3,068 research outputs found
Regular rapidly decreasing nonlinear generalized functions. Application to microlocal regularity
We present new types of regularity for nonlinear generalized functions, based
on the notion of regular growth with respect to the regularizing parameter of
Colombeau's simplified model. This generalizes the notion of G^{\infty
}-regularity introduced by M. Oberguggenberger. A key point is that these
regularities can be characterized, for compactly supported generalized
functions, by a property of their Fourier transform. This opens the door to
microanalysis of singularities of generalized functions, with respect to these
regularities. We present a complete study of this topic, including properties
of the Fourier transform (exchange and regularity theorems) and relationship
with classical theory, via suitable results of embeddings.Comment: Submitted to the Journal of Mathematical Analysis and Application
Remarks on the embedding of spaces of distributions into spaces of Colombeau generalized functions
We present some remarks about the embedding of spaces of Schwartz
distributions into spaces of Colombeau generalized functions. We show that the
various constructions of such embeddings existing in the literature lead in
fact to the same one.Comment: 13 page
Alpha-invariant of Toric Line Bundles
We generalize the work of Jian Song to compute the alpha invariant of any
(nef and big) toric line bundle in terms of the associated polytope. We use the
analytic version of the computation of the log canonical threshold of monomial
ideals to give the log canonical threshold of any non-negatively curved
singular hermitian metric on the line bundle, and deduce the alpha invariant
from this.Comment: 13 pages. Minor corrections, and references added. Published versio
Generalized Integral Operators and Schwartz Kernel Theorem
In connection with the classical Schwartz kernel theorem, we show that in the
framework of Colombeau generalized functions a large class of linear mappings
admit integral kernels. To do this, we need to introduce news spaces of
generalized functions with slow growth and the corresponding adapted linear
mappings. Finally, we show that in some sense Schwartz' result is contained in
our main theorem.Comment: 18 page
Semi-pointed partition posets and Species
We define semi-pointed partition posets, which are a generalisation of
partition posets and show that they are Cohen-Macaulay. We then use multichains
to compute the dimension and the character for the action of the symmetric
groups on their homology. We finally study the associated incidence Hopf
algebra, which is similar to the Fa{\`a} di Bruno Hopf algebra.Comment: 27 page
Pulmonary arterial hypertension: the burden of disease and impact on quality of life.
Pulmonary arterial hypertension (PAH) is a debilitating disease that pervades all aspects of a patients daily life. It is also increasingly acknowledged that the burden of PAH extends to older patients and carers. Until recently, the adverse effect of disease symptoms on the physical, emotional and social factors governing patient health-related quality of life (HRQoL) remained largely unrecognised. With a shift in therapeutic objectives to longer term improvements and HRQoL benefits, clinical trials now frequently include HRQoL measures as study end-points. Most HRQoL instruments used in patients with PAH are generic or non-disease-specific questionnaires and therefore may not accurately capture PAH disease burden. New PAH-specific HRQoL instruments currently undergoing validation include emPHasis-10 and Pulmonary Arterial Hypertension-Symptoms and Impact (PAH-SYMPACT; Actelion Pharmaceuticals Ltd, Allschwil, Switzerland). Using various HRQoL measures, pharmacological therapies have been shown to improve HRQoL in patients with PAH. Patients also derive HRQoL benefits from nonpharmacological strategies, which include the emotional support provided by multidisciplinary care and support groups that is fundamental to patient wellbeing. Looking to the future, validated PAH-specific HRQoL instruments together with dedicated guidelines and procedures are essential to support the translation of HRQoL scores to the clinic, thus enabling a holistic treatment approach to the management of patients with PAH
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