Eigenfunctions of the weighted Laplacian and a vanishing theorem on gradient steady Ricci soliton

The aim of this note has two folds. First, we show a gradient estimate of the higher eigenfunctions of the weighted Laplacian on smooth metric measure spaces. In the second part, we consider a gradient steady Ricci soliton and prove that there exists a positive constant c(n)$c(n)$ depending only on the dimension n   of the soliton such that there is no nontrivial harmonic 1-form (hence harmonic function) which is in L^p$L^p$ on such a soliton for any 2<p<c(n)$2<p<c(n)$.     

Adsorption properties and surface chemistry of MgO

The adsorption properties of MgO, which is used as a sorbent and catalyst support, were studied using gas chromatography. The test absorbents used were n-alkanes (which show only nonspecific dispersion interactions when physisorbed on any adsorbent) and adsorbates whose molecules are capable of specific interactions with the surface reactive sites of MgO. Adsorption isotherms were measured for CHCl₃, CH₃NO₂, CH₃CN, (CH₃)₂CO, CH₃COOC₂H₅, and (C₂H₅)₂O on MgO at 50–100°C. Differential molar enthalpy changes (?ΔH), equal to molar heats of adsorption, were determined. For polar adsorbates, contributions from dispersive and specific interactions into ?ΔH were determined. The electron-acceptor and electron-donor abilities of the MgO surface were estimated.     

Determination of α and f for k0-NAA in irradiation sites with high thermalized neutrons

We have measured the ⁵⁷Fe Mössbauer spectra of the Hofmann pyridine complex Fe(pyridine)₂Ni(CN)₄ sample before and after exposure to high pressure of gaseous xenon. The temperature dependence of the high spin molar fraction has been determined from the ⁵⁷Fe Mössbauer spectra. The spin transition of the sample without the high pressure treatment occurs between 175 and 220 K with a hysteresis width of 15 K. Although the ⁵⁷Fe Mössbauer spectra suggest that the spin crossover behavior of the sample before and after the high pressure treatment are almost the same, the hysteresis of the latter sample is somewhat larger.     

Transparency enhancement for an active knee orthosis by a constraint-free mechanical design and a gait phase detection based predictive control

This paper proposes a novel mechanical design of a lower limb exoskeleton device which prevents the residual stresses due to arthro-kinematics movements of synovial joints and by the way allows effective compensation for dynamic disturbances in osteo-kinematic movements of the wearer. Here, the exoskeleton is only actuated at the knee joints to provide assistive torques, which are required to assist the anatomical joint motion and to increase the transparency of the device. Dynamic simulations of a virtual human equipped with this exoskeleton are used to quantify the disturbances induced by the device during locomotion and to show the benefit of passive mechanisms introduced in the mechanical attaches as well. The authors also demonstrated how the device’s transparency can be improved by providing the motor torques in order to compensate the inertial and gravitational effects. This can be done rely on the knowledge of the locomotion movement phases. A robust gait phase detection method was implemented on the experimental device in order to identify specific gait phases in real time. This method exploits the K-nearest neighbors algorithm to identify the k-closest trained vectors, coupling with a discrete time Markov chain to determine the phases shift probability during the gait cycle. This gait detection algorithm was tested with a percentage of success of more than 95% when the subjects walked with constant and variable stride lengths.     

Implementation of the <Emphasis Type="Italic">k</Emphasis><Subscript>0</Subscript>-NAA method by using <Emphasis Type="Italic">k</Emphasis><Subscript>0</Subscript>-IAEA software and the NAA#3 irradiation hole at the HANARO research reactor

This study intended to demonstrate the use of k ₀-IAEA software with the NAA#3 irradiation hole in the HANARO research reactor and the gamma-ray spectrometers at the NAA laboratory in the Korea Atomic Energy Research Institute (KAERI). NIST SRM 2586-Soil was chosen as a sample to validate the analytical protocol by using the k ₀-IAEA software. Twenty four elements were determined and the resultant deviations between the experimental results and the certified values were all within 10% except for Dy. In addition, an analysis of three types of synthetic multielement standards (SMELS) prepared by the Institute for Reference Materials and Measurements (IRMM) and Institute of Nuclear Science (INW) in Belgium was executed. The analytical results agreed well with the assigned values and the U-scores for most of the elements were lower than 2.     

Iterative methods for stabilized discrete convection-diffusion problems

In this paper we study the computational cost of solving theconvection-diffusion equation using various discretization strategiesand iteration solution algorithms. The choice of discretizationinfluences the properties of the discrete solution and alsothe choice of solution algorithm. The discretizations consideredhere are stabilized low-order finite element schemes using streamlinediffusion, crosswind diffusion and shock-capturing. The latter,shock-capturing discretizations lead to nonlinear algebraicsystems and require nonlinear algorithms. We compare variouspreconditioned Krylov subspace methods including Newton-Krylovmethods for nonlinear problems, as well as several preconditionersbased on relaxation and incomplete factorization. We find thatalthough enhanced stabilization based on shock-capturing requiresfewer degrees of freedom than linear stabilizations to achievecomparable accuracy, the nonlinear algebraic systems are morecostly to solve than those derived from a judicious combinationof streamline diffusion and crosswind diffusion. Solution algorithmsbased on GMRES with incomplete block-matrix factorization preconditioningare robust and efficient.     

Determination of phytoextraction potential of plant species for toxic elements in soils of abandoned sulphide-mining areas

This study has determined contamination levels in soils and plants from the São Domingos mining area, Portugal, by k ₀-INAA. Total concentrations of As, Sb, Cr, Hg, Cu, Zn and Fe in soils were very high, exceeding the maximum limits in Portuguese legislation. Concentrations of toxic elements like As, Sb and Zn were highest in roots of Erica andevalensis, Juncus acutus, Agrostis castellana and Nicotiana glauca. Additionally, As, Br, Cr, Fe, Sb and Zn in all organs of most plants were above toxicity levels. Those species that accumulated relatively high concentrations of toxic elements in roots (and tops) may be cultivated for phytostabilisation of similar areas.     

On the boundedness of the Hardy operator in the weighted space BMO

The result of Golubov [5, Theorem 2] on the boundedness of the Hardy-Littlewood operator $$ \mathcal{B}f(x): = \frac{1} {x}\int_0^x {f(t)} dt $$ in the space BMO(?) is well known. The author of the present paper solves the analogous problem in the weighted space BMO on the semi-axis ?₊ for the operator $$ T_w f(x): = \frac{1} {{W(x)}}\int_0^x {f(t)w(t)} dt $$ and also in the classical space BMO(?₊) for a class of integral operators involving, for example, the Riemann-Liouville fractional integral.