Search results for "PSC"
showing 10 items of 183 documents
Monotonicity-based inversion of the fractional Schr\"odinger equation II. General potentials and stability
2019
In this work, we use monotonicity-based methods for the fractional Schr\"odinger equation with general potentials $q\in L^\infty(\Omega)$ in a Lipschitz bounded open set $\Omega\subset \mathbb R^n$ in any dimension $n\in \mathbb N$. We demonstrate that if-and-only-if monotonicity relations between potentials and the Dirichlet-to-Neumann map hold up to a finite dimensional subspace. Based on these if-and-only-if monotonicity relations, we derive a constructive global uniqueness results for the fractional Calder\'on problem and its linearized version. We also derive a reconstruction method for unknown obstacles in a given domain that only requires the background solution of the fractional Sch…
MR2553995 (2010h:26008): Mihail, Alexandru The Arzela-Ascoli theorem for partial defined functions. An. Univ. Bucureşti Mat. 57 (2008), no. 2, 259–26…
2008
In this paper the author gives a generalization of the Arzela-Ascoli theorem for partial defined functions, i.e., for functions defined in a nonempty subset of a metric space X and taking values in a metric space Y. To this end suitable definitions of local and uniform convergence for partial defined functions are introduced. As an application a different proof of a known result concerning the existence of Lipschitz selections for Lipschitz multifunctions is given. Reviewed by Luisa Di Piazza
Nitric Acid Trihydrate (NAT) formation at low NAT supersaturation in Polar Stratospheric Clouds (PSCs)
2005
International audience; A PSC was detected on 6 February 2003 in the Arctic stratosphere by in-situ measurements onboard the high-altitude research aircraft Geophysica. Low number densities (~10-4cm-3) of small nitric acid (HNO3) containing particles (dTNAT, these NAT particles have the potential to grow further and to remove HNO3 from the stratosphere, thereby enhancing polar ozone loss. Interestingly, the NAT particles formed in less than a day at temperatures just slightly below TNAT (T>TNAT-3.1K). This unique measurement of PSC formation at extremely low NAT saturation ratios (SNAT?10) constrains current NAT nucleation theories. We suggest, that the NAT particles have formed heterogeneo…
Atomic Decomposition of Weighted Besov Spaces
1996
We find the atomic decomposition of functions in the weighted Besov spaces under certain factorization conditions on the weight. Introduction. After achieving the atomic decomposition of Hardy spaces (see [8,22, 33]), many of the function saces have been shown to admit similar decompositions. Let us mention the decomposition of B.M.O. (see [32, 25]), Bergman spaces (see [9, 23]), the predual of Bloch space (see [ 11]), Besov spaces (see [15, 4, 10]), Lipschitz spaces (see [18]), Triebel-Lizorkin spaces (see [16, 31]),... They are obtained by quite different methods, but there is a unified and beautiful approach to get the decomposition for most of the spaces. This is the use of a formula du…
Uniqueness of diffusion on domains with rough boundaries
2016
Let $\Omega$ be a domain in $\mathbf R^d$ and $h(\varphi)=\sum^d_{k,l=1}(\partial_k\varphi, c_{kl}\partial_l\varphi)$ a quadratic form on $L_2(\Omega)$ with domain $C_c^\infty(\Omega)$ where the $c_{kl}$ are real symmetric $L_\infty(\Omega)$-functions with $C(x)=(c_{kl}(x))>0$ for almost all $x\in \Omega$. Further assume there are $a, \delta>0$ such that $a^{-1}d_\Gamma^{\delta}\,I\le C\le a\,d_\Gamma^{\delta}\,I$ for $d_\Gamma\le 1$ where $d_\Gamma$ is the Euclidean distance to the boundary $\Gamma$ of $\Omega$. We assume that $\Gamma$ is Ahlfors $s$-regular and if $s$, the Hausdorff dimension of $\Gamma$, is larger or equal to $d-1$ we also assume a mild uniformity property for $\Omega$ i…
The validity of the “liminf” formula and a characterization of Asplund spaces
2014
Abstract We show that for a given bornology β on a Banach space X the following “ lim inf ” formula lim inf x ′ ⟶ C x T β ( C ; x ′ ) ⊂ T c ( C ; x ) holds true for every closed set C ⊂ X and any x ∈ C , provided that the space X × X is ∂ β -trusted. Here T β ( C ; x ) and T c ( C ; x ) denote the β-tangent cone and the Clarke tangent cone to C at x. The trustworthiness includes spaces with an equivalent β-differentiable norm or more generally with a Lipschitz β-differentiable bump function. As a consequence, we show that for the Frechet bornology, this “ lim inf ” formula characterizes in fact the Asplund property of X. We use our results to obtain new characterizations of T β -pseudoconve…
Stronger proprioceptive BOLD-responses in the somatosensory cortices reflect worse sensorimotor function in adolescents with and without cerebral pal…
2020
Graphical abstract
The influence of water and of alkali promotor on the carbon number distribution of fischer-tropsch products formed over iron catalysts
1987
The carbon number distribution of Fischer-Tropsch products formed over an alkalized precipitated iron catalyst has been studied as a function of the water vapor pressure of the synthesis gas. The carbon number distribution of formed hydrocarbons is characterized by a bimodal Schulz-Flory distribution of growth probabilities P1 ≈ 0.6 and P2 ≈ 0.87 attributed to unpromoted and promoted (alkalized) sites on the catalyst surface. Promoted sites are more stable with respect to oxidation (deactivation) by water than unpromoted sites. The growth probability of unpromoted sites decreases with increasing ratio P/P — Studies using Mossbauer spectroscopy have shown that iron foils treated with water c…
Semmes surfaces and intrinsic Lipschitz graphs in the Heisenberg group
2018
A Semmes surface in the Heisenberg group is a closed set $S$ that is upper Ahlfors-regular with codimension one and satisfies the following condition, referred to as Condition B. Every ball $B(x,r)$ with $x \in S$ and $0 < r < \operatorname{diam} S$ contains two balls with radii comparable to $r$ which are contained in different connected components of the complement of $S$. Analogous sets in Euclidean spaces were introduced by Semmes in the late $80$'s. We prove that Semmes surfaces in the Heisenberg group are lower Ahlfors-regular with codimension one and have big pieces of intrinsic Lipschitz graphs. In particular, our result applies to the boundary of chord-arc domains and of redu…
Local regularity for time-dependent tug-of-war games with varying probabilities
2016
We study local regularity properties of value functions of time-dependent tug-of-war games. For games with constant probabilities we get local Lipschitz continuity. For more general games with probabilities depending on space and time we obtain H\"older and Harnack estimates. The games have a connection to the normalized $p(x,t)$-parabolic equation $(n+p(x,t))u_t=\Delta u+(p(x,t)-2) \Delta_{\infty}^N u$.