Non-linear parabolic problem associated with the penetration of a magnetic field into a substance

We study the following initial and boundary value problem: In section 1, with u₀ in L²(Ω), f continuous such that f(u) + ? non-decreasing for ? positive, we prove the existence of a unique solution on (0,T), for each T > 0. In section 2 it is proved that the unique soluition u belongs to L²(0, T; H ∩ H²) ∩ L^∞(0, T; H) if we assume u₀ in H and f in C¹(?,?). Numerical results are given for these two cases.     

Versatile photosensitization system for 1O2-mediated oxidation of alkenes based on nafion-supported platinum(II) terpyridyl acetylide complex

[structure: see text] Platinum(II) terpyridyl acetylide complex (1) was incorporated into Nafion membranes as a photosensitizer, and the Nafion was immersed in an aqueous or organic solution of 7-dehydrocholesterol, alpha-pinene, or cyclopentadiene. This photosensitizer system can generate singlet oxygen ((1)O(2)) in high quantum yield to oxidize the alkenes in the solution outside the Nafion and can be easily removed from the reaction vessel at the end of the photooxidation.     

Hierarchical assembly of homochiral porous solids using coordination and hydrogen bonds

A family of homochiral metal carboxylate coordination polymers have been synthesized by treating 2,2'-dihydroxy-1,1'-binaphthalene-6,6'-dicarboxylic acid (H(2)BDA) with metal salts at elevated temperatures. BDA ligands link adjacent metal centers to form 1D coordination polymeric chains using the carboxylate functionality, while the hydroxyl groups of BDA ligands form H-bonds with carboxylate oxygen atoms to link 1D coordination polymeric chains into open frameworks of higher dimensionality. We also present evidence for the important role played by H-bonds in the stabilization of open framework structures which allows for the hierarchical assembly of chiral porous solids.