In the thesis we investigate the connections between arbitrary functions and their realizing polynomials over finite algebras. We study functionally complete algebras, i.e. algebras over which every function can be realized by a polynomial expression. We characterize functional completeness by the so called Stone-Weierstrass property, and we determine the functionally complete semigroups and semirings. Then we investigate the computational perspective of the function-polynomial relationships over finite groups. We consider the efficient representability, the equivalence, and the equation solvability problems. We approach the efficient representability problem from three directions. We consider the length of functions, we investigate the circuit complexity of functions, and we analyse the finite-state sequential machine representation of Boolean functions. From each of these viewpoints we give bounds on the potential efficiency of computations based on functionally complete groups compared to computations based on the two-element Boolean algebra. Neither the equivalence problem nor the equation solvability problem has been completely characterized for finite groups. The complexity of the equivalence problem was only known for nilpotent groups. In the thesis we determine the complexity of the equivalence problem for certain meta-Abelian groups and for all non-solvable groups. The complexity of the equation solvability problem is known for nilpotent groups and for non-solvable groups. There are no results about the complexity of the equation solvability problem for solvable non-nilpotent groups apart from the case of certain meta-cyclic groups that we present in the thesis. Moreover, we determine the complexity of the equation solvability problem for all functionally complete algebra. The idea of the extended equivalence problem emerges from the observation that the commutator might significantly change the length of group-polynomials. We characterize the complexity of the extended equivalence problem for finite groups. For many finite groups we determine the complexity of the equivalence problem if the commutator is considered as the basic operation of the group.

Tsang Hing Wa = 梯度粒子系統的扭轉運動 / 曾慶華. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (leaves 66-68). / Text in English; abstracts in English and Chinese. / Tsang Hing Wa = Ti du li zi xi tong de niu zhuan yun dong / Zeng Qinghua. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Localization --- p.1 / Chapter 1.1.1 --- Localization by Potential Confinement --- p.1 / Chapter 1.1.2 --- Localization by Interference --- p.2 / Chapter 1.2 --- Graded Materials --- p.2 / Chapter 1.3 --- Rotational Motion --- p.3 / Chapter 2 --- Torsional Motion of Rotating Particles with Graded Couplings / Chapter 2.1 --- Linear Couplings --- p.5 / Chapter 2.1.1 --- Model and Formalism --- p.5 / Chapter 2.1.2 --- Gradient in Coupling Constant --- p.7 / Chapter 2.1.3 --- Gradient in Moment of Inertia --- p.8 / Chapter 2.1.4 --- Numerical Results --- p.9 / Chapter 2.1.5 --- Discussion and Conclusion --- p.14 / Chapter 2.2 --- Non-Linear Couplings --- p.14 / Chapter 2.2.1 --- Model and Formalism --- p.14 / Chapter 2.2.2 --- Gradient in Coupling Constant --- p.16 / Chapter 2.2.3 --- Gradient in Moment of Inertia --- p.16 / Chapter 2.2.4 --- Numerical Results --- p.17 / Chapter 2.2.5 --- Discussion and Conclusion --- p.29 / Chapter 3 --- Torsional Motion of Rotating Particles with graded potential --- p.30 / Chapter 3.1 --- Linear Interaction --- p.30 / Chapter 3.1.1 --- Model and Formalism --- p.30 / Chapter 3.1.2 --- Gradient in On-site Torsional Potential --- p.32 / Chapter 3.1.3 --- Numerical Results --- p.33 / Chapter 3.1.4 --- Discussion and Conclusion --- p.43 / Chapter 3.2 --- Non-linear Interaction --- p.43 / Chapter 3.2.1 --- Model and Formalism --- p.43 / Chapter 3.2.2 --- Numerical Results --- p.45 / Chapter 3.2.3 --- Chaotic Effect --- p.62 / Chapter 3.2.4 --- Discussion and Conclusion --- p.64 / Chapter 4 --- Conclusion --- p.65 / Bibliography --- p.66

Fracture mechanics plays an important role in understanding the performance of all types of materials including Functionally Graded Materials (FGMs). Recently, FGMs have attracted the attention of various scholars and engineers around the world since its specific material properties can smoothly vary along the geometries. In this thesis, the Finite Block Method (FBM), based on a 1D differential matrix derived from the Lagrangian Interpolation Method, has been presented for the evaluation of the mechanical properties of FGMs on both static and dynamic analysis. Additionally, the coefficient differential matrix can be determined by a normalized local domain, such as a square for 2D, a cubic for 3D. By introducing the mapping technique, a complex real domain can be divided into several blocks, and each block is possible to transform from Cartesian coordinate (xyz) to normalized coordinate (ξησ) with 8 seeds for two dimensions and 20 seeds for three dimensions. With the aid of coefficient differential matrix, the differential equation is possible to convert to a series of algebraic functions. The accuracy and convergence have been approved by comparison with other numerical methods or analytical results. Besides, the stress intensity factor and T-stresses are introduced to assess the fracture characteristics of FGMs. The Crack Opening displacement is applied for the calculation of the stress intensity factor with the FBM. In addition, a singular core is adopted to combine with the blocks for the simulation of T stresses. Numerical examples are introduced to verify the accuracy of the FBM, by comparing with Finite Element Methods or analytical results. Finally, the FBM is applied for wave propagation problems in two- and three-dimensional porous mediums considering their poroelasticities. To demonstrate the accuracy of the present method, a one-dimensional analytical solution has been derived for comparison.

Controlling fields and properties has attracted ever increasing interest over past decades due to the rapid advancement of nanofabrication techniques. In the field of nano-optics, to overcome the limit of signal processing speed and device scale of traditional electronic devices, optical devices using photon as the signal carriers have been chosen as the potential candidates. However, the diffraction limit of light has limited the integration of the micro-meter photonic components into electronic chips. Plasmonics offer the possibility to control electromagnetic fields at the subwavelength scale. Moreover , this controlling become tunable by introducing gradient into the material and/or structure, i.e., taking the concept of functionally graded materials (FGM) to design materials. / Gradon confinements in graded materials and/or systems open a door for tunable fields-controlling, which have potential applications in a variety of fields. Our research methods and results provide an effective way to understand field localization in a variety of systems, and they can be applied to design and manufacture thermal devices and even on-chip plasmonic-optical devices. / Gradon confinements, or referred as frequency-controlled localization of fields are investigated in various graded plasmonic lattices. The correspondences between gradon confinements and Bloch oscillations as well as nonBloch oscillations are explored. By taking into account retardation and loss effects, the asymmetric localization behavior and broadband localizat ion due to graded host permittivity are studied. / This thesis will concentrate on gradon confinements, which make controlling fields and properties tunable in graded materials and/or systems. We start with investigating gradon modes and their properties in graded elastic lattices. Using the quantum-classical analogue method, the analytic envelope function is obtained and can be used to analyze the system-size dependence of inverse participation ratio of gradon modes. In damping graded elastic lattices , the frequency-dependent behavior of relaxation rate are studied analytically and numerically. / We continue to study the three-dimensional graded plasmonic lattices with fully retarded electromagnetic interactions. A generalized Ewald-Kornfeld summation formula is developed to deal with the long-range interaction. In the quasistatic limit, various plasmonic gradon modes are investigated. Taking retardation and loss into account, field localization and enhancement are calculated in three-dimensional graded plasmonic lattices with graded size, spacing, and/or host permittivity in one direction. / Zheng, Mingjie = 弹性和等离子体梯度子禁闭研究 / 郑明杰. / Adviser: Kin Wah Yu. / Source: Dissertation Abstracts International, Volume: 72-11, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 117-124) and index. / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese. / Zheng, Mingjie = Tan xing he deng li zi ti ti du zi jin bi yan jiu / Zheng Mingjie.

In this thesis, we will discuss the possibility of wave manipulation by graded materials and/or systems. In contrast to the traditional inhomogeneous media, i.e. periodically modulated system and randomly disordered system, graded system demonstrates a unique way to control wave, resulting in a new type of localization-delocalization transition, which can confine the primary excitations (e.g., photons, phonons, and surface plasmons) and redistribute them spatially. This is not only of fundamental significance, but will also pave new avenue for various applications, for example, in surface elastic waves, nanooptics, and plasmonics. It also has implications with practical problems in industry such as oil probing and earthquake study. / Manipulating waves (e.g., elastic or electromagnetic) inside nanostructures has attracted ever increasing interest over the past decades due to the rapid advancement of nanofabrication techniques. Particularly, interactions of light with structures modulated at the wavelength or subwavelength scale offer an opportunity to achieve novel properties and designated functionalities in nanophotonics. Notable examples include photonic crystals, various metamaterials, and plasmonic devices. / Moreover, we consider to combine the novel properties of gradons and surface plasmons (SPs), in an attempt to explore new mechanisms to manipulate SP. Firstly, we study an incrementally-spaced nanoparticle chain waveguide, in which coupled plasmon waves show a localization-delocalization transition, in analogy to the elastic gradons. Secondly, we propose waveguides using periodic plasmonic chains immersed in a graded host which can sustain "light", "heavy", and "light-heavy" plasmonic gradons. Existence of tunable passband is demonstrated in these systems. / Thus, in view of the success, we discuss many potential applications in plasmonics, such as junctions, transistors, and even on-chip integrated plasmonic-dielectric devices. In this regard, we further study the most commonly used coplanar photonic elements, i.e., ring resonators and their integrated devices. To explore the interactions between various gradons and typical excitations would be very interesting and rewarding. Our findings have important ramifications for understanding excitations with transition spectra in many condensed matter systems, ranging from ultrasonic waves, seismic waves to light waves, microwaves, as well as quantum waves. / We started with one-dimensional graded networks of coupled harmonic oscillators. By examining the vibrational mode characteristics, we have identified a new kind of vibrational excitations, which are named "gradons". The features of elastic gradon are elab orated. Gradon localization is also different from well-known mechanisms of localization transition, such as defect(s) and Anderson-type localization. Gradons in higher dimensional graded elastic networks show more intriguing behaviors; we proved the existence of "soft", "hard", and "soft-hard" gradons in two dimensional cases. / Xiao Junjun = 新型调波功能材料 : 梯度子及其在纳米光学中的应用 / 肖君军. / "May 2006." / Adviser: Kin Wah Yu. / Source: Dissertation Abstracts International, Volume: 68-03, Section: B, page: 1694. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (p. 108-118). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307. / Xiao Junjun = Xin xing diao bo gong neng cai liao : ti du zi ji qi zai na mi guang xue zhong de ying yong / Xiao Junjun.

It has been argued that a secure and comfortable atmosphere is essential in order for a therapeutic or learning environment to be beneficial (Bakken 1998). In Functionally Oriented Music Therapy (FMT) there are arguably certain elements that help create this kind of atmosphere. By looking at the nature of FMT, what these elements might be, and FMT with two different clients, this paper tries to obtain a clearer idea of what creates a secure and comfortable atmosphere in FMT.

Thesis (Ph.D.)--McMaster University, 2005. / Supervisor: Patrick S. Nicholson. Includes bibliographical references (leaves 162-181). Also available online.

Thesis (Ph. D.)--University of California, San Diego and San Diego State University, 2006. / Includes bibliographical references (leaves 178-191).

In this paper, we study the nonlocal linear bending behavior of functionally graded beams subjected to distributed loads. A finite element formulation for an improved first-order shear deformation theory for beams with five independent variables is proposed. The formulation takes into consideration 3D constitutive equations. Eringen's nonlocal differential model is used to rewrite the nonlocal stress resultants in terms of displacements. The finite element formulation is derived by means of the principle of virtual work. High-order nodal-spectral interpolation functions were utilized to approximate the field variables, which minimizes the locking problem. Numerical results and comparisons of the present formulation with those found in the literature for typical benchmark problems involving nonlocal beams are found to be satisfactory and show the validity of the developed finite element model.

京都大学 / 新制・論文博士 / 博士(医学) / 乙第13465号 / 論医博第2252号 / 新制||医||1055(附属図書館) / (主査)教授 伊達 洋至, 教授 小西 靖彦, 教授 山下 潤 / 学位規則第4条第2項該当 / Doctor of Medical Science / Kyoto University / DFAM