Dirac type condition and Hamiltonian graphs

2010 Mathematics Subject Classification: 05C38, 05C45.

A maximal operator, Carleson's embedding, and tent spaces for vector-valued functions

This thesis is concerned with the area of vector-valued Harmonic Analysis, where the central theme is to determine how results from classical Harmonic Analysis generalize to functions with values in an infinite dimensional Banach space. The work consists of three articles and an introduction. The first article studies the Rademacher maximal function that was originally defined by T. Hytönen, A. McIntosh and P. Portal in 2008 in order to prove a vector-valued version of Carleson's embedding theorem. The boundedness of the corresponding maximal operator on Lebesgue-(Bochner) -spaces defines the RMF-property of the range space. It is shown that the RMF-property is equivalent to a weak type inequality, which does not depend for instance on the integrability exponent, hence providing more flexibility for the RMF-property. The second article, which is written in collaboration with T. Hytönen, studies a vector-valued Carleson's embedding theorem with respect to filtrations. An earlier proof of the dyadic version assumed that the range space satisfies a certain geometric type condition, which this article shows to be also necessary. The third article deals with a vector-valued generalizations of tent spaces, originally defined by R. R. Coifman, Y. Meyer and E. M. Stein in the 80's, and concerns especially the ones related to square functions. A natural assumption on the range space is then the UMD-property. The main result is an atomic decomposition for tent spaces with integrability exponent one. In order to suit the stochastic integrals appearing in the vector-valued formulation, the proof is based on a geometric lemma for cones and differs essentially from the classical proof. Vector-valued tent spaces have also found applications in functional calculi for bisectorial operators. In the introduction these three themes come together when studying paraproduct operators for vector-valued functions. The Rademacher maximal function and Carleson's embedding theorem were applied already by Hytönen, McIntosh and Portal in order to prove boundedness for the dyadic paraproduct operator on Lebesgue-Bochner -spaces assuming that the range space satisfies both UMD- and RMF-properties. Whether UMD implies RMF is thus an interesting question. Tent spaces, on the other hand, provide a method to study continuous time paraproduct operators, although the RMF-property is not yet understood in the framework of tent spaces.

Numerical modeling of the contaminant Transport through stratified soil

The transport processes of the dissolved chemicals in stratified or layered soils have been studied for several decades. In case of the solute transport through stratified layers, interface condition plays an important role in determining appropriate transport parameters. First‐ type and third‐ type interface conditions are generally used in the literature. A first‐type interface condition will result in a continuous concentration profile across the interface at the expense of solute mass balance. On the other hand, a discontinuity in concentration develops when a third‐ type interface condition is used. To overcome this problem, a combined first‐ and third‐ type condition at the interface has been widely employed which yields second‐ type condition. This results in a similar break‐through curve irrespective of the layering order, which is non‐physical. In this work, an interface condition is proposed which satisfies the mass balance implicitly and brings the distinction between the breakthrough curves for different layering sequence corroborating with the experimental observations. This is in disagreement with the earlier work by H. M. Selim and co‐workers but, well agreement with the hypothetical result by Bosma and van der Zee; and Van der Zee.

A service evaluation of the role of complementary therapies for patients with cancer - By Action Cancer

Advances in the diagnosis and treatment of cancer has resulted in longer survival, meaning that cancer patients are now living with what may be termed a chronic type condition. As a result of this the needs of patients living with a cancer diagnosis has changed, placing a greater emphasis on survivorship which in turn has an effect on quality of life and sleep patterns. Evidence suggests that counselling and complementary therapies have a positive impact not only on the cancer patient’s quality of life but also on family members and friends.

The aim of this study was to determine if there is an improvement in client’s quality of life and sleep patterns after availing of counselling and complementary therapy services as offered by a local cancer charity.

All clients availing of the counselling or complementary therapies offered by the charity were invited to participate in a Service Evaluation. The regulations relating to research involving human participants as outlined by the “Research Governance Framework” at a local university were also adhered to. A seven piece questionnaire was used for evaluation of services.

Access to anonymous data from the cancer patients, their families and carers was granted by the Research and Development Officer within Action Cancer.
A total of 507 participants completed the initial questionnaires immediately before therapy and 255 participants completed the questionnaires immediately after therapy, the total matched sample is 230. When considering counselling and complementary therapies together (therapeutic services) there were statistically significant results indicating improved quality of life and sleep patterns between the two sets of data. However this was not the trend when considering counselling and complementary therapies alone.

While some of the findings closely reflect the literature and on the whole supports the use of therapeutic services in having a positive effect on cancer patient’s quality of life and sleep patterns.

Who accesses complementary therapies and why?: An evaluation of a cancer care service

Introduction

Advances in cancer diagnosis and treatment have resulted in longer survival, meaning patients are living with a chronic-type condition. Therefore the needs of such patients have changed placing greater emphasis on survivorship, such as impact on quality of life and sleep patterns. Evidence suggests complementary therapies positively impact not only on the cancer patient's quality of life but also on family members and friends.

Methodology

This service evaluation examines self-reported benefits following a course of complementary therapy offered by a local cancer charity.

Results

Analysis of self-reported sleep scores and perceived quality of life experiences confirmed a number of trends relating to the demographics of people accessing the complementary therapy service.

Conclusion

Results suggest the complementary therapies provided by Action Cancer significantly improved clients' quality of life. Based on these findings the authors make a number of recommendations in relation to the use of complementary therapies by cancer patients.

Toeplitz operators on Bergman spaces with locally integrable symbols

We study the boundedness of Toeplitz operators $T_a$ with locally integrable symbols on Bergman spaces $A^p(\mathbb{D})$, $1 < p < \infty$. Our main result gives a sufficient condition for the boundedness of $T_a$ in terms of some ``averages'' (related to hyperbolic rectangles) of its symbol. If the averages satisfy an ${o}$-type condition on the boundary of $\mathbb{D}$, we show that the corresponding Toeplitz operator is compact on $A^p$. Both conditions coincide with the known necessary conditions in the case of nonnegative symbols and $p=2$. We also show that Toeplitz operators with symbols of vanishing mean oscillation are Fredholm on $A^p$ provided that the averages are bounded away from zero, and derive an index formula for these operators.

Toeplitz operators on Dirichlet-Besov spaces

We study Toeplitz operators on the Besov spaces in the case of the open unit disk. We prove that a symbol satisfying a weak Lipschitz type condition induces a bounded Toeplitz operator. Such symbols do not need to be bounded functions or have continuous extensions to the boundary of the open unit disk. We discuss the problem of the existence of nontrivial compact Toeplitz operators, and also consider Fredholm properties and prove an index formula.

Comportamento dinâmico não-linear de um sistema mecânico com vibrações associadas a uma transição brusca na rigidez

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Harnack inequalities in sub-Riemannian settings

In the present thesis, we discuss the main notions of an axiomatic approach for an invariant Harnack inequality. This procedure, originated from techniques for fully nonlinear elliptic operators, has been developed by Di Fazio, Gutiérrez, and Lanconelli in the general settings of doubling Hölder quasi-metric spaces. The main tools of the approach are the so-called double ball property and critical density property: the validity of these properties implies an invariant Harnack inequality. We are mainly interested in the horizontally elliptic operators, i.e. some second order linear degenerate-elliptic operators which are elliptic with respect to the horizontal directions of a Carnot group. An invariant Harnack inequality of Krylov-Safonov type is still an open problem in this context. In the thesis we show how the double ball property is related to the solvability of a kind of exterior Dirichlet problem for these operators. More precisely, it is a consequence of the existence of some suitable interior barrier functions of Bouligand-type. By following these ideas, we prove the double ball property for a generic step two Carnot group. Regarding the critical density, we generalize to the setting of H-type groups some arguments by Gutiérrez and Tournier for the Heisenberg group. We recognize that the critical density holds true in these peculiar contexts by assuming a Cordes-Landis type condition for the coefficient matrix of the operator. By the axiomatic approach, we thus prove an invariant Harnack inequality in H-type groups which is uniform in the class of the coefficient matrices with prescribed bounds for the eigenvalues and satisfying such a Cordes-Landis condition.

In-situ stress conditions at ODP Site 131-808

Shipboard laboratory index property data, shore-based consolidation tests, and in-situ stress and pore-pressure measurements are used in this study to constrain the stress conditions at ODP Site 808, Nankai Trough. Results of these tests are presented along with additional interpretations of porosity rebound and permeability. The sediment at Site 808 is highly affected by excess fluid pressures throughout the sediment column. Excess fluid pressure is severe below the major fault boundary, the décollement. The in-situ measurement of lateral stresses, which are shallow in the sediment section, confirms that the principal stress direction is rotated from a "normal" basin-type condition where the principal stress direction is vertical.

DNS of EGR-type turbulent flame in MILD condition

Three-dimensional direct numerical simulation (DNS) of exhaust gas recirculation (EGR)-type turbulent combustion operated in moderate and intense low-oxygen dilution (MILD) condition has been carried out to study the flame structure and flame interaction. In order to achieve adequate EGR-type initial/inlet mixture fields, partially premixed mixture fields which are correlated with the turbulence are carefully preprocessed. The chemical kinetics is modelled using a skeletal mechanism for methane-air combustion. The results suggest that the flame fronts have thin flame structure and the direct link between the mean reaction rate and scalar dissipation rate remains valid in the EGR-type combustion with MILD condition. However, the commonly used canonical flamelet is not fully representative for MILD combustion. During the flame-flame interactions, the heat release rate increases higher than the maximum laminar flame value, while the gradient of progress variable becomes smaller than laminar value. It is also proposed that the reaction rate and the scalar gradient can be used as a marker for the flame interaction. © 2012 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Type 2 Diabetes Elicits Lower Nitric Oxide, Bradykinin Concentration and Kallikrein Activity Together with Higher DesArg(9)-BK and Reduced Post-Exercise Hypotension Compared to Non-Diabetic Condition

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Associations of Forest Type, Parasitism and Body Condition of Two European Passerines, Fringilla coelebs and Sylvia atricapilla

Human-induced forest modification can alter parasite-host interactions and might change the persistence of host populations. We captured individuals of two widespread European passerines (Fringilla coelebs and Sylvia atricapilla) in southwestern Germany to disentangle the associations of forest types and parasitism by haemosporidian parasites on the body condition of birds. We compared parasite prevalence and parasite intensity, fluctuating asymmetries, leukocyte numbers, and the heterophil to lymphocyte ratio (H/L-ratio) among individuals from beech, mixed-deciduous and spruce forest stands. Based on the biology of bird species, we expected to find fewer infected individuals in beech or mixed-deciduous than in spruce forest stands. We found the highest parasite prevalence and intensity in beech forests for F. coelebs. Although, we found the highest prevalence in spruce forests for S. atricapilla, the highest intensity was detected in beech forests, partially supporting our hypothesis. Other body condition or health status metrics, such as the heterophil to lymphocyte ratio (H/L-ratio), revealed only slight differences between bird populations inhabiting the three different forest types, with the highest values in spruce for F. coelebs and in mixed-deciduous forests for S. atricapilla. A comparison of parasitized versus non-parasitized individuals suggests that parasite infection increased the immune response of a bird, which was detectable as high H/L-ratio. Higher infections with blood parasites for S. atricapilla in spruce forest indicate that this forest type might be a less suitable habitat than beech and mixed-deciduous forests, whereas beech forests seem to be a suboptimal habitat regarding parasitism for F. coelebs.