A Note on Transformed Density Rejection

In this paper we describe a version of transformed density rejection that requires less uniform random numbers. Random variates below the squeeze are generated by inversion. For the expensive part between squeeze and density an algorithm that uses a covering with triangles is introduced. Received August 23, 1999; revised March 6, 2000     

Analysis of Some Elementary Algorithms for Prime Factorization

For factoring a positive integer n into primes, four variants of the elementary algorithm are analysed. The worst-case time complexities vary from Θ() up to Θ(). The average time complexities vary from Θ() up to Θ(). Received August 21, 1998; revised September 14, 2000     

Volume Maximization and Orthoconvex Approximation of Orthogons

Let n axes-parallel hyperparallelepipeds (also called blocks) of the d-dimensional Euclidean space and a positive integer r be given. The volume maximization problem (VMP) selects at most r blocks such that the volume of their union becomes maximum. VMP is shown to be -hard in the 2-dimensional case and polynomially solvable for the line via a constrained critical path problem (CCPP) in an acyclic digraph. This CCPP leads to further well solvable special cases of the maximization problem. In particular, the following approximation problem (OAP) becomes polynomially solvable: given an orthogon P (i.e., a simple polygon in the plane which is a union of blocks) and a positive integer q, find an orthoconvex orthogon with at most q vertices and minimum area, which contains P. Received: September 7, 1998     

Relations Between Forcing Sequences and Inexact Newton Iterates in Banach Space

We use inexact Newton iterates to approximate a solution of a nonlinear equation in a Banach space. Solving a nonlinear equation using Newton iterates at each stage is very expensive in general. That is why we consider inexact Newton methods, where the Newton equations are solved only approximately and in some unspecified manner. In the elegant paper [6] natural assumptions under which the forcing sequence is uniformly less than one were given based on the first-Fréchet derivative of the operator involved. Here, we use assumptions on the second Fréchet-derivative. This way, we essentially reproduce all results found earlier. However, our upper error bounds on the distances involved are smaller. Received: March 3, 1998; revised April 23, 1999     

Minimal Expansions in Redundant Number Systems and Shortest Paths in Graphs

We consider digit expansions in redundant number systems to base q with and consider such an expansion as minimal, if is minimal. We describe an efficient algorithm for determining a minimal representation and give an explicit characterization of optimal representations for odd q. Received: July 20, 1999; revised August 23 1999     

An Approach to Evaluating E-Business Information Systems Projects

Capital investments in the e-business infrastructure add complexity to the IT payoff question because e-business interorganizational investments are deployed across multiple platforms, projects, vendors and partners. Traditional MIS research has been devoted to measuring the payoff from information technology (IT) investment without any specific focus on e-business. Flaws in the mature MIS performance measures seem to yield weak guidance for managers when evaluating IT success, thus diluting the potential for these measures to be adapted for use in the new e-business environment. A review of the conventional MIS payoff literature indicates that these measures may be incomplete, inaccurate, or inefficient for application to electronic commerce investments. This paper brings four new points to the e-business IT investment evaluation dialogue: (1) we first explore performance measurement validity flaws in our long established measures; (2) the paper discusses a two-by-two matrix delineating the gap between the quantitative versus qualitative performance measures of management information systems (MIS) initiatives; (3) sample e-business payoff techniques are discussed and reviewed in light of these historical imperfections, and (4) fourth, the paper proposes and describes an innovative framework derived from production theory economics for future research in evaluating e-business MIS implementations.     

Liouvillian solutions of third order differential equations

The Kovacic algorithm and its improvements give explicit formulae for the Liouvillian solutions of second order linear differential equations. Algorithms for third order differential equations also exist, but the tools they use are more sophisticated and the computations more involved. In this paper we refine parts of the algorithm to find Liouvillian solutions of third order equations. We show that, except for four finite groups and a reduction to the second order case, it is possible to give a formula in the imprimitive case. We also give necessary conditions and several simplifications for the computation of the minimal polynomial for the remaining finite set of finite groups (or any known finite group) by extracting ramification information from the character table. Several examples have been constructed, illustrating the possibilities and limitations.     

Edge-fault-tolerant bipanconnectivity of hypercubes

This paper shows that for any two distinct vertices u and v with distance d in the hypercube Q_n (n?3) with at most faulty edges and each vertex incident with least two fault-free edges, there exist fault-free uv-paths of length ? in Q_n for every ? with d+4???2ⁿ-1 and . This result improves some known results on edge-fault bipanconnectivity of hypercubes. The proof is based on the recursive structure of Q_n.     

Computation of travelling wave solutions of scalar conservation laws with a stiff source term

In this paper we propose a nonoscillatory numerical technique to compute the travelling wave solution of scalar conservation laws with a stiff source term. This procedure is based on the dynamical behavior described by the associated stationary ODE and it reduces/avoids numerical errors usually encountered with these problems, i.e., spurious oscillations and incorrect wave propagation speed. We combine this treatment with either the first order Lax-Friedrichs scheme or the second order Nessyahu-Tadmor scheme. We have tested several model problems by LeVeque and Yee for which the stiffness coefficient can be increased. We have also tested a problem with a nonlinear flux and a discontinuous source term.