In the present paper we construct differential invariants for generic rank 2 vector distributions on n-dimensional manifold. In the case n = 5 (the first case containing functional parameters) E. Cartan found in 1910 the covariant fourth-order tensor invariant for such distributions, using his ”reduction-prolongation” procedure (see [12]). After Cartan’s work the following questions remained op...

A method is presented to easily derive von Neumann stability conditions for a wide variety of time discretization schemes for the convection-di usion equation. Spatial discretization is by the -scheme or the fourth order central scheme. The use of the method is illustrated by application to multistep, Runge-Kutta and implicit-explicit methods, such as are in current use for ow computations, and...

Equivalences between conformal foliations on Euclidean 3-space, Hermitian structures on Euclidean 4-space, shear-free ray congruences on Minkowski 4-space, and holomorphic foliations on complex 4-space are explained geometrically and twistorially; these are used to show that 1) any real-analytic complex-valued harmonic morphism without critical points defined on an open subset of Minkowski spac...

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...

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...