We present a subtraction scheme for eliminating the ultraviolet, soft, and collinear divergences in the numerical calculation of an arbitrary one-loop QCD amplitude with an arbitrary number of external legs. The subtractions consist of local counter terms in the space of the four-dimensional loop momentum. The ultraviolet subtraction terms reproduce MS renormalization. The key point in the meth...

The energy of a graph is the sum of the absolute values of the eigenvalues of its adjacency matrix. The edge grafting operation on a graph is a kind of edge moving between two vertices of the graph. In this paper, we introduce two new edge grafting operations and show how the graph energy changes under these edge grafting operations. Let G(n) be the set of all unicyclic graphs with n vertices. ...

We study criteria which ensure that Gibbs states (often also called generalized vacuum states) on distance-regular graphs are positive. Our main criterion assumes the graph can be embedded into a growing family of graphs. For proof positivity we then use polynomial hypergroup theory and translate this problem whether for [Formula: see text] function has positive integral representation w.r.t. o...

A multibond graph element for a general single moving body is derived. A multibody system can easily be described as an interconnection of these elements. 3-D mechanical systems usually contain dependent inertias having both differential and integral causality. A method is described for the transformation of inertias with dt@erential causality to an integral form, using formula manipulation. Th...

Visualization has become an integral part in a wide array of application areas, and papers are solicited both for original visualization research and for the application of visualization towards the understanding of domain-specific data. Our main objective is the visual representation of a directed finite graph with labels attached to edges based on the structure properties of the graph. In par...

We prove that for a graph G = (V,E) without bad K4 subdivision, and for b ∈ Z ∪E + , the b-stable set polytope is determined by the system of constraints determined by the vertices, edges and odd circuits. We also prove that this system is totally dual integral. This relates to t-perfect graphs. Let G = (V,E) be a graph and let b ∈ ZV ∪E + . Then a b-stable set in G is a vector x ∈ Z+ satisfyin...

in this paper, we present an efficient method for determining the solution of the stochastic second kind volterra integral equations (svie) by using the taylor expansion method. this method transforms the svie to a linear stochastic ordinary differential equation which needs specified boundary conditions. for determining boundary conditions, we use the integration technique. this technique give...

We give an especially simple proof of a theorem in graph theory that forms the key part of the solution to a problem in commutative algebra, on how to characterize the integral closure of a polynomial ring generated by quadratic monomials. Forms of this theorem were proved independently by two groups of researchers, who submitted their results [3, 5] two months apart, in 1997. The techniques of...

In this paper, we consider the harmonic extension problem, which is widely used in many applications of machine learning. We find that the transitional method of graph Laplacian fails to produce a good approximation of the classical harmonic function. To tackle this problem, we propose a new method called the point integral method (PIM). We consider the harmonic extension problem from the point...