We study the geometric classi&#64257;cation of Banach spaces via Lipschitz, uniformly continuous, and coarse mappings. We prove that a Banach space which is uniformly homeomorphic to a linear quotient of lp is itself a linear quotient of lp when p<2. We show that a Banach space which is Lipschitz universal for all separable metric spaces cannot be asymptotically uniformly convex. Next we consider coarse embedding maps as de&#64257;ned by Gromov, and show that lp cannot coarsely embed into a Hilbert space when p> 2. We then build upon the method of this proof to show that a quasi-Banach space coarsely embeds into a Hilbert space if and only if it is isomorphic to a subspace of L0(??) for some probability space (&#937;,B,??).

This research explores the impact of kinematic structural nonlinearities on the dynamics of a highly deformable cantilevered wing. Two different theoretical formulations are presented and analysed for nonlinear behavior. The first formulation, which is more conventional, assumes zero equilibrias and structural nonlinearities occur as terms up to third order in the Taylor series expansion of structural nonlinearities. In the second approach, no prior assumption about equilibria states of the wing is made. Kinematic nonlinearities due to curvature and inertia were retained in their exact form. Thus, the former becomes a special case of the latter. This nonlinear formulation permits the analysis of dynamics about nonzero trims. Nonzero trim states are computed as a system parameter is varied using a continuation software tool. The stability characteristics of these trim states are also ascertained. Various bifurcation points of the system are determined. Limit-cycle oscillations are also investigated for and are characterized in terms of amplitude of vibration. The research in particular examines the impact of in-plane degree of freedom on the stability of nonzero trim states. The effect of variation of system parameters such as stiffness ratio, aspect ratio and root angle of attack is also studied. The method of direct eigenanalysis of nonzero equilibria is novel and new for an aeroelastic system.

This work presents a control algorithm developed from the mammalian emotional processing network. Emotions are processed by the limbic system in the mammalian brain. This system consists of several components that carry out different tasks. The system level understanding of the limbic system has been previously captured in a discrete event computational model. This computational model was modified suitably to be used as a feedback mechanism to regulate the output of a continuous-time first order plant. An extension to a class of nonlinear plants is also discussed. The combined system of the modified model and the linear plant are represented as a set of bilinear differential equations valid in a half space of the 3-dimensional real space. The bounding plane of this half space is the zero level of the square of the plant output. This system of equations possesses a continuous set of equilibrium points which lies on the bounding plane of the half space. The occurrence of a connected equilibrium set is uncommon in control engineering, and to prove stability for such cases one needs an extended Lyapunov-like theorem, namely LaSalle's Invariance Principle. In the process of using this Principle, it is shown that this set of equations possesses a first integral as well. A first integral is identified using the compatibility method, and this first integral is utilized to prove asymptotic stability for a region of the connect equilibrium set.

This thesis studies the nonlinear characteristics of microwave devices by Volterra series because it can analyze the nonlinear devices with memory. And a nonlinear model was established by measurement data for Volterra series analysis. This content is composed of three parts. The first part devote to introduce the nonlinear phenomenon and theories of nonlinear analysis. The difference between power series and Volterra series could be realized by deriving them. The second part is to introduce the physical characteristics of pHEMTs and demonstrate the procedure of establishing small signal model and fitting nonlinear equations of currents and capacitances, and a process of nonlinear model analysis by Volterra series is shown. The third part is to describe the experimental arrangements and analyze nonlinear characteristics of pHEMTs actually with above methods. And the relationship among nonlinear sources was discussed. The device was fabricated by WIN 0.15£gm InGaAs process and measured by on wafer measurements.

Thesis (Ph. D.)--Lehigh University, 2000. / Includes vita. Includes bibliographical references (leaves 191-203).

Thesis (M. Phil.)--University of Hong Kong, 2010. / Includes bibliographical references (leaves 72-80). Also available in print.

Thesis (doctoral)--Friedrich-Alexanders-Universität Erlangen, 1911. / Vita. Includes bibliographical references.

Thesis (Honors)--College of William and Mary, 2009. / Includes bibliographical references (leaf 37). Also available via the World Wide Web.

Thesis (Ph. D.)--University of Texas at Austin, 2002. / Vita. Includes bibliographical references. Available also in a digital version from UMI Company.

Thesis (Ph. D.)--University of Texas at Austin, 2002. / Vita. Includes bibliographical references (leaves 133-146). Available also in a digital version from Dissertation Abstracts.