The Trotter-Kato theorem and approximation of PDEs

We present formulations of the Trotter-Kato theorem for approximation of linear C-semigroups which provide very useful framework when convergence of numerical approximations to solutions of PDEs are studied. Applicability of our results is demonstrated using a first order hyperbolic equation, a wave equation and Stokes' equation as illustrative examples.

     

Iron-catalysed green synthesis of carboxylic esters by the intermolecular addition of carboxylic acids to alkenes

Iron triflate, in situ-formed from FeCl3 and triflic acid, or FeCl3 and silver triflate efficiently catalyse the intermolecular addition of carboxylic acids to various alkenes to yield carboxylic esters; the reaction is applicable to the synthesis of unstable esters, such as acrylates.     

A caffeine-sensitive membrane electrode: previous misleading report and present approach

Although a previous study [S.S.M. Hassan, M.A. Ahmed, M.M. Saoudi, Anal. Chem. 57 (1985) 1126] had shown that a caffeine-sensitive electrode made with picrylsulfonate and 1-octanol as a cation-exchanger and a solvent mediator, respectively, had a wide working pH range (5.5–9.5) and exhibited a Nernstian response, we could not find such response in this electrode. The present result was reasonable, because the pK_a value of caffeinium ion was reported to be around 0.7 and the neutral form of caffeine was predominant in the pH range examined. Thus, we reinvestigated the response characteristics of a caffeine electrode, taking into consideration the pK_a value, and constructed a new electrode with a combination of the lipophilic cation-exchanger, tetrakis[3,5-bis(2-methoxyhexafluoro-2-propyl)phenyl]borate (HFPB), and the solvent mediator with high degree of dielectric constant, 2-fluoro-2′-nitrodiphenyl ether (FNDPE). This electrode showed a pH-dependent response to caffeinium ion and gave a detection limit of 50 μM with a slope of 55 mV per concentration decade at pH 2. The use of other solvent mediators was less effective than that of FNDPE. The electrode was applied for the determination of caffeine in some central stimulants.     

On a semi-smooth Newton method and its globalization

This paper addresses the globalization of the semi-smooth Newton method for non-smooth equations F(x)  =  0 in with applications to complementarity and discretized ℓ¹-regularization problems. Assuming semi-smoothness it is shown that super-linearly convergent Newton methods can be globalized, if appropriate descent directions are used for the merit function |F(x)|². Special attention is paid to directions obtained from the primal-dual active set strategy. K. Ito’s research was partially supported by the Army Research Office under DAAD19-02-1-039.     

The Sensitivity Analysis for the Flow Past Obstacles Problem with Respect to the Reynolds Number

In this paper, numerical sensitivity analysis with respect to the Reynolds number for the flow past obstacle problem is presented. To carry out such analysis, at each time step, we need to solve the incompressible Navier-Stokes equations on irregular domains twice, one for the primary variables; the other is for the sensitivity variables with homogeneous boundary conditions. The Navier-Stokes solver is the augmented immersed interface method for Navier-Stokes equations on irregular domains. One of the most important contributions of this paper is that our analysis can predict the critical Reynolds number at which the vortex shading begins to develop in the wake of the obstacle. Some interesting experiments are shown to illustrate how the critical Reynolds number varies with different geometric settings.     

MTV-G experiment: Probing non-standard strong gravitational field at nuclear scale using geodetic precession

A new experiment named MTV-G, probing a large electron spin-precession due to a possible strong gravitational field, which predicted by large extra dimension model, is started at TRIUMF from 2011. In an electron-nuclear scattering experiment, a strong gravitational field is tested as a large spin precession effect caused by geodetic precession predicted by general relativity theory as a result of a warped space-time around nuclei. Experimental design using spin polarized electron source and Mott-spin analyzer, commissioning experiment and the preliminary results are described.     

Relative contributions of porosity and mineralized matrix properties to the bulk axial ultrasonic wave velocity in human cortical bone

Velocity of ultrasound waves has proved to be a useful indicator of bone biomechanical competence. A detailed understanding of the dependence of ultrasound parameters such as velocity on bone characteristics is a key to the development of bone quantitative ultrasound (QUS). The objective of this study is to investigate the relative contributions of porosity and mineralized matrix properties to the bulk compressional wave velocity (BCV) along the long bone axis. Cross-sectional slabs from the diaphysis of four human femurs were included in the study. Seven regions of interest (ROIs) were selected in each slab. BCV was measured in through-transmission at 5 MHz. Impedance of the mineralized matrix (Z_m) and porosity (Por) were obtained from 50 MHz scanning acoustic microscopy. Por and Z_m had comparable effects on BCV along the bone axis (R = −0.57 and R = 0.72, respectively).     

Color change (yellow \documentclass{article}\pagestyle{empty}\begin{document}$\rightleftharpoons$\end{document} orange) of 4,6,7-tri(alkoxy-substituted aryl)-1,2,5-thiadiazolo[3,4-c]pyridines in the solid phase

Reversible color change of 4,6,7-tri(alkoxy-substituted phenyl)-1,2,5-thiadiazolo[3,4-c]pyridines 5 in the solid state was observed: on grinding, yellow crystals of 5 became an orange amorphous solid which, on heating or washing with an appropriate solvent, gave the original yellow crystals.     

On the stationary semiconductor equations arising in modeling an LBIC technique

In this paper by using anL estimate for elliptic equations, we study the well-posedness of the stationary semiconductor equations arising from modeling a nondestructive testing technique LBIC. It is shown that when the extra source term is small, the system has a unique weak solution, and the solution is continuously dependent on this source term. The validity of an approximate model derived for the study of the inverse problem is established. The existence result is then extended to the case of constant mobilities without the assumption on the size of the source term.Parts of this work were completed while the authors were members of the Center for Applied Mathematical Sciences at the University of Southern California, and was supported by Air Force Office of Scientific Research Grant AFOSR-90-0091.