Computation Of Orlik-Solomon Algebra And Hypergeometric Function Expressions For The Molecule-Micropore Potential

The thesis consists of two parts. The first part is about arrangements of hyperplanes and is divided into three chapters. The second part is about hypergeometric functions which are studied in chapters 5 and 6. These two parts are not interrelated clearly in real space, but they have essential relations in complex space. Some notes in chapter 4 are intended to serve as simple expositions of the connections between the two parts.The information about arrangements related Orlik-Solomon algebra is introduced briefly in chapter 1. In chapter 2, an algorithm for computing NBC basis of Orlik-Solomon algebra is given by using the pseudocode language, including the necessary notes and analyses. Some applications of the algorithm are given in chapter 3. Signed complete graphic arrangements A(ΣΚ_n) with n < 7 vertices are classified under π-equivalence, and the Poincare polynomials of their representatives are worked out by this algorithm. The Poincare polynomial of hyperplane arrangements associated with a class of signed complete graphs is computed. Finally, a counter-example is addressed to a conjecture which says that if G and G are not switching equivalent, then for all n > 4, A(G) is free if and if A(G) is not free, where G is a signed complete graph and G is the negative graph of G.The information about the mesoscopic scale and Lennard-Jones...