BACH TO BASICS: A PERFORMANCE STUDY OF THE SUITES FOR SOLO CELLO BY JOHANN SEBASTIAN BACH, BWV 1007-1012

This dissertation project focuses on J.S. Bach's Six Suites and explores the ideology of the Suites as etudes versus concert pieces. It is my belief that the evolution of the rank of the Suites in a cellist's repertoire today represents more than just historical coincidence. My premise is that the true genius of the Suites lies in their dual role as !&I efficient teaching pieces and superior performance works. Consequently, the maximum use of Bach's Six Suites as pedagogical material heightens both technical ability and deeper appreciation of the art. The dual nature of the Suites must always be emphasized: not only do these pieces provide innumerable opportunities for building cello technique, but they also offer material for learning the fundamentals of melody, harmony, dynamics, phrasing and texture. It is widely accepted among academic musicians that Bach's keyboard music serves as perfect compositions -- the model for music theory, music form and music counterpoint. I argue that we should employ the Cello Suites to this same end. The order in which the Suites are presented was deliberately chosen to highlight the contrasts in the pieces. Because the technical demands of each suite grow progressively from the previous one, they were performed non-consecutively in order to balance the difficulty and depth of each recital. The first compact disc consists of the Third Suite in C Major and Fifth Suite in C minor (with scordatura tuning), emphasizing the parallel keys. The Second Suite in D Minor and the Fourth Suite in E-flat Major comprises the compact disc. Finally, in the third compact disc, the First Suite in G Major and the Sixth Suite in D Major (composed for the five string cello piccola, but played here on a four-string cello) highlights the progression of the Suites.

AN ENTROPIC THEORY OF DAMAGE WITH APPLICATIONS TO CORROSION-FATIGUE STRUCTURAL INTEGRITY ASSESSMENT

This dissertation demonstrates an explanation of damage and reliability of critical components and structures within the second law of thermodynamics. The approach relies on the fundamentals of irreversible thermodynamics, specifically the concept of entropy generation due to materials degradation as an index of damage. All failure mechanisms that cause degradation, damage accumulation and ultimate failure share a common feature, namely energy dissipation. Energy dissipation, as a fundamental measure for irreversibility in a thermodynamic treatment of non-equilibrium processes, leads to and can be expressed in terms of entropy generation. The dissertation proposes a theory of damage by relating entropy generation to energy dissipation via generalized thermodynamic forces and thermodynamic fluxes that formally describes the resulting damage. Following the proposed theory of entropic damage, an approach to reliability and integrity characterization based on thermodynamic entropy is discussed. It is shown that the variability in the amount of the thermodynamic-based damage and uncertainties about the parameters of a distribution model describing the variability, leads to a more consistent and broader definition of the well know time-to-failure distribution in reliability engineering. As such it has been shown that the reliability function can be derived from the thermodynamic laws rather than estimated from the observed failure histories. Furthermore, using the superior advantages of the use of entropy generation and accumulation as a damage index in comparison to common observable markers of damage such as crack size, a method is proposed to explain the prognostics and health management (PHM) in terms of the entropic damage. The proposed entropic-based damage theory to reliability and integrity is then demonstrated through experimental validation. Using this theorem, the corrosion-fatigue entropy generation function is derived, evaluated and employed for structural integrity, reliability assessment and remaining useful life (RUL) prediction of Aluminum 7075-T651 specimens tested.

Strong shift equivalence, algebraic K-theory, and isolating zero-dimensional dynamics on manifolds

We study the relations of shift equivalence and strong shift equivalence for matrices over a ring $\mathcal{R}$, and establish a connection between these relations and algebraic K-theory. We utilize this connection to obtain results in two areas where the shift and strong shift equivalence relations play an important role: the study of finite group extensions of shifts of finite type, and the Generalized Spectral Conjectures of Boyle and Handelman for nonnegative matrices over subrings of the real numbers. We show the refinement of the shift equivalence class of a matrix $A$ over a ring $\mathcal{R}$ by strong shift equivalence classes over the ring is classified by a quotient $NK_{1}(\mathcal{R}) / E(A,\mathcal{R})$ of the algebraic K-group $NK_{1}(\calR)$. We use the K-theory of non-commutative localizations to show that in certain cases the subgroup $E(A,\mathcal{R})$ must vanish, including the case $A$ is invertible over $\mathcal{R}$. We use the K-theory connection to clarify the structure of algebraic invariants for finite group extensions of shifts of finite type. In particular, we give a strong negative answer to a question of Parry, who asked whether the dynamical zeta function determines up to finitely many topological conjugacy classes the extensions by $G$ of a fixed mixing shift of finite type. We apply the K-theory connection to prove the equivalence of a strong and weak form of the Generalized Spectral Conjecture of Boyle and Handelman for primitive matrices over subrings of $\mathbb{R}$. We construct explicit matrices whose class in the algebraic K-group $NK_{1}(\mathcal{R})$ is non-zero for certain rings $\mathcal{R}$ motivated by applications. We study the possible dynamics of the restriction of a homeomorphism of a compact manifold to an isolated zero-dimensional set. We prove that for $n \ge 3$ every compact zero-dimensional system can arise as an isolated invariant set for a homeomorphism of a compact $n$-manifold. In dimension two, we provide obstructions and examples.