Search results for "obol"
showing 10 items of 228 documents
Characterization of Cobalt Catalysts on Biomass-Derived Carbon Supports
2017
Cobalt catalysts are known to have a high activity and selectivity in the Fischer–Tropsch reaction converting synthesis gas to higher hydrocarbons (C5+). These catalysts have been supported by different porous materials. Porous carbon materials like activated carbon (AC) have physical and chemical surface properties that affect the preparation of supported metal catalysts and can easily be tailored. In this study, AC was produced by carbonization and steam activation of lignin, a waste fraction from the Kraft pulping process. A series of Co/AC-catalysts was produced and characterized by several techniques. According to the results, tailored properties (high surface area, mesoporosity) were …
Ligand mediated evolution of size dependent magnetism in cobalt nanoclusters.
2018
We use density functional theory to model the impact of a ligand shell on the magnetic properties of CoN (15 ≤ N ≤ 55) nanoclusters. We study three different ligand shells on each nanocluster core size, each known to have different electronic interactions with the surface: pure Cl ligand shells (X-type), pure PH3 ligand shells (L-type), and two component ligand shells with mixtures of Cl and PH3 ligands. The simulations show that the identity, arrangement, and total coverage of the ligand shell controls the distribution of local magnetic moments across the CoN core. On the surface of an unpassivated CoN nanocluster, the Co-Co coordination number (CN) is known to determine the local magnetic…
Synthesis of isomorphous cobalt and nickel thiocyanate coordination compounds: Effect of metals on compound properties
2019
The reaction of 2-methylpiperazine with the thiocyanate ligand and two transition metals leads to the production of two new isomorphous [ML2SCN4] where L is the 2-methylpiperazine and [M =Co (1), and Ni (2)], presenting an octahedral configuration. These compounds were characterized by single crystal X-ray crystallography, TG-DTA analysis, as well as infrared and UV-Vis spectroscopy and TG-DTA. The magnetic and antibacterial properties were also determined. Through the link with N-H···S hydrogen bonds, a global 3D network was established. The studied compounds show the metal center’s impact leading to different properties. Indeed, the first compound shows high spin orbit coupling, whereas t…
Experimental and Computational Study of Unique Tetranuclear µ3-Chloride and µ-Phenoxo/Chloro-Bridged Defective Dicubane Cobalt(II) Clusters
2016
Two tetranuclear CoII clusters [Co4(L)2(µ3-Cl)2Cl2] have been prepared by using multidentate diaminobisphenolate ligands. The solid-state structures of the complexes were determined by single-crystal X-ray diffraction. The cores of the cluster compounds can be defined as a two-vertex-deficient dicubane geometry (pseudo-dicubane). In the central unit, the cobalt(II) cations are linked through phenoxide oxygen (outer bridges) and chloride anions (inner bridges), previously unprecedented in this type of cobalt cluster. The magnetic properties were studied by both experimental and computational methods. By using a combination of techniques, we were able to determine the nature and strength of t…
On Limits at Infinity of Weighted Sobolev Functions
2022
We study necessary and sufficient conditions for a Muckenhoupt weight $w \in L^1_{\mathrm{loc}}(\mathbb R^d)$ that yield almost sure existence of radial, and vertical, limits at infinity for Sobolev functions $u \in W^{1,p}_{\mathrm{loc}}(\mathbb R^d,w)$ with a $p$-integrable gradient $|\nabla u|\in L^p(\mathbb R^d,w)$. The question is shown to subtly depend on the sense in which the limit is taken. First, we fully characterize the existence of radial limits. Second, we give essentially sharp sufficient conditions for the existence of vertical limits. In the specific setting of product and radial weights, we give if and only if statements. These generalize and give new proofs for results of…
Differential of metric valued Sobolev maps
2020
We introduce a notion of differential of a Sobolev map between metric spaces. The differential is given in the framework of tangent and cotangent modules of metric measure spaces, developed by the first author. We prove that our notion is consistent with Kirchheim's metric differential when the source is a Euclidean space, and with the abstract differential provided by the first author when the target is $\mathbb{R}$.
The fractional Calderón problem: Low regularity and stability
2017
The Calder\'on problem for the fractional Schr\"odinger equation was introduced in the work \cite{GSU}, which gave a global uniqueness result also in the partial data case. This article improves this result in two ways. First, we prove a quantitative uniqueness result showing that this inverse problem enjoys logarithmic stability under suitable a priori bounds. Second, we show that the results are valid for potentials in scale-invariant $L^p$ or negative order Sobolev spaces. A key point is a quantitative approximation property for solutions of fractional equations, obtained by combining a careful propagation of smallness analysis for the Caffarelli-Silvestre extension and a duality argumen…
The higher order fractional Calderón problem for linear local operators : Uniqueness
2020
We study an inverse problem for the fractional Schr\"odinger equation (FSE) with a local perturbation by a linear partial differential operator (PDO) of order smaller than the order of the fractional Laplacian. We show that one can uniquely recover the coefficients of the PDO from the Dirichlet-to-Neumann (DN) map associated to the perturbed FSE. This is proved for two classes of coefficients: coefficients which belong to certain spaces of Sobolev multipliers and coefficients which belong to fractional Sobolev spaces with bounded derivatives. Our study generalizes recent results for the zeroth and first order perturbations to higher order perturbations.
Assouad Type Dimensions in Geometric Analysis
2021
We consider applications of the dual pair of the (upper) Assouad dimension and the lower (Assouad) dimension in analysis. We relate these notions to other dimensional conditions such as a Hausdorff content density condition and an integrability condition for the distance function. The latter condition leads to a characterization of the Muckenhoupt Ap properties of distance functions in terms of the (upper) Assouad dimension. It is also possible to give natural formulations for the validity of Hardy–Sobolev inequalities using these dual Assouad dimensions, and this helps to understand the previously observed dual nature of certain cases of these inequalities. peerReviewed
p-Laplacen operaattorin ominaisarvo-ongelmasta
2016
Tämän tutkielman tarkoitus on tutustua epälineaarisiin ominaisarvo-ongelmiin p-Laplacen operaattorin ominaisarvo-ongelman kautta. p-Laplacen operaattori on Laplacen operaattorin eräs yleistys ja tarkastelun kohteena oleva ominaisarvo-ongelma on Dirichletin ominaisarvo-ongelman yleistys. Tutkielmassa kerrataan ensin tarvittavia taustatietoja Sobolevin avaruuksista ja funktionaalianalyysistä, ja keskitytään sitten itse ongelmaan. Päätulokset koskevat ensimmäistä ominaisarvoa, ja ne ovat ensimmäisen ominaisarvon olemassaolo, ensimmäisen ominaisarvon karakterisointi Rayleighin osamäärän avulla, ensimmäisen ominaisfunktion yksinkertaisuus, ja se, että ensimmäinen ominaisfunktio on ainoa ominaisf…