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Dynamical Coherence and Strain-Deformation Curvature View on Gravity 重力的动力相干性和应变-变形曲率观
Geometry, Integrability and Quantization Pub Date : 2023-01-01 DOI: 10.7546/giq-26-2023-1-25
Stoil Donev
{"title":"Dynamical Coherence and Strain-Deformation Curvature View on Gravity","authors":"Stoil Donev","doi":"10.7546/giq-26-2023-1-25","DOIUrl":"https://doi.org/10.7546/giq-26-2023-1-25","url":null,"abstract":"","PeriodicalId":53425,"journal":{"name":"Geometry, Integrability and Quantization","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135611065","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}
引用次数: 0
Clifford Algebras, Hypercomplex Numbers and Nonlinear Equations in Physics 物理学中的Clifford代数、超复数和非线性方程
Geometry, Integrability and Quantization Pub Date : 2023-01-01 DOI: 10.7546/giq-25-2023-47-72
Ying-Qiu Gu
{"title":"Clifford Algebras, Hypercomplex Numbers and Nonlinear Equations in Physics","authors":"Ying-Qiu Gu","doi":"10.7546/giq-25-2023-47-72","DOIUrl":"https://doi.org/10.7546/giq-25-2023-47-72","url":null,"abstract":"Hypercomplex number systems are vector algebras with the definition of multiplication and division of vectors, satisfying the associativity and distributive law. In this paper, some new types of hypercomplex numbers and their fundamental properties are introduced, the Clifford algebra formalisms of hydrodynamics and gauge field equations are established, and some novel consistent conditions helpful to understand the properties of solutions to nonlinear physical equations are derived. The coordinate transformation and covariant derivatives of hypercomplex numbers are also discussed. The basis elements of the hypercomplex numbers have group-like properties and satisfy a structure equation $A^2=nA$. The hypercomplex number system integrates the advantages of algebra, geometry and analysis, and provides a unified, standard and elegant language and tool for scientific theories and engineering technology, so it is easy to learn and use. The description of mathematical, physical and engineering problems by hypercomplex numbers is of neat formalism, symmetric structure and standard derivation, which is especially suitable for the efficient processing of the higher dimensional complicated systems.","PeriodicalId":53425,"journal":{"name":"Geometry, Integrability and Quantization","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82533792","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}
引用次数: 1
Star Product Deformation of Gamma Function 函数的星积变形
Geometry, Integrability and Quantization Pub Date : 2023-01-01 DOI: 10.7546/giq-26-2023-53-63
Tsukasa Takeuchi, Naoko Yoshimi, Akira Yoshioka
{"title":"Star Product Deformation of Gamma Function","authors":"Tsukasa Takeuchi, Naoko Yoshimi, Akira Yoshioka","doi":"10.7546/giq-26-2023-53-63","DOIUrl":"https://doi.org/10.7546/giq-26-2023-53-63","url":null,"abstract":"","PeriodicalId":53425,"journal":{"name":"Geometry, Integrability and Quantization","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135611073","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}
引用次数: 0
Geometry of the Ovoids: Reptilian Eggs and Similar Symmetric Forms 卵形的几何:爬行动物的卵和类似的对称形式
Geometry, Integrability and Quantization Pub Date : 2023-01-01 DOI: 10.7546/giq-25-2023-95-116
C. Mladenova, I. Mladenov
{"title":"Geometry of the Ovoids: Reptilian Eggs and Similar Symmetric Forms","authors":"C. Mladenova, I. Mladenov","doi":"10.7546/giq-25-2023-95-116","DOIUrl":"https://doi.org/10.7546/giq-25-2023-95-116","url":null,"abstract":"Despite the longstanding interest in the shapes of the eggs since the ancient time till nowadays, the available parametric descriptions in the modern literature are given only via purely empirical formulas without any clear relationships with their measurable physical parameters. Here we present a geometrical model of the eggs based on Perseus spirics which were known as well since the ancient time but their analytical parameterizations were absent in the meantime. Such parameterizations have been found recently and the present work is based on the idea to use the spirics as a geometrical model of the egg's shapes. Explicit formulas for the volume, surface area and the curvatures of the eggs are derived from the first principles and these have been compared with the available empirical formulas and experimental data.","PeriodicalId":53425,"journal":{"name":"Geometry, Integrability and Quantization","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75364861","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}
引用次数: 0
On the Spectrum of the Discrete Bilaplacian with Rank-One Perturbation 具有秩一摄动的离散Bilaplacian的谱
Geometry, Integrability and Quantization Pub Date : 2023-01-01 DOI: 10.7546/giq-26-2023-39-52
Mardon Pardabaev, Firdavs Almuratov
{"title":"On the Spectrum of the Discrete Bilaplacian with Rank-One Perturbation","authors":"Mardon Pardabaev, Firdavs Almuratov","doi":"10.7546/giq-26-2023-39-52","DOIUrl":"https://doi.org/10.7546/giq-26-2023-39-52","url":null,"abstract":"","PeriodicalId":53425,"journal":{"name":"Geometry, Integrability and Quantization","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135611068","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}
引用次数: 0
On the Dynamics of the Solar System III: Perihelion Precession and Eccentricity Variation 太阳系动力学ⅲ:近日点进动和偏心率变化
Geometry, Integrability and Quantization Pub Date : 2023-01-01 DOI: 10.7546/giq-25-2023-1-45
R. G. Calvet
{"title":"On the Dynamics of the Solar System III: Perihelion Precession and Eccentricity Variation","authors":"R. G. Calvet","doi":"10.7546/giq-25-2023-1-45","DOIUrl":"https://doi.org/10.7546/giq-25-2023-1-45","url":null,"abstract":"","PeriodicalId":53425,"journal":{"name":"Geometry, Integrability and Quantization","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83031136","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}
引用次数: 0
Explicit Solutions for Geodetic Problems on the Deformed Sphere as Reference Model for the Geoid 以变形球为参考模型的大地测量问题的显式解
Geometry, Integrability and Quantization Pub Date : 2023-01-01 DOI: 10.7546/giq-25-2023-73-94
V. Kovalchuk, I. Mladenov
{"title":"Explicit Solutions for Geodetic Problems on the Deformed Sphere as Reference Model for the Geoid","authors":"V. Kovalchuk, I. Mladenov","doi":"10.7546/giq-25-2023-73-94","DOIUrl":"https://doi.org/10.7546/giq-25-2023-73-94","url":null,"abstract":"In this article, we consider deformed spheres as a new reference model for the geoid, alternatively to the classical ellipsoidal one. The parametrization of deformed spheres is furnished through the incomplete elliptic integrals. From the other side, the solutions for geodesics on those surfaces are given entirely via elementary analytical functions, contrary to the case of ellipsoids of revolution. We explicitly described algorithms (all necessary computational steps) for the solution of the direct and inverse geodetic problems on the deformed spheres. Finally, we presented a few illustrative numerical solutions of the inverse geodetic problems for two conceptual cases of near and far points. It had turned out that even in the non-optimized case we obtained the good agreement with the predictions of the World Geodetic System 1984's ellipsoidal reference model.","PeriodicalId":53425,"journal":{"name":"Geometry, Integrability and Quantization","volume":"28 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88074630","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}
引用次数: 0
Coupled Fixed Points in Partial Metric Spaces 部分度量空间中的耦合不动点
Geometry, Integrability and Quantization Pub Date : 2023-01-01 DOI: 10.7546/giq-26-2023-27-38
Atanas Ilchev, Diana Nedelcheva-Arnaudova
{"title":"Coupled Fixed Points in Partial Metric Spaces","authors":"Atanas Ilchev, Diana Nedelcheva-Arnaudova","doi":"10.7546/giq-26-2023-27-38","DOIUrl":"https://doi.org/10.7546/giq-26-2023-27-38","url":null,"abstract":"","PeriodicalId":53425,"journal":{"name":"Geometry, Integrability and Quantization","volume":"105 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135611066","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}
引用次数: 1
Octonionic Planes and Real Forms of $G_2$, $F_4$ and $E_6$ $G_2$， $F_4$和$E_6$的八元平面和实形式
Geometry, Integrability and Quantization Pub Date : 2022-03-05 DOI: 10.7546/giq-23-2022-39-57
Daniele Corradetti, A. Marrani, David Chester, Raymond Aschheim
{"title":"Octonionic Planes and Real Forms of $G_2$, $F_4$ and $E_6$","authors":"Daniele Corradetti, A. Marrani, David Chester, Raymond Aschheim","doi":"10.7546/giq-23-2022-39-57","DOIUrl":"https://doi.org/10.7546/giq-23-2022-39-57","url":null,"abstract":"In this work we present a useful way to introduce the octonionic projective and hyperbolic plane $mathbb{O}P^{2}$ through the use of Veronese vectors. Then we focus on their relation with the exceptional Jordan algebra $mathfrak{J}_{3}^{mathbb{O}}$ and show that the Veronese vectors are the rank-one elements of the algebra. We then study groups of motions over the octonionic plane recovering all real forms of $text{G}_{2}$, $text{F}_{4}$ and $text{E}_{6}$ groups and finally give a classification of all octonionic and split-octonionic planes as symmetric spaces.","PeriodicalId":53425,"journal":{"name":"Geometry, Integrability and Quantization","volume":"172 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82939664","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}
引用次数: 7
(Co)Homology Groups and Categorified Eigenvalues (1)同调群与分类特征值
Geometry, Integrability and Quantization Pub Date : 2022-01-01 DOI: 10.7546/giq-23-2022-59-74
Jumpei Gohara, Yuji Hirota, Keisui Ino, Akifumi Sako
{"title":"(Co)Homology Groups and Categorified Eigenvalues","authors":"Jumpei Gohara, Yuji Hirota, Keisui Ino, Akifumi Sako","doi":"10.7546/giq-23-2022-59-74","DOIUrl":"https://doi.org/10.7546/giq-23-2022-59-74","url":null,"abstract":"We discuss the relationship between (co)homology groups and categorical diagonalization. We consider the category of chain complexes in the category of finite-dimensional vector spaces over a fixed field. For a fixed chain complex with zero maps as an object, a chain map from the object to another chain complex is defined, and the chain map introduce a mapping cone. The fixed object is isomorphic to the (co)homology groups of the codomain of the chain map if and only if the chain map is injective to the cokernel of differentials of the codomain chain complex and the mapping cone is homotopy equivalent to zero. On the other hand, it was found that the fixed object can be regarded as a categorified eigenvalue of the chain complex in the context of the categorical diagonalization, recently. It is found that (co)homology groups are constructed as the eigenvalue of a chain complex.","PeriodicalId":53425,"journal":{"name":"Geometry, Integrability and Quantization","volume":"39 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82663727","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}
引用次数: 0
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