A cyclic ketene acetal is an olefin that is substituted at one end by two electrondonating hetero atoms, like O, N, S, where these heteroatoms are connected together by a chain. Delocalization of the lone pair electrons of the two hetero atoms to the double bond makes the β-carbon (the exocyclic methylene carbon) electron rich and nucleophilic. A major goal of cyclic ketene acetal chemistry is to provide functionalized cyclic ketene acetal monomers as precursors to polymers of desired properties. The cyclic ketene-N,O-acetal 3-methyl-2-methylene-oxazolidine, generated in situ from 2-methyl-2-oxazolinium iodide and triethylamine, reacted with aryl isocyanates in refluxing THF to give α,α-bis(N-arylamido) lactams via the iodide-catalyzed rearrangement of β,β–bis(N-arylamido) cyclic ketene-N,O-acetal intermediates. However, similar β,β–bis(N-arylamido) cyclic ketene-N,O-acetals having two methyl substituents at C-4, did not rearrange due to hindrance of the iodide attack on C-5. 3,4,4-Trimethyl-2-methylene-oxazolidine reacted with aryl chloroformates to form both mono- and di-aryloxycarbonylation adducts. The two methyl groups at C-4 Template Created By: Damen Peterson 2009 hindered the alternative polymerization route. 3-Methyl-2-methylene-oxazolidine, which does not have two methyl groups at C-4, underwent cationic polymerization under identical conditions. Benzoylation of 2-methyl-2-oxazoline with benzoyl chloride gave a ring-opened N,C,O-trisbenzoylation product via O-benzoylation of the N,C-bisbenzoylated intermediate, followed by chloride attack on C-5. The N,C,O-trisbenzoylated product underwent N,O-double debenzoylation by KOH to give the cyclic ketene-N,O-acetal, 2- oxazolidin-2-ylidene-1-phenylethanone. This compound (an ambident nucleophile), upon deprotonation, reacted with benzoyl chloride to give the β,β-bisbenzoylated cyclic ketene-N,O-acetal, and reacted with phenyl chloroformate to give a novel heterocycle, [1,3]oxazine-2,4-dione. The benzoylation of 2-methyl-2-oxazine gave a similar ringopened N,C,O-trisbenzoylation product. Reactions of 2-methyl-2-oxazoline, 2,4,4-trimethyl-2-oxazoline and 2-methyl-2- thiazoline with trifluoroacetyl anhydride gave C-trifluoroacetylated cyclic ketene-N,O(S)- acetals. However, trifluoroacetylation of 2-methyl-2-oxazine gave the β,β- bistrifluoroacetylated cyclic ketene-N,O-acetal. In summary, a novel iodide-catalyzed rearrangement of β,β–bis(N- arylamido)- cyclic ketene-N,O-acetals was found. The [1,3]oxazine-2,4-dione heterocycle synthesized during this research also demonstrates the synthetic potential of cyclic ketene acetal chemistry in pharmaceutical industry. Functionalization of cyclic ketene acetals based on the chemistry developed in this work will find applications in polymer industry.

<p> This thesis is a contribution to the theory of Steiner quadruple systems. S-cyclic Steiner quadruple systems are defined and then as a main result it is shown that there exists exactly one S-cyclic Steiner quadruple system of order 20.</p> / Thesis / Master of Science (MSc)

<p> This thesis is concerned with the existence of cyclic block designs with parameters (b, v, r, k, λ) where λ = 1 , r = 2k and 3 ≤ k ≤ 6.</p> <p> It gives the proofs of the non-existence of cyclic block designs with k = 6, λ = 1 and r = 9, 10 and 12.</p> / Thesis / Master of Science (MSc)

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Yes / This work presents an efficient and fast method for achieving cyclic animation using Partial Differential Equations (PDEs). The boundary-value nature associ- ated with elliptic PDEs offers a fast analytic solution technique for setting up a framework for this type of animation. The surface of a given character is thus cre- ated from a set of pre-determined curves, which are used as boundary conditions so that a number of PDEs can be solved. Two different approaches to cyclic ani- mation are presented here. The first consists of using attaching the set of curves to a skeletal system hold- ing the animation for cyclic motions linked to a set mathematical expressions, the second one exploits the spine associated with the analytic solution of the PDE as a driving mechanism to achieve cyclic animation, which is also manipulated mathematically. The first of these approaches is implemented within a framework related to cyclic motions inherent to human-like char- acters, whereas the spine-based approach is focused on modelling the undulatory movement observed in fish when swimming. The proposed method is fast and ac- curate. Additionally, the animation can be either used in the PDE-based surface representation of the model or transferred to the original mesh model by means of a point to point map. Thus, the user is offered with the choice of using either of these two animation repre- sentations of the same object, the selection depends on the computing resources such as storage and memory capacity associated with each particular application.

The classical n-bugs problem has attracted considerable attention from researchers. This problem stems from the study of movement of a group of animals. In the context of multi- agent systems the problem has been modelled as cyclic pursuit. Under this paradigm, every agent, indexed i, chases its unique leader, agent i + 1 (modulo n), with n being the total number of agents. In the existing literature, cyclic pursuit has been studied for homogeneous agents where each agent’s velocity is proportional to the distance separating it from its leader and is directed along the line joining it to its leader. The constant of proportionality, initially chosen to be the same for all the agents, resulted in consensus in position, without the need for any centralized controller. Later, the constant of proportionality, alternately called the gain, was allowed to be heterogeneous and positional consensus was still achieved. Moreover, it was shown that the point of convergence, where the agents rendezvous, could be chosen at will, except for some diagnostic cases. In this thesis, besides admitting heterogeneous gains, the agents are assumed to pursue their respective leaders with an angle of deviation from the line joining them to their corresponding leaders. This expands the reachability set (set of points where the agents can rendezvous) for the system of agents to include points that were hitherto unreachable. Sufficient conditions for stability of such systems have been derived in this thesis. Detailed analysis of the reachability set has also been carried out. Some researchers have also investigated hierarchical cyclic pursuit, where there are multiple levels of pursuit. For instance, in the two level hierarchical pursuit, the agents are divided into m groups of n agents each, where each agent in a group chases its leader within the group as well as a similarly indexed agent in its leading group. Thus, groups of agents are also in cyclic pursuit. So far, only homogeneous gains were considered under this paradigm. The present thesis admits heterogeneous gains and establishes necessary and sufficient conditions for the stability of heterogeneous hierarchical cyclic pursuit, that generalize existing results. Reachable sets are also derived for this case. It is proved that the existing results can be derived as special cases of the ones considered in this thesis. As an extension to a realistic application, the importance of expansion in reachable set vis-a`-vis capturing a moving target is highlighted in this thesis. It has been shown that if the target’s initial position is reachable, then using a control law proposed in the thesis, the target can be captured. This control law is essentially an augmented cyclic pursuit law with the target’s velocity information fed to each agent in addition to the conventional cyclic pursuit command. Analysis has been carried out for agents with double integrator dynamics as well. A control law in conjunction with an algorithm is proposed that helps ensure global reachability of agents, with double integrator dynamics, in cyclic pursuit. Another application, in which cyclic pursuit and a closely related topology called platooning have been coupled together to track the boundaries of unknown regions and constantly monitor them, is addressed in this thesis. This problem is especially important in monitoring forest fire, marine contamination, volcanic ash eruptions, etc., and can protect human life by cordoning off unsafe regions using multiple autonomous agents. Lastly, discrete time cyclic pursuit laws are analyzed to obtain results similar to the continuous time counterparts that exist in the literature. Moreover, heterogeneous gains and deviations are admitted similar to the continuous time version considered in this thesis. Gershgorin’s theorem is used extensively to arrive at sufficient conditions for the stability of such discrete time deviated cyclic pursuit systems. Reachability sets are also derived. In case of discrete time systems, loss of synchronization due to no common clock for autonomous agents is a very realistic scenario. This thesis obtains some results on the stability of such asynchronous cyclic pursuit systems and indicates that special precautions are needed for dealing with heterogeneous cyclic pursuit systems even when one gain is negative, since the system may not converge, depending on the initial positions of the agents and the sequence of updates.

Thesis (Ph. D.)--University of Washington, 2003. / Vita. Includes bibliographical references (leaves 101-113).

Chan Ho Yu, Richard. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 115-122). / Abstracts in English and Chinese. / Declaration --- p.i / Acknowledgements --- p.ii / Abstract --- p.iii / 摘要 --- p.v / Table of Contents --- p.vii / Chapter Chapter 1: --- Introduction --- p.1 / Chapter 1.1 --- Potassium Channels --- p.1 / Chapter 1.1.1 --- Potassium Ions --- p.1 / Chapter 1.1.2 --- Potassium Channels --- p.1 / Chapter 1.1.3 --- Structure of K Channels --- p.2 / Chapter 1.1.4 --- Classification ofK Channels --- p.3 / Chapter 1.1.5 --- Mechanisms Contributed to K Channel Functions and Diversity --- p.5 / Chapter 1.1.5.1 --- RNA Editing --- p.5 / Chapter 1.1.5.2 --- Alternative Splicing --- p.6 / Chapter 1.1.5.3 --- Heteromultimeric Assembly of Principal Subunits --- p.6 / Chapter 1.1.5.4 --- Auxiliary Subunits --- p.7 / Chapter 1.1.5.5 --- Posttranslational Modifications --- p.7 / Chapter 1.2 --- Voltage-gated Potassium (Kv) Channels --- p.9 / Chapter 1.2.1 --- Diversity of Kv Channel Structure --- p.9 / Chapter 1.2.2 --- Early Origin of the Kv Family --- p.10 / Chapter 1.2.3 --- Structural Diversity of Kv Channels in Drosophila --- p.11 / Chapter 1.2.4 --- Structural Diversity of Kv Channels in Mammals --- p.11 / Chapter 1.2.5 --- Phylogenetic Tree of Kv Family --- p.13 / Chapter 1.2.6 --- Tissue Expression of Kv Channels --- p.13 / Chapter 1.2.7 --- "Three Main Functions of Kv Channels as Signaling Proteins: Ion Permeation, Gating and Sensing" --- p.16 / Chapter 1.2.7.1 --- Ion Permeation --- p.16 / Chapter 1.2.7.2 --- Gating --- p.18 / Chapter 1.2.7.2.1 --- Gating at the S6 Bundle Crossing --- p.18 / Chapter 1.2.7.2.2 --- Ball-and-Chain Gating --- p.19 / Chapter 1.2.7.2.3 --- Gating at the Selectivity Filter --- p.19 / Chapter 1.2.7.3 --- Sensing Mechanisms --- p.20 / Chapter 1.2.7.3.l --- Voltage Sensor --- p.20 / Chapter 1.2.7.3.2 --- Gating Sensors for Ligands --- p.21 / Chapter 1.3 --- KCNA10 --- p.22 / Chapter 1.3.1 --- "Rabbit Homologue of KCNA10, Kcnl" --- p.22 / Chapter 1.3.2 --- Genomic Localization of Human KCNA10 --- p.23 / Chapter 1.3.3 --- Human Gene for KCNA10 --- p.23 / Chapter 1.3.4 --- Basic Kinetic and Pharmacological Properties of KCNA10 --- p.25 / Chapter 1.3.5 --- "Regulation of KCNAlO by KCNA4B, a β -subunit" --- p.27 / Chapter 1.4 --- Aim of the Present Study --- p.30 / Chapter Chapter2: --- Materials and Methods --- p.31 / Chapter 2.1 --- Molecular Sub-Cloning ofKCNAlO --- p.31 / Chapter 2.1.1 --- Polymerase Chain Reaction (PCR) ofKCNA10 Fragment from KCNA Clone --- p.10 / Chapter 2.1.2 --- Separation and Purification of PCR Products --- p.32 / Chapter 2.1.2.1 --- Separation --- p.32 / Chapter 2.1.2.2 --- Purification --- p.33 / Chapter 2.1.3 --- Polishing the Purified PCR Products --- p.33 / Chapter 2.1.4 --- Ligation of PCR Products and pPCR-Script Amp SK(+) Cloning Vector --- p.34 / Chapter 2.1.5 --- Transformation --- p.34 / Chapter 2.1.6 --- Preparing Glycerol Stocks Containing the Bacterial Clones --- p.35 / Chapter 2.1.7 --- Plasmid DNA Preparation --- p.35 / Chapter 2.1.8 --- Clones Confirmation --- p.36 / Chapter 2.1.8.1 --- Restriction Enzyme Digestion --- p.36 / Chapter 2.1.8.2 --- Automatic Sequencing --- p.37 / Chapter 2.2 --- In situ Hybridization --- p.39 / Chapter 2.2.1 --- Probe Preparation --- p.39 / Chapter 2.2.1.1 --- Antisense KCNA10 RNA Probe --- p.39 / Chapter 2.2.1.2 --- Sense KCNA10 RNA Probe (Control Probe) --- p.40 / Chapter 2.2.2 --- Testing of DIG-Labeled RNA Probes --- p.43 / Chapter 2.2.3 --- Paraffin Sections Preparation --- p.43 / Chapter 2.2.4 --- In situ Hybridization: Pretreatment --- p.44 / Chapter 2.2.5 --- "Pre-hybridization, Hybridization and Post-hybridization" --- p.45 / Chapter 2.2.5.1 --- Pre-hybridization --- p.45 / Chapter 2.2.5.2 --- Hybridization --- p.45 / Chapter 2.2.5.3 --- Post-hybridization --- p.46 / Chapter 2.2.6 --- Colourimetnc Detection of Human KCNA10 --- p.46 / Chapter 2.3 --- Cell Culture --- p.47 / Chapter 2.3.1 --- Human Kidney Proximal Epithelial Cell Line (OK) --- p.47 / Chapter 2.3.2 --- Mouse Micro-vessel Endothelial Cell Line (H5V) --- p.48 / Chapter 2.3.3 --- Mouse Neuroblastoma Cell Line (NG108-15) --- p.48 / Chapter 2.3.4 --- Human Bladder Epithelial Cell Line (ECV304) --- p.48 / Chapter 2.3.5 --- Human T Cell Leukemia Cell Line (Jurkat) --- p.49 / Chapter 2.4 --- Total RNA Extraction --- p.49 / Chapter 2.5 --- Reverse Transcription from Cell Line --- p.51 / Chapter 2.6 --- Polymerase Chain Reaction (PCR) ofKCNAl 0 Fragment from Frist Strand cDNA --- p.51 / Chapter 2.7 --- Northern Hybridization --- p.52 / Chapter 2.7.1 --- Probe Preparation --- p.52 / Chapter 2.7.2 --- Separating RNA on an Agarose Gel --- p.52 / Chapter 2.7.3 --- RNA Transfer and Fixation --- p.52 / Chapter 2.7.4 --- Hybridization --- p.54 / Chapter 2.7.5 --- Post-hybridization --- p.54 / Chapter 2.7.6 --- Chemiluminescent Detection --- p.55 / Chapter 2.8 --- Intracellular Free Calcium Ion ([Ca2+］i) Measurement by Confocal Imaging System --- p.56 / Chapter 2.8.1 --- Bathing Solutions --- p.56 / Chapter 2.8.2 --- Preparation of Cells for [Ca2+]i Measurement --- p.56 / Chapter 2.8.3 --- Confocal Imaging System --- p.57 / Chapter 2.8.3.1 --- Fluo-3/AM Dye Loading --- p.57 / Chapter 2.8.3.2 --- [Ca2+]i Measurement --- p.57 / Chapter Chapter3: --- Results --- p.59 / Chapter 3.1 --- Phylogenetic Tree Reconstruction ofKCNAl0 --- p.59 / Chapter 3.2 --- Hydropathy Analysis ofKCNAl0 --- p.60 / Chapter 3.3 --- Molecular Sub-Cloning ofKCNAl0 --- p.61 / Chapter 3.3.1 --- Polymerase Chain Reaction (PCR) ofKCNAl0 Fragment from KCNA10 Clone --- p.61 / Chapter 3.3.2 --- Clones Confirmation --- p.63 / Chapter 3.4 --- In situ Hybridization Analysis ofKCNAl0 mRNAExpression --- p.65 / Chapter 3.4.1 --- Expression ofKCNAl0 in Human Kidney (Nephron) --- p.66 / Chapter 3.4.2 --- Expression ofKCNAl0 in Human Cerebral Artery --- p.69 / Chapter 3.4.3 --- Expression ofKCNAl0 in Human Cerebellum --- p.71 / Chapter 3.4.4 --- Expression ofKCNAl0 in Human Hippocampus --- p.73 / Chapter 3.4.5 --- Expression ofKCNAl0 in Human Occipital Cortex --- p.75 / Chapter 3.4.6 --- Expression ofKCNAl0 in Human Esophagus --- p.77 / Chapter 3.4.7 --- Expression ofKCNAl0 in Human Lung --- p.79 / Chapter 3.4.8 --- Expression ofKCNAl0 in Human Thyroid Glands --- p.81 / Chapter 3.4.9 --- Expression ofKCNAl0 in Human Adrenal Glands --- p.83 / Chapter 3.4.10 --- Expression ofKCNAl0 in Human Spleen --- p.86 / Chapter 3.5 --- RT-PCR ofKCNAl0 Fragment from Different Tissues --- p.88 / Chapter 3.6 --- Northern Blot Analysis of KCNA10 in Different Tissues --- p.90 / Chapter 3.7 --- Effects of Blocking KCNA10 on Ca2+ influx in Human Renal Proximal Tubule Epithelial Cells --- p.91 / Chapter Chapter4: --- Discussion --- p.97 / Chapter 4.1 --- Phylogency ofKCNAlO --- p.97 / Chapter 4.2 --- Hydropathy Plot for KCNA10 --- p.97 / Chapter 4.3 --- Expression ofKCNAl0 --- p.98 / Chapter 4.3.1 --- In situ Hybridization --- p.98 / Chapter 4.3.2 --- RT-PCR & Northern Blot Analysis --- p.99 / Chapter 4.4 --- Functional Implication of KCNA10 Expression in Different Human Tissues --- p.100 / Chapter 4.4.1 --- Unique Functional Properties ofKCNAlO --- p.100 / Chapter 4.4.2 --- Role ofKCNAlO in Renal Proximal Tubule --- p.101 / Chapter 4.4.2.1 --- Functions ofK+ Channels in Kidney --- p.101 / Chapter 4.4.2.2 --- The Function ofKCNAlO --- p.104 / Chapter 4.4.3 --- Role ofKCNAl0 in Blood Vessels --- p.106 / Chapter 4.4.3.1 --- Endothelial Cells --- p.106 / Chapter 4.4.3.2 --- Smooth Muscle Cells --- p.108 / Chapter 4.4.4 --- Role ofKCNA10 in CNS --- p.109 / Chapter 4.4.5 --- Role ofKCNAl0 in Secretory Cells --- p.111 / Chapter 4.4.6 --- Role ofKCNAl0 in Lung --- p.112 / Chapter 4.5 --- Conclusion --- p.114 / Chapter Chapter5： --- Reference --- p.115