UNIQUENESS OF SOLUTIONS TO SCHRODINGER EQUATIONS ON H-TYPE GROUPS

This paper deals with the Schrodinger equation i partial derivative(s)u(z, t; s) - Lu(z, t; s) = 0; where L is the sub-Laplacian on the Heisenberg group. Assume that the initial data f satisfies vertical bar f(z, t)vertical bar less than or similar to q(alpha)(z, t), where q(s) is the heat kernel associated to L. If in addition vertical bar u(z, t; s(0))vertical bar less than or similar to q(beta)(z, t), for some s(0) is an element of R \textbackslash {0}, then we prove that u(z, t; s) = 0 for all s is an element of R whenever alpha beta < s(0)(2). This result holds true in the more general context of H-type groups. We also prove an analogous result for the Grushin operator on Rn+1.

Evolution and propagation of density waves on galactic disk .1. General evolution equation of wavelet and discussion of its solution

This paper presents a general self-consistent theory of evolution and propagation of wavelets on the galactic disk. A simplified model for this theory, i. e. the thin transition-layer approximation is proposed.There are three types of solutions to the basic equation governing the evolution of wavelets on the disk: (ⅰ) normal propagating type; (ⅱ) swing type; (ⅲ) general evolving type. The results show that the first two types are applicable to a certain domain on the galactic disk and a certain region of the wave number of wavelets. The third is needed to join the other two types and to yield a coherent total picture of the wave motion. From the present theory, it can be seen that the well-known "swing theory" of the G-L sheet model holds only for a certain class of basic states of galaxies.

Detailed properties of high redshift galaxies

Galaxies evolve throughout the history of the universe from the first star-forming sources, through gas-rich asymmetric structures with rapid star formation rates, to the massive symmetrical stellar systems observed at the present day. Determining the physical processes which drive galaxy formation and evolution is one of the most important questions in observational astrophysics. This thesis presents four projects aimed at improving our understanding of galaxy evolution from detailed measurements of star forming galaxies at high redshift.

We use resolved spectroscopy of gravitationally lensed z ≃ 2 - 3 star forming galaxies to measure their kinematic and star formation properties. The combination of lensing with adaptive optics yields physical resolution of ≃ 100 pc, sufficient to resolve giant Hii regions. We find that ~ 70 % of galaxies in our sample display ordered rotation with high local velocity dispersion indicating turbulent thick disks. The rotating galaxies are gravitationally unstable and are expected to fragment into giant clumps. The size and dynamical mass of giant Hii regions are in agreement with predictions for such clumps indicating that gravitational instability drives the rapid star formation. The remainder of our sample is comprised of ongoing major mergers. Merging galaxies display similar star formation rate, morphology, and local velocity dispersion as isolated sources, but their velocity fields are more chaotic with no coherent rotation.

We measure resolved metallicity in four lensed galaxies at z = 2.0 − 2.4 from optical emission line diagnostics. Three rotating galaxies display radial gradients with higher metallicity at smaller radii, while the fourth is undergoing a merger and has an inverted gradient with lower metallicity at the center. Strong gradients in the rotating galaxies indicate that they are growing inside-out with star formation fueled by accretion of metal-poor gas at large radii. By comparing measured gradients with an appropriate comparison sample at z = 0, we demonstrate that metallicity gradients in isolated galaxies must flatten at later times. The amount of size growth inferred by the gradients is in rough agreement with direct measurements of massive galaxies. We develop a chemical evolution model to interpret these data and conclude that metallicity gradients are established by a gradient in the outflow mass loading factor, combined with radial inflow of metal-enriched gas.

We present the first rest-frame optical spectroscopic survey of a large sample of low-luminosity galaxies at high redshift (L < L*, 1.5 < z < 3.5). This population dominates the star formation density of the universe at high redshifts, yet such galaxies are normally too faint to be studied spectroscopically. We take advantage of strong gravitational lensing magnification to compile observations for a sample of 29 galaxies using modest integration times with the Keck and Palomar telescopes. Balmer emission lines confirm that the sample has a median SFR ∼ 10 M_sun yr^−1 and extends to lower SFR than has been probed by other surveys at similar redshift. We derive the metallicity, dust extinction, SFR, ionization parameter, and dynamical mass from the spectroscopic data, providing the first accurate characterization of the star-forming environment in low-luminosity galaxies at high redshift. For the first time, we directly test the proposal that the relation between galaxy stellar mass, star formation rate, and gas phase metallicity does not evolve. We find lower gas phase metallicity in the high redshift galaxies than in local sources with equivalent stellar mass and star formation rate, arguing against a time-invariant relation. While our result is preliminary and may be biased by measurement errors, this represents an important first measurement that will be further constrained by ongoing analysis of the full data set and by future observations.

We present a study of composite rest-frame ultraviolet spectra of Lyman break galaxies at z = 4 and discuss implications for the distribution of neutral outflowing gas in the circumgalactic medium. In general we find similar spectroscopic trends to those found at z = 3 by earlier surveys. In particular, absorption lines which trace neutral gas are weaker in less evolved galaxies with lower stellar masses, smaller radii, lower luminosity, less dust, and stronger Lyα emission. Typical galaxies are thus expected to have stronger Lyα emission and weaker low-ionization absorption at earlier times, and we indeed find somewhat weaker low-ionization absorption at higher redshifts. In conjunction with earlier results, we argue that the reduced low-ionization absorption is likely caused by lower covering fraction and/or velocity range of outflowing neutral gas at earlier epochs. This result has important implications for the hypothesis that early galaxies were responsible for cosmic reionization. We additionally show that fine structure emission lines are sensitive to the spatial extent of neutral gas, and demonstrate that neutral gas is concentrated at smaller galactocentric radii in higher redshift galaxies.

The results of this thesis present a coherent picture of galaxy evolution at high redshifts 2 ≲ z ≲ 4. Roughly 1/3 of massive star forming galaxies at this period are undergoing major mergers, while the rest are growing inside-out with star formation occurring in gravitationally unstable thick disks. Star formation, stellar mass, and metallicity are limited by outflows which create a circumgalactic medium of metal-enriched material. We conclude by describing some remaining open questions and prospects for improving our understanding of galaxy evolution with future observations of gravitationally lensed galaxies.

Descriptive set theory and the ergodic theory of countable groups

The primary focus of this thesis is on the interplay of descriptive set theory and the ergodic theory of group actions. This incorporates the study of turbulence and Borel reducibility on the one hand, and the theory of orbit equivalence and weak equivalence on the other. Chapter 2 is joint work with Clinton Conley and Alexander Kechris; we study measurable graph combinatorial invariants of group actions and employ the ultraproduct construction as a way of constructing various measure preserving actions with desirable properties. Chapter 3 is joint work with Lewis Bowen; we study the property MD of residually finite groups, and we prove a conjecture of Kechris by showing that under general hypotheses property MD is inherited by a group from one of its co-amenable subgroups. Chapter 4 is a study of weak equivalence. One of the main results answers a question of Abért and Elek by showing that within any free weak equivalence class the isomorphism relation does not admit classification by countable structures. The proof relies on affirming a conjecture of Ioana by showing that the product of a free action with a Bernoulli shift is weakly equivalent to the original action. Chapter 5 studies the relationship between mixing and freeness properties of measure preserving actions. Chapter 6 studies how approximation properties of ergodic actions and unitary representations are reflected group theoretically and also operator algebraically via a group's reduced C^*-algebra. Chapter 7 is an appendix which includes various results on mixing via filters and on Gaussian actions.

Normal structures and automorphism groups of t-designs

Combinatorial configurations known as t-designs are studied. These are pairs ˂B, ∏˃, where each element of B is a k-subset of ∏, and each t-design occurs in exactly λ elements of B, for some fixed integers k and λ. A theory of internal structure of t-designs is developed, and it is shown that any t-design can be decomposed in a natural fashion into a sequence of “simple” subdesigns. The theory is quite similar to the analysis of a group with respect to its normal subgroups, quotient groups, and homomorphisms. The analogous concepts of normal subdesigns, quotient designs, and design homomorphisms are all defined and used.

This structure theory is then applied to the class of t-designs whose automorphism groups are transitive on sets of t points. It is shown that if G is a permutation group transitive on sets of t letters and ф is any set of letters, then images of ф under G form a t-design whose parameters may be calculated from the group G. Such groups are discussed, especially for the case t = 2, and the normal structure of such designs is considered. Theorem 2.2.12 gives necessary and sufficient conditions for a t-design to be simple, purely in terms of the automorphism group of the design. Some constructions are given.

Finally, 2-designs with k = 3 and λ = 2 are considered in detail. These designs are first considered in general, with examples illustrating some of the configurations which can arise. Then an attempt is made to classify all such designs with an automorphism group transitive on pairs of points. Many cases are eliminated of reduced to combinations of Steiner triple systems. In the remaining cases, the simple designs are determined to consist of one infinite class and one exceptional case.

Leadership of healthcare commissioning networks in England: a mixed-methods study on clinical commissioning groups.

To explore the relational challenges for general practitioner (GP) leaders setting up new network-centric commissioning organisations in the recent health policy reform in England, we use innovation network theory to identify key network leadership practices that facilitate healthcare innovation.

Coordinated motion design on lie groups

The present paper proposes a unified geometric framework for coordinated motion on Lie groups. It first gives a general problem formulation and analyzes ensuing conditions for coordinated motion. Then, it introduces a precise method to design control laws in fully actuated and underactuated settings with simple integrator dynamics. It thereby shows that coordination can be studied in a systematic way once the Lie group geometry of the configuration space is well characterized. Applying the proposed general methodology to particular examples allows to retrieve control laws that have been proposed in the literature on intuitive grounds. A link with Brockett's double bracket flows is also made. The concepts are illustrated on SO(3), SE(2) and SE(3). © 2010 IEEE.

AN ALGEBRAIC METHOD TO ESTIMATE GENERAL TYPE OF PHASES OF STRUCTURE FACTORS

The algebraic formulas of 1.5 and 2.5 rank are given for four space groups P2(1), Pn, Pna2(1), P2(1)2(1)2(1). It is better that the results of applying them to estimating general type of phases for four correspondent crystal structures. And a method of transforming algebraic formulas from 1.5(2.5) rank is proposed.

Development of a general internet attitude scale and internet self-efficacy scale

The measurement of users’ attitudes towards and confidence with using the Internet is an important yet poorly researched topic. Previous research has encountered issues that serve to obfuscate rather than clarify. Such issues include a lack of distinction between the terms ‘attitude’ and ‘self-efficacy’, the absence of a theoretical framework to measure each concept, and failure to follow well-established techniques for the measurement of both attitude and self-efficacy. Thus, the primary aim of this research was to develop two statistically reliable scales which independently measure attitudes towards the Internet and Internet self-efficacy. This research addressed the outlined issues by applying appropriate theoretical frameworks to each of the constructs under investigation. First, the well-known three component (affect, behaviour, cognition) model of attitudes was applied to previous Internet attitude statements. The scale was distributed to four large samples of participants. Exploratory factor analyses revealed four underlying factors in the scale: Internet Affect, Internet Exhilaration, Social Benefit of the Internet and Internet Detriment. The final scale contains 21 items, demonstrates excellent reliability and achieved excellent model fit in the confirmatory factor analysis. Second, Bandura’s (1997) model of self-efficacy was followed to develop a reliable measure of Internet self-efficacy. Data collected as part of this research suggests that there are ten main activities which individuals can carry out on the Internet. Preliminary analyses suggested that self-efficacy is confounded with previous experience; thus, individuals were invited to indicate how frequently they performed the listed Internet tasks in addition to rating their feelings of self-efficacy for each task. The scale was distributed to a sample of 841 participants. Results from the analyses suggest that the more frequently an individual performs an activity on the Internet, the higher their self-efficacy score for that activity. This suggests that frequency of use ought to be taken into account in individual’s self-efficacy scores to obtain a ‘true’ self-efficacy score for the individual. Thus, a formula was devised to incorporate participants’ previous experience of Internet tasks in their Internet self-efficacy scores. This formula was then used to obtain an overall Internet self-efficacy score for participants. Following the development of both scales, gender and age differences were explored in Internet attitudes and Internet self-efficacy scores. The analyses indicated that there were no gender differences between groups for Internet attitude or Internet self-efficacy scores. However, age group differences were identified for both attitudes and self-efficacy. Individuals aged 25-34 years achieved the highest scores on both the Internet attitude and Internet self-efficacy measures. Internet attitude and self-efficacy scores tended to decrease with age with older participants achieving lower scores on both measures than younger participants. It was also found that the more exposure individuals had to the Internet, the higher their Internet attitude and Internet self-efficacy scores. Examination of the relationship between attitude and self-efficacy found a significantly positive relationship between the two measures suggesting that the two constructs are related. Implication of such findings and directions for future research are outlined in detail in the Discussion section of this thesis.

D-Amino acid peptide residualizing agents bearing N-hydroxysuccinimido- and maleimido-functional groups and their application for trastuzumab radioiodination.

INTRODUCTION: Proteins that undergo receptor-mediated endocytosis are subject to lysosomal degradation, requiring radioiodination methods that minimize loss of radioactivity from tumor cells after this process occurs. To accomplish this, we developed the residualizing radioiodination agent N(ϵ)-(3-[(*)I]iodobenzoyl)-Lys(5)-N(α)-maleimido-Gly(1)-D-GEEEK (Mal-D-GEEEK-[(*)I]IB), which enhanced tumor uptake but also increased kidney activity and necessitates generation of sulfhydryl moieties on the protein. The purpose of the current study was to synthesize and evaluate a new D-amino acid based agent that might avoid these potential problems. METHODS: N(α)-(3-iodobenzoyl)-(5-succinimidyloxycarbonyl)-D-EEEG (NHS-IB-D-EEEG), which contains 3 D-glutamates to provide negative charge and a N-hydroxysuccinimide function to permit conjugation to unmodified proteins, and the corresponding tin precursor were produced by solid phase peptide synthesis and subsequent conjugation with appropriate reagents. Radioiodination of the anti-HER2 antibody trastuzumab using NHS-IB-D-EEEG and Mal-D-GEEEK-IB was compared. Paired-label internalization assays on BT474 breast carcinoma cells and biodistribution studies in athymic mice bearing BT474M1 xenografts were performed to evaluate the two radioiodinated D-peptide trastuzumab conjugates. RESULTS: NHS-[(131)I]IB-D-EEEG was produced in 53.8%±13.4% and conjugated to trastuzumab in 39.5%±7.6% yield. Paired-label internalization assays with trastuzumab-NHS-[(131)I]IB-D-EEEG and trastuzumab-Mal-D-GEEEK-[(125)I]IB demonstrated similar intracellular trapping for both conjugates at 1h ((131)I, 84.4%±6.1%; (125)I, 88.6%±5.2%) through 24h ((131)I, 60.7%±6.8%; (125)I, 64.9%±6.9%). In the biodistribution experiment, tumor uptake peaked at 48 h (trastuzumab-NHS-[(131)I]IB-D-EEEG, 29.8%±3.6%ID/g; trastuzumab-Mal-D-GEEEK-[(125)I]IB, 45.3%±5.3%ID/g) and was significantly higher for (125)I at all time points. In general, normal tissue levels were lower for trastuzumab-NHS-[(131)I]IB-D-EEEG, with the differences being greatest in kidneys ((131)I, 2.2%±0.4%ID/g; (125)I, 16.9%±2.8%ID/g at 144 h). CONCLUSION: NHS-[(131)I]IB-D-EEEG warrants further evaluation as a residualizing radioiodination agent for labeling internalizing antibodies/fragments, particularly for applications where excessive renal accumulation could be problematic.

Ecological equivalence of species within phytoplankton functional groups

1.There are tens of thousands of species of phytoplankton found throughout the tree of life. Despite this diversity, phytoplankton are often aggregated into a few functional groups according to metabolic traits or biogeochemical role. We investigate the extent to which phytoplankton species dynamics are neutral within functional groups. 2.Seasonal dynamics in many regions of the ocean are known to affect phytoplankton at the functional group level leading to largely predictable patterns of seasonal succession. It is much more difficult to make general statements about the dynamics of individual species. 3.We use a 7 year time-series at station L4 in the Western English Channel with 57 diatom and 17 dinoflagellate species enumerated weekly to test if the abundance of diatom and dinoflagellate species vary randomly within their functional group envelope or if each species is driven uniquely by external factors. 4.We show that the total biomass of the diatom and dinoflagellate functional groups is well predicted by irradiance and temperature and quantify trait values governing the growth rate of both functional groups. The biomass dynamics of the functional groups are not neutral and each has their own distinct responses to environmental forcing. Compared to dinoflagellates, diatoms have faster growth rates, and grow faster under lower irradiance, cooler temperatures, and higher nutrient conditions. 5.The biomass of most species vary randomly within their functional group biomass envelope, most of the time. As a consequence, modelers will find it difficult to predict the biomass of most individual species. Our analysis supports the approach of using a single set of traits for a functional group and suggests that it should be possible to determine these traits from natural communities.

Evaluation of extended training for general practice in Northern Ireland: qualitative study.

Objective To evaluate participants' perceptions of the impact on them of an additional six months' training beyond the standard 12 month general practice vocational training scheme. Design Qualitative study using focus groups. Setting General practice vocational training in Northern Ireland. Participants 13 general practitioner registrars, six of whom participated in the additional six months' training, and four trainers involved in the additional six months' training. Main outcome measures: Participants' views about their experiences in 18 month and 12 month courses. Results Participants reported that the 12 month course was generally positive but was too pressurised and focused on examinations, and also that it had a negative impact on self care. The nature of the learning and assessment was reported to have left participants feeling averse to further continuing education and lacking in confidence. In contrast, the extended six month component was reported to have restimulated learning by focusing more on patient care and promoting self directed learning. It developed confidence, promoted teamwork, and gave experience of two practice contexts, and was reported as valuable by both ex-registrars and trainers. However, both the 12 and 18 month courses left participants feeling underprepared for practice management and self care. Conclusions 12 months' training in general practice does not provide doctors with the necessary competencies and confidence to enter independent practice. The extended period was reported to promote greater professional development, critical evaluation skills, and orientation to lifelong learning but does not fill all the gaps.

Challenge of culture, conscience, and contract to general practitioners' care of their own health: qualitative study

Objective: To explore general practitioners' perceptions of the effects of their profession and training on their attitudes to illness in themselves and colleagues. Design: Qualitative study using focus groups and indepth interviews. Setting: Primary care in Northern Ireland. Participants: 27 general practitioners, including six recently appointed principals and six who also practised occupational medicine part time. Main outcome measures: Participants' views about their own and colleagues' health. Results: Participants were concerned about the current level of illness within the profession. They described their need to portray a healthy image to both patients and colleagues. This hindered acknowledgement of personal illness and engaging in health screening. Embarrassment in adopting the role of a patient and concerns about confidentiality also influenced their reactions to personal illness. Doctors' attitudes can impede their access to appropriate health care for themselves, their families, and their colleagues. A sense of conscience towards patients and colleagues and the working arrangements of the practice were cited as reasons for working through illness and expecting colleagues to do likewise. Conclusions: General practitioners perceive that their professional position and training adversely influence their attitudes to illness in themselves and their colleagues. Organisational changes within general practice, including revalidation, must take account of barriers experienced by general practitioners in accessing health care. Medical education and culture should strive to promote appropriate self care among doctors.

The SPHERE Study: Secondary prevention of heart disease in general practice: protocol of a randomised controlled trial of tailored practice and patient care plans with parallel qualitative, economic and policy analyses. [ISRCTN24081411]

Background: The aim of the SPHERE study is to design, implement and evaluate tailored practice and personal care plans to improve the process of care and objective clinical outcomes for patients with established coronary heart disease (CHD) in general practice across two different health systems on the island of Ireland.CHD is a common cause of death and a significant cause of morbidity in Ireland. Secondary prevention has been recommended as a key strategy for reducing levels of CHD mortality and general practice has been highlighted as an ideal setting for secondary prevention initiatives. Current indications suggest that there is considerable room for improvement in the provision of secondary prevention for patients with established heart disease on the island of Ireland. The review literature recommends structured programmes with continued support and follow-up of patients; the provision of training, tailored to practice needs of access to evidence of effectiveness of secondary prevention; structured recall programmes that also take account of individual practice needs; and patient-centred consultations accompanied by attention to disease management guidelines.

Methods: SPHERE is a cluster randomised controlled trial, with practice-level randomisation to intervention and control groups, recruiting 960 patients from 48 practices in three study centres (Belfast, Dublin and Galway). Primary outcomes are blood pressure, total cholesterol, physical and mental health status (SF-12) and hospital re-admissions. The intervention takes place over two years and data is collected at baseline, one-year and two-year follow-up. Data is obtained from medical charts, consultations with practitioners, and patient postal questionnaires. The SPHERE intervention involves the implementation of a structured systematic programme of care for patients with CHD attending general practice. It is a multi-faceted intervention that has been developed to respond to barriers and solutions to optimal secondary prevention identified in preliminary qualitative research with practitioners and patients. General practitioners and practice nurses attend training sessions in facilitating behaviour change and medication prescribing guidelines for secondary prevention of CHD. Patients are invited to attend regular four-monthly consultations over two years, during which targets and goals for secondary prevention are set and reviewed. The analysis will be strengthened by economic, policy and qualitative components.

Using the opinions of coronary heart disease patients in designing a health education booklet for use in general practice consultations.

Objective This study explored how coronary heart disease (CHD) patients’ views would inform the design of an information booklet aimed at providing patients and practitioners with a resource to help influence positively patients’ health behaviour outcomes. Methods Opinions of patients (N=23) with CHD about their information needs, particularly lifestyle advice, were explored using a qualitative approach in four general practices. This information was used in designing a booklet for a pilot study intervention aimed at promoting healthy lifestyle behaviours and medication adherence among people with CHD. Subsequent focus groups explored patients’ (N=17) opinions about the booklet’s ‘fitness for purpose’; semi-structured interviews with practitioners (N=10) examined their views on the booklet’s usefulness. Results In initial focus groups patients identified gaps in their information provision regarding coping with stress, available local community support and medication purpose. A booklet, prepared on the basis of previous literature, was modified to address these gaps. Pilot study patients were satisfied with the re-designed booklet and practitioners reported that its use in consultations enabled change implementation and facilitated patients’ understanding of connections between lifestyle and health outcomes. Conclusion Acknowledging the opinions of CHD patients in producing health information booklets which emphasised a patient centred approach supported practitioner-patient partnerships for choosing healthy lifestyle choices.