This thesis is concerned with extensions and refinements of the Katznelson-Tzafriri theorem, a cornerstone of the asymptotic theory of operator semigroups which recently has received renewed interest in the context of damped wave equations. The thesis comprises three main parts. The key results in the first part are a version of the Katznelson-Tzafriri theorem for bounded C_0-semigroups in which a certain function appearing in the original statement of the result is allowed more generally to be a bounded Borel measure, and bounds on the rate of decay in an important special case. The second part deals with the discrete version of the Katznelson-Tzafriri theorem and establishes upper and lower bounds on the rate of decay in this setting too. In an important special case these general bounds are then shown to be optimal for general Banach spaces but not on Hilbert space. The third main part, finally, turns to general operator semigroups. It contains a version of the Katznelson-Tzafriri theorem in the Hilbert space setting which relaxes the main assumption of the original result. Various applications and extensions of this general result are also presented.

The aim of this work is the study of the existence and multiplicity of sign changing nonradial solutions to elliptic boundary value problems on annular domains.

In 1909, F. Riesz succeeded in giving an integral represntation for continuous linear functionals on C[0,1]. Although other authors, notably Hadamard and Frechet, had given representations for continuous linear functionals on C[0,1], their results lacked the clarity, elegance, and some of the substance (uniqueness) of Riesz's theorem. Subsequently, the integral representation of continuous linear functionals has been known as the Riesz Representation Theorem. In this paper, three different proofs of the Riesz Representation Theorem are presented. The first approach uses the denseness of the Bernstein polynomials in C[0,1] along with results of Helly to write the continuous linear functionals as Stieltjes integrals. The second approach makes use of the Hahn-Banach Theorem in order to write the functional as an integral. The paper concludes with a detailed presentation of a Daniell integral development of the Riesz Representation Theorem.

Study 1 evaluated agreement among five respondents using the Functional Analysis Screening Tool (FAST), the Motivation Assessment Scale (MAS) and Questions About Behavioral Function (QABF). Respondents provided ratings for 20 target behaviors exhibited by 10 individuals. At least 4/5 raters agreed on the primary maintaining variable in 80% of cases with the FAST, 70% of cases with the MAS, and 55% of cases with the QABF. Study 2 evaluated correspondence between results of anecdotal assessments and experimental functional analysis for 10 target behaviors selected from Study 1. Correspondence between the experimental functional analyses was 60% with the FAST and the MAS, 50% with the QABF.

We study a nonlinear kinetic model describing the interactions of particles in a granular medium, i.e. inelastic systems where kinetic energy is not conserved due to internal friction. Examples of particles that fall into this category are sand, ground coffee and many others. Originally studied by Benedetto, Caglioti and Pulvirenti in the one-dimensional setting (RAIRO Model. Math. Anal. Numer, 31(5): 615-641, (1997)) the original model contained inconsistencies later accounted for and corrected by invoking a mollifier (Modelisation Mathematique et Analyse Numerique, M2AN, Vol. 33, No 2, pp. 439–441 (1999)). This thesis approximates the generalized model presented by Agueh (Arch. Rational Mech., Anal. 221, pp. 917-959 (2016)) with the added assumption of a spatial mollifier present in the kinetic equation. In dimension d ≥ 1 this model reads as ∂tf + v · ∇xf = divv(f([ηα∇W] ∗(x,v) f)) where f is a non-negative particle density function, W is a radially symmetric class C2 velocity interaction potential, and and ηα is a mollifier. A physical interpretation of this approximation is that the particles are spheres of radius α > 0 as opposed to the original assumption of being point-masses. Properties lost by this approximation and macroscopic quantities that remain conserved are discussed in greater detail and contrasted. The main result of this thesis is a proof of the weak global existence and uniqueness. An argument utilizing the tools of Optimal Transport allows simple construction of a weak solution to the kinetic model by transporting an initial measure under the characteristic flow curves. Concluding regularity arguments and restrictions on the velocity interaction potential ascertain that global classical solutions are obtained. / Graduate

Após um levantamento inicial com 24 sujeitos, em uma instituição, foram observadas as ocorrências das auto-agressões de uma criança profundamente retardada, em diferentes situações do dia-­a-dia na instituição. Outras respostas da mesma criança foram também observadas e relacionadas com as auto-agressões. Dois grupamentos de ações foram identificados. Morder-se, juntamente com outras ações, aumentava diante de exigências de desempenho e restrição à locomoção; diminuía na presença de um pianinho ou quando havia música tocando. Bater-se na cabeça, juntamente com outras ações, pareceu ser controlado por estimulação auditiva. O conceito de auto-agressão foi discutido, sugerindo-se que comportamentos auto-lesivos (termo proposto, mais descritivo) poderiam ser auto-estimulatórios ou modalidades de agressão. Concluiu-se que o entendimento dos determinantes de comportamentos auto-lesivos pode dar-se através de sua análise funcional, feita em situação natural, pela análise de múltiplas respostas em múltiplas situações. Tal estudo pode trazer implicações para a elaboração de intervenções que promovam ganho significativos, múltiplos e permanentes. / A review of the existing literature showed a variety of self-aggressive acts*, which relate to other actions of the same individual. The same review showed furthermore that there are many situations in which such acts occur, with no agreement as to what originates and maintains self-aggression. After an initial survey in an institution including 24 subjects, the occurrence of self-aggressive acts was observed in a profoundly retarded child in different day-to-day situations at the institution. Other responses of the same child were also observed and related to the self-aggressive episodes. Most of the actions observed can be grouped into two classes of response. Biting herself and other related act ions increased in frequency when requirements were made and locomotion restricted, and decreased when a small piano was given to her or when music was playing. Hitting on the head and other related actions were seemingly controlled by auditory stimulation. The concept of self-aggression was discussed and self-injurious behavior (a more descriptive proposed expression) presented as either self-stimulation or a modality of aggression. It was concluded that an understanding of the determinants of self-injurious behavior can be achieved through functional analysis under natural conditions, including multiple responses in multiple situations. Such a study may have an impact on the development of measures that may lead to significant, multiple and permanent gains. * Self-injurious behavior is referred to, \"self-aggressive\" behavior.

by Wai-Shing Luk. / Thesis (Ph.D.)--Chinese University of Hong Kong, 1996. / Includes bibliographical references (leaves 104-113). / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Functional Extension of Iterative Methods --- p.2 / Chapter 1.2 --- Applications in Circuit Simulation --- p.2 / Chapter 1.3 --- Multigrid Acceleration --- p.3 / Chapter 1.4 --- Why Hilbert Space? --- p.4 / Chapter 1.5 --- Parallel Implementation --- p.5 / Chapter 1.6 --- Domain Decomposition --- p.5 / Chapter 1.7 --- Contributions of This Thesis --- p.6 / Chapter 1.8 --- Outlines of the Thesis --- p.7 / Chapter 2 --- Waveform Relaxation Methods --- p.9 / Chapter 2.1 --- Basic Idea --- p.10 / Chapter 2.2 --- Linear Operators between Banach Spaces --- p.14 / Chapter 2.3 --- Waveform Relaxation Operators for ODE's --- p.16 / Chapter 2.4 --- Convergence Analysis --- p.19 / Chapter 2.4.1 --- Continuous-time Convergence Analysis --- p.20 / Chapter 2.4.2 --- Discrete-time Convergence Analysis --- p.21 / Chapter 2.5 --- Further references --- p.24 / Chapter 3 --- Waveform Krylov Subspace Methods --- p.25 / Chapter 3.1 --- Overview of Krylov Subspace Methods --- p.26 / Chapter 3.2 --- Krylov Subspace methods in Hilbert Space --- p.30 / Chapter 3.3 --- Waveform Krylov Subspace Methods --- p.31 / Chapter 3.4 --- Adjoint Operator for WBiCG and WQMR --- p.33 / Chapter 3.5 --- Numerical Experiments --- p.35 / Chapter 3.5.1 --- Test Circuits --- p.36 / Chapter 3.5.2 --- Unstructured Grid Problem --- p.39 / Chapter 4 --- Parallel Implementation Issues --- p.50 / Chapter 4.1 --- DECmpp 12000/Sx Computer and HPF --- p.50 / Chapter 4.2 --- Data Mapping Strategy --- p.55 / Chapter 4.3 --- Sparse Matrix Format --- p.55 / Chapter 4.4 --- Graph Coloring for Unstructured Grid Problems --- p.57 / Chapter 5 --- The Use of Inexact ODE Solver in Waveform Methods --- p.61 / Chapter 5.1 --- Inexact ODE Solver for Waveform Relaxation --- p.62 / Chapter 5.1.1 --- Convergence Analysis --- p.63 / Chapter 5.2 --- Inexact ODE Solver for Waveform Krylov Subspace Methods --- p.65 / Chapter 5.3 --- Experimental Results --- p.68 / Chapter 5.4 --- Concluding Remarks --- p.72 / Chapter 6 --- Domain Decomposition Technique --- p.80 / Chapter 6.1 --- Introduction --- p.80 / Chapter 6.2 --- Overlapped Schwarz Methods --- p.81 / Chapter 6.3 --- Numerical Experiments --- p.83 / Chapter 6.3.1 --- Delay Circuit --- p.83 / Chapter 6.3.2 --- Unstructured Grid Problem --- p.86 / Chapter 7 --- Conclusions --- p.90 / Chapter 7.1 --- Summary --- p.90 / Chapter 7.2 --- Future Works --- p.92 / Chapter A --- Pseudo Codes for Waveform Krylov Subspace Methods --- p.94 / Chapter B --- Overview of Recursive Spectral Bisection Method --- p.101 / Bibliography --- p.104

BACKGROUND: Immune cells promote periodontal bone loss through an unresolved inflammatory response to bacterial pathogens. The limited availability of ex vivo gingival immune cells severely impedes identification of cell types and cell-specific functions that drive human periodontitis and thus impedes the development of effective pharmacotherapeutics. Previous studies have largely relied on mRNA analysis and confocal microscopy to imprecisely estimate gingival immune cell function. The aim of the study was to develop a cell type-specific technique to quantitate function of resident gingival immune cells. METHODS: Diseased tissues from chronic periodontitis in non-diabetes or type 2 diabetes subjects or relatively healthy gingival tissues were removed during standard-of-care surgery for pocket reduction surgery or crown lengthening, respectively. Gingiva was dissociated with collagenase to generate single cell suspensions, then 9-color flow cytometry was used quantitate and/or isolate myeloid cells (CD11b+), B cells (CD20+), T cells (CD4+ or CD8+) and natural killer (NK) cells (CD56+). We stimulated the sorted cells with lineage-appropriate activators for 36 hrs and measured cytokine production by ELISPOT, an assay that identifies individual cytokine-producing cells by fixed “spots” on a solid support. RESULTS: A higher proportion of gingival CD4+ T helper cells and not CD8+cytoxic T cells from subjects with periodontal disease with or without type 2 diabetes produce pro-inflammatory cytokines compared to CD4+ T cells from crown lengthening subjects. CD4+ T cells were the dominant cell population in gingiva from all three groups, and all groups contained similar proportions of cytotoxic (CD8+) T cells, myeloid cells (CD11b+), B cells (CD20+) and natural killer cells (CD56+). CONCLUSION: The combination of flow cytometry, cell sorting and ELISPOT identified CD4+ T cells as dominant immune cells in human periodontal lesions, and identified T cell cytokines that may uniquely promote periodontitis in type 2 diabetes.

Thesis. 1976. Ph.D.--Massachusetts Institute of Technology. Dept. of Mathematics. / Microfiche copy available in Archives and Science. / Vita. / Includes bibliographical references. / by Robert R. Reitano. / Ph.D.

Thesis. 1977. M.Arch.A.S.--Massachusetts Institute of Technology. Dept. of Architecture. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ROTCH. / Blank leaf bound in after leaf 5; no leaf 148. / Includes bibliographical references. / M.Arch.A.S.