79 research outputs found
<i>H<sup>p</sup></i>-bounds for spectral multipliers on Riemannian manifolds
No full textAbstractLet M be a Riemannian manifold which satisfies the doubling volume property. Let Δ be the Laplace–Beltrami operator on M and m(λ), λ∈R, a multiplier satisfying the Mikhlin–Hörmander condition. We also assume that the heat kernel satisfies certain upper Gaussian estimates and we prove that there is a geometric constant p0<1, such that the spectral multiplier m(Δ) is bounded on the Hardy spaces Hp for all p∈(p0,1]
Key environmental stress biomarker candidates for the optimisation of chemotherapy treatment of leukaemia
No full textThe impact of fluctuations of environmental parameters
such as oxygen and starvation on the evolution of leukaemia
is analysed in the current review. These fluctuations may occur
within a specific patient (in different organs) or across patients
(individual cases of hypoglycaemia and hyperglycaemia). They
can be experienced as stress stimuli by the cancerous population,
leading to an alteration of cellular growth kinetics, metabolism
and further resistance to chemotherapy. Therefore, it is of high
importance to elucidate key mechanisms that affect the evolution
of leukaemia under stress. Potential stress response mechanisms
are discussed in this review. Moreover, appropriate cell biomarker
candidates related to the environmental stress response and/or
further resistance to chemotherapy are proposed. Quantification
of these biomarkers can enable the combination of macroscopic kinetics
with microscopic information, which is specific to individual
patients and leads to the construction of detailed mathematical
models for the optimisation of chemotherapy. Due to their nature,
these models will be more accurate and precise (in comparison
to available macroscopic/black box models) in the prediction of
responses of individual patients to treatment, as they will incorporate
microscopic genetic and/or metabolic information which is
patient-specific.peer-reviewe
Spectral multipliers on spaces of distributions associated with non-negative self-adjoint operators
No full textWe consider spaces of homogeneous type associated with a non-negative self-adjoint operator whose heat kernel satisfies certain upper Gaussian bounds. Spectral multipliers are introduced and studied on distributions associated with this operator. The boundedness of spectral multipliers on Besov and Triebel–Lizorkin spaces with full range of indices is established too. As an application, we obtain equivalent norm characterizations for the spaces mentioned above. Non-classical spaces as well as Lebesgue, Hardy, (generalized) Sobolev and Lipschitz spaces are also covered by our approach
Embeddings between Triebel-Lizorkin Spaces on Metric Spaces Associated with Operators
No full textWe consider the general framework of a metric measure space satisfying the doubling volume property, associated with a non-negative self-adjoint operator, whose heat kernel enjoys standard Gaussian localization. We prove embedding theorems between Triebel-Lizorkin spaces associated with operators. Embeddings for non-classical Triebel-Lizorkin and (both classical and non-classical) Besov spaces are proved as well. Our result generalize the Euclidean case and are new for many settings of independent interest such as the ball, the interval and Riemannian manifolds
A Lattice Boltzmann method model of diffusion-weighted magnetic resonance imaging in skeletal muscle
No full textAging and obesity is associated with reduction in muscle mass and increase in fat mass, leading to decline in both physical function and health. Probing the cellular microstructure of skeletal muscle with noninvasive methods is paramount in developing effective therapeutic procedures for the elderly, such as physical exercise. Using special proton magnetic resonance imaging (MRI) protocols we can investigate non-invasively diffusion phenomena within skeletal muscle. This project focuses on the numerical study of the effect of microstructure on the effective diffusion coefficient via a Lattice Boltzmann model (LBM). Specifically, we aim to characterize how variations in microstructure and mass transport properties affect the local apparent diffusion coefficient of water measured with Diffusion Tensor Imaging (DTI).
A numerical model is developed to solve the Bloch-Torrey equation in a periodic domain containing muscle cells surrounded by permeable membranes. This model is shown to be convergent in both time and space at the theoretical truncation error rate and to agree with analytical solutions of limiting cases. The effect of membrane permeability is investigated and found to be consistent in trend with prior experimental investigations.
A simpler two-compartment exchange model is also investigated and compared with the LBM model. It is found that qualitative agreement exists in terms of variations in ellipticity and permeability, however, there is qualitative disagreement in the model for changes in cell volume fraction. This disagreement is investigated systematically and the numerical source of the disagreement between the two models is identified. Our results demonstrate that the continuum LBM model is superior to the two-compartmental model for human muscle MRI.Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2018-05-01The student, Noel Naughton, accepted the attached license on 2016-04-26 at 16:57.The student, Noel Naughton, submitted this Thesis for approval on 2016-04-26 at 17:08.This Thesis was approved for publication on 2016-04-28 at 08:20.DSpace SAF Submission Ingestion Package generated from Vireo submission #9531 on 2016-07-07 at 14:18:05Made available in DSpace on 2016-07-07T21:18:08Z (GMT). No. of bitstreams: 2
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Previous issue date: 2016-04-28Embargo set by: Seth Robbins for item 93321
Lift date: 2018-07-07T21:18:16Z
Reason: Author requested closed access (OA after 2yrs) in Vireo ETD systemLimited Restriction Lifted for Item 93321 on 2018-07-08T09:15:20Z
Fourier multipliers on anisotropic mixed-norm spaces of distributions
No full textA new general Hörmander type condition involving anisotropies and mixed norms is introduced, and boundedness results for Fourier multipliers on anisotropic Besov and Triebel-Lizorkin spaces of distributions with mixed Lebesgue norms are obtained. As an application, the continuity of such operators is established on mixed Sobolev and Lebesgue spaces too. Some lifting properties and equivalent norms are obtained as well
Molecular decomposition of anisotropic homogeneous mixed-norm spaces with applications to the boundedness of operators
No full textAnisotropic homogeneous mixed-norm Besov and Triebel–Lizorkin spaces are introduced and their properties are explored. A discrete adapted ϕ-transform decomposition is obtained. An associated class of almost diagonal operators is introduced and a boundedness result for such operators is obtained. Molecular decompositions for all the considered spaces are derived with the help of the algebra of almost diagonal operators. As an application, we obtain boundedness results on the considered spaces for Fourier multipliers and for pseudodifferential operators with suitable adapted homogeneous symbols using the molecular decomposition theory
Fourier Multipliers on Decomposition Spaces of Modulation and Triebel–Lizorkin Type
No full textThe family of anisotropic decomposition spaces of modulation and Triebel–Lizorkin type on Rn is a large family of smoothness spaces that include classical Besov, Triebel–Lizorkin, modulation and α-modulation spaces. The decomposition space approach allows for a unified treatment of such smoothness spaces in both the isotropic and an anisotropic setting. We derive a boundedness result for Fourier multipliers on anisotropic decomposition spaces of modulation and Triebel–Lizorkin type. As an application, we obtain equivalent quasi-norm characterizations for this class of decomposition spaces
Anisotropic mixed-norm Hardy spaces
No full textWe introduce and explore Hardy spaces defined by mixed Lebesgue norms and anisotropic dilations. We prove that the definitions of these spaces in terms of smooth, non-tangential, auxiliary, grand, and Poisson maximal operators coincide. We also study the relation between anisotropic mixed-norm Hardy spaces and mixed-norm Lebesgue spaces
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