Some Isoperimetric Inequalities in Electrochemistry and Hele Shaw Flows

Isoperimetric inequalities are applied to a moving-boundaryproblem for doubly-connected domains. This problem occurs forexample in electrochemistry, in which case the domains in questionare the electrolyte of an electrolytic cell. The two electrodessurrounding the electrolyte are assumed to grow or dissolve,at different rates in general, by electrochemical reaction.We obtain optimal estimates showing, for example, that the leastchange in volume of each electrode always occurs in sphericalsymmetry.     

Reaction mechanism governing formation of 1,3-bis(diphenylphosphino)propane-protected gold nanoclusters

This report outlines the determination of a reaction mechanism that can be manipulated to develop directed syntheses of gold monolayer-protected clusters (MPCs) prepared by reduction of solutions containing 1,3-bis(diphenylphosphino)propane (L(3)) ligand and Au(PPh(3))Cl. Nanocluster synthesis was initiated by reduction of two-coordinate phosphine-ligated [Au(I)LL'](+) complexes (L, L' = PPh(3), L(3)), resulting in free radical complexes. The [Au(0)LL'](?) free radicals nucleated, forming a broad size distribution of ligated clusters. Timed UV-vis spectroscopy and electrospray ionization mass spectrometry monitored the ligated Au(x), 6 ≤ x ≤ 13, clusters, which comprise reaction intermediates and final products. By employing different solvents and reducing agents, reaction conditions were varied to highlight the largest portion of the reaction mechanism. We identified several solution-phase reaction classes, including dissolution of the gold precursor, reduction, continuous nucleation/core growth, ligand exchange, ion-molecule reactions, and etching of colloids and larger clusters. Simple theories can account for the reaction intermediates and final products. The initial distribution of the nucleation products contains mainly neutral clusters. However, the rate of reduction controls the amount of reaction overlap occurring in the system, allowing a clear distinction between reduction/nucleation and subsequent solution-phase processing. During solution-phase processing, the complexes undergo core etching and core growth reactions, including reactions that convert neutral clusters to cations, in a cyclic process that promotes formation of stable clusters of specific metal nuclearity. These processes comprise "size-selective" processing that can narrow a broad distribution into specific nuclearities, enabling development of tunable syntheses.     

MODELING CLIMATE CHANGE AND THE EFFECT ON THE NORWEGIAN SALMON FARMING INDUSTRY

Abstract Global warming is expected to affect the ecosystem in the Northeast Atlantic, and substantial changes will also affect the aquaculture industry. Farming of salmon and trout is the biggest aquaculture industry in Norway, with an export value of about 3 billion US dollars in 2007. The objective of the paper is to analyze the potential economic effect a general increase in sea temperature can have on the Norwegian salmon aquaculture industry. The assessment of the economic impact of global warming is made possible by estimating a growth function, which explicitly includes sea water temperature. The analysis compares the economic effect of a climate change on fish farming plants in the south and the north of Norway. The scenarios are based on a model with monthly seasonal variation in temperature.     

Addition reactions of allyl stannanes to an indolo[2′,3′:3,4]pyrido[1,2‐b]isoquinoline imminium salt

The addition of organometallic reagents to the 13b‐position of the indolo[2′,3′:3,4]pyrido[1,2‐b]isoquinoline imminium salt 4 is described. Reaction of 4 with tetraallyl tin in 2‐methoxyethanol gave the allyl adduct 7 in moderate yield. Further elaboration of 7 yielded the pentacyclic benzylidene alcohols 13 and 14 . Structure elucidation of the compounds prepared was achieved by a combination of ¹H nmr spec troscopy and X‐ray crystallography.