Modification of mainframe BOAST II

BOAST II is a black-oil, applied-simulation tool used routinely for performing evaluation and design work in modern petroleum reservoir engineering. Personnel from the Louisiana State University Computer Science Department worked on modifying the mainframe version of this program through the simulation of two-phase flow of slightly compressible fluids in a three-dimensional porous medium. This included the construction of a FORTRAN program that uses 3-D finite elements to approximate the governing equations. The existing finite element code was adapted so that virtually any size of element could easily be incorporated into the solution scheme. This gave increased flexibility and made it possible to utilize mesh refinement techniques. Modifications to the mainframe version also involved the development and integration of radial grid systems suitable for the investigations proposed in the project

Explicitly searching for useful inventions: dynamic relatedness and the costs of connecting versus synthesizing

Inventions combine technological features. When features are barely related, burdensomely broad knowledge is required to identify the situations that they share. When features are overly related, burdensomely broad knowledge is required to identify the situations that distinguish them. Thus, according to my first hypothesis, when features are moderately related, the costs of connecting and costs of synthesizing are cumulatively minimized, and the most useful inventions emerge. I also hypothesize that continued experimentation with a specific set of features is likely to lead to the discovery of decreasingly useful inventions; the earlier-identified connections reflect the more common consumer situations. Covering data from all industries, the empirical analysis provides broad support for the first hypothesis. Regressions to test the second hypothesis are inconclusive when examining industry types individually. Yet, this study represents an exploratory investigation, and future research should test refined hypotheses with more sophisticated data, such as that found in literature-based discovery research

Lie Generators for Semigroups of Transformations on a Polish Space

. Let X be a separable complete metric space. We characterize completely the infinitesimal generators of semigroups of linear transformations in C b (X), the bounded real-valued continuous functions on X, that are induced by strongly continuous semigroups of continuous transformations in X. In order to do this, C b (X) is equipped with a locally convex topology known as the strict topology. Introduction. A strongly continuous semigroup of transformations on a topological space X is a function T from [0; 1) into the collection of continuous transformations from X into X such that (1) T (0) = I, the identity transformation on X, (2) T (t) ffi T (s) = T (t + s) for all t; s 0, and (3) if x 2 X, then the function T (\Delta)x is continuous from [0; 1) into X. We will follow the standard practice writing the semigroup as a collection and denoting such a semigroup as fT (t) : t 0g or just fT (t)g. Since at least the time of Sophus Lie, mathematicians have been investigating generators, ..

Stochastic problems with unbounded control set

We describe a change of time technique for stochastic control problems with unbounded control set. We demonstrate the technique on a class of maximization problems that do not have optimal controls. Given such a problem, we introduce an extended problem which has the same value function as the original problem and for which there exist optimal controls that are expressible in simple terms. This device yields a natural sequence of suboptimal controls for the original problem. By this we mean a sequence of controls for which the payoff functions approach the value function

Theory of Strongly Continuous Semigroups in Terms of Generators

this paper does not. This paper is more nearly "self-contained" in that it does not appeal to any theory of strongly continuous semigroups in topological vector spaces, whereas [6] did. Furthermore, [6] did not establish the exponential formula. A theory like that in [6] is given in [4] in the case X is a locally compact Hausdorff space, not necessarily metric. The paper [5] contains a relevant result on the strict topology. In [9], it was proved that if A is the Lie generator of T 2 S(X), then f(T (t)x) = li

A Technique for Stochastic Control Problems with Unbounded Control Set

We describe a change of time technique for stochastic control problems with unbounded control set. We demonstrate the technique on a class of maximization problems that do not have optimal controls. Given such a problem, we introduce an extended problem which has the same value function as the original problem and for which there exist optimal controls that are expressible in simple terms. This device yields a natural sequence of suboptimal controls for the original problem. By this we mean a sequence of controls for which the payoff functions approach the value function

Diffusions with positive unbounded controls

We give a preliminary sketch for a theory of impulsive stochastic controls based on a time substitution

A Technique for Stochastic Control Problems with Unbounded Control Set

We describe a change of time technique for stochastic control problems with unbounded control set. We demonstrate the technique on a class of maximization problems that do not have optimal controls. Given such a problem, we introduce an extended problem which has the same value function as the original problem and for which there exist optimal controls that are expressible in simple terms. This device yields a natural sequence of suboptimal controls for the original problem. By this we mean a sequence of controls for which the payoff functions approach the value function. 1 Introduction Let H denote a bounded piecewise-continuous real-valued function on IR such that H(x) 1 for all x and H(x) = 1 for all x in some nondegenerate closed interval I. Let f; g; oe; ¯ be Lipschitz continous real-valued functions on IR, with oe and ¯ positive and bounded away from zero. For any reference probability system =(\Omega ; F ; fF t g; P; W ) (see [5, pages 159,160,171]), Research supported ..