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Physical Sciences and Mathematics Commons™
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Articles 1 - 7 of 7
Full-Text Articles in Physical Sciences and Mathematics
Early Investigations In Conformal And Differential Geometry, Raymond T. Walter
Early Investigations In Conformal And Differential Geometry, Raymond T. Walter
Inquiry: The University of Arkansas Undergraduate Research Journal
The present article introduces fundamental notions of conformal and differential geometry, especially where such notions are useful in mathematical physics applications. Its primary achievement is a nontraditional proof of the classic result of Liouville that the only conformal transformations in Euclidean space of dimension greater than two are Möbius transformations. The proof is nontraditional in the sense that it uses the standard Dirac operator on Euclidean space and is based on a representation of Möbius transformations using 2x2 matrices over a Clifford algebra. Clifford algebras and the Dirac operator are important in other applications of pure mathematics and mathematical physics, …
Where Does It All End? Boundaries Beyond Euclidean Space, Jonathan Thompson
Where Does It All End? Boundaries Beyond Euclidean Space, Jonathan Thompson
Inquiry: The University of Arkansas Undergraduate Research Journal
No abstract provided.
Equations Of Variation For Ordinary Differential Equations On Manifolds, J. B. Bennett
Equations Of Variation For Ordinary Differential Equations On Manifolds, J. B. Bennett
Journal of the Arkansas Academy of Science
No abstract provided.
Faces, Edges, Vertices Of Some Polyhedra, Charles H. Harbison
Faces, Edges, Vertices Of Some Polyhedra, Charles H. Harbison
Journal of the Arkansas Academy of Science
A proof that: for any given polyhedron so shaped that every closed non-self intersecting broken line composed of edges of the polyhedron divides the surface of the polyhedron into precisely two disjoint regions each of which is bounded by the closed broken line, v - e + f = 2, where v is the number of vertices of the polyhedron, e the number of edges and f the number of faces.
Simple Algebraic Extensions And Characteristics Polynomials, Don Stokes
Simple Algebraic Extensions And Characteristics Polynomials, Don Stokes
Journal of the Arkansas Academy of Science
No abstract provided.
Exact Test For Simple Correlation In Analysis Of Dispersion, James E. Dunn
Exact Test For Simple Correlation In Analysis Of Dispersion, James E. Dunn
Journal of the Arkansas Academy of Science
No abstract provided.
What Is A Riemmian Manifold?, Frederick Griffin
What Is A Riemmian Manifold?, Frederick Griffin
Journal of the Arkansas Academy of Science
No abstract provided.