Search results for "Function"

The Calderón problem for the fractional Schrödinger equation

2020

We show global uniqueness in an inverse problem for the fractional Schr\"odinger equation: an unknown potential in a bounded domain is uniquely determined by exterior measurements of solutions. We also show global uniqueness in the partial data problem where the measurements are taken in arbitrary open, possibly disjoint, subsets of the exterior. The results apply in any dimension $\geq 2$ and are based on a strong approximation property of the fractional equation that extends earlier work. This special feature of the nonlocal equation renders the analysis of related inverse problems radically different from the traditional Calder\'on problem.

Real-time clothoid approximation by Rational Bezier curves

2008

This paper presents a novel technique for implementing Clothoidal real-time paths for mobile robots. As first step, rational Bezier curves are obtained as approximation of the Fresnel integrals. By rescaling, rotating and translating the previously computed RBC, an on-line Clothoidal path is obtained. In this process, coefficients, weights and control points are kept invariant. This on-line approach guarantees that an RBC has the same behavior as the original Clothoid using a low curve order. The resulting Clothoidal path allows any two arbitrary poses to be joined in a plane. RBCs working as Clothoids are also used to search for the shortest bounded-curvature path with a significant comput…

Comparative Study of the a Posteriori Error Estimators for the Stokes Problem

2007

The research presented is focused on a comparative study of a posteriori error estimation methods to various approximations of the Stokes problem. Mainly, we are interested in the performance of functional type a posterior error estimates and their comparison with other methods. We show that functional type a posteriori error estimators are applicable to various types of approximations (including non-Galerkin ones) and robust with respect to the mesh structure, type of the finite element and computational procedure used. This allows the construction of effective mesh adaptation procedures in all cases considered. Numerical tests justify the approach suggested.

Using tools effectively despite defective hand posture: A single-case study.

2019

Apraxia, a cognitive disorder of motor control, can severely impair transitive actions (object-related) and may lead to action errors (e.g., rubbing a hammer on a nail instead of pounding it) and hand posture errors (e.g., grasping a tool in a wrong way). Here, we report a rare observation of a left-handed patient, left-lateralized for language, who developed a severe apraxia following a right brain lesion. Interestingly the patient showed a significant number of hand posture errors, while she perfectly demonstrated the actual use of tools. This case stressed the predictions made by the current theories of tool use. According to the manipulation-based approach, the hand posture errors shoul…

Insight into the Mechanism of Action of Marine Cytotoxic Thiazinoquinones

2017

The electrochemical response of four natural cytotoxic thiazinoquinones isolated from the Aplidium species was studied using conventional solution-phase and solid-state techniques, based on the voltammetry of immobilized particles methodology. The interaction with O-2 and electrochemically generated reactive oxygen species (ROS) was electrochemically monitored. At the same time, a molecular modeling study including density functional theory (DFT) calculations was performed in order to analyze the conformational and electronic properties of the natural thiazinoquinones, as well as those of their reduced intermediates. The obtained electrochemical and computational results were analyzed and c…

Synthesis, Characterization, and Catalysis of β3-[(CoIIO4)W11O31(O2)4],10- the First Keggin-Based True Heteropoly Dioxygen (Peroxo) Anion. Spectrosco…

1999

Reactions of hydrogen peroxide with several lacunary polyoxometalates of the 1:11 series, XW11O39m- (X = Co3+, Ga3+, Fe3+, Si4+, and P5+), are reported. Synthetic pathways to new polyoxotungstates incorporating dioxygen moieties (peroxo and/or superoxo) are developed. The key step involves treating lacunary precursors with H2O2 in strongly buffered aqueous solutions. Upon reaction of H2O2 with α-[Co3+W11O39],9- (a) the central tetrahedral Co3+ is reduced to Co2+ and (b) each of the four unshared oxygens surrounding the vacancy are replaced by a peroxide group, yielding salts of the tetraperoxide anion β3-[(Co2+O4)W11O31(O2)4]10- (1). These results are unequivocally established by a combinat…

A quantum mechanics-molecular mechanics study of dissociative electron transfer : The methylchloride radical anion in aqueous solution

2002

The dissociative electron transfer reaction CH3Cl+e−→CH3•+Cl− in aqueous solution is studied by using a QM/MM method. In this work the quantum subsystem (a methylchloride molecule plus an electron) is described using density functional theory while the solvent (300 water molecules) is described using the TIP3P classical potential. By means of molecular dynamics simulations and the thermodynamic integration technique we obtained the potential of mean force (PMF) for the carbon–chlorine bond dissociation of the neutral and radical anion species. Combining these two free energy curves we found a quadratic dependence of the activation free energy on the reaction free energy in agreement with Ma…

Hole Localization and Thermochemistry of Oxidative Dehydrogenation of Aqueous Rutile TiO2(110)

2012

The Silica-Water Interface: How the Silanols Determine the Surface Acidity and Modulate the Water Properties.

2015

Silica is the most abundant metal oxide and the main component of the Earth's crust. Its behavior in contact with water plays a critical role in a variety of geochemical and environmental processes. Despite its key role, the details of the aqueous silica interface at the microscopic molecular level are still elusive. Here we provide such a detailed understanding of the molecular behavior of the silica-water interface, using density functional theory based molecular dynamics (DFTMD) simulations, where a consistent treatment of the electronic structure of solvent and surface is provided. We have calculated the acidity of the silanol groups at the interface directly from the DFTMD simulations,…

Polyfunctional Tetraaza-Macrocyclic Ligands: Zn(II), Cu(II) Binding and Formation of Hybrid Materials with Multiwalled Carbon Nanotubes

2017

The binding properties of HL1, HL2, and HL3 ligands toward Cu(II) and Zn(II) ions, constituted by tetraaza-macrocyclic rings decorated with pyrimidine pendants, were investigated by means of potentiometric and UV spectrophotometric measurements in aqueous solution, with the objective of using the related HL-M(II) (HL = HL1–HL3; M = Cu, Zn) complexes for the preparation of hybrid MWCNT-HL-M(II) materials based on multiwalled carbon nanotubes (MWCNTs), through an environmentally friendly noncovalent procedure. As shown by the crystal structure of [Cu(HL1)](ClO4)2, metal coordination takes place in the macrocyclic ring, whereas the pyrimidine residue remains available for attachment onto the s…