Advances in Applied Clifford Algebras最新文献

Hilbert Boundary Value Problems for Monogenic Functions on the Hyperplane 超平面上单基因函数的Hilbert边值问题

IF 1.2 2区数学

Advances in Applied Clifford Algebras Pub Date : 2025-10-03 DOI: 10.1007/s00006-025-01411-9

Pei Dang, Jinyuan Du, Tao Qian

引用次数: 0

Cauchy theorems for solutions to polynomial Dirac equations with (alpha )-weight in superspace 超空间中(alpha ) -权的多项式狄拉克方程解的柯西定理

IF 1.2 2区数学

Advances in Applied Clifford Algebras Pub Date : 2025-09-15 DOI: 10.1007/s00006-025-01408-4

Yonghong Xie, Shuoxing He, Xiaojing Du

引用次数: 0

Transmutation Operator for the Radial Maxwell System in Inhomogeneous Media 非均匀介质中径向Maxwell系统的嬗变算子

IF 1.2 2区数学

Advances in Applied Clifford Algebras Pub Date : 2025-09-14 DOI: 10.1007/s00006-025-01410-w

Doan Cong Dinh

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A Geometric Algebra-Based Machine Learning Method for Typhoon Intensity Forecasting 基于几何代数的台风强度预测机器学习方法

IF 1.2 2区数学

Advances in Applied Clifford Algebras Pub Date : 2025-08-30 DOI: 10.1007/s00006-025-01400-y

Haiyan Chen, Yadi Huang, Dongshuang Li, Wen Luo, Zhaoyuan Yu, Linwang Yuan

{"title":"A Geometric Algebra-Based Machine Learning Method for Typhoon Intensity Forecasting","authors":"Haiyan Chen, Yadi Huang, Dongshuang Li, Wen Luo, Zhaoyuan Yu, Linwang Yuan","doi":"10.1007/s00006-025-01400-y","DOIUrl":"10.1007/s00006-025-01400-y","url":null,"abstract":"<div>Machine learning is well-suited for forecasting typhoon intensity due to its capacity to model complex nonlinear relationships. However, current deep learning methodologies often treat vector field components independently, neglecting the geometric relationships between them. This oversight results in a loss of information and less accurate typhoon intensity forecasts. In contrast, geometric algebra considers multidimensional variables holistically, preserving internal correlations and relevant inductive biases pertinent to wind field data. To address this limitation, this study develops a geometric algebra-based method for typhoon intensity forecasting. Initially, wind field data, encompassing both longitudinal and latitudinal components across various isobaric levels, are represented as multivector inputs. Geometric algebra convolution is subsequently employed to capture the spatial features of typhoon wind speed data. Following this, a geometric algebra-based spatial attention mechanism is introduced to dynamically focus on regions with significant wind speed variations. This is followed by a geometric algebra convolutional fusion, which enhances the representation of typhoon features by integrating data across different stages. Finally, a Wide and Deep framework is utilized to incorporate both two-dimensional and three-dimensional typhoon characteristics, modeling the interrelationships between these variables and typhoon intensity, thereby establishing a forecasting model. A comparative analysis utilizing best track and reanalysis datasets from the North-Western Pacific region (2015–2018) demonstrates that our model not only enhances prediction accuracy but also reduces the number of required parameters. This study offers new insights and advances in the application of geometric algebra for feature extraction and prediction of multidimensional correlated geoscientific data.</div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"35 4","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144918584","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}

引用次数: 0

Determinant, Characteristic Polynomial, and Inverse in Commutative Analogues of Clifford Algebras Clifford代数交换类似物中的行列式、特征多项式和逆

IF 1.2 2区数学

Advances in Applied Clifford Algebras Pub Date : 2025-08-25 DOI: 10.1007/s00006-025-01406-6

Heerak Sharma, Dmitry Shirokov

引用次数: 0

In Memoriam of Yuri M. Grigor’ev: An Overview of his Research 纪念尤里·格里戈尔耶夫：他的研究综述

IF 1.2 2区数学

Advances in Applied Clifford Algebras Pub Date : 2025-08-23 DOI: 10.1007/s00006-025-01404-8

Dmitrii Legatiuk, Heikki Orelma

引用次数: 0

The B–P Formula and Cauchy Integral Formula for Weighted Inframonogenic Functions(dag ) 加权次致函数的B-P公式和Cauchy积分公式(dag )

IF 1.2 2区数学

Advances in Applied Clifford Algebras Pub Date : 2025-08-14 DOI: 10.1007/s00006-025-01405-7

Ying Li, Liping Wang, Xin Jiang, Xiaojia Yang

引用次数: 0

On a Certain Boundary Value Problem in a Plane Excluding Axes 不含轴平面上的边值问题

IF 1.2 2区数学

Advances in Applied Clifford Algebras Pub Date : 2025-07-30 DOI: 10.1007/s00006-025-01396-5

Vladimir Vasilyev, Alexander Vasilyev, Nataliya Agarkova

引用次数: 0

Hyperquaternionic Unitary Symplectic Groups: A Unifying Tool for Physics 超四元元酉辛群：物理学的统一工具

IF 1.2 2区数学

Advances in Applied Clifford Algebras Pub Date : 2025-07-21 DOI: 10.1007/s00006-025-01402-w

Patrick R. Girard, Patrick Clarysse, Romaric Pujol, Philippe Delachartre

{"title":"Hyperquaternionic Unitary Symplectic Groups: A Unifying Tool for Physics","authors":"Patrick R. Girard, Patrick Clarysse, Romaric Pujol, Philippe Delachartre","doi":"10.1007/s00006-025-01402-w","DOIUrl":"10.1007/s00006-025-01402-w","url":null,"abstract":"<div>The mathematical tools of physics, based on group theory, are in permanent evolution. Major covariance groups are the orthogonal, unitary and symplectic groups. These groups are generally expressed in terms of real and complex matrices. Here we shall develop a new representation of the unitary symplectic groups USp(n) in terms of Clifford algebras constituted by tensor products of quaternion algebras called hyperquaternions. Concise expressions of the generators are obtained and a concrete example USp(4) is provided. Isomorphic quaternion matrix representations will also be used in the applications. The first application concerns classical mechanics. The Hamiltonian formalism, Poisson brackets and canonical transforms are related to the unitary symplectic groups. The 1D and 2D harmonic oscillators are examined within that framework. The second application concerns quantum mechanics. The Schrödinger and Heisenberg equations are derived in a new hyperquaternionic unitary symplectic way, the complex imaginary i being replaced by the quaternion k in phase space. The 1D and 2D quantum harmonic oscillators are treated within that formalism. Allowing a representation of both classical and quantum mechanics, it is hoped that the hyperquaternion algebras might deepen our mathematical comprehension of the foundational principles of physics.</div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"35 4","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145167904","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}

引用次数: 0

First Order Differential Calculus on the Jordanian Twisted (star )-Hopf Supersymmetry Algebra jordan扭曲(star ) -Hopf超对称代数的一阶微分

IF 1.2 2区数学

Advances in Applied Clifford Algebras Pub Date : 2025-07-19 DOI: 10.1007/s00006-025-01398-3

H. Fakhri, S. Laheghi

{"title":"First Order Differential Calculus on the Jordanian Twisted (star )-Hopf Supersymmetry Algebra","authors":"H. Fakhri, S. Laheghi","doi":"10.1007/s00006-025-01398-3","DOIUrl":"10.1007/s00006-025-01398-3","url":null,"abstract":"<div>A Jordanian deformation of the (N=2) supersymmetry algebra and its first-order noncommutative differential calculus is obtained from the q-deformed Hopf supersymmetry algebra via a singular limit of a linear transformation. We show that the Jordanian (N=2) supersymmetry algebra carries a Hopf superalgebra structure. It is enhanced to a twisted Hopf star superalgebra by four inequivalent families of (star )-structures. It is demonstrated that these star operations induce four types of (star )-involutions on the differential one-forms and partial derivatives. We introduce an appropriate Jordanian super-Hopf algebra that includes two even and two odd generators equipped with four different types of (star )-structures and its corresponding supergroup on the Hopf (N=2) supersymmetry algebra. It is shown that the noncommutative differential calculus over the Jordanian (N=2) supersymmetry algebra is left-covariant with respect to the Jordanian supergroup. The (star )-structures of the supergroup are (star )-preserving on the supersymmetry algebra only for zero values of their parameters.</div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"35 4","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145166531","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}

引用次数: 0