Search results for "A10"
showing 10 items of 62 documents
Weyl's Theorems and Extensions of Bounded Linear Operators
2012
A bounded operator $T\in L(X)$, $X$ a Banach space, is said to satisfy Weyl's theorem if the set of all spectral points that do not belong to the Weyl spectrum coincides with the set of all isolated points of the spectrum which are eigenvalues and having finite multiplicity. In this article we give sufficient conditions for which Weyl's theorem for an extension $\overline T$ of $T$ (respectively, for $T$) entails that Weyl's theorem holds for $T$ (respectively, for $\overline T$).
Harnack and Shmul'yan pre-order relations for Hilbert space contractions
2015
We study the behavior of some classes of Hilbert space contractions with respect to Harnack and Shmul'yan pre-orders and the corresponding equivalence relations. We give some conditions under which the Harnack equivalence of two given contractions is equivalent to their Shmul'yan equivalence and to the existence of an arc joining the two contractions in the class of operator-valued contractive analytic functions on the unit disc. We apply some of these results to quasi-isometries and quasi-normal contractions, as well as to partial isometries for which we show that their Harnack and Shmul'yan parts coincide. We also discuss an extension, recently considered by S.~ter~Horst [\emph{J. Operato…
On the topology of surfaces with the generalised simple lift property.
2020
In this paper, we study the geometry of surfaces with the generalised simple lift property. This work generalises previous results by Bernstein and Tinaglia, and it is motivated by the fact that leaves of a minimal lamination obtained as a limit of a sequence of properly embedded minimal disks satisfy the generalised simple lift property.
A Kato's second type representation theorem for solvable sesquilinear forms
2017
Kato's second representation theorem is generalized to solvable sesquilinear forms. These forms need not be non-negative nor symmetric. The representation considered holds for a subclass of solvable forms (called hyper-solvable), precisely for those whose domain is exactly the domain of the square root of the modulus of the associated operator. This condition always holds for closed semibounded forms, and it is also considered by several authors for symmetric sign-indefinite forms. As a consequence, a one-to-one correspondence between hyper-solvable forms and operators, which generalizes those already known, is established.
Dynamics of the scenery flow and geometry of measures
2015
We employ the ergodic theoretic machinery of scenery flows to address classical geometric measure theoretic problems on Euclidean spaces. Our main results include a sharp version of the conical density theorem, which we show to be closely linked to rectifiability. Moreover, we show that the dimension theory of measure-theoretical porosity can be reduced back to its set-theoretic version, that Hausdorff and packing dimensions yield the same maximal dimension for porous and even mean porous measures, and that extremal measures exist and can be chosen to satisfy a generalized notion of self-similarity. These are sharp general formulations of phenomena that had been earlier found to hold in a n…
Resonances for nonanalytic potentials
2009
We consider semiclassical Schr"odinger operators on $R^n$, with $C^infty$ potentials decaying polynomially at infinity. The usual theories of resonances do not apply in such a non-analytic framework. Here, under some additional conditions, we show that resonances are invariantly defined up to any power of their imaginary part. The theory is based on resolvent estimates for families of approximating distorted operators with potentials that are holomorphic in narrow complex sectors around $R^n$.
miRNA Signature and Dicer Requirement during Human Endometrial Stromal Decidualization In Vitro
2012
Decidualization is a morphological and biochemical transformation of endometrial stromal fibroblast into differentiated decidual cells, which is critical for embryo implantation and pregnancy establishment. The complex regulatory networks have been elucidated at both the transcriptome and the proteome levels, however very little is known about the post-transcriptional regulation of this process. miRNAs regulate multiple physiological pathways and their de-regulation is associated with human disorders including gynaecological conditions such as endometriosis and preeclampsia. In this study we profile the miRNAs expression throughout human endometrial stromal (hESCs) decidualization and analy…
Quantifying energy demand and greenhouse gas emissions of road infrastructure projects: An LCA case study of the Oslo fjord crossing in Norway
2016
The road sector consumes large amounts of materials and energy and produces large quantities of greenhouse gas emissions, which can be reduced with correct information in the early planning stages of road project. An important aspect in the early planning stages is the choice between alternative road corridors that will determine the route distance and the subsequent need for different road infrastructure elements, such as bridges and tunnels. Together, these factors may heavily influence the life cycle environmental impacts of the road project. This paper presents a case study for two prospective road corridor alternatives for the Oslo fjord crossing in Norway and utilizes in a streamlined…
Designing mobility in a city in transition : challenges from the case of Palermo
2014
Transport policy is one of the most crucial sectors in the process of adaptation of contemporary cities to the challenge of sustainable development. For its close relation with social habits and people behaviors, in fact, innovation in transports play a strategic role both in the decreasing of the environmental impact of mobility and in the improvement of the quality of the built environment. To do so, however, cities need to reach a more effective integration between transport policy and land-use planning, as well as taking full advantage by the spreading of new technologies. In this context, this paper discusses the challenges provided by the reshaping of the transport system in the metro…
Interior Eigenvalue Density of Jordan Matrices with Random Perturbations
2017
International audience; We study the eigenvalue distribution of a large Jordan block subject to a small random Gaussian perturbation. A result by E. B. Davies and M. Hager shows that as the dimension of the matrix gets large, with probability close to 1, most of the eigenvalues are close to a circle.We study the expected eigenvalue density of the perturbed Jordan block in the interior of that circle and give a precise asymptotic description.; Nous étudions la distribution de valeurs propres d’un grand bloc de Jordan soumis à une petite perturbation gaussienne aléatoire. Un résultat de E. B. Davies et M. Hager montre que quand la dimension de la matrice devient grande, alors avec probabilité…