In this paper, we propose to write a source term in the divergence form. A conservation law with a source term can then be written as a single divergence form. We demonstrate that it enables to discretize both the conservation law and the source term in the same framework, and thus greatly simplifies the construction of numerical schemes. To illustrate the advantage of the divergence formulatio...

In the paper we present an application of the homotopy analysis method for solving the two-phase inverse Stefan problem. In the proposed approach a series is created, having elements which satisfy some differential equation following from the investigated problem. We reveal, in the paper, that if this series is convergent then its sum determines the solution of the original equation. A sufficie...

The termination problem of a logic program can be addressed in either a static or a dynamic way. A static approach performs termination analysis at compile time, while a dynamic approach characterizes and tests termination of a logic program by applying a loop checking technique. In this paper, we present a novel dynamic approach to termination analysis for general logic programs with moded que...

The class of well-behaved evaluation functions simpliies and makes eecient the handling of numerical attributes; for them it suuces to concentrate on the boundary points in searching for the optimal partition. This holds always for binary partitions and also for multisplits if only the function is cumulative in addition to being well-behaved. A large portion of the most important attribute eval...

In this paper, we investigate the termination problem of a family of polynomial programs, in which all assignments to program variables are polynomials, and test conditions of loops and conditional statements are polynomial equations. Our main result is that the non-terminating inputs of such a polynomial program is algorithmically computable according to a strictly descending chain of algebrai...

For i.i.d. univariate observations a new estimation method, the maximum spacing (MSP) method, was defined in Ranneby (1984) and independently by Cheng and Amin (1983). The idea behind the method, as described by Ranneby (1984), is to approximate the Kullback-Leibler information so each contribution is bounded from above. In the present paper the MSP-method is extended to multivariate observatio...

This paper presents a new tool for fitting a divergence-free vector field tangent to a two dimensional orientable surface P ∈ R to samples of such a field taken at scattered sites on P . This method, which involves a kernel constructed from radial basis functions, has applications to problems in geophysics, and has the advantage of avoiding problems with poles. Numerical examples testing the me...

This work presents a systematic study of objective evaluations of abstaining classifications using Information-Theoretic Measures (ITMs). First, we define objective measures for which they do not depend on any free parameter. This definition provides technical simplicity for examining “objectivity” or “subjectivity” directly to classification evaluations. Second, we propose twenty four normaliz...

The author proposes a general method for evaluating the fit of a model for functional data. His approach consists of embedding the proposed model into a larger family of models, assuming the true process generating the data is within the larger family, and then computing a posterior distribution for the Kullback-Leibler distance between the true and the proposed models. The technique is illustr...

We propose a clustering algorithm that effectively utilizes feature order preferences, which have the form that feature s is more important than feature t. Our clustering formulation aims to incorporate feature order preferences into prototype-based clustering. The derived algorithm automatically learns distortion measures parameterized by feature weights which will respect the feature order pr...