Identification of nonlinear elliptic equations

An optimization theoretic approach and algorithm for the estimation of state-dependent coefficients in nonlinear elliptic equation is presented. It is based on a splitting method combined with convex analysis techniques. Convergence of the algorithm is established and numerical examples are included.The research of K. Kunisch was supported in part by a grant from the Bundesministerium für Wissenschaft und Forschung, Austria.     

Existence and Ergodicity for the Two-Dimensional Stochastic Magneto-Hydrodynamics Equations

The paper proves the existence of solutions to the magneto-hydrodynamics equations driven by random exterior forcing terms both in the velocity and in the magnetic field. The existence and uniqueness of an invariant measure is also obtained via coupling methods.     

Adaptive efficient estimation for generalized semi-Markov big data models

Annals of the Institute of Statistical Mathematics - In this paper we study generalized semi-Markov high dimension regression models in continuous time, observed at fixed discrete time moments. The...     

Existence and asymptotic results for a system of integro-partial differential equations

A non-Fourier phase field model is considered. A global existence result for a Dirichlet, or generalized Neumann, initial-boundary value problem is obtained, followed by a discussion of the regularity and asymptotic properties of solutions ast.This research was supported in part by the National Science Foundation under Grant DMS 91-11794 and in part by the Italian M.U.R.S.T. project Problemi non lineari...Part of this author's work was done while visiting Ohio University.     

Reaction of bis(phosphine)(hydrotris(3,5-dimethylpyrazolyl)borato)rhodium(I) with phenylacetylene,p-nitrobenzaldehyde,and triphenyltin hydride: structures of [Rh(Tp)(PPh(3))(2)], [Rh(Tp)(H)(C(2)Ph)(P(4-C(6)H(4)F)(3))], [Rh(Tp)(H)(COC(6)H(4)-4-NO(2))(PPh(3))], and [Rh(Tp)(H)(SnPh(3))(PPh(3))

The complexes [Rh(Tp)(PPh(3))(2)] (1a) and [Rh(Tp)(P(4-C(6)H(4)F)(3))(2)] (1b) combine with PhC(2)H, 4-NO(2)-C(6)H(4)CHO and Ph(3)SnH to give [Rh(Tp)(H)(C(2)Ph)(PR(3))] (R = Ph, 2a; R = 4-C(6)H(4)F, 2b), [Rh(Tp)(H)(COC(6)H(4)-4-NO(2))(PR(3))] (R = Ph, 3a), and [Rh(Tp)(H)(SnPh(3))(PR(3))] (R = Ph, 4a; R = 4-C(6)H(4)F, 4b) in moderate to good yield. Complexes 1a, 2b, 3a, and 4a have been structurally characterized. In 1a the Tp ligand is bidentate, in 2b, 3a, and 4a it is tridentate. Crystal data for 1a: space group P2(1)/c; a = 11.9664(19), b = 21.355(3), c = 20.685(3) A; beta = 112.576(7) degrees; V = 4880.8(12) A(3); Z = 4; R = 0.0441. Data for 2b: space group P(-)1; a = 10.130(3), b = 12.869(4), c = 17.038(5) A; alpha = 78.641(6), beta = 76.040(5), gamma = 81.210(6) degrees; V = 2100.3(11) A(3); Z = 2; R = 0.0493. Data for 3a: space group P(-)1; a = 10.0073(11), b = 10.5116(12), c = 19.874(2) A; alpha = 83.728(2), beta = 88.759(2), gamma = 65.756(2) degrees; V =1894.2(4) A(3); Z = 2; R = 0.0253. Data for 4a: space group P2(1)/c; a = 15.545(2), b = 18.110(2), c = 17.810(2) A; beta = 95.094(3) degrees; V = 4994.1(10) A(3); Z = 4; R = 0.0256. NMR data ((1)H, (31)P, (103)Rh, (119)Sn) are also reported.     

Practical aspects of the uncertainty and traceability of spectrochemical measurement results by electrothermal atomic absorption spectrometry

The determination of trace elements concentration in water by electrothermal atomic absorption spectrometry (ETAAS) is a common and well established technique in many chemical testing laboratories. However, the evaluation of measurement uncertainty results is not systematically implemented. The paper presents an easy step-by-step example leading to the evaluation of the combined standard uncertainty of copper determination in water using ETAAS. The major contributors to the overall measurement uncertainty are identified due to amount of copper in water sample that mainly depends on the absorbance measurements, due to certified reference material and due to auto-sampler volume measurements. The practical aspects how the traceability of copper concentration in water can be established and demonstrated are also pointed out.     

Correlation between Small-Angle X-ray Scattering spectra and apparent diffusion coefficients in the study of structure and interaction of sodium taurodeoxycholate micelles

Small-Angle X-ray Scattering (SAXS) and Dynamic Light Scattering (DLS) measurements were carried out on aqueous micellar solutions of the ionic biological detergent sodium taurodeoxycholate (NaTDC). Apparent diffusion coefficients (D(app)) and SAXS spectra of NaTDC 0.1 M solutions at different ionic strengths (0.1-0.3 M NaCl) were reported. A comparative analysis of SAXS spectra and D(app) data was performed to infer information on particle structure and interaction potential. Uniform particles with a spherical, an oblate, and a prolate symmetry were used to model the micelles in the data interpretation. A hard-core interaction shell of suitable thickness and a screened Coulomb potential of the electric double layer (EDL potential) were alternatively used to represent the long-range repulsive tail of the interaction potential. The Percus Yevick and the Rescaled Mean Spherical Approximation were applied. To compare the data of the two techniques, for each sample, a D(app) was calculated from the SAXS best-fitting geometrical parameters and interparticle structure factor of the micelles. Hence, a fitting procedure involving both the scattering and D(app) data was performed. The interpretation of SAXS spectra does not allow the discrimination between the oblate and the prolate symmetries of the aggregates. On the other hand, the comparison of calculated and experimental D(app) values indicates that the prolate ellipsoid is better suited to represent the micelle shape. Moreover, the agreement between calculated and experimental D(app) values is sensitively better at the lowest NaCl concentration when the EDL potential is used. A rodlike micellar growth and a progressive screening of the electrostatic interactions is testified by the trends of best-fitting parameters as a function of the added electrolyte.     

Robust adaptive efficient estimation for semi-Markov nonparametric regression models

Statistical Inference for Stochastic Processes - We consider the nonparametric robust estimation problem for regression models in continuous time with semi-Markov noises. An adaptive model...     

The obtaining of NiCr2O4 nanoparticles by unconventional synthesis methods

This paper presents a study regarding the obtaining of NiCr₂O₄ by two new unconventional synthesis methods: (i) the first method is based on the formation of Cr(III) and Ni(II) carboxylate-type precursors in the redox reaction between the nitrate ion and 1,3-propanediol. The thermal decomposition of these complex combinations, at ~300 °C, leads to an oxide mixture of Cr₂O_3+x and NiO, with advanced homogeneity, small particles and high reactivity. On heating this mixture at 500 °C, Cr₂O₃ reacts with NiO to form NiCr₂O₄, which was evidenced by FT-IR and X-ray diffractometry (XRD) analysis; (ii) the second method starts from a mechanical mixture of (NH₄)₂Cr₂O₇ and Ni(NO₃)₂·6H₂O. On heating this mixture, a violent decomposition at 240 °C with formation of an oxides mixture (Cr₂O₃ + CrO₃) and NiO takes place. On thermal treatment up to 500 °C, an intermediary phase NiCrO₄ is formed, which by decomposition at ~700 °C leads to NiCr₂O₄, evidenced by FT-IR and XRD analysis. NiCr₂O₄ is formed, in both cases, starting with a temperature higher than 400 °C, when the non-stoichiometric chromium oxide (Cr₂O_3+x ) loses the oxygen excess and turns to stoichiometric chromium oxide (Cr₂O₃), which further reacts with NiO.