Search results for "A12"
showing 10 items of 60 documents
On Radon transforms on compact Lie groups
2016
We show that the Radon transform related to closed geodesics is injective on a Lie group if and only if the connected components are not homeomorphic to $S^1$ nor to $S^3$. This is true for both smooth functions and distributions. The key ingredients of the proof are finding totally geodesic tori and realizing the Radon transform as a family of symmetric operators indexed by nontrivial homomorphisms from $S^1$.
The Geodesic Ray Transform on Spherically Symmetric Reversible Finsler Manifolds
2023
We show that the geodesic ray transform is injective on scalar functions on spherically symmetric reversible Finsler manifolds where the Finsler norm satisfies a Herglotz condition. We use angular Fourier series to reduce the injectivity problem to the invertibility of generalized Abel transforms and by Taylor expansions of geodesics we show that these Abel transforms are injective. Our result has applications in linearized boundary rigidity problem on Finsler manifolds and especially in linearized elastic travel time tomography.
Pestov identities and X-ray tomography on manifolds of low regularity
2021
We prove that the geodesic X-ray transform is injective on scalar functions and (solenoidally) on one-forms on simple Riemannian manifolds $(M,g)$ with $g \in C^{1,1}$. In addition to a proof, we produce a redefinition of simplicity that is compatible with rough geometry. This $C^{1,1}$-regularity is optimal on the H\"older scale. The bulk of the article is devoted to setting up a calculus of differential and curvature operators on the unit sphere bundle atop this non-smooth structure.
Normal forms and embeddings for power-log transseries
2016
First return maps in the neighborhood of hyperbolic polycycles have their asymptotic expansion as Dulac series, which are series with power-logarithm monomials. We extend the class of Dulac series to an algebra of power-logarithm transseries. Inside this new algebra, we provide formal normal forms of power-log transseries and a formal embedding theorem. The questions of classifications and of embeddings of germs into flows of vector fields are common problems in dynamical systems. Aside from that, our motivation for this work comes from fractal analysis of orbits of first return maps around hyperbolic polycycles. This is a joint work with Pavao Mardešić, Jean-Philippe Rolin and Vesna Župano…
Existence and uniqueness of nontrivial collocation solutions of implicitly linear homogeneous Volterra integral equations
2011
We analyze collocation methods for nonlinear homogeneous Volterra-Hammerstein integral equations with non-Lipschitz nonlinearity. We present different kinds of existence and uniqueness of nontrivial collocation solutions and we give conditions for such existence and uniqueness in some cases. Finally we illustrate these methods with an example of a collocation problem, and we give some examples of collocation problems that do not fit in the cases studied previously.
Localization of the spectra of dual frames multipliers
2022
This paper concerns dual frames multipliers, i.e. operators in Hilbert spaces consisting of analysis, multiplication and synthesis processes, where the analysis and the synthesis are made by two dual frames, respectively. The goal of the paper is to give some results about the localization of the spectra of dual frames multipliers, i.e. to individuate regions of the complex plane containing the spectra using some information about the frames and the symbols.
Controversial roles of methylenetetrahydrofolate reductase polymorphisms and folate in breast cancer disease
2014
Abstract Breast cancer (BC) represents a highly heterogeneous tumour at both the clinical and molecular levels. Single-nucleotide polymorphisms (SNPs) of the folate-metabolising enzyme methylenetetrahydrofolate-reductase (MTHFR) may modify the association between folate intake and BC and influence plasma folate concentration. The role of folate in BC is equivocal, association studies between the common MTHFR SNPs C677T and A1298C and BC risk are controversial. In this study, I have reviewed observed associations between folate intake, as well as its blood levels, and BC. The purpose of this review is to analyse the role of folate and the two SNPs associated with reduced enzyme activity in B…
Identification of novel mutations in the ABCA12 gene, c.1857delA and c.5653–5655delTAT, causing harlequin ichthyosis
2013
Abstract Harlequin ichthyosis (HI) is a severe autosomal recessive developmental disorder of the skin that is frequently but not always fatal in the first few days of life. In HI, mutations in both ABCA12 gene alleles must have a severe impact on protein function and most mutations are truncating. The presence of at least one nontruncating mutation (predicting a residual protein function) usually causes a less severe congenital ichthyosis (lamellar ichthyosis or congenital ichthyosiform erythroderma). Here we report on a girl with severe HI diagnosed by prenatal ultrasound at 33 5/7 week gestation. Ultrasound findings included ectropion, eclabium, deformed nose, hands and feet, joint contra…
The forgotten mathematical legacy of Peano
2019
International audience; The formulations that Peano gave to many mathematical notions at the end of the 19th century were so perfect and modern that they have become standard today. A formal language of logic that he created, enabled him to perceive mathematics with great precision and depth. He described mathematics axiomatically basing the reasoning exclusively on logical and set-theoretical primitive terms and properties, which was revolutionary at that time. Yet, numerous Peano’s contributions remain either unremembered or underestimated.
Local conical dimensions for measures
2012
AbstractWe study the decay of μ(B(x,r)∩C)/μ(B(x,r)) asr↓ 0 for different kinds of measures μ on ℝnand various conesCaroundx. As an application, we provide sufficient conditions that imply that the local dimensions can be calculated via cones almost everywhere.