The small dispersion limit of the focusing nonlinear Schroödinger equation (fNLS) exhibits a rich structure with rapid oscillations at microscopic scales. Due to the non self-adjoint scattering problem associated to fNLS, very few rigorous results exist in the semiclassical limit. The asymptotics for reectionless WKB-like initial data was worked out in [KMM03] and for the family q(x, 0) = sech^(1+(i/∈)μ in [TVZ04]. In both studies the authors observed sharp breaking curves in the space-time separating regions with disparate asymptotic behaviors. In this paper we consider another exactly solvable family of initial data, specifically the family of centered square pulses, q(x; 0) = qx[-L,L] for real amplitudes q. Using Riemann- Hilbert techniques we obtain rigorous pointwise asymptotics for the semiclassical limit of fNLS globally in space and up to an O(1) maximal time. In particular, we find breaking curves emerging in accord with the previous studies. Finally, we show that the discontinuities in our initial data regularize by the immediate generation of genus one oscillations emitted into the support of the initial data. This is the first case in which the genus structure of the semiclassical asymptotics for fNLS have been calculated for non-analytic initial data.

Prof. Potter examines the implications of the Charter 08 manifesto issued by leading Chinese intellectuals. The Communist Party is faced with a challenge that, in time, offers it a way around the governance roadblocks that threaten China’s further development.

The study of combinatorial patterns of words has raised great interest since the early 20th century. In this master's thesis presentation we study two combinatorial patterns. The first pattern is “abelian k-th power free” and the second one is “representability of sets of words of equal length”. For the first pattern we study the context-freeness of non-abelian k-th powers. A word is a non-abelian k-th power if it cannot be factorized in the form w1w2...wk where the wi are permutations of w1 for 2 ≤ i ≤ k. We show that neither the language of non-abelian squares nor the language of non- abelian cubes is context-free. For the second pattern we study the representability of a set of words of fixed length. A set S of words of length n is representable if there exists some word w such that the set of length-n factors of w equals S. We will give lower and upper bounds for the number of such representable sets. Furthermore, we study a variation of the problem: we fix a length t, and try to evaluate the number of sets of words of length n such that there exists some word w of length t such that the set of length-n factors of w equals S. We give a closed-form formula in the case where n ≤ t < 2n. In particular, we give a characterization on two distinct words having the same subset of length-n factors.

An incomplete Latin square is a v x v array with an empty n x n subarray with every row and every column containing each symbol at most once and no row or column with an empty cell containing one of the last n symbols. A set of t incomplete mutually orthogonal Latin squares of order v and hole size n is a set of t incomplete Latin squares (containing the same empty subarray on the same set of symbols) with a natural extension to the condition of orthogonality. The existence of such sets have been previously explored only for small values of t. We determine an asymptotic result for the existence of t incomplete mutually orthogonal Latin squares for general t requiring large holes, which we develop from our results on incomplete pairwise balanced designs and incomplete group divisible designs. / Graduate

The mystery of Canis Major overdensity is addressed. We discuss concurrent methods and their limitations on the determination of interstellar reddening. We establish a new way to determine line of sight interstellear reddening by observing stellar spectral lines and UBV colors. We observe and analyze spectra of 22 stars in different open clusters. We find that Hydrogen Balmer line at 4861 angstrom can predict the stellar atmospheric parameters and intrinsic colors with reasonable accuracy. Comparing with observed colors we derive the reddening of the stars. We compare our results with standard database WEBDA and find that within 90% probability limit the standard deviation of the error is 0.102798. This is improved by taking the absolute maximum probabilities and the scatter becomes 0.0688865.

Studies of minimalist multi-robot systems consider multiple robotic agents, each with limited individual capabilities, but with the capacity for self-organization in order to collectively perform coordinated tasks. Object clustering is a widely studied task in which self-organized robots form piles from dispersed objects. Our work considers a variation of an object clustering derived from the influential ant-inspired work of Beckers, Holland and Deneubourg which proposed stigmergy as a design principle for such multi-robot systems. Since puck mechanics contribute to cluster accrual dynamics, we studied a new scenario with square objects because these pucks into clusters differently from cylindrical ones. Although central clusters are usually desired, workspace boundaries can cause perimeter cluster formation to dominate. This research demonstrates successful clustering of square boxes - an especially challenging instance since flat edges exacerbate adhesion to boundaries - using simpler robots than previous published research. Our solution consists of two novel behaviours, Twisting and Digging, which exploit the objects’ geometry to pry boxes free from boundaries. Physical robot experiments illustrate that cooperation between twisters and diggers can succeed in forming a single central cluster. We empirically explored the significance of different divisions of labor by measuring the spatial distribution of robots and the system performance. Data from over 40 hours of physical robot experiments show that different divisions of labor have distinct features, e.g., one is reliable while another is especially efficient.

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Thesis (M.Arch.)--University of Hong Kong, 1994. / Includes bibliographical references. Also available in print.

Thesis (Ph.D.)--McGill University, 1998. / Mode of access: World Wide Web. Includes bibliographical references.