Search results for "DOMAIN"
showing 10 items of 2485 documents
Jacobian of weak limits of Sobolev homeomorphisms
2016
Abstract Let Ω be a domain in ℝ n {\mathbb{R}^{n}} , where n = 2 , 3 {n=2,3} . Suppose that a sequence of Sobolev homeomorphisms f k : Ω → ℝ n {f_{k}\colon\Omega\to\mathbb{R}^{n}} with positive Jacobian determinants, J ( x , f k ) > 0 {J(x,f_{k})>0} , converges weakly in W 1 , p ( Ω , ℝ n ) {W^{1,p}(\Omega,\mathbb{R}^{n})} , for some p ⩾ 1 {p\geqslant 1} , to a mapping f. We show that J ( x , f ) ⩾ 0 {J(x,f)\geqslant 0} a.e. in Ω. Generalizations to higher dimensions are also given.
Biorthogonal Wavelet Transforms Originating from Discrete and Discrete-Time Splines
2018
This chapter describes how to generate families of biorthogonal wavelet transforms in spaces of periodic signals using prediction p-filters originating from discrete-time and discrete splines. The transforms are generated by the lifting scheme (Sweldens (Wavelet applications in signal and image processing III, vol 2569, 1995, [7]), Sweldens (Appl Comput Harmon Anal 3:186–200, 1996, [8]), Sweldens (SIAM J Math Anal 29:511–546, 1997, [9]), see also Sect. 7.1 of this volume). The discrete-time wavelets related to those transforms are (anti)symmetric, well localized in time domain and have flat spectra. These families comprise wavelets with any number of local discrete vanishing moments (LDVMs)…
A density problem for Sobolev spaces on Gromov hyperbolic domains
2017
We prove that for a bounded domain $\Omega\subset \mathbb R^n$ which is Gromov hyperbolic with respect to the quasihyperbolic metric, especially when $\Omega$ is a finitely connected planar domain, the Sobolev space $W^{1,\,\infty}(\Omega)$ is dense in $W^{1,\,p}(\Omega)$ for any $1\le p<\infty$. Moreover if $\Omega$ is also Jordan or quasiconvex, then $C^{\infty}(\mathbb R^n)$ is dense in $W^{1,\,p}(\Omega)$ for $1\le p<\infty$.
Existence and multiplicity results for semilinear elliptic Dirichlet problems in exterior domains
1995
A Note on States and Traces from Biorthogonal Sets
2019
In this paper, following Bagarello, Trapani, and myself, we generalize the Gibbs states and their related KMS-like conditions. We have assumed that H 0 , H are closed and, at least, densely defined, without giving information on the domain of these operators. The problem we address in this paper is therefore to find a dense domain D that allows us to generalize the states of Gibbs and take them in their natural environment i.e., defined in L &dagger
Optimal lower bounds for eigenvalues of linear and nonlinear Neumann problems
2013
In this paper we prove a sharp lower bound for the first non-trivial Neumann eigenvalue μ1(Ω) for the p-Laplace operator (p > 1) in a Lipschitz bounded domain Ω in ℝn. Our estimate does not require any convexity assumption on Ω and it involves the best isoperimetric constant relative to Ω. In a suitable class of convex planar domains, our bound turns out to be better than the one provided by the Payne—Weinberger inequality.
Geometrical control of pure spin current induced domain wall depinning.
2017
[EN] We investigate the pure spin-current assisted depinning of magnetic domain walls in half ring based Py/Al lateral spin valve structures. Our optimized geometry incorporating a patterned notch in the detector electrode, directly below the Al spin conduit, provides a tailored pinning potential for a transverse domain wall and allows for a precise control over the magnetization configuration and as a result the domain wall pinning. Due to the patterned notch, we are able to study the depinning field as a function of the applied external field for certain applied current densities and observe a clear asymmetry for the two opposite field directions. Micromagnetic simulations show that this …
The era of reference genomes in conservation genomics
2022
Progress in genome sequencing now enables the large-scale generation of reference genomes. Various international initiatives aim to generate reference genomes representing global biodiversity. These genomes provide unique insights into genomic diversity and architecture, thereby enabling comprehensive analyses of population and functional genomics, and are expected to revolutionize conservation genomics.
Zebrafish as a Model to Evaluate a CRISPR/Cas9-Based Exon Excision Approach as a Future Treatment Option for EYS-Associated Retinitis Pigmentosa
2021
Retinitis pigmentosa (RP) is an inherited retinal disease (IRD) with an overall prevalence of 1 in 4000 individuals. Mutations in EYS (Eyes shut homolog) are among the most frequent causes of non-syndromic autosomal recessively inherited RP and act via a loss-of-function mechanism. In light of the recent successes for other IRDs, we investigated the therapeutic potential of exon skipping for EYS-associated RP. CRISPR/Cas9 was employed to generate zebrafish from which the region encompassing the orthologous exons 37-41 of human EYS (eys exons 40-44) was excised from the genome. The excision of these exons was predicted to maintain the open reading frame and to result in the removal of exactl…
A Comparative Study on Nickel Binding to Hpn-like Polypeptides from Two Helicobacter pylori Strains
2021
Combined potentiometric titration and isothermal titration calorimetry (ITC) methods were used to study the interactions of nickel(II) ions with the N-terminal fragments and histidine-rich fragments of Hpn-like protein from two Helicobacter pylori strains (11637 and 26695). The ITC measurements were performed at various temperatures and buffers in order to extract proton-independent reaction enthalpies of nickel binding to each of the studied protein fragments. We bring up the problem of ITC results of nickel binding to the Hpn-like protein being not always compatible with those from potentiometry and MS regarding the stoichiometry and affinity. The roles of the ATCUN motif and multiple His…