A master integral in four parameters

A Contracted Path Integral Solution of the Discrete Master Equation

A new representation of the exact time dependent solution of the discrete master equation is derived. This representation can be considered as contraction of the path integral solution of Haken. It allows the calculation of the probability distribution of the occurence time for each path and is suitable as basis of new computational solution methods. Typeset using REVTEX 1

A Hilbert Integral-Type Inequality with Parameters

Cubes of Integral Vectors in Dimension Four

A system of m nonzero vectors in Zn is called an m-icube if they are pairwise orthogonal and have the same length. The paper describes m-icubes in Z for 2 ≤ m ≤ 4 using Hurwitz integral quaternions, counts the number of them with given edge length, and proves that unlimited extension is possible in Z.

An Integral with Three Parameters

In this paper we give an exact expression for the integral

Half-integral Flows in a Planar Graph with Four Holes

Suppose that G = (1/G, EG) is a planar graph embedded in the euclidean plane, that I, J, K, 0 are four of its faces (called holes in G), that sl, , s,, t, , , t, are vertices of G such that each pair {si, ti} belongs to the boundary of some of I,J, K, 0, and that the graph (I/G, EGu{ {.slr fl}, ___ ,{.r,, t,}}) is eulerian. We prove that if the multi(commodity)flow problem in G with unit demand...