Thesis (Ph.D)--Mathematics, Georgia Institute of Technology, 2009. / Committee Chair: Yi, Yingfei; Committee Member: Chow, Shui-Nee; Committee Member: Dieci, Luca; Committee Member: Verriest, Erik; Committee Member: Weiss, Howie. Part of the SMARTech Electronic Thesis and Dissertation Collection.

El presente trabajo tiene como finalidad exponer la discusión entre Kierkegaard y Hegel en torno a la noción de libertad, de acuerdo con la interpretación que ofrece concretamente sobre la misma el filósofo italiano Cornelio Fabro. De este modo, se mencionarán primeramente algunos de los puntos principales de estudio que aborda el filósofo italiano en su obra. Posteriormente se analizarán las posiciones especulativas que Hegel y Kierkegaard desarrollan, respectivamente, sobre el tema en cuestión. Por último, se realizarán algunas apreciaciones sobre la instancia existencial que presenta el pensador danés y que Fabro destaca.

<p>This work provides a theory of singular reference based on the idea that the function of a referring expression is to get an audience to think of some particular item. Although this obvious fact has not escaped anyone's notice, many believe that the considerations associated with this communicatory function do not belong to "semantics" but to "pragmatics". Others regard such considerations as relating to "perlocutionary", as opposed to "illocutionary", effects. By contrast the framework presented, which can be described as "Gricean", puts forward the theory of communication as the primary arena of semantics. I take the view (derived from Wittgenstein) that representation is to be explained in terms of agency. </p><p> Starting from a simple condition for paradigm acts of reference, the theory is developed by considering three areas of contemporary concern: names, definite descriptions and intentional contexts. While the "cluster" theory is upheld as an insight into the problem of determining the conventional bearer of a name, it is conceded that names function semantically in a manner postulated by Mill. Donnellan's distinction between referential and attributive uses of definite descriptions is redrawn; unlike recent accounts of this distinction, the account proposed represents the distinction as a sharp one The account of intentional contexts introduces an approac which exploits the Gricean model for analyzing a speaker' strategy. This approach differs significantly from other published accounts of intentional contexts.</p> / Thesis / Doctor of Philosophy (PhD)

We prove the existence and nonexistence of radial solutions of singular semilinear equations Δu + k(x)f(u)=0 with boundary condition on the exterior of the ball with radius R>0 in ℝ^N such that lim r →∞ u(r)=0, where f: ℝ \ {0} →ℝ is an odd and locally Lipschitz continuous nonlinear function such that there exists a β >0 with f <0 on (0, β), f >0 on (β, ∞), and K(r) ~ r^-α for some α >0.

Flutter suppression is a problem of considerable interest in modern avionics. Flutter is a vibration caused by energy in the airstream being absorbed by a non-rigid wing. Active control is one possible method of suppressing flutter. However, due to unmeasurable aerodynamic-lag states, developing an active control using full-state feedback is not viable. The use of a state-estimator is a more practical way of developing active controllers. In this paper we investigate two control methods using state-estimators. We also use simple models of disturbances to test attenuation and robustness of each control method. Finally, a method of quantitative robust analysis is reviewed and then applied to each of the controlled systems. / Master of Science

The research contained in this thesis can be divided into two related, but distinct parts. The rst chapter deals with block Toeplitz operators de ned by rational matrix function symbols on discrete sequence spaces. Here we study sequences of operators that converge to the inverses of these Toeplitz operators via an invertibility result involving a special representation of the symbol of these block Toeplitz operators. The second part focuses on a special class of matrices generated by banded Toeplitz matrices, i.e., Toeplitz matrices with a nite amount of non-zero diagonals. The spectral theory of banded Toeplitz matrices is well developed, and applied to solve questions regarding the behaviour of the singular values of Toeplitz-generated matrices. In particular, we use the behaviour of the singular values to deduce bounds for the growth of the norm of the inverse of Toeplitz-generated matrices. In chapter 2, we use a special state-space representation of a rational matrix function on the unit circle to de ne a block Toeplitz operator on a discrete sequence space. A discrete Riccati equation can be associated with this representation which can be used to prove an invertibility theorem for these Toeplitz operators. Explicit formulas for the inverse of the Toeplitz operators are also derived that we use to de ne a sequence of operators that converge in norm to the inverse of the Toeplitz operator. The rate of this convergence, as well as that of a related Riccati di erence equation is also studied. We conclude with an algorithm for the inversion of the nite sections of block Toeplitz operators. Chapter 3 contains the main research contribution of this thesis. Here we derive sharp growth rates for the norms of the inverses of Toeplitz-generated matrices. These results are achieved by employing powerful theory related to the Avram-Parter theorem that describes the distribution of the singular values of banded Toeplitz matrices. The investigation is then extended to include the behaviour of the extreme and general singular values of Toeplitz-generated matrices. We conclude with Chapter 4, which sets out to answer a very speci c question regarding the singular vectors of a particular subclass of Toeplitz-generated matrices. The entries of each singular vector seems to be a permutation (up to sign) of the same set of real numbers. To arrive at an explanation for this phenomenon, explicit formulas are derived for the singular values of the banded Toeplitz matrices that serve as generators for the matrices in question. Some abstract algebra is also employed together with some results from the previous chapter to describe the permutation phenomenon. Explicit formulas are also shown to exist for the inverses of these particular Toeplitz-generated matrices as well as algorithms to calculate the norms and norms of the inverses. Finally, some additional results are compiled in an appendix. / PhD (Mathematics), North-West University, Potchefstroom Campus, 2015

The research contained in this thesis can be divided into two related, but distinct parts. The rst chapter deals with block Toeplitz operators de ned by rational matrix function symbols on discrete sequence spaces. Here we study sequences of operators that converge to the inverses of these Toeplitz operators via an invertibility result involving a special representation of the symbol of these block Toeplitz operators. The second part focuses on a special class of matrices generated by banded Toeplitz matrices, i.e., Toeplitz matrices with a nite amount of non-zero diagonals. The spectral theory of banded Toeplitz matrices is well developed, and applied to solve questions regarding the behaviour of the singular values of Toeplitz-generated matrices. In particular, we use the behaviour of the singular values to deduce bounds for the growth of the norm of the inverse of Toeplitz-generated matrices. In chapter 2, we use a special state-space representation of a rational matrix function on the unit circle to de ne a block Toeplitz operator on a discrete sequence space. A discrete Riccati equation can be associated with this representation which can be used to prove an invertibility theorem for these Toeplitz operators. Explicit formulas for the inverse of the Toeplitz operators are also derived that we use to de ne a sequence of operators that converge in norm to the inverse of the Toeplitz operator. The rate of this convergence, as well as that of a related Riccati di erence equation is also studied. We conclude with an algorithm for the inversion of the nite sections of block Toeplitz operators. Chapter 3 contains the main research contribution of this thesis. Here we derive sharp growth rates for the norms of the inverses of Toeplitz-generated matrices. These results are achieved by employing powerful theory related to the Avram-Parter theorem that describes the distribution of the singular values of banded Toeplitz matrices. The investigation is then extended to include the behaviour of the extreme and general singular values of Toeplitz-generated matrices. We conclude with Chapter 4, which sets out to answer a very speci c question regarding the singular vectors of a particular subclass of Toeplitz-generated matrices. The entries of each singular vector seems to be a permutation (up to sign) of the same set of real numbers. To arrive at an explanation for this phenomenon, explicit formulas are derived for the singular values of the banded Toeplitz matrices that serve as generators for the matrices in question. Some abstract algebra is also employed together with some results from the previous chapter to describe the permutation phenomenon. Explicit formulas are also shown to exist for the inverses of these particular Toeplitz-generated matrices as well as algorithms to calculate the norms and norms of the inverses. Finally, some additional results are compiled in an appendix. / PhD (Mathematics), North-West University, Potchefstroom Campus, 2015

This study examined the relationship between family status and child behavior and the relationship between the primary caregiver groups and child behavior. In total, there were 40 non-randomly selected participants who took part in a cross-sectional design. The Final Survey consisted of a combined questionnaire of the Child Behavior Checklist and the Eyberg Child Behavior Inventory. This study found that there were no statistically significant differences between singular and dual households in regards to child behavior (p =.222) and no statistically significant differences between the primary caregiver groups in regards to child behavior (p= .312). The conclusions drawn from the findings suggest that living arrangements and the primary caregiver groups do not influence maladaptive child behavior.

The chemical master equation (CME) represents the accepted stochastic description of chemical reaction kinetics in mesoscopic systems. As its exact solution – which gives the corresponding probability density function – is possible only in very simple cases, there is a clear need for approximation techniques. Here, we propose a novel perturbative three-step approach which draws heavily on graph theory: (i) we expand the eigenvalues of the transition state matrix in the CME as a series in a non-dimensional parameter that depends on the reaction rates and the reaction volume; (ii) we derive an analogous series for the corresponding eigenvectors via a graph-based algorithm; (iii) we combine the resulting expansions into an approximate solution to the CME. We illustrate our approach by applying it to a reversible dimerization reaction; then, we formulate a set of conditions, which ensure its applicability to more general reaction networks. We follow attempting to apply the results to a more complicated system, namely push-pull, but the problem reveals too complex for a complete solution. Finally, we discuss the limitations of the methodology.

by Lau Shui-kong, Francis. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 95-98). / Abstracts in English and Chinese. / Chapter 1 --- General Theory of Wavelets --- p.8 / Chapter 1.1 --- Introduction --- p.8 / Chapter 1.2 --- Multiresolution Analysis and Wavelets --- p.9 / Chapter 1.3 --- Orthonormal Bases of Compactly Supported Wavelets --- p.12 / Chapter 1.3.1 --- Example : The Daubechies Wavelets --- p.15 / Chapter 1.4 --- Wavelets in Higher Dimensions --- p.20 / Chapter 1.4.1 --- Tensor product method --- p.20 / Chapter 1.4.2 --- Multiresolution Analysis in Rd --- p.21 / Chapter 1.5 --- Generalization to frames --- p.25 / Chapter 2 --- Wavelet Bases Numerical Algorithm --- p.27 / Chapter 2.1 --- The Algorithm in Wavelet Bases --- p.27 / Chapter 2.1.1 --- Definitions and Notations --- p.28 / Chapter 2.1.2 --- Fast Wavelet Transform --- p.31 / Chapter 2.2 --- Wavelet-Based Quadratures --- p.33 / Chapter 2.3 --- "The Integral Operator, Standard and Non-standard Form" --- p.39 / Chapter 2.3.1 --- The Standard Form --- p.40 / Chapter 2.3.2 --- The Non-standard Form --- p.41 / Chapter 2.4 --- The Calderon-Zygmund Operator and Numerical Cal- culation --- p.45 / Chapter 2.4.1 --- Numerical Algorithm to Construct the Non- standard Form --- p.45 / Chapter 2.4.2 --- Numerical Calculation and Compression of Op- erators --- p.45 / Chapter 2.5 --- Differential Operators in Wavelet Bases --- p.48 / Chapter 3 --- T(l)-Theorem of David and Journe --- p.55 / Chapter 3.1 --- Definitions and Notations --- p.55 / Chapter 3.1.1 --- T(l) Operator --- p.56 / Chapter 3.2 --- The Wavelet Proof of the T(l)-Theorem --- p.59 / Chapter 3.3 --- Proof of the T(l)-Theorem (Continue) --- p.64 / Chapter 3.4 --- Some recent results on the T(l)-Theorem --- p.70 / Chapter 4 --- Singular Values of Compact Pseudodifferential Op- erators --- p.72 / Chapter 4.1 --- Background --- p.73 / Chapter 4.1.1 --- Singular Values --- p.73 / Chapter 4.1.2 --- Schatten Class Ip --- p.73 / Chapter 4.1.3 --- The Ambiguity Function and the Wigner Dis- tribution --- p.74 / Chapter 4.1.4 --- Weyl Correspondence --- p.76 / Chapter 4.1.5 --- Gabor Frames --- p.78 / Chapter 4.2 --- Singular Values of Lσ --- p.82 / Chapter 4.3 --- The Calderon-Vaillancourt Theorem --- p.87 / Chapter 4.3.1 --- Holder-Zygmund Spaces --- p.87 / Chapter 4.3.2 --- Smooth Dyadic Resolution of Unity --- p.88 / Chapter 4.3.3 --- The proof of the Calderon-Vaillancourt The- orem --- p.89 / Bibliography