Convergence rates for Tikhonov regularization of a two-coefficient identification problem in an elliptic boundary value problem

We investigate the convergence rates for Tikhonov regularization of the problem of simultaneously estimating the coefficients q and a in the Neumann problem for the elliptic equation \({{-{\rm div}(q \nabla u) + au = f \;{\rm in}\; \Omega, q{\partial u}/{\partial n} = g}}\) on the boundary \({{\partial\Omega, \Omega \subset \mathbb{R}^d, d \geq 1}}\) , when u is imprecisely given by \({{{z^\delta} \in {H^1}(\Omega), \|u-z^\delta\|_{H^1(\Omega)}\le\delta, \delta > 0}}\). We regularize this problem by minimizing the strictly convex functional of (q, a)

$\begin{array}{lll}\int\limits_{\Omega}\left(q| \nabla (U(q,a)-z^{\delta})|^2 + a(U(q,a)-z^{\delta})^2\right)dx\\\quad+\rho\left(\|q-q^*\|^2_{L^2(\Omega)} + \|a-a^*\|^2_{L^2(\Omega)}\right)\end{array}$

over the admissible set K, where ρ > 0 is the regularization parameter and (q*, a*) is an a priori estimate of the true pair (q, a) which is identified, and consider the unique solution of these minimization problem as the regularized one to that of the inverse problem. We obtain the convergence rate \({{{\mathcal {O}}(\sqrt{\delta})}}\), as δ → 0 and ρ ~ δ, for the regularized solutions under the simple and weak source condition

${\rm there\;is\;a\;function}\;w^* \in V^*\;{\rm such\;that}\;{U^\prime (q^ \dagger, a^\dagger)}^*w^* = (q^\dagger - q^*, a^\dagger - a^*)$

with \({{(q^\dagger, a^\dagger)}}\) being the (q*, a*)-minimum norm solution of the coefficient identification problem, U′(·, ·) the Fréchet derivative of U(·, ·), V the Sobolev space on which the boundary value problem is considered. Our source condition is without the smallness requirement on the source function which is popularized in the theory of regularization of nonlinear ill-posed problems. Furthermore, some concrete cases of our source condition are proved to be simply the requirement that the sought coefficients belong to certain smooth function spaces.

     

Chemical constituents of the Vietnamese inedible mushroom Xylaria intracolorata

Investigation of the methanolic extract of Vietnamese inedible Xylariaceous mushroom Xylaria intracolorata resulted in the isolation of two new compounds named coloratin A [3,5-dimethoxy-2-(6-oxo-5-pentyl-6H-pyran-3-carbonyl)-benzoic acid] (1) and coloratin B (2-carbomethoxyl-3,5-dimethoxybenzoic acid) (2). Their structures were elucidated by 2D-NMR, MS, IR, and UV spectroscopy. Coloratin A (1) showed strong antimicrobial activity.     

Origin of the variability of the mechanical properties of silk fibres: 2 The nanomechanics of single silkworm and spider fibres

The variability in mechanical stress–strain behaviour of various silks obtained from Bombyx mori silkworm and Nephila madagascarensis spider fibres has been studied by high resolution Raman analysis using the Raman shift induced by application of a controlled strain on the νN–H mode as a probe. Silk fibres exhibiting typical 1, 2, 3 and 4 Types have been selected from their characteristic tensile stress–strain behaviour. A perfect relationship between the nanomechanic (at the scale of the chemical bond) and macroscopic (silk single fibre) behaviour is observed as in the case of other polyamide fibres (natural keratin and synthetic PA66). Copyright © 2012 John Wiley & Sons, Ltd.     

First-principles study of the magnetic properties of nitrogen-doped alkaline earth metal oxides

We present a first-principles study of the magnetic properties of N-doped MgO, CaO and SrO, which have been proposed to constitute a new class of dilute magnetic semiconductors (DMSs) with no magnetic elements. In this study, it was found that under a homogeneously distributed condition, Curie temperatures could reach room temperature at sufficient N concentrations in the range of 20–30 at.%; however, an inhomogeneous N distribution in these DMSs is the favored configuration, which indicates that spinodal decomposition leads to a room-temperature blocking temperature at smaller N concentrations than those estimated for room-temperature ferromagnetism in the homogeneous distribution condition.     

Short-pulse laser deposition of diamond-like carbon thin films

The high intensities present in and the non-thermal nature of ultrashort-pulse laser ablation provide a nearly ideal source for thin-film deposition. The high kinetic energies and high ion content in the ablation plume suggest that it would be useful for the creation of diamond thin films. We used a 120 fs, 3 W, 1 kHz laser to ablate a graphite target and characterized the resulting films. We were able to grow amorphous films of up to 18 7m thick and free from graphite particulates with no annealing necessary and at rates up to 25 7m/hr. The films had 40-50% sp³ bonds as measured by using EELS and had properties typical of PLD-generated diamond-like carbon films.     

Impact of MHD on hybrid nanomaterial free convective flow within a permeable region

Journal of Thermal Analysis and Calorimetry - Computational modeling was employed to scrutinize the nanomaterial influence of flow patterns and thermal treatment within a porous region....     

Dissipativity and stability for semilinear anomalous diffusion equations involving delays

We analyze the dissipativity and stability of solutions to a class of semilinear anomalous diffusion equations involving delays. The existence of absorbing set, the stability, and weak stability will be shown under suitable assumptions on the nonlinearity. Our analysis is based on new Halanay-type inequality, local estimates, and fixed-point arguments.