A simple algorithm is presented for the tensorial reduction of oneloop diagrams with massless external momenta. At most rank one tensor integrals with the initial number of denominators appear, plus, eventually, higher rank integrals with less denominators. The number of Gram determinants in the tensorial decomposition is then reduced, giving a better numerical stability of the results. In some...

We develop a theory of difference approximations to absorbing boundary conditions for the scalar wave equation in several space dimensions. This generalizes the work of the author described in [8]. The theory is based on a representation of analytical absorbing boundary conditions proven in [8]. These conditions are defined by compositions of first-order, one-dimensional differential operators....

We derive a formula for an n-th order divided difference of the inverse of a function. The formula has a simple and surprising structure: it is a sum over partitions of a convex polygon with n+1 vertices. The formula provides a numerically stable method of computing divided differences of k-th roots. It also provides a new way of enumerating all partitions of a convex polygon of a certain type,...

In this paper, we consider the robust stability analysis and synthesis problems for closed-loop vibrational control. In the analysis problem, we derive an upper bound on the allowable unstructured uncertainty which preserves the stability of a closed-loop vibrationally stabilized system. In the synthesis problem, we establish a necessary and sufficient condition for the existence of a single vi...

Recently, hierarchical capacitance extraction algorithms have been shown an efficient and accurate capacitance extraction algorithm. An improved algorithm is also proposed to remove its runtime dependency on the number of conductors by a combination of hierarchical and multipole expansion algorithm. In this paper, we show that with the introduction of hierarchical merging operation and supernod...

Canonical Correlation Analysis(CCA) is a useful tool to discover relationship between different sources of information represented by vectors. The solution of the underlying optimisation problem involves a generalised eigenproblem and is nonconvex. We will show a sequence of transformations which turn CCA into a convex maximum margin problem. The new formulation can be applied for the same clas...

The use of threshold pivoting with the purpose to reduce fill-in during sparse Gaussian elimination has been generally acknowledged. Here we describe the application of threshold pivoting in dense Gaussian elimination for improving the performance of a parallel implementation. We discuss the effect on the numerical stability and conclude that the consequences are only of minor importance as lon...

A firm facing price dependent stochastic demand aims to maximize its total expected profit over a planning horizon. In addition to the regular unit selling price, the firm can utilize quantity discounts to increase sales. We refer to this dual-pricing strategy as quantity-based price differentiation. At the beginning of each period, the firm needs to make three decisions: replenish the inventor...

A fourth-order accurate embedded boundary method for the scalar wave equation with Dirichlet or Neumann boundary conditions is described. The method is based on a compact Pade-type discretization of spatial derivatives together with a Taylor series method (modified equation) in time. A novel approach for enforcing boundary conditions is introduced which uses interior boundary points instead of ...

The aim of this note is to give a type of characterization of Banach spaces in terms of the stability of functional equations. More precisely, we prove that a normed space X is complete if there exists a functional equation of the type n ∑ i=1 aif(φi(x1, . . . , xk)) = 0 (x1, . . . , xk ∈ D) with given real numbers a1, . . . , an, given mappings φ1 . . . , φn : D k → D and unknown function f : ...