Search results for "geometry."
showing 10 items of 4386 documents
On the Landis conjecture for the fractional Schrödinger equation
2023
In this paper, we study a Landis-type conjecture for the general fractional Schrödinger equation ((−P)s+q)u=0. As a byproduct, we also prove the additivity and boundedness of the linear operator (−P)s for non-smooth coefficents. For differentiable potentials q, if a solution decays at a rate exp (−∣x∣1+), then the solution vanishes identically. For non-differentiable potentials q, if a solution decays at a rate exp (−∣x∣4s−14s+), then the solution must again be trivial. The proof relies on delicate Carleman estimates. This study is an extension of the work by Rüland and Wang (2019). peerReviewed
Fractional Maximal Functions in Metric Measure Spaces
2013
Abstract We study the mapping properties of fractional maximal operators in Sobolev and Campanato spaces in metric measure spaces. We show that, under certain restrictions on the underlying metric measure space, fractional maximal operators improve the Sobolev regularity of functions and map functions in Campanato spaces to Hölder continuous functions. We also give an example of a space where fractional maximal function of a Lipschitz function fails to be continuous.
Quasiconformal geometry and removable sets for conformal mappings
2020
We study metric spaces defined via a conformal weight, or more generally a measurable Finsler structure, on a domain $\Omega \subset \mathbb{R}^2$ that vanishes on a compact set $E \subset \Omega$ and satisfies mild assumptions. Our main question is to determine when such a space is quasiconformally equivalent to a planar domain. We give a characterization in terms of the notion of planar sets that are removable for conformal mappings. We also study the question of when a quasiconformal mapping can be factored as a 1-quasiconformal mapping precomposed with a bi-Lipschitz map.
Quasisymmetric extension on the real line
2015
We give a geometric characterization of the sets $E\subset \mathbb{R}$ that satisfy the following property: every quasisymmetric embedding $f: E \to \mathbb{R}^n$ extends to a quasisymmetric embedding $f:\mathbb{R}\to\mathbb{R}^N$ for some $N\geq n$.
A note on some fundamental results in complete gauge spaces and application
2015
We discuss the extension of some fundamental results in nonlinear analysis to the setting of gauge spaces. In particular, we establish Ekeland type and Caristi type results under suitable hypotheses for mappings and cyclic mappings. Our theorems generalize and complement some analogous results in the literature, also in the sense of ordered sets and oriented graphs. We apply our results to establishing the existence of solution to a second order nonlinear initial value problem.
Sparse relative risk survival modelling
2016
Cancer survival is thought to closed linked to the genimic constitution of the tumour. Discovering such signatures will be useful in the diagnosis of the patient and may be used for treatment decisions and perhaps even the development of new treatments. However, genomic data are typically noisy and high-dimensional, often outstripping the number included in the study. Regularized survival models have been proposed to deal with such scenary. These methods typically induce sparsity by means of a coincidental match of the geometry of the convex likelihood and (near) non-convex regularizer.
Digital and Interactive Learning and Teaching Methods in Descriptive Geometry
2013
Abstract During the course of “Fundamentals and applications of Science of Representation - Geometric drawing” (held at the Faculty of Engineering at the University of Palermo) we successfully tested the adoption of informatics tools to enhance the comprehension and the critical analysis of complex figures in the geometrical space. The peculiarity in the teaching methodology was the adoption of interactive software products (Cabri Geometre and GeoGebra concerning dynamic and geometrical constructions; the well-known Rhinoceros plug-in, Grasshopper, about generating algorithms; Linceo regarding implementing the graphic display of complex solids in augmented reality). According to our experie…
<title>Modified crossed-cylinder aberroscope</title>
2001
We report a technique to estimate eye aberrations, based mainly on the subjective crossed-cylinder method. In order to obtain accurate coordinates of cross sections of the aberration distorted grid image on the retinal plane, needed in subjective methods, fusion of two images is used. The image seen by the eye under investigation is fused by the patient with a similar grid generated and reshaped in the appropriate way on the computer screen. The computer simulated image is viewed either by the second eye (in order to avoid eye rivalry and suppression processes, that are typical for such conditions, stimuli for both eyes are discontinuous and are displayed sequentially with a frequency of 50…
An unbounded family of log Calabi–Yau pairs
2016
We give an explicit example of log Calabi-Yau pairs that are log canonical and have a linearly decreasing Euler characteristic. This is constructed in terms of a degree two covering of a sequence of blow ups of three dimensional projective bundles over the Segre-Hirzebruch surfaces ${\mathbb F}_n$ for every positive integer $n$ big enough.
Volcanic Gas Emissions Along the Colombian Arc Segment of the Northern Volcanic Zone (CAS-NVZ): Implications for volcano monitoring and volatile budg…
2019
Studying spatial and temporal trends in volcanic gas compositions and fluxes is crucial both to volcano monitoring and to constrain the origin and recycling efficiency of volatiles at active convergent margins. New volcanic gas compositions and volatile fluxes are here reported for Nevado del Ruiz, Galeras, and Purace, three of the most persistently degassing volcanoes located in the Colombian Arc Segment of the Northern Volcanic Zone. At Nevado del Ruiz, from 2014 to 2017, plume emissions showed an average molar CO2/S-T ratio of 3.9 +/- 1.6 (S-T is total sulfur, S). Contemporary, fumarolic chemistry at Galeras progressively shifted toward low-temperature, S-depleted fumarolic gas discharge…