Precision of Raman depolarization and optical attenuation measurements of sound tooth enamel

The demineralization of enamel that is associated with early caries formation affects the optical properties of the enamel. Polarized Raman spectroscopy and optical coherence tomography have been used to detect these changes and potentially offer a means to detect and monitor early caries development. The total optical attenuation coefficient as measured by optical coherence tomography and the polarization anisotropy of the Raman peak arising from the symmetric ν₁ vibration of at approximately 959 cm⁻¹ have been demonstrated as being sensitive markers of early caries. This ex vivo study on extracted human teeth demonstrates that these measurements can be made with reasonable precision with concomitantly good repeatability and reproducibility in sound enamel. Such reliability is crucial for these techniques to have a practical clinical value.     

Study on the base-catalyzed reverse vinylogous aldol reaction of (4abeta,5beta)-4,4a,5,6,7,8-hexahydro-5-hydroxy-1,4a-dimethylnaphthalen-2(3H)-one under Robinson annulation conditions

[reaction: see text] We have proposed a pathway for the base-catalyzed reverse vinylogous aldol reaction of (-)-(4abeta,5beta)-4,4a,5,6,7,8-hexahydro-5-hydroxy-1,4a-dimethylnaphthalen-2(3H)-one [(-)-8] under Robinson annulation conditions. For confirmation, 4-(2,6-dimethyl-3-oxocyclohex-1-enyl)butanal (11) and 4-(2,6-dimethyl-5-oxocyclohex-1-enyl)butanal (12), both of which potentially produce enolate I, were synthesized regioselectively. Unexpectedly, 11 gave a complex mixture, including only a trace amount of (+/-)-8 (less than 5% yield), under these basic conditions. To the contrary, 12 cleanly afforded (+/-)-8 in 66% yield. This result provides evidence for our proposed mechanism of the above reaction.     

Pseudo-steady-state solutions for solidification in a wedge

Polubarinova-Kochina's analytical differential equation methodis used to determine the pseudo-steady-state solution to problemsinvolving the freezing (solidification) of wedges of liquidwhich are initially at their fusion temperature. In particular,we consider four distinct problems for wedges which are: freezingwith the same constant boundary temperature, freezing with thesame constant boundary heat fluxes, freezing with distinct constantboundary temperatures and freezing with distinct constant fluxesat the boundaries. For the last two problems, a Heun's differentialequation with an unknown singularity is derived, which in bothcases admits a particularly elegant simple solution for thespecial case when the wedge angle is . The moving boundariesobtained are shown pictorially.     

On the roles of minimization and linearization in least-squares finite element models of nonlinear boundary-value problems

In this paper we examine the roles of minimization and linearization in the least-squares finite element formulations of nonlinear boundary-values problems. The least-squares principle is based upon the minimization of the least-squares functional constructed via the sum of the squares of appropriate norms of the residuals of the partial differential equations (in the present case we consider L₂ norms). Since the least-squares method is independent of the discretization procedure and the solution scheme, the least-squares principle suggests that minimization should be performed prior to linearization, where linearization is employed in the context of either the Picard or Newton iterative solution procedures. However, in the least-squares finite element analysis of nonlinear boundary-value problems, it has become common practice in the literature to exchange the sequence of application of the minimization and linearization operations. The main purpose of this study is to provide a detailed assessment on how the finite element solution is affected when the order of application of these operators is interchanged. The assessment is performed mathematically, through an examination of the variational setting for the least-squares formulation of an abstract nonlinear boundary-value problem, and also computationally, through the numerical simulation of the least-squares finite element solutions of both a nonlinear form of the Poisson equation and also the incompressible Navier–Stokes equations. The assessment suggests that although the least-squares principle indicates that minimization should be performed prior to linearization, such an approach is often impractical and not necessary.