Search results for "obol"
showing 10 items of 228 documents
Sobolev homeomorphic extensions
2021
Let $\mathbb X$ and $\mathbb Y$ be $\ell$-connected Jordan domains, $\ell \in \mathbb N$, with rectifiable boundaries in the complex plane. We prove that any boundary homeomorphism $\varphi \colon \partial \mathbb X \to \partial \mathbb Y$ admits a Sobolev homeomorphic extension $h \colon \overline{\mathbb X} \to \overline{\mathbb Y}$ in $W^{1,1} (\mathbb X, \mathbb C)$. If instead $\mathbb X$ has $s$-hyperbolic growth with $s>p-1$, we show the existence of such an extension lies in the Sobolev class $W^{1,p} (\mathbb X, \mathbb C)$ for $p\in (1,2)$. Our examples show that the assumptions of rectifiable boundary and hyperbolic growth cannot be relaxed. We also consider the existence of $W^{…
Isoperimetric inequality from the poisson equation via curvature
2012
In this paper, we establish an isoperimetric inequality in a metric measure space via the Poisson equation. Let (X,d,μ) be a complete, pathwise connected metric space with locally Ahlfors Q-regular measure, where Q > 1, that supports a local L2-Poincare inequality. We show that, for the Poisson equation Δu = g, if the local L∞-norm of the gradient Du can be bounded by the Lorentz norm LQ,1 of g, then we obtain an isoperimetric inequality and a Sobolev inequality in (X,d,μ) with optimal exponents. By assuming a suitable curvature lower bound, we establish such optimal bounds on . © 2011 Wiley Periodicals, Inc.
Transformation of the dermatophyte Trichophyton mentagrophytes to hygromycin B resistance.
1989
A transformation system for the ringworm-producing dermatophyte Trichophyton mentagrophytes has been developed. The system employs the plasmid pHIS, which contains a bacterial hygromycin B phosphotransferase gene linked to Cochliobolus heterostrophus regulatory sequences (B. G. Turgeon, R. C. Garber, and O. C. Yoder, Mol. Cell. Biol. 7:3297-3305, 1987). This plasmid confers hygromycin B resistance to T. mentagrophytes. The DNA was stably integrated into the fungal genome, and the number and sites of integrations varied among transformants. Transformant clones were capable of infecting guinea pigs. This system opens the way for the molecular genetic analysis of the interaction of T. mentagro…
Continuous spectrum for a two phase eigenvalue problem with an indefinite and unbounded potential
2020
Abstract We consider a two phase eigenvalue problem driven by the ( p , q ) -Laplacian plus an indefinite and unbounded potential, and Robin boundary condition. Using a modification of the Nehari manifold method, we show that there exists a nontrivial open interval I ⊆ R such that every λ ∈ I is an eigenvalue with positive eigenfunctions. When we impose additional regularity conditions on the potential function and the boundary coefficient, we show that we have smooth eigenfunctions.
Mappings of Finite Distortion:¶Discreteness and Openness
2001
We establish a sharp integrability condition on the partial derivatives of a mapping with L p -integrable distortion for some p>n− 1 to guarantee discreteness and openness. We also show that a mapping with exponentially integrable distortion and integrable Jacobian determinant is either constant or both discrete and open. We give an example demonstrating the preciseness of our criterion.
Medical student ultrasound education: a WFUMB position paper, part I
2019
The introduction of ultrasound into medical student education is well underway in many locations around the world, but is still in its infancy or has yet to begin in others. Proper incorporation of ultrasound education into medical training requires planning and resources, both capital and human. In this article, we discuss the state of the art of ultrasound in medical education throughout the world, as well as various methodologies utilized to improve student education and to incorporate ultrasound into every facet of training. Experiences from various educational systems and available evidence regarding the impact of ultrasound education are summarized. Representing multiple societies and…
Nodal Solutions for Supercritical Laplace Equations
2015
In this paper we study radial solutions for the following equation $$\Delta u(x)+f (u(x), |x|) = 0,$$ where $${x \in {\mathbb{R}^{n}}}$$ , n > 2, f is subcritical for r small and u large and supercritical for r large and u small, with respect to the Sobolev critical exponent $${2^{*} = \frac{2n}{n-2}}$$ . The solutions are classified and characterized by their asymptotic behaviour and nodal properties. In an appropriate super-linear setting, we give an asymptotic condition sufficient to guarantee the existence of at least one ground state with fast decay with exactly j zeroes for any j ≥ 0. Under the same assumptions, we also find uncountably many ground states with slow decay, singular gro…
H2-TPR, XPS and TEM Study of the Reduction of Ru and Re promoted Co/γ-Al2O3, Co/TiO2 and Co/SiC Catalysts
2016
<p class="1Body">Effects of Ru and Re promoters on Co-CoO<sub>x </sub>catalysts supported on γ-Al<sub>2</sub>O<sub>3</sub>, TiO<sub>2</sub> and SiC were investigated to improve the understanding of the role of promoters of the active phase of Co-CoO<sub>x</sub>-Ru and Co-CoO<sub>x</sub>-Re. The influence of promoter addition on the composition and activity of the catalysts was characterized by several methods, such as H<sub>2</sub>-TPR, XPS, chemisorption and TEM. Furthermore, the role of support and metal-support interaction was especially studied and different support materials were compared.</p&g…
Loomis-Whitney inequalities in Heisenberg groups
2021
This note concerns Loomis-Whitney inequalities in Heisenberg groups $\mathbb{H}^n$: $$|K| \lesssim \prod_{j=1}^{2n}|\pi_j(K)|^{\frac{n+1}{n(2n+1)}}, \qquad K \subset \mathbb{H}^n.$$ Here $\pi_{j}$, $j=1,\ldots,2n$, are the vertical Heisenberg projections to the hyperplanes $\{x_j=0\}$, respectively, and $|\cdot|$ refers to a natural Haar measure on either $\mathbb{H}^n$, or one of the hyperplanes. The Loomis-Whitney inequality in the first Heisenberg group $\mathbb{H}^1$ is a direct consequence of known $L^p$ improving properties of the standard Radon transform in $\mathbb{R}^2$. In this note, we show how the Loomis-Whitney inequalities in higher dimensional Heisenberg groups can be deduced…
Infinitesimal Hilbertianity of Weighted Riemannian Manifolds
2018
AbstractThe main result of this paper is the following: anyweightedRiemannian manifold$(M,g,\unicode[STIX]{x1D707})$,i.e., a Riemannian manifold$(M,g)$endowed with a generic non-negative Radon measure$\unicode[STIX]{x1D707}$, isinfinitesimally Hilbertian, which means that its associated Sobolev space$W^{1,2}(M,g,\unicode[STIX]{x1D707})$is a Hilbert space.We actually prove a stronger result: the abstract tangent module (à la Gigli) associated with any weighted reversible Finsler manifold$(M,F,\unicode[STIX]{x1D707})$can be isometrically embedded into the space of all measurable sections of the tangent bundle of$M$that are$2$-integrable with respect to$\unicode[STIX]{x1D707}$.By following the…