Risk averse elastic shape optimization with parametrized fine scale geometry

Shape optimization of the fine scale geometry of elastic objects is investigated under stochastic loading. Thus, the object geometry is described via parametrized geometric details placed on a regular lattice. Here, in a two dimensional set up we focus on ellipsoidal holes as the fine scale geometric details described by the semiaxes and their orientation. Optimization of a deterministic cost functional as well as stochastic loading with risk neutral and risk averse stochastic cost functionals are discussed. Under the assumption of linear elasticity and quadratic objective functions the computational cost scales linearly in the number of basis loads spanning the possibly large set of all realizations of the stochastic loading. The resulting shape optimization algorithm consists of a finite dimensional, constraint optimization scheme where the cost functional and its gradient are evaluated applying a boundary element method on the fine scale geometry. Various numerical results show the spatial variation of the geometric domain structures and the appearance of strongly anisotropic patterns.     

Binding modes of carboxylate- and acetylacetonate-linked chromophores to homodisperse polyoxotitanate nanoclusters

The binding of carboxylate- and acetylacetonate-linked chromophores to homodisperse polyoxotitanate nanoclusters with 17 Ti atoms or more are surveyed and found to be limited to chelate-bidentate and the bridging modes, the former being dominant for the acetylacetonate-linked chromophores, the latter for the carboxylate linkers. Chromophores with acetylacetonate linking groups invariably bind in the chelate mode, whereas carboxylic acid terminated chromophores more frequently are observed to have the bridging mode, with the exception of three cases in which a strong electron-donating substituent is present on two different sensitizers. The calculations for isonicotinateand nitrophenylacetylacetonate functionalized Ti17 clusters show the observed binding modes to correspond to the lower energy functionalized clusters, but do not predict the difference between the cinnamic acid and dimethylaminocinnamic acid binding to Ti17, which are bridging and chelate respectively. Both binding modes were never observed to occur for a single chromophore, even when synthetic conditions were varied. Density of state calculations show broadening and splitting of the chromophore LUMO on complexation due to interaction with the cluster's conduction band, as well as frequent penetration of sensitizer orbitals into the bandgap of the functionalized nanoparticle.     

Palladium-catalyzed sequential indole synthesis using sterically hindered amines

A palladium catalyst derived from a bulky N-heterocyclic carbene ligand enabled a modular synthesis of indoles bearing sterically hindered N-alkyl or N-aryl substituents through a reaction sequence comprising an intermolecular N-arylation and an intramolecular hydroamination.     

A Literature Review of Science and Mathematics Integration

Integrated curricula has gained a great deal of acceptance among educators. Many educators provide testimonials about the effectiveness of units they teach, and many professional organizations stress integration across the curriculum. However, few empirical studies exist to support the notion that an integrated curriculum is any better than a well-designed traditional curriculum. Some educators question integration across the curriculum, because in the effort to integrate topics, science and mathematics content becomes superficial and trivial. This paper presents a review of the literature on integrated curricula. It concludes with a call to action for members of School Science and Mathematics Association.     

Efficient Cu(I) acetate‐catalyzed cycloaddition of multifunctional alkynes and azides: From solution to bulk polymerization

“Click” chemistry is an effective and commonly used technique in polymer chemistry for the synthesis and modification of polymers. In this study, the bulk polymerization of multifunctional alkynes and azides was achieved by the copper(I)‐catalyzed alkyne–azide 1,3‐dipolar cycloaddition. The influence of different catalyst systems on the polymerization kinetics of the “click”reaction were evaluated by differential scanning calorimetry. Surprisingly, Cu(I) acetate showed the most efficient catalytic behavior among the applied Cu(I) salts. The polymerization kinetics in solution were investigated by 1H NMR spectroscopy and size exclusion chromatography. According to the 1H NMR investigation the copper(I)‐catalyzed cycloaddition follows a second‐order kinetics with external catalysis. Additionally, the mechanical properties of the resulting polymers were investigated by depth sensing indentation. Thereby the polymerizations of the alkyne tripropargylamine with the azides 1,3‐bis(azidomethyl)benzene and 1,4‐bis(azidomethyl)benzene resulted in mechanical hard materials. Furthermore, the combination of the alkynes tripropargylamine and di(prop‐2‐yn‐1‐yl) isophorone dicarbamate and polymerization with 1,2‐bis(2‐azidoethoxy)ethane resulted in high indentation moduli. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 239–247     

Some Remarks on Signs in Functional Equations

We discuss the computation of the sign in certain functional equations.