Thesis (M.Sc.) - Carleton University, 2007. / Includes bibliographical references (p. 70-75). Also available in electronic format on the Internet.

Thesis (M.S.)--Worcester Polytechnic Institute. / Keywords: sequences, Escher, Catalan, Collatz, integer. Includes bibliographical references (p.27-28).

Thesis (Ph. D.)--Ohio State University, 2005. / Title from first page of PDF file. Document formatted into pages; contains xiv, 260 p.; also includes graphics (some col.). Includes bibliographical references (p. 210-217). Available online via OhioLINK's ETD Center

<p> </p><p>The aim of this project has been to develop a new method that can be used for optimising the sequences of operations in flexible manufacturing cells. The method combines existing methods and available software tools from three research areas, optimisation, flexibility and virtual manufacturing. This method is named SIMBOSeer and it combines genetic algorithms in discrete event simulation together with continuous robot simulation. SIMBOSeer has been implemented at an existing workcell at Volvo Powertrain, Skövde, and it has successfully shown to be able to find possible improvements of the sequences of operations. SIMBOSeer has shown to be a successful combination of different virtual manufacturing tools. It has a great ability to find an optimal solution of the sequence of operations in a flexible manufacturing cell. SIMBOSeer not only gives a fast answer on how to produce different variants it also offers the possibility to generate the robot code automatically.</p>

For any two differential modules M and N over a graded differential k-algebra Λ (k a commutative ring), there Is a spectral sequence Er, called the Eilenberg-Moore spectral sequence, having the following properties: Er converges to Tor Λ (M,N) and E2=TorH(Λ) (H(M),H(N)). This algebraic set-up gives rise to a "geometric" spectral sequence in algebraic topology. Starting with a commutative diagram of topological spaces [diagram omitted] where B Is simply connected, one gets a spectral sequence Er converging to the cohomology H*(X xBY) of the space X xBY, and for which E₂=TorH*(B) (H*(X),H*(Y)). In this thesis we outline a generalization of the above geometric spectral sequence obtained, by first extending the category of topological spaces and then, extending the cohomology theory H* to this larger category. The convergence of the extended spectral sequence does not depend, on any topological conditions of the spaces involved. It follows algebraically from the way the exact couple (from which the spectral sequence Is derived) Is set up and from the Suspension Axiom of the extended cohomology theory. / Science, Faculty of / Mathematics, Department of / Graduate

RNA molecules that can fold into two or more predefined alternative metastable structures can be designed rationally. We outline an algorithm for this task that reduces the problem to vertex coloring the union of all prescribed outerplanar secondary structure graphs. Starting from an ear decomposition of this composite graph colorings are produced by a dynamic programming procedure. Sequences can then be optimized for particular properties by means of standard optimization heuristics.

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Generators of pseudorandom sequences are widely used objects, not in the least place because of their application in stream ciphers. One of the ways to improve resistance to different types of attack is to use compression on the generated sequence in order to remove redundant information, that might lead to an attack against the generator. In this work we try to explore from a wider perspective the theoretical foundations for compressing pseudorandom sequences created thus far. Using this general view we will examine some known attacks against the PRN generators and look for a way to resist such attacks.

Counting problems lead naturally to integer sequences. For example if one asks for the number of subsets of an $n$-set, the answer is $2^n$, or the integer sequence $1,~2,~4,~8,~ldots$. Conversely, given an integer sequence, or part of it, one may ask if there is an associated counting problem. There might be several different counting problems that produce the same integer sequence. To illustrate the nature of mathematical research involving integer sequences, we will consider Escher's counting problem and a generalization, as well as counting problems associated with the Catalan numbers, and the Collatz conjecture. We will also discuss the purpose of the On-Line-Encyclopedia of Integer Sequences.