# Browse by Subject "Mathematics"

• (1989)
This thesis describes a new class of Intelligent Tutoring Systems (ITS) which I call the Learning Companion Systems (LCS). In the learning environment of such a system, there are three agents involved, namely, the human ...
PDF (7MB)
• (1994)
Finite difference techniques are used to solve a variety of differential equations. For the neutron diffusion equation, the typical local truncation error for standard finite difference approximation is on the order of the ...
PDF (4MB)
• (1991)
This dissertation proposes a unification-based formalism to provide a common basis for a computational realization of different linguistic theories, GPSG, HPSG, and LFG in particular, both as a means of theory testing and ...
PDF (10MB)
• (1995)
In this thesis, the concept of the regular (or Riesz) norm on ordered real Banach spaces is generalized to matrix ordered complex operator spaces in a way that respects the matricial structure of the operator space. A norm ...
PDF (5MB)
• (1994)
The metric entropy of a set is a measure of its size in terms of the minimal number of sets of diameter not exceeding 2$\varepsilon$ which cover the set. We calculate the asymptotic order of the metric entropy as $\varepsilon\ ... PDF (1MB) • (1996) It has long been suspected that the conjectural motivic cohomology groups of a smooth variety X are related to the algebraic K-groups of X. Explicitly, it is expected that there is a spectral sequence whose terms are the ... PDF (5MB) • (1991) A transitive permutation representation of a finite group G is said to be multiplicity-free if each irreducible constituent of the associated permutation character of G occurs with multiplicity one. If H is a subgroup of ... PDF (3MB) • (1990) In Chapter I we shall prove a new upper bound in the linear sieve. Our purpose in Chapter II is to explain our method in greater detail than was done in Chapter I. Let x be a large number. We consider$\pi\sb2$(x)--the ... PDF (2MB) • (1996) This thesis introduces a new set theory referred to as the graph-isomorphism set theory (GST). GST does not satisfy the foundation axiom. Peter Aczel has presented several non-well-founded (NWF) set theories within a unified ... PDF (5MB) • (1989) Consider the nonlinear, singularly perturbed, vector boundary relation problem x$\sp\prime$= f(t,x,y,$\epsilon$),$\epsilon$y$\sp\prime$= g(t,x,y,$\epsilon$), L(x(0),y(0),$\epsilon$) =$\alpha\sb0$, R(x(1),y(1),$\epsilon$) ... PDF (7MB) • (1989) Ideas and techniques from nonstandard theories of measure spaces and Banach spaces are brought together to develop a nonstandard theory of Banach space valued measures. In particular, constructions of countably additive ... PDF (3MB) • (1994) We describe an extension of the Bochner integral. Bochner integrable functions can be approximated by simple functions. Using Nonstandard Analysis, we investigate internal simple functions from an internal measure space ... PDF (3MB) • (1994) Let f be a meromorphic function in the complex plane C. We consider the normality of the family of integer translations of f,$\{ f(z + n):n = 0,\pm 1,\pm2,\...\}$. If the family is normal on a set G in C, then the set G ... PDF (1MB) • (1996) Let$\pi$be orthogonal projection of$\IR\sp{d}$onto a hyperplane and let P be a d-polytope in$\IR\sp{d}$. The following relations hold on the numbers of facets$f\sb{d-1}(P)$of P and$f\sb{d-2}(\pi(P))$of ... PDF (6MB) • (1992) Numerical modeling of nonstationary transport effects using partial differential equations derived from the Boltzmann Transport Equation (BTE) is investigated. Augmented drift-diffusion (ADD) models and improved energy ... PDF (3MB) • (1989) In Chapter 1, we define discrete objects like$\delta$-tangents,$\delta$-normals and$\delta$-curvatures which are analogues of smooth objects in differential geometry. These are incorporated into numerical methods for ... PDF (3MB) • (1996) The purpose of this dissertation is to define homology functors for the category of definable sets and definable continuous maps in an o-minimal expansion of an ordered field. Both simplicial and singular homology functors ... PDF (2MB) • (1996) Let C be a class of finite groups closed under the operations of taking subgroups, quotients, and extensions. Let H and K be pro-C-groups and let$G=H*K\$ be their free pro-C-product. An open question in the theory of ...
PDF (3MB)
• (1995)
In the first part of this thesis I prove some results on elementary pairs of o-minimal structures.
PDF (4MB)
• (1990)
In this manuscript we consider multigraded modules. Chapter 1 gives the necessary definitions and examples that develop the theory of multigraded modules. A multigraded module has a multigraded minimal resolution. We give ...
PDF (2MB)