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ON SETS OF ZEROES OF clifford algebra-VALUED POLYNOMIALS

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Acta Mathematica Scientia 2010年第3期30卷 1004-1012页

作者：杨燕钱涛 School of Mathematics and Computational Science Sun Yat-Sen University Department of Mathematics Faculty of Science and Technology University of Macao

In this note, we study zeroes of clifford algebra-valued polynomials. We prove that if such a polynomial has only real coefficients, then it has two types of zeroes： the real isolated zeroes and the spherical conjugate ones. The total number of zeroes does not exceed the degree of the polynomial. We also present a technique for computing the zeroes.

关键词： clifford algebra zeroes of polynomials

Coverage analysis for sensor networks based on clifford algebra

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Science in China(Series F) 2008年第5期51卷 460-475页

作者： XIE WeiXin CAO WenMing MENG Shan ATR Key Laboratory of Defense Technology Shenzhen University Shenzhen 518060 China

The coverage performance is the foundation of information acquisition in distributed sensor networks. The previously proposed coverage work was mostly based on unit disk coverage model or ball coverage model in 2D or 3D space, respectively. However, most methods cannot give a homogeneous coverage model for targets with hybrid types. This paper presents a coverage analysis approach for sensor networks based on clifford algebra and establishes a homogeneous coverage model for sensor networks with hybrid types of targets. The effectiveness of the approach is demonstrated with examples.

关键词： sensor network clifford algebra coverage analysis rotation operator distance measure

A Representation of sl(2;C) on clifford algebra of Even Dimension

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Wuhan University Journal of Natural Sciences 2011年第6期16卷 461-464页

作者： HE Fuli DU Jinyuan WANG Ying School of Mathematics Science and Computing Technology Central South University Changsha 410083 Hunan China School of Mathematics and Statistics Wuhan UniversityWuhan 430072 Hubei China School of Statistics and Mathematics Zhongnan Universityof Economics and Law Wuhan 430073 Hubei China

Under the foundation of Hermitean clifford setting, we define the fundamental operators for complex clifford algebra valued fimctions, obtain some properties of these operators, and discuss a representation of sl（2;... 详细信息

关键词： clifford algebra Lie algebra representation

Rapid Satellite Selection Algorithm Based On clifford algebra

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Rapid Satellite Selection Algorithm Based On Clifford Algebr...

GAUSS-MEAN VALUE FORMULA FOR TRIHARMONIC FUNCTIONS AND ITS APPLICATIONS IN clifford ANALYSIS

第十三届中国卫星导航年会

作者： Shuaikang Lv Kezhao Li Ning Wang Yingxiang Jiao School of Surveying and Land Information Engineering Henan Polytechnic University

GNSS Multi-system provide more visible satellites, however, the amount of computation will increase exponentially and the realtime requirement of navigation solution will be affected when all visible satellites are used for computing the three-dimensional position. Reasonable satellite selection algorithm can meet the accuracy of navigation, as well as the efficiency of navigation. Based on this, according to the characteristics and shortcomings of the elevation angle satellite selection algorithm, combined with the representation advantages of clifford algebra, a rapid satellite selection algorithm based on clifford algebra is proposed here. The specific idea of the algorithm is as follows: taking the station center as the vertex, combining with the regional division of high, medium, and low angle of the elevation angle satellite selection algorithm, an umbrella matching benchmark model for low angle area to select satellites is constructed based on clifford algebra;the coordinates of the visible satellites about local Cartesian coordinates coordinate system are calculated, and the multi vector set of visible satellites is constructed based on clifford algebra theory;the matching threshold angle is calculated according to the designed total number of selected satellites and the number of zenith satellites first. Based on C1 ifford algebra theory, multiple vector sets of visible satellites are constructed. According to the preset total number of selected satellites and the number of top satellites, the matching threshold angle is calculated. Based on the vector angle operation of clifford algebra, the multiple vector sets visible satellites and the umbrella model are matched and selected satellites. When the total number of the low elevation angle area and the high elevation area visible satellites is smaller than the designed total number, the visible satellites of the medium elevation angle area will be added, until the total number of the visible satellites reaches the number of the designed total selected sat

关键词： clifford algebra Global navigation satellite system GNSS Satellite selection Geometric dilution precision GDOP

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Acta Mathematica Scientia 2013年第5期33卷 1419-1430页

作者：谷龙飞张忠祥 School of Mathematics and Statistics Wuhan University

In this paper, the integral representation for some polyharmonic functions with values in a universal clifford algebra Cl（Vn,n） is studied and Gauss-mean value formula for triharmonic functions with values in a clifford algebra Cl（Vn,n） are proved by using Stokes formula and higher order Cauchy-Pompeiu formula. As application some results about growth condition at infinity are obtained.

关键词： triharmonic function clifford algebra Gauss-mean value forrrmla

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Acta Mathematica Sinica,English Series 2006年第1期22卷 289-300页

作者： Yong Ge TIAN School of Economics Shanghai University of Finance and Economics 777 Guoding Road Shanghai 200433 P. R. China

For any element a in a generalized 2^n-dimensional clifford algebra Lln （F） over an arbitrary field F of characteristic not equal to two, it is shown that there exits a universal invertible matrix Pn over Lln（F） such that Pn^-1DnPn= φ（α）∈F^2n×2n, where φ（a） is a matrix representation of α over and Dα is a diagonal matrix consisting of a or its conjugate.

关键词： algebraic isomorphism Quaternionic algebra clifford algebra Matrix representation Universal similarity factorization equality

BOUNDARY BEHAVIOR OF CAUCHY-TYPE INTEGRALS IN clifford ANALYSIS

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Acta Mathematica Scientia 2009年第1期29卷 210-224页

作者：杜金元许娜张忠祥 Department of Mathematics Wuhan University

In this article,the authors discussed the boundary behavior for the Cauchy- type integrals with values in a clifford algebra,obtained some Sochocki–Plemelj formulae and Privalov–Muskhelishvili theorems for the Cauch... 详细信息

关键词： clifford algebra Cauchy-type integral Sochocki–Plemelj formula Privalov– Muskhelishvili theorem

A Laurent Expansion and Residue Theorems of k-Regular Functions in clifford Analysis

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Wuhan University Journal of Natural Sciences 2009年第2期14卷 97-102页

作者： KU Min DU Jinyuan School of Mathematics and Statistics Wuhan UniversityWuhan 430072 Hubei China

In this context, we mainly study the behavior in the neighborhood of finite singular points for k-regular functions in R1^n with values in R0、n. We get a Laurent expansion of them in an open set, prove its uniqueness, give the definitions of k-poles, isolated and essential singular points and removable singularity, discuss some properties, and further obtain the residue theorems.

关键词： clifford algebra k-regular functions Laurent expansion residue theorems singularity

Dirac Operators on Quadratic Lie Superalgebras

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Acta Mathematica Sinica,English Series 2021年第8期37卷 1229-1253页

作者： Yi Fang KANG Zhi Qi CHEN Institute of Mathematics and Physics Central South University of Forestry and TechnologyChangsha 410004P.R.China School of Mathematical Sciences and LPMC Nankai UniversityTianjin 300071P.R.China

Assume thatτis a finite dimensional complex Lie superalgebra with a non-degenerate super-symmetric invariant bilinear form,p is a finite dimensional complex super vector space with a nondegenerate super-symmetric bilinear form,and v:τ→osp(p)is a homomorphism of Lie superalgebras.In this paper,we give a necessary and sufficient condition forτ■p to be a quadratic Lie superalgebra.Then,we define the cubic Dirac operator D(g,τ)on g and give a formula of(D(g,τ))^(2).Finally,we get the Vogan’s conjecture for quadratic Lie superalgebras by D(g,τ).

关键词： Quadratic Lie superalgebra exterior algebra clifford algebra Dirac operator