A system is described which learns to compose sequences of operators into episodes for problem solving. The system incrementally learns when and why operators are applied. Episodes are segmented so that they are generalizable and reusable. The idea of *augmenting the instance language with higher level concepts is introduced. The technique of perturbation is described for discovering the essent...

In this paper, we consider distribution solutions to the aggregation equation ρt + div(ρu) = 0, u = −∇V ∗ρ in R where the density ρ concentrates on a co-dimension one manifold. We show that an evolution equation for the manifold itself completely determines the dynamics of such solutions. We refer to such solutions aggregation sheets. When the equation for the sheet is linearly well-posed, we s...

However it is possible to use of numerical methods such as beta-Newmark in order to investigate the structural response behavior of the dynamic systems under random sea wave loads but because of necessity to analysis the offshore systems for extensive time to fatigue study it is important to use of simple stable methods for numerical integration. The modified Euler method (MEM) is a simple nume...

in this paper, a  fuzzy numerical procedure for solving fuzzy linear volterra integro-differential equations of the second kind under strong  generalized differentiability is designed. unlike the existing numerical methods, we do not replace the original fuzzy equation by a $2times 2$ system ofcrisp equations, that is the main difference between our method  and other numerical methods.error ana...

In this paper we propose a strategy to obtain the solutions of a scalar equation f (x) = 0 through solving an associated system of two equations. In this way, the solutions of the associated system lying on the identity line provide solutions of the given equation. In most cases, the associated system cannot be solved exactly. Solving this system with the Newton method for systems may result mo...

Last time, we talked about a very simple solver for Laplacian-based systems of linear equations, i.e., systems of linear equations of the form Ax = b, where the constraint matrix A is the Laplacian of a graph. This is not fully-general—Laplacians are SPSD matrices of a particular form—but equations of this form arise in many applications, certain other SPSD problems such as those based on SDD m...

This paper presents two models typical of two different approaches often used for modelling the advective-dispersive transport of multiple ions in variably-saturated porous media. The first approach assumes that all solute reactions can be incorporated directly into the governing transport equations (the one-step method), while the second approach divides the mathematical solution process into ...