No description available.

A natural problem that arises in the study of derivations on a Banach algebra is to classify the commutators in the algebra. The problem as stated is too broad and we will only consider the algebra of operators acting on a given Banach space X. In particular, we will focus our attention to the spaces $\lambda I and $\linf$. The main results are that the commutators on $\ell_1$ are the operators not of the form $\lambda I + K$ with $\lambda\neq 0$ and $K$ compact and the operators on $\linf$ which are commutators are those not of the form $\lambda I + S$ with $\lambda\neq 0$ and $S$ strictly singular. We generalize Apostol's technique (1972, Rev. Roum. Math. Appl. 17, 1513 - 1534) to obtain these results and use this generalization to obtain partial results about the commutators on spaces $\mathcal{X}$ which can be represented as $\displaystyle \mathcal{X}\simeq \left ( \bigoplus_{i=0}^{\infty} \mathcal{X}\right)_{p}$ for some $1\leq p\leq\infty$ or $p=0$. In particular, it is shown that every non - $E$ operator on $L_1$ is a commutator. A characterization of the commutators on $\ell_{p_1}\oplus\ell_{p_2}\oplus\cdots\oplus\ell_{p_n}$ is also given.

Thesis (M. Phil.)--Hong Kong University of Science and Technology, 2004. / Includes bibliographical references. Also available in electronic version. Access restricted to campus users.

Thesis (M.S.)--Oregon State University, 2008. / Printout. Includes bibliographical references (leaves [51-54]). Also available on the World Wide Web.

No description available.

Among all stochastic processes with independent increments, essentially only Brownian motion and Poisson process have a chaotic representation property. In the case of a Levy process, several approaches have been proposed in order to construct an orthogonal decomposition of the corresponding L2-space. In this dissertation, we deal with orthogonal (chaotic) decompositions for generalized processes with independent values. We do not suppose stationarity of the process, as a result the Levy measure of the process depends on points of the space. We first construct, in Chapter 3, a unitary isomorphism between a certain symmetric Fock space and the space L2 (D',mu). Here D' is a co-nuclear space of generalized functions (distributions), and mu is a generalized stochastic process with independent values. This isomorphism is constructed by employing the projection spectral theorem for an (uncountable) family of commuting self-adjoint operators. We next derive, in Chapter 4, a counterpart of the Nualart Schoutens decomposition for generalized stochastic process with independent values. Our results here extend those in the papers of Nualart Schoutens and Lytvynov. In Chapter 5, we construct an orthogonal decomposition of the space L2 (D',mu) in terms of orthogonal polynomials on D'. We observe a deep relation between this decomposition and the results of the two previous chapters. Finally, in Chapter 6, we briefly discuss the situation of the generalized stochastic processes of Meixner's type.

No description available.

A tree decomposition is a tool which allows for analysis of the underlying tree structure of graphs which are not trees. Given a class of graphs with bounded tree width, many NP-complete problems can be computed in linear time for graphs in the class. Clique width of a graph G is a measure of the number of labels required to construct G using several particular graph operations. For any integer k, both the class of graphs with tree width at most k and the class of graphs with clique width at most k have a decidable monadic second order theory. In this paper we explore some recent results in applying these graph measures and their relation to monadic second order logic.

Multiphase pipe flow is investigated using proper orthogonal decomposition for tomographic X-ray data, where holdup, cross-sectional phase distributions and phase interface characteristics within the pipe are obtained. Six cases of stratified and mixed flow with water content of 10%, 30% and 80% are investigated to gain insight into effects of velocity and proportion of water on the flow fields. Dispersed and slug flows are separately analyzed to consider the added interface complexity of the flow fields. These regimes are also highly applicable to industry operational flows. Instantaneous and fluctuating phase fractions of the four flow regime are analyzed and reduced order dynamical descriptions are generated. Stratified flow cases display coherent structures that highlight the liquid-liquid interface location while the mixed flow cases show minimal coherence of the eigenmodes. The dispersed flow displays coherent structures for the first few modes near the horizontal center of the pipe, representing the liquid-liquid interface location while the slug flow case shows coherent structures that correspond to the cyclical formation and break up of the slug in the first 5 modes. The low order descriptions of the high water content, stratified flow field indicates that main characteristics can be captured with minimal degrees of freedom. Reconstructions of the dispersed flow and slug flow cases indicate that dominant features are observed in the low order dynamical description utilizing less than 1% of the full order model. POD temporal coefficients a1, a2 and a3 show a high level of interdependence for the slug flow case. The coefficients also describe the phase fraction holdup as a function of time for both dispersed and slug flow. The second coefficient, a2, and the centerline holdup profile show a mean percent difference below 9% between the two curves. The mathematical description obtained from the decomposition will deepen the understanding of multiphase flow characteristics and is applicable to long distance multiphase transport pipelines, fluidized beds, hydroelectric power and nuclear processes to name a few.

Thesis (Ph. D.)--University of Rhode Island, 2006. / Includes bibliographical references (leaves 108-112).