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Titlebook: Applications of Algebraic Topology; Graphs and Networks. S. Lefschetz Book 1975 Springer Science+Business Media New York 1975 Algebraic.Alg

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Empirical Modelling in Regional ScienceA complex analytic 2n-manifold M. is a connected space defined by the following properties:
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Joacim Andersson,Jim Garrison,Leif ÖstmanThe structure of a Feynman integral is dictated by a certain special graph. I must, therefore, discuss these graphs.
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A Résumé of Linear AlgebraTwo elements dominate linear algebra: matrices and vectors. One may identify vectors with certain matrices but not .. Thus matrices are the dominant feature. We shall, therefore, first deal with matrices and then with vectors.
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Duality in Vector SpacesThe idea of duality occurs in many parts of mathematics. Its earliest appearance (some 125 years ago) was in projective geometry where it permitted to halve the number of theorems to be proved. It also played a most important role in analysis, for example in Banach spaces. In topology, beginning with Poincaré its role has been no less important.
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Topological PreliminariesThere are many approaches to topology. One of the most accessible is by means of the notion of distance. Our purpose in the present chapter is to sketch this approach and a few of the general concepts derivable from it. It may be said that this material amply covers our future needs.
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Graph Algebra. The first step in dealing with graph algebra is to orient the graph G. This means assigning to each branch b. with endpoints n.,n. one of the two, say, n. as . point and the other n. as . point. Hereafter G will always be assumed oriented.
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