We derive many necessary conditions for minimizers of a functional depending on free discontinuities, free gradient discontinuities and second derivatives, which is related to image segmentation.

The ability for density functional theory with the B3LYP lanl2dz basis set to predict 1st (Wave 1) and 2nd 2) reductions of diazine ring in a series thirty-seven (37) 1,4-di-N-oxide quinoxaline-2-carboxamide derivatives dimethylformamide was examined. B3LYP/lanl2dz method had strong correlation low experimental potentials Wave 1 2, respectively. There are nine identifiable analogs based on simi...

Inverse problems are of utmost importance in many fields of science and engineering. In the variational approach inverse problems are formulated as PDE-constrained optimization problems, where the optimal estimate of the uncertain parameters is the minimizer of a certain cost functional subject to the constraints posed by the model equations. The numerical solution of such optimization problems...

To tailor highly-functionalized gold nanoparticle (GNP) networks, we investigated the GNP network formation with functionalized spacer group via click chemistry. This is based on its high reactivity and mild reaction conditions. The feature of this protocol is the easy approach to versatile GNP functionalization on the basis of the excellent accessibility and good stability of functional dialky...

In this paper, we consider a discontinuous, fully nonlinear, higher-order equation on the half-line, together with functional boundary conditions, given by general continuous functions dependence several derivatives and asymptotic information (n−1)th derivative of unknown function. These conditions generalize usual data allow other types global assumptions function its derivatives, such as nonl...

Zerumbone 1 is an 11-membered cyclic sesquiterpene obtained from the rhizomes of Zingiber zerumbet SMITH (Zingiberaceae). In this study, we investigated the structure-activity relationship of 1, α-humulene (2), tetrahydrozerumbone stereoisomers (3-5), and tetrahydrozerumbone derivatives (6-9). The oxygen-containing functional groups and the configurations at C1 and C2 contributed to the spontan...

Neamine is normally found as a core structure of aminoglycoside antibiotics. In order to understand the relationship between the antibiotic activity and the configurations of the functional groups of neamine, a series of novel neamine analogues with functional group manipulations on the 2-deoxystreptamine (2-DOS) ring or the sugar ring were designed and synthesized. The synthetic approach invol...

A molecularly imprinted polymer (MIP) with dual dopamine/serotonin-like binding sites (DS-MIP) was synthesized for use as a receptor model of study the drug-interaction of biological mixed receptors at a molecular level. The polymer material was produced using methacrylic acid (MAA) and acrylamide (ACM) as functional monomers, N,N'-methylene bisacrylamide (MBAA) as cross-linker, methanol/water ...

Sulfones feature prominently in biologically active molecules and are key functional groups for organic synthesis. We report a mild, photoredox-catalyzed reaction for sulfonylation of aniline derivatives with sulfinate salts, and demonstrate the utility of the method by the late-stage functionalization of drugs. Key features of the method are the straightforward generation of sulfonyl radicals ...