we give geometric descriptions of the maximal-dimensional orbits in the coadjoint representation of all considered Lie groups. Next, we prove that, for each considered group, the family of the generic coadjoint orbits forms a measurable foliation in the sense of Connes. Finally, the topological classification of all these foliations is also provided.
{"title":"Measurable Foliations Associated to the Coadjoint Representation of a Class of Seven-Dimensional Solvable Lie Groups","authors":"V. Le, Tu T. C. Nguyen, T. Nguyen","doi":"10.7546/jgsp-65-2023-41-65","DOIUrl":"https://doi.org/10.7546/jgsp-65-2023-41-65","url":null,"abstract":"We consider connected and simply connected seven-dimensional Lie groups whose Lie algebras have nilradical $g_{5,2}$ of Dixmier. First, we give geometric descriptions of the maximal-dimensional orbits in the coadjoint representation of all considered Lie groups. Next, we prove that, for each considered group, the family of the generic coadjoint orbits forms a measurable foliation in the sense of Connes. Finally, the topological classification of all these foliations is also provided.","PeriodicalId":43078,"journal":{"name":"Journal of Geometry and Symmetry in Physics","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41829177","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 : 2023-03-30DOI: 10.7546/jgsp-65-2023-93-108
S. Nikolov, V. Vassilev
Nonlinear dynamical systems can be studied in many different directions: i)~finding integrable cases and their analytical solutions, ii)~investigating the algebraic nature of the integrability, iii)~topological analysis of integrable systems, and so on. The aim of the present paper is to find integrable cases of a dynamical system describing the rider and the swing pumped (from the seated position) as a compound pendulum. As a result of our analytical calculations, we can conclude that this system has two integrable cases when: 1)~the dumbbell lengths and point-masses meet a special condition; 2)~the gravitational force is neglected.
{"title":"Integrability in a Nonlinear Model of Swing Oscillatory Motion","authors":"S. Nikolov, V. Vassilev","doi":"10.7546/jgsp-65-2023-93-108","DOIUrl":"https://doi.org/10.7546/jgsp-65-2023-93-108","url":null,"abstract":"Nonlinear dynamical systems can be studied in many different directions: i)~finding integrable cases and their analytical solutions, ii)~investigating the algebraic nature of the integrability, iii)~topological analysis of integrable systems, and so on. The aim of the present paper is to find integrable cases of a dynamical system describing the rider and the swing pumped (from the seated position) as a compound pendulum. As a result of our analytical calculations, we can conclude that this system has two integrable cases when: 1)~the dumbbell lengths and point-masses meet a special condition; 2)~the gravitational force is neglected.","PeriodicalId":43078,"journal":{"name":"Journal of Geometry and Symmetry in Physics","volume":"27 9","pages":""},"PeriodicalIF":0.4,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41270047","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 : 2023-01-01DOI: 10.7546/jgsp-66-2023-47-58
L. Stepien
{"title":"Some Exact Solutions of (ABC) and Martínez Alonso-Shabat Equations","authors":"L. Stepien","doi":"10.7546/jgsp-66-2023-47-58","DOIUrl":"https://doi.org/10.7546/jgsp-66-2023-47-58","url":null,"abstract":"","PeriodicalId":43078,"journal":{"name":"Journal of Geometry and Symmetry in Physics","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71197993","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 : 2023-01-01DOI: 10.7546/jgsp-66-2023-1-34
Ying-Qiu Gu
{"title":"Spinor Equation and Operator Algebra","authors":"Ying-Qiu Gu","doi":"10.7546/jgsp-66-2023-1-34","DOIUrl":"https://doi.org/10.7546/jgsp-66-2023-1-34","url":null,"abstract":"","PeriodicalId":43078,"journal":{"name":"Journal of Geometry and Symmetry in Physics","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71197761","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 : 2023-01-01DOI: 10.7546/jgsp-66-2023-35-45
C. Mladenova, I. Mladenov
{"title":"Yet Another Mathematical Model of Eggs: Two-Parametric Brandt's Shapes","authors":"C. Mladenova, I. Mladenov","doi":"10.7546/jgsp-66-2023-35-45","DOIUrl":"https://doi.org/10.7546/jgsp-66-2023-35-45","url":null,"abstract":"","PeriodicalId":43078,"journal":{"name":"Journal of Geometry and Symmetry in Physics","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71198344","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 : 2022-12-30DOI: 10.7546/jgsp-66-2023-59-70
T. Wada
The gradient-flow equations with respect to the potential functions in information geometry are reconsidered from the perspective of the Weyl integrable geometry. The pre-geodesic equations associated with the gradient-flow equations are regarded as the general pre-geodesic equations in the Weyl integrable geometry.
{"title":"Weyl Geometric Approach to the Gradient-Flow Equations in Information Geometry","authors":"T. Wada","doi":"10.7546/jgsp-66-2023-59-70","DOIUrl":"https://doi.org/10.7546/jgsp-66-2023-59-70","url":null,"abstract":"The gradient-flow equations with respect to the potential functions in information geometry are reconsidered from the perspective of the Weyl integrable geometry. The pre-geodesic equations associated with the gradient-flow equations are regarded as the general pre-geodesic equations in the Weyl integrable geometry.","PeriodicalId":43078,"journal":{"name":"Journal of Geometry and Symmetry in Physics","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43524501","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 : 2022-01-01DOI: 10.7546/jgsp-64-2022-29-37
Clementina D. Mladenova, Ivaïlo M. Mladenov
Dynamical orbits of the harmonic oscillator potential in the plane are ellipses which depend on a real parameter. Some time ago in this journal it has been proven by purely geometrical methods that the locus of the focuses of these ellipses are Cassinian ovals. Here we present several explicit analytic parameterizations of these remarkable curves. Nominally, their forms depend on the magnitude of the initial distance from the center of attraction and the magnitude of the initial velocity. We have found a few parameterizations in which the roles of the size and shapes can be clearly distinguished.
{"title":"Explicit Solution of the Focus Locus Problem for the Harmonic Oscillator Orbits in the Plane","authors":"Clementina D. Mladenova, Ivaïlo M. Mladenov","doi":"10.7546/jgsp-64-2022-29-37","DOIUrl":"https://doi.org/10.7546/jgsp-64-2022-29-37","url":null,"abstract":"Dynamical orbits of the harmonic oscillator potential in the plane are ellipses which depend on a real parameter. Some time ago in this journal it has been proven by purely geometrical methods that the locus of the focuses of these ellipses are Cassinian ovals. Here we present several explicit analytic parameterizations of these remarkable curves. Nominally, their forms depend on the magnitude of the initial distance from the center of attraction and the magnitude of the initial velocity. We have found a few parameterizations in which the roles of the size and shapes can be clearly distinguished.","PeriodicalId":43078,"journal":{"name":"Journal of Geometry and Symmetry in Physics","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71197440","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 : 2022-01-01DOI: 10.7546/jgsp-64-2022-1-8
Rukmini Dey
{"title":"Quantization of the Seiberg-Witten Moduli Space on Product of a Riemann Surface","authors":"Rukmini Dey","doi":"10.7546/jgsp-64-2022-1-8","DOIUrl":"https://doi.org/10.7546/jgsp-64-2022-1-8","url":null,"abstract":"","PeriodicalId":43078,"journal":{"name":"Journal of Geometry and Symmetry in Physics","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71197656","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 : 2022-01-01DOI: 10.7546/jgsp-63-2022-21-37
V. Jain, R. Rani, Rakesh Kumar
We study generalized Cauchy-Riemann (GCR)-lightlike submanifolds of indefinite Kaehler manifolds admitting a quarter-symmetric non-metric connection. We derive a condition for a totally umbilical GCR-lightlike submanifold of indefinite Kaehler manifolds admitting a quarter-symmetric non-metric connection to be a totally geodesic submanifold. We study minimal GCR-lightlike submanifolds and obtain characterization theorem for a GCR-lightlike submanifold to be a GCR-lightlike product manifold.
{"title":"On GCR-Lightlike Submanifolds of Indefinite Kaehler Manifolds","authors":"V. Jain, R. Rani, Rakesh Kumar","doi":"10.7546/jgsp-63-2022-21-37","DOIUrl":"https://doi.org/10.7546/jgsp-63-2022-21-37","url":null,"abstract":"We study generalized Cauchy-Riemann (GCR)-lightlike submanifolds of indefinite Kaehler manifolds admitting a quarter-symmetric non-metric connection. We derive a condition for a totally umbilical GCR-lightlike submanifold of indefinite Kaehler manifolds admitting a quarter-symmetric non-metric connection to be a totally geodesic submanifold. We study minimal GCR-lightlike submanifolds and obtain characterization theorem for a GCR-lightlike submanifold to be a GCR-lightlike product manifold.","PeriodicalId":43078,"journal":{"name":"Journal of Geometry and Symmetry in Physics","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71197051","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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