Search results for " Functional"
showing 10 items of 1811 documents
Diameter 2 properties and convexity
2015
We present an equivalent midpoint locally uniformly rotund (MLUR) renorming $X$ of $C[0,1]$ on which every weakly compact projection $P$ satisfies the equation $\|I-P\| = 1+\|P\|$ ($I$ is the identity operator on $X$). As a consequence we obtain an MLUR space $X$ with the properties D2P, that every non-empty relatively weakly open subset of its unit ball $B_X$ has diameter 2, and the LD2P+, that for every slice of $B_X$ and every norm 1 element $x$ inside the slice there is another element $y$ inside the slice of distance as close to 2 from $x$ as desired. An example of an MLUR space with the D2P, the LD2P+, and with convex combinations of slices of arbitrary small diameter is also given.
Rotationally symmetric p -harmonic maps fromD2toS2
2013
We consider rotationally symmetric p-harmonic maps from the unit disk D2⊂R2 to the unit sphere S2⊂R3, subject to Dirichlet boundary conditions and with 1<p<∞. We show that the associated energy functional admits a unique minimizer which is of class C∞ in the interior and C1 up to the boundary. We also show that there exist infinitely many global solutions to the associated Euler–Lagrange equation and we completely characterize them.
Prevention of Functional Decline by Reframing the Role of Nursing Homes?
2017
Institutionalization is generally a consequence of functional decline driven by physical limitations, cognitive impairments, and/or loss of social supports. At this stage, intervention to reverse functional losses is often too late. To be more effective, geriatric medicine must evolve to intervene at an earlier stage of the disability process. Could nursing homes (NHs) transform from settings in which many residents dwell to settings in which the NH residents and those living in neighboring communities benefit from staff expertise to enhance quality of life and maintain or slow functional decline? A task force of clinical researchers met in Toulouse on December 2, 2015, to address some of t…
Observer-Based Stabilization of Stochastic Systems with Limited Communication
2012
Published version of an article in the journal: Mathematical Problems in Engineering. Also available from Hindawi: http://dx.doi.org/10.1155/2012/781542 Open Access This paper studies the problem of observer-based stabilization of stochastic nonlinear systems with limited communication. A communication channel exists between the output of the plant and the input of the dynamic controller, which is considered network-induced delays, data packet dropouts, and measurement quantization. A new stability criterion is derived for the stochastic nonlinear system by using the Lyapunov functional approach. Based on this, the design procedure of observer-based controller is presented,which ensures asy…
Reactivity of the Superheavy Element 115, Mc, and Its Lighter Homologue, Bi, with Respect to Gold and Hydroxylated Quartz Surfaces from Periodic Rela…
2021
Adsorption energies (Eads) of the superheavy element (SHE) Mc, its lighter homologue (Bi), as well as of another superheavy element Nh and some lighter homologues of SHEs on gold and hydroxylated quartz surfaces are predicted via periodic relativistic density functional theory calculations. The aim of this study is to support "one-atom-at-a-time" gas-phase chromatography experiments that are examining the reactivity and volatility of Mc. The obtained Eads values of the Bi and Mc atoms on the Au(111) surface are >200 kJ/mol. On the hydroxylated quartz surface, Mc should adsorb with a minimal energy of 58 kJ/mol. On both types of surfaces, Eads(Mc) should be ∼100 kJ/mol smaller than Eads(Bi) …
Six-coordinate [CoIII(L)2]z (z = 1−, 0, 1+) complexes of an azo-appended o-aminophenolate in amidate(2−) and iminosemiquinonate π-radical (1−) redox-…
2018
Aerobic reaction of the ligand H2L1, 2-(2-phenylazo)-anilino-4,6-di-tert-butylphenol, CoCl2·6H2O and Et3N in MeOH under refluxing conditions produces, after work-up and recrystallization, black crystals of [Co(L1)2] (1). When examined by cyclic voltammetry, 1 displays in CH2Cl2 three one-electron redox responses: two oxidative, E11/2 = 0.30 V (peak-to-peak separation, ΔEp = 100 mV) and E21/2 = 1.04 V (ΔEp = 120 mV), and one reductive E1/2 = −0.27 V (ΔEp = 120 mV) vs. SCE. Consequently, 1 is chemically oxidized by 1 equiv. of [FeIII(η5-C5H5)2][PF6], affording the isolation of deep purple crystals of [Co(L1)2][PF6]·2CH2Cl2 (2), and one-electron reduction with [CoII(η5-C5H5)2] yielded bluish-b…
[CuII{(LISQ)˙−}2] (H2L: thioether-appended o-aminophenol ligand) monocation triggers change in donor site from N2O2 to N2O(2)S and valence-tautomerism
2019
Using a potentially tridentate o-aminophenol-based redox-active ligand H2L1 (2-[2-(benzylthio)phenylamino]-4,6-di-tert-butylphenol) in its deprotonated form, [Cu(L1)2] has been synthesized and crystallized as [CuII(L1)2]·CH2Cl2 (1·CH2Cl2). A cyclic voltammetry experiment (in CH2Cl2; V vs. SCE (saturated calomel electrode)) on 1·CH2Cl2 exhibits two oxidative (E = 0.20 V (peak-to-peak separation, ΔEp = 100 mV) and E = 0.90 V (ΔEp = 140 mV)) and two reductive (E = -0.52 V (ΔEp = 110 mV) and E = -0.92 V (ΔEp = 120 mV)) responses. Upon oxidation using a stoichiometric amount of [FeIII(η5-C5H5)2](PF6), 1·CH2Cl2 yielded [Cu(L1)2](PF6) (2). Structural analysis (100 K) reveals that 1·CH2Cl2 is a fou…
New light on an old debate: does the RCN–PtCl2 bond include any back-donation? RCN←PtCl2 backbonding vs. the IR νCN blue-shift dichotomy in organoni…
2019
For a series of organonitrile [RCN (R = Me, CF3, Ph, CH3Ph, CF3Ph)] ligands, the nature of the N–Pt bond in the related cis-/trans-(RCN)2PtCl2 complexes has been computationally investigated by Density Functional Theory. A fragment based bond analysis has been performed in the canonical Kohn–Sham molecular orbitals framework, and it has been ultimately assessed that this bond is characterized both by N→Pt σ and by N←Pt π contributions. Voronoi Deformation Density charges further confirms the occurrence of N←Pt π interactions. Moreover, the Energy Decomposition Analysis-Natural Orbital for Chemical Valence (EDA-NOCV) method shows that the strength of the N←Pt π interaction is not negligible …
Electronic and optical properties of CeO 2 from first principles calculations
2016
International audience; First-principles calculations of the electronic structure of CeO2 nanoparticles (NPs) were performed to investigate published experimental data obtained by different spectroscopies. The main features of the valence and conduction bands have been analyzed from the total and partial density of states. Several functionals were applied to interpret and quantify the optical properties, including the dielectric function, extinction coefficient and refractive index. It is found that the on-site hybrid functional B3PW91 modelled most suitably the band gap region of CeO2 NPs and consequently gave a more accurate band gap value. It also agreed very well with the experimental v…
Absolute acidity of clay edge sites from ab-initio simulations
2012
International audience; We provide a microscopic understanding of the solvation structure and reactivity of the edges of neutral clays. In particular we address the tendency to deprotonation of the different reactive groups on the (0 1 0) face of pyrophyllite. Such information cannot be inferred directly from titration experiments, which do not discriminate between different sites and whose interpretation resorts to macroscopic models. The determination of the corresponding pKa then usually relies on bond valence models, sometimes improved by incorporating some structural information from ab-initio simulations. Here we use density functional theory based molecular dynamics simulations, comb…