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Overview and introduction to dynamical systems. Local and global theory of maps. Attractors and limit sets. Lyapunov exponents and dimensions. Fractals: definition and examples. Lorentz attractor, Hamiltonian systems, homoclinic orbits and Smale horseshoe orbits. Chaos in finite dimensions and in PDEs. Can be used to fulfill the senior seminar requirement in applied mathematics. Prerequisites: Differential equations and linear algebra.

APMA 2811A. Directed Methods in Control and System Theory. Various general techniques have been developed for control and system problems. Many of the methods are indirect. For example, control problems are reduced to a problem involving a differential equation (such as the partial differential equation of Dynamic Programming) or to a system of differential equations (such as the canonical system of the Maximum Principle). Since these indirect methods are not always effective alternative approaches are necessary. In particular, direct methods are of interest. We deal with two general classes, namely: 1.) Integration Methods; and, 2.) Representation Methods. Integration methods deal with the integration of function space differential equations. Perhaps the most familiar is the so-called Gradient Method or curve of steepest descent approach. Representation methods utilize approximation in function spaces and include both deterministic and stochastic finite element methods. Our concentration will be on the theoretical development and less on specific numerical procedures. The material on representation methods for Levy processes is new.

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The theory of large deviations attempts to estimate the probability of rare events and identify the most likely way they happen. The course will begin with a review of the general framework, standard techniques (change-of-measure, subadditivity, etc.), and elementary examples (e.g., Sanov's and Cramer's Theorems). We then will cover large deviations for diffusion processes and the Wentsel-Freidlin theory. The last part of the course will be one or two related topics, possibly drawn from (but not limited to) risk-sensitive control; weak convergence methods; Hamilton-Jacobi-Bellman equations; Monte Carlo methods. Prerequisites: AM 263 and 264.

The next chapter presents an evaluation of the REST architecture through the experience and lessons learned from applying REST to the design, specification, and deployment of the modern Web architecture. This work included authoring the current Internet standards-track specifications of the Hypertext Transfer Protocol (HTTP/1.1) and Uniform Resource Identifiers (URI), and implementing the architecture through the libwww-perl client protocol library and Apache HTTP server.

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Brown University Library archives dissertations in accordance with the Graduate School policy. Type. 1968 Doctoral Dissertation; 144 Masters Thesis

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PhD Dissertations. Click here to access the Brown University Digital Repository of Theses and Dissertations French Studies PhD Dissertations 1990 - Present

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Brown University Library archives dissertations in accordance with the Brown Graduate School policy. Type. 1968 Doctoral Dissertation; 144 Masters Thesis

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The early Web architecture, as portrayed by the diagram in [], was defined by the client-cache-stateless-server set of constraints. That is, the design rationale presented for the Web architecture prior to 1994 focused on stateless client-server interaction for the exchange of static documents over the Internet. The protocols for communicating interactions had rudimentary support for non-shared caches, but did not constrain the interface to a consistent set of semantics for all resources. Instead, the Web relied on the use of a common client-server implementation library (CERN libwww) to maintain consistency across Web applications.

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