The rotavirus NSP4 protein is the first described viral enterotoxin. Abundant data from our laboratory reveals that NSP4 binds both the N- and C-termini of caveolin- 1 (aa2-31 and 161-178, respectively). Yeast two-hybrid and peptide binding analysis mapped the caveolin-1 binding site to three hydrophobic residues within the amphipathic a-helix, enterotoxic peptide domain (aa114-135). The research studies herein utilized peptides to investigate the interaction between NSP4 and caveolin-1. Peptides were synthesized corresponding to the amphipathic a-helix and caveolin-1 binding domain of NSP4 (aa112-140) and to the N- (aa2-20 and 19-40) and C- (161-178) termini of caveolin-1, and were utilized in structural and functional studies. Fluorescence binding assays revealed that NSP4 (aa112-140) binds to the N-terminus (aa19-40) of caveolin-1 with a stronger affinity than the C-terminus (aa161-178). In addition, this assay further delineated the NSP4 binding domain on caveolin-1 to aa19-40. Secondary structural changes following NSP4-caveolin-1 peptide-peptide interactions were investigated by circular dichroism analysis. Changes in a-helix formation were observed only upon interaction of the NSP4112-140 peptide with the C-terminal caveolin-1 peptide (C-Cav161- 178). The NSP4112-140 peptide contains a potential cholesterol recognition amino acid consensus (CRAC) sequence. Therefore this peptide was examined for cholesterol binding. Results of the binding assay revealed NSP4 binds cholesterol with a Kd of 7.67 +/- 1.49nM and this interaction occurs via aa112-140. Mutation of amino acid residues within the CRAC motif resulted in weaker binding affinities between each of the corresponding mutant peptides and cholesterol. NSP4 peptides containing mutations within the hydrophobic and charged faces of the amphipathic a-helix, enterotoxic peptide and caveolin-1 binding domain of NSP4 were examined for changes in secondary structure as well as diarrhea induction in mouse pups. Circular dichroism analysis revealed that mutation of hydrophobic residues resulted in a decrease in a-helix formation, whereas mutation of acidic and basic charged residues caused little to no change in a-helical content. When tested for diarrhea induction in mouse pups, the peptides containing mutations of either the hydrophobic or basic charged residues did not cause diarrhea. Taken together, the results of this research suggest a complex interplay between NSP4 secondary structure, caveolin-1 and cholesterol binding and diarrheagenic function.

This thesie discusses uniquely circular colourable and uniquely fractional colourable graphs. Suppose G = (V;E) is a graph and r ¸ 2 is a real number. A circular r-colouring of G is a mapping f : V (G) ! [0; r) such that for any edge xy of G, 1 ¡P jf(x) ¡ f(y)j ¡P r ¡ 1. We say G is uniquely circular r-colourable if there is a circular r-colouring f of G and any other circular r-colouring of G can obtained from f by a rotation or a ¢Xip of the colours. Let I(G) denote the family of independent sets of G. A fractional r-colouring of G is a mapping f : I(G) ! [0; 1] such that for any vertex x, Px2I f(I) = 1 and PI2I(G) f(I) ¡P r. A graph G is called uniquely fractional r-colourable if there is exactly one fractional r-colouring of G. Uniquely circular r-colourable graphs have been studied extensively in the literature. In particular, it is known that for any r ¸ 2, for any integer g, there is a uniquely circular r- colourable graph of girth at least g. Uniquely fractional r-colouring of graphs is a new concept. In this thesis, we prove that for any r ¸ 2 for any integer g, there is a uniquely fractional r-colourable graph of girth at least g. It is well-known that for any graph G, Âf (G) ¡P Âc(G). We prove that for any rational numbers r ¸ r0 > 2 and any integer g, there is a graph G of girth at least g, which is uniquely circular r-colourable and at the same time uniquely fractional r0-colourable.

In the proposed project¡Athe three - dimensional vibration of circular and annular plates is analyzed by a mixed finite element¡C Stresses¡Aas well as displacements¡A are primary variables in the mixed finite element formulation¡Atherefore¡Aall the stress and displacement boundary conditions can be imposed exactly¡CMeanwhile¡Athe proposed finite element is a modification of axisymmetric finite element which is based on three ¡V dimensional elasticity¡Aso general results of both axisymmetric and unaxisymmetric vibration of circular and annular plates can be obtained¡C Results of the present project will be compared to those by conventional displacement ¡V type finite element¡ARitz method and series method to show the difference among these theories¡CEspecially¡Athe effect of satisfying the stress boundary conditions on the unaxisymmetric vibration analyses can be demonstrated¡Awhich is not available in the literature up to date¡C

In this thesis, we shall propose heuristic algorithms to construct evolutionary trees under the distance base model. For a distance matrix of any type, the problem of constructing a minimum ultrametric tree (MUT), whose scoring function is the minimum tree size, is NP-hard. Furthermore, the problem of constructing an approximate ultrametric tree with approximation error ratio within $n^{epsilon}, epsilon > 0$, is also NP-hard. When the distance matrix is metric, the problem is called the triangle minimum ultrametric tree problem ($ riangle$MUT). For the $ riangle$MUT, there is a previous approximation algorithm, with error ratio $leq 1.5 ( lceil log n ceil + 1 )$. And we shall propose an improvement, with error ratio $leq lceil log_{alpha} n ceil + 1 cong 1.44 lceil log n ceil + 1$, where $alpha = frac{sqrt{5}+1}{2}$ for solving the $ riangle$MUT problem. We shall also propose a heuristic algorithm to obtain a good leaf node circular order. The heuristic algorithm is based on the clustering scheme. And then we shall design a dynamic programming algorithm to construct the optimal ultrametric tree with some fixed leaf node circular order. The time complexity of the dynamic programming is $O(n^3)$, if the scoring function is the minimum tree size or $L^1$-min increment.

ABSTRACT In the present study, it is emphasized that mixed-type finite element formulation, which is different from the conventional displacement-type formulation, has both displacements and stresses as its primary variables. Therefore, stress, as well as displacement boundary conditions, can be imposed easily and exactly. Except around the outer edge where support is placed, stresses obtained by both displacement and mixed formulation are close to each other when the circular plate is subject to transverse uniform loading. However, large discrepancies exist around the locations of constraints, where the stresses are always significant and critical. Since mixed formulation of the present study can completely satisfy the stress and displacement boundary conditions, it can theoretically provide more accurate stress analysis and should be considered as a more appropriate analysis tool.

The bevel gears have been widely used for the intersected-axial transmission system for a long time. But mostly them are limited in the category of involute tooth profiles. It is believed that bevel gears with circular-arc tooth profile, similar to the Wildhaber-Novikov circular-arc helical gears, will improve the load capacity of the gear set. The bevel gears with circular-arc tooth profiles was firstly proposed by Kuo and Tsai in 2001. Although these new type of bevel gears can increase the load capacity of transmission, the expensive manufacturing process is still the problem. In this paper, the design parameters of bevel gear with circular-arc profiles developed by Kuo and Tsai are modified. Bevel gear set with spiral point contact path is developed. This improvement makes it possible to manufacturing the newly developed bevel gears in just a simple milling or/and grinding process with circular cutting edges. The manufacturing process is then cost down quit a lot. A method for checking the gear interference is also proposed. Finally, the 3D solid models of the bevel gear with circular-arc tooth profiles as well as the grinding wheel are constructed by using the computer software ¡§Pro/E¡¨. It is believed that the mathematical models and the design method developed in the thesis will provide a useful foundation for the further studies.

The objective of the study is to investigate the capability of PANS (Partially Averaged Navier-Stokes Simulation) model over a wide range of Reynolds numbers and flow physics. In this regard, numerical simulations of turbulent flow past a circular cylinder are performed at ReD 140,000 and ReD 3900 using the PANS model. The high Reynolds number PANS results are compared with experimental results from Cantwell and Coles, Large Eddy Simulation results from Breuer, and Detached Eddy Simulation results from Travin et al. Low Reynolds number PANS results are compared with experimental results from Ong and Wallace and Large Eddy Simulation results from Breuer. The effects of the various PANS parameters (fk, fε, σku, σεu) on the ability to capture turbulence physics at various Reynolds numbers are studied. It is confirmed, as previously predicted from theoretical considerations that: (i) for high Reynolds number flow fε = 1 and σku = σk × fk2 / fε are most appropriate; and (ii) for low Reynolds number flow fε = fk and σku = σk are most suitable. These choices for the parameters stem from the fact that there is no clear separation of scales between the energy scales and the dissipation scales at low Reynolds number unlike in the high Reynolds number where there is a clear separation of scales between the energy containing scales and the dissipation scales. Also, in both cases it is found that decreasing fk leads to improved accuracy in predicting the flow statistics.

In this thesis two different research topics are undertaken, both in the area of compact RF/microwave circuits design. The first topic involves the design of a compact circularly polarized (CP) slot-ring antenna. A study of several compact CP microstrip and slotline antennas reported in the past has been carried out. In this research, a method of reducing the size of a printed slot-ring antenna is proposed. The reduction in size is achieved by introducing meandered-slot sections in the ring. Circular polarization is achieved by introducing an asymmetry, also a meandered-slot section, and feeding the antenna at an angle of 45o from the asymmetry using a microstrip feed line. The minimum axial ratio of 0.4 dB is obtained at 2.46 GHz, which is the operating frequency of the antenna. The size of the proposed antenna is reduced by about 50% compared to a conventional CP slot-ring antenna and it displays a CP bandwidth of about 2.5%. The simulated and measured results are presented, and they are in good agreement. The small size of the antenna makes it very suitable for use in modern RF/microwave wireless systems which require compact, low cost, and high performance circuits. Moreover, its CP behavior makes it more attractive for applications such as satellite communications. The second topic in the thesis involves the design of a compact microstrip bandpass filter using triangular open-loop resonators. A new compact three-pole microstrip bandpass filter using four triangular open-loop resonators is presented. A fourth resonator is placed to provide cross-coupling in the structure which gives a better skirt rejection. The measured pass-band center frequency is 2.85 GHz. The filter demonstrates about 7% bandwidth with insertion loss of less than 1 dB in the passband, a return loss of greater than 15 dB and out-of-band rejection of greater than 30 dB. The simulated and measured results are in good agreement. The proposed filter is very attractive for use in modern wireless systems which require bandpass filters having compact size, low insertion loss, high selectivity, and good out-of-band rejection.

A three-link, single-degree-of-freedom mechanism, named the Spirograph linkage, is investigated in this thesis. What is special about this open-chain mechanism is that, by the use of a chain and two sprockets and therefore maintaining a constant angular velocity ratio between the two rotating links, the path traced by this mechanism can be shown to be either an epitrochoid or a hypotrochoid. Through the understanding of the formulations of the trochoids, the relations between the design parameters of the Spirograph linkage and the corresponding path patterns are derived. With certain design parameter combinations, the Spirograph linkage is able to feature paths with cusps, which means dwells and are useful in applications. A design chart for such cusp-generating Spirograph linkages is then included in the thesis for the sake of convenience. In addition, by matching the link-length ratio with the angular velocity ratio, ways for finding closed single-loop paths of the Spirograph linkage are also studied. As for the path generation problems concerning only a fraction of the entire path, we compare results given by the classical precision point scheme with assorted combinations of initial conditions. In the latter part of the thesis, non-circular sprockets are also introduced to provide the Spirograph linkage additional freedom to cope with the demand of more flexible, i.e., non-symmetrical shapes of the path. However, many constraints are to be imposed on the design process of such linkages, and these design limitations are elaborated in the thesis. At last, the use of Newton¡¦s method, the selection of the proper type of trochoids, the application of the envelop method for obtaining the profile of the non-circular sprocket, the analyses of angular velocity ratios, etc. are all exemplified in the several numerical examples of the thesis.

This research is aimed to investigate the fluid-elastic instability of the motion simulation using a single cylinder and two cylinders within the context of shear flows. T/D, shear parameter and mass ratio are parameters to be investigated. Besides, cylindrical motion treks and the amplitude are also analyzed. Continuity equation and momentum equations are solved alternatively using a CFD package, Fluent 6.3.26. The force caused by the flow interacts with the cylindrical motion. Thus Motion meshing techniques together with the cylindrical motion equations are employed in the simulation. Under different flow conditions, flow types and cylindrical motion models, lock-in and fluid-elastic instability are studied. The results show that motion and flow types of a single cylinder within the context of the uniform flow have a general agreement with the related literatures. In terms of the shear flow, however, as the shear parameter increases, the fluid-elastic instability is caused, and thus amplitude of the cylinder augments considerably. Further, double cylinders in the shear flow are studied. Double cylinder arrangements( classified as side-by-side and tandem) and the distance between cylinders are the factors to cause fluid-elastic instability. Compared with the single cylindrical motion, double cylindrical motion¡¦s critical flow velocity is smaller than the single cylindrical motion, which means double cylindrical motion are more subject to fluid-elastic instability.