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Articles 1 - 3 of 3
Full-Text Articles in Applied Mathematics
The Octonions And The Exceptional Lie Algebra G2, Ian M. Anderson
The Octonions And The Exceptional Lie Algebra G2, Ian M. Anderson
Research Vignettes
The octonions O are an 8-dimensional non-commutative, non-associative normed real algebra. The set of all derivations of O form a real Lie algebra. It is remarkable fact, first proved by E. Cartan in 1908, that the the derivation algebra of O is the compact form of the exceptional Lie algebra G2. In this worksheet we shall verify this result of Cartan and also show that the derivation algebra of the split octonions is the split real form of G2.
PDF and Maple worksheets can be downloaded from the links below.
The Geometry Of Homological Triangles, Florentin Smarandache, Ion Patrascu
The Geometry Of Homological Triangles, Florentin Smarandache, Ion Patrascu
Branch Mathematics and Statistics Faculty and Staff Publications
This book is addressed to students, professors and researchers of geometry, who will find herein many interesting and original results. The originality of the book The Geometry of Homological Triangles consists in using the homology of triangles as a “filter” through which remarkable notions and theorems from the geometry of the triangle are unitarily passed. Our research is structured in seven chapters, the first four are dedicated to the homology of the triangles while the last ones to their applications. In the first chapter one proves the theorem of homological triangles (Desargues, 1636), one survey the remarkable pairs of homological …
Cardinal Functions And Integral Functions, Florentin Smarandache, Mircea Selariu, Marian Nitu
Cardinal Functions And Integral Functions, Florentin Smarandache, Mircea Selariu, Marian Nitu
Branch Mathematics and Statistics Faculty and Staff Publications
This paper presents the correspondences of the eccentric mathematics of cardinal and integral functions and centric mathematics, or ordinary mathematics. Centric functions will also be presented in the introductory section, because they are, although widely used in undulatory physics, little known. In centric mathematics, cardinal sine and cosine are dened as well as the integrals. Both circular and hyperbolic ones. In eccentric mathematics, all these central functions multiplies from one to innity, due to the innity of possible choices where to place a point. This point is called eccenter S(s;") which lies in the plane of unit circle UC(O;R = …