We present and analyze a linearly implicit finite-difference scheme for computing approximate solutions and interface curves for the porous medium equation in one space variable. Our scheme requires only that linear, tridiagonal systems of equations be solved at each time step. We derive error bounds for the approximate interface curves as well as for the approximate solutions under the rather ...

A new logic of belief (in the “Only knowing” family) with confidence levels is presented. The logic allows a natural distinction between explicit and implicit belief representations, where the explicit form directly expresses its models. The explicit form can be found by applying a set of equivalence preserving rewriting rules to the implicit form. The rewriting process is performed entirely wi...

Design is a complex and ill-structured activity, which makes difficult the creation of efficient computational design systems. One way to enhance design systems capabilities is using machine learning techniques. In this paper we analyze machine learning in design from three different perspectives. We first use the process/product viewpoint, inferring some important aspects. The other perspectiv...

Two experiments investigated the effect of prior knowledge on implicit and explicit learning. Implicit as opposed to explicit learning is sometimes characterized as unselective or purely statistical. During training, one group of participants was presented with category exemplars whose features could be tied together by integrative knowledge, whereas another group saw category exemplars with un...

In this paper, we introduce the concept of constant time updateability for the functional operations that can be used for constructing functions. We believe that constant time updateability will be important in the future for guaranteeing interactive modeling of implicit surfaces that are defined by functional construction of functions. We have developed several tests to determine if a function...

J.-L. Loday has used w-cubes of fibrations, where n is a non-negative integer, in his study of spaces with finitely many non-trivial homotopy groups [4]. His main result is the construction of an algebraic category equivalent to the weak homotopy category of path-connected spaces Z with TI^Z = 0 for / > w+1 [4, 1.7]. One step in the proof [4, 3.5] requires the construction of certain «-cubes of...

The paper presents a new enclosure method for initial value problems in systems of ordinary di erential equations. Like the common enclosure methods (eg Lohner's algorithm AWA), it is based on Taylor expansion. In contrast to them, however, it is an implicit method. The solution sets of nonlinear inequalities have to be enclosed by a Newton-like algorithm. As the presented examples show, the ne...

We give a general construction for the classical limit of a quantum system defined in terms of generators of an arbitrary compact semisimple Lie algebra, generalizing known results for the su2 and su3 cases. The classical limit depends on the physical problem in question and is determined by the sequence of representations by which it is reached. Only in the simplest cases it is unique. We pres...

In this paper, we propose an e cient technique for the animation of exible thin objects. Massspring model was employed to represent the exible objects. Many techniques have used the mass-spring model to generate plausible animation of soft objects. The easiest approach to animation with mass-spring model is explicit Euler method, but the explicit Euler method has serious disadvantage that it su...

Distributions of the first-exit times from a region with non-linear upper boundary are discussed for ordinary and compound Poisson processes. Explicit formulae are developed for the case of ordinary Poisson processes. Recursive formulae are given for the compound Poisson case, where the jumps are positive, having continuous distributions with finite means. Applications to sequential point estim...