Search results for "102"
showing 10 items of 2892 documents
On vibrating thin membranes with mass concentrated near the boundary: an asymptotic analysis
2018
We consider the spectral problem \begin{equation*} \left\{\begin{array}{ll} -\Delta u_{\varepsilon}=\lambda(\varepsilon)\rho_{\varepsilon}u_{\varepsilon} & {\rm in}\ \Omega\\ \frac{\partial u_{\varepsilon}}{\partial\nu}=0 & {\rm on}\ \partial\Omega \end{array}\right. \end{equation*} in a smooth bounded domain $\Omega$ of $\mathbb R^2$. The factor $\rho_{\varepsilon}$ which appears in the first equation plays the role of a mass density and it is equal to a constant of order $\varepsilon^{-1}$ in an $\varepsilon$-neighborhood of the boundary and to a constant of order $\varepsilon$ in the rest of $\Omega$. We study the asymptotic behavior of the eigenvalues $\lambda(\varepsilon)$ and the eige…
A Dirichlet problem for the Laplace operator in a domain with a small hole close to the boundary
2016
We study the Dirichlet problem in a domain with a small hole close to the boundary. To do so, for each pair $\boldsymbol\varepsilon = (\varepsilon_1, \varepsilon_2 )$ of positive parameters, we consider a perforated domain $\Omega_{\boldsymbol\varepsilon}$ obtained by making a small hole of size $\varepsilon_1 \varepsilon_2 $ in an open regular subset $\Omega$ of $\mathbb{R}^n$ at distance $\varepsilon_1$ from the boundary $\partial\Omega$. As $\varepsilon_1 \to 0$, the perforation shrinks to a point and, at the same time, approaches the boundary. When $\boldsymbol\varepsilon \to (0,0)$, the size of the hole shrinks at a faster rate than its approach to the boundary. We denote by $u_{\bolds…
Discontinuous Gradient Constraints and the Infinity Laplacian
2012
Motivated by tug-of-war games and asymptotic analysis of certain variational problems, we consider a gradient constraint problem involving the infinity Laplace operator. We prove that this problem always has a solution that is unique if a certain regularity condition on the constraint is satisfied. If this regularity condition fails, then solutions obtained from game theory and $L^p$-approximation need not coincide.
Parametric and nonparametric A-Laplace problems: Existence of solutions and asymptotic analysis
2021
We give sufficient conditions for the existence of weak solutions to quasilinear elliptic Dirichlet problem driven by the A-Laplace operator in a bounded domain Ω. The techniques, based on a variant of the symmetric mountain pass theorem, exploit variational methods. We also provide information about the asymptotic behavior of the solutions as a suitable parameter goes to 0 + . In this case, we point out the existence of a blow-up phenomenon. The analysis developed in this paper extends and complements various qualitative and asymptotic properties for some cases described by homogeneous differential operators.
Two properties of Müntz spaces
2017
Abstract We show that Müntz spaces, as subspaces of C[0, 1], contain asymptotically isometric copies of c0 and that their dual spaces are octahedral.
TGF-β signalling is required for CD4⁺ T cell homeostasis but dispensable for regulatory T cell function.
2013
Signalling by the cytokine TGF-β regulates mature CD4+ T cell populations but is not involved in the survival and function of regulatory T cells.
Automorphism Groups of Certain Rational Hypersurfaces in Complex Four-Space
2014
The Russell cubic is a smooth contractible affine complex threefold which is not isomorphic to affine three-space. In previous articles, we discussed the structure of the automorphism group of this variety. Here we review some consequences of this structure and generalize some results to other hypersurfaces which arise as deformations of Koras–Russell threefolds.
Metabolomics of Human Amniotic Fluid and Maternal Plasma during Normal Pregnancy
2016
Metabolic profiles of amniotic fluid and maternal blood are sources of valuable information about fetus development and can be potentially useful in diagnosis of pregnancy disorders. In this study, we applied 1H NMR-based metabolic profiling to track metabolic changes occurring in amniotic fluid (AF) and plasma (PL) of healthy mothers over the course of pregnancy. AF and PL samples were collected in the 2nd (T2) and 3rd (T3) trimester, prolonged pregnancy (PP) until time of delivery (TD). A multivariate data analysis of both biofluids reviled a metabolic switch-like transition between 2nd and 3rd trimester, which was followed by metabolic stabilization throughout the rest of pregnancy proba…
Dental disease and dietary isotopes of individuals from St Gertrude Church cemetery, Riga, Latvia.
2018
This research explores oral health indicators and stable carbon and nitrogen isotope data to explore diet, and differences in diet, between people buried in the four different contexts of the St Gertrude Church cemetery (15th– 17th centuries AD): the general cemetery, two mass graves, and a collective mass burial pit within the general cemetery. The main aim is to assess whether people buried in the mass graves were rural immigrants, or if they were more likely to be the victims of plague (or another epidemic) who lived in Riga and its suburbs. The data produced (from dental disease assessments and isotope analyses) were compared within, as well as between, the contexts. Most differences em…
Representable and Continuous Functionals on Banach Quasi *-Algebras
2017
In the study of locally convex quasi *-algebras an important role is played by representable linear functionals; i.e., functionals which allow a GNS-construction. This paper is mainly devoted to the study of the continuity of representable functionals in Banach and Hilbert quasi *-algebras. Some other concepts related to representable functionals (full-representability, *-semisimplicity, etc) are revisited in these special cases. In particular, in the case of Hilbert quasi *-algebras, which are shown to be fully representable, the existence of a 1-1 correspondence between positive, bounded elements (defined in an appropriate way) and continuous representable functionals is proved.