Measure functions for frames

This paper addresses the natural question: “How should frames be compared?” We answer this question by quantifying the overcompleteness of all frames with the same index set. We introduce the concept of a frame measure function: a function which maps each frame to a continuous function. The comparison of these functions induces an equivalence and partial order that allows for a meaningful comparison of frames indexed by the same set. We define the ultrafilter measure function, an explicit frame measure function that we show is contained both algebraically and topologically inside all frame measure functions. We explore additional properties of frame measure functions, showing that they are additive on a large class of supersets—those that come from so called non-expansive frames. We apply our results to the Gabor setting, computing the frame measure function of Gabor frames and establishing a new result about supersets of Gabor frames.     

Application of the continuum shell finite element SHB8PS to sheet forming simulation using an extended large strain anisotropic elastic–plastic formulation

This paper proposes an extension of the SHB8PS solid–shell finite element to large strain anisotropic elasto-plasticity, with application to several non-linear benchmark tests including sheet metal forming simulations. This hexahedral linear element has an arbitrary number of integration points distributed along a single line, defining the “thickness” direction; and to control the hourglass modes inherent to this reduced integration, a physical stabilization technique is used. In addition, the assumed strain method is adopted for the elimination of locking. The implementation of the element in Abaqus/Standard via the UEL user subroutine has been assessed through a variety of benchmark problems involving geometric non-linearities, anisotropic plasticity, large deformation and contact. Initially designed for the efficient simulation of elastic–plastic thin structures, the SHB8PS exhibits interesting potentialities for sheet metal forming applications—both in terms of efficiency and accuracy. The element shows good performance on the selected tests, including springback and earing predictions for Numisheet benchmark problems.     

A stable high-order Spectral Difference method for hyperbolic conservation laws on triangular elements

Numerical schemes using piecewise polynomial approximation are very popular for high order discretization of conservation laws. While the most widely used numerical scheme under this paradigm appears to be the Discontinuous Galerkin method, the Spectral Difference scheme has often been found attractive as well, because of its simplicity of formulation and implementation. However, recently it has been shown that the scheme is not linearly stable on triangles. In this paper we present an alternate formulation of the scheme, featuring a new flux interpolation technique using Raviart–Thomas spaces, which proves stable under a similar linear analysis in which the standard scheme failed. We demonstrate viability of the concept by showing linear stability both in the semi-discrete sense and for time stepping schemes of the SSP Runge–Kutta type. Furthermore, we present convergence studies, as well as case studies in compressible flow simulation using the Euler equations.     

A palladium-catalyzed three-component cross-coupling of conjugated dienes or terminal alkenes with vinyl triflates and boronic acids

A three-component coupling of vinyl triflates and boronic acids to alkenes catalyzed by palladium is reported. Using 1,3-dienes, selective 1,2-alkene difunction-alization is observed, whereas the use of terminal alkenes results in 1,1-alkene difunctionalization. The reaction outcome is attributed to the formation of stabilized, cationic Pd-π-allyl intermediates to regulate β-hydride elimination.     

Titanium isopropoxide as efficient catalyst for the aza-Baylis-Hillman reaction. Selective formation of alpha-methylene-beta-amino acid derivatives

The direct formation of alpha-methylene-beta-amino acid derivatives is achieved using the aza version of the Baylis-Hillman protocol. The products are readily formed in a three-component one-pot reaction between arylaldehydes, sulfonamides, and alpha,beta-unsaturated carbonyl compounds. The reaction is efficiently catalyzed by titanium isopropoxide and 2-hydroxyquinuclidine in the presence of molecular sieves. The protocol allows for structural variation of the substrates, tolerating electron-poor and electron-rich arylaldehydes and various Michael acceptors.     

A Novel siloxane-containing dicarboxylic acid, 1,3-bis(p-carboxyphenylene-ester-methylene)tetramethyldisiloxane,and its derivatives: ester macrocycle and supramolecular structure with a copper complex

The new dicarboxylic acid, 1,3-bis(p-carboxyphenylene-ester-methylene)tetramethyldisiloxane (H₂L, 1) was obtained by treating 1,3-bis(chloromethyl)-1,1,3,3-tetramethyldisiloxane with a mixture of terephthalic acid and terephthalic acid sodium salt in a 1:1 ratio. In this approach, besides the desired compound 1 (33 wt % yield), the condensation cyclic dimer 2 (7 wt % yield) and an oligomer 3 (10 wt % yield) resulted. The reaction between dicarboxylic acid H₂L, where L is the carboxylate ligand, along with imidazole as co-ligand, and copper hydroxide resulted in the formation of a coordination compound [Cu(HIm)₄(H₂O)₂]L·4.5H₂O (4). Single-crystal X-ray crystallography has revealed that the crystal structure of 4 is a self-assembled H-bonded three-dimensional supramolecular structure. FTIR and NMR spectral techniques were also used to characterize the formed structures. Optical and thermal properties of all compounds were studied. The stability of the supramolecular structure in solution (methanol) and with temperature was studied using ATR-FTIR. The ability of the macrocycle 2 to bind potassium cations in solution was investigated by UV–vis spectrophotometry.     

Electrochemical Behaviour and Rapid Determination of L‐Dopa at Electrochemically Pretreated Screen Printed Carbon Electrode

A simple and rapid voltammetric method based on a disposable electrochemically pretreated screen‐printed carbon electrode is proposed for the determination of L ‐dopa. Under optimum differential pulse voltammetry conditions a limit of detection of 3.6×10^?7 M for L ‐dopa was obtained. The method was successfully applied to the determination of L ‐dopa in a commercial pharmaceutical formulation.     

Benzotriazole derivatives as long wavelength photosensitizers for diaryliodonium salt initiators

Two benzotriazole derivative dyes 4,7‐bis(2,3‐dihydrothieno[3,4‐b][1,4]dioxin‐5‐yl)‐2‐dodecyl‐2H‐benzo[1,2,3]triazole, and 2‐dodecyl‐4,7‐bis(4‐hexylthiophen‐2‐yl)‐2H‐benzo[d][1,2,3]triazole are shown to work as efficient photosensitizers for a diphenyliodonium salt initiator in cationic photopolymerization of epoxide and vinyl monomers. Substituted thienyl groups are attached to benzotriazole backbone to extend conjugation and enhance electron density of the molecules. Thereby, it was possible to initiate polymerizations at room temperature using long wavelength UV and visible light. The progress of photopolymerizations was monitored using optical pyrometry. The photopolymerization of an epoxide monomer using solar irradiation was also demonstrated. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

Syntheses and optoelectronic properties of quinoxaline polymers: The effect of donor unit

Tuning the bandgap of electrochromic polymers is one of the important research topics in electrochromism. To understand clearly the effect of donor unit in donor–acceptor–donor‐type polymers, 2,3‐bis(4‐tert‐butylphenyl)‐5,8‐di(thiophen‐2‐yl)quinoxaline and 2,3‐bis(4‐tert‐butylphenyl)‐5‐(2,3‐dihydrothieno[3,4‐b][1,4]dioxin‐ 5‐yl)‐8‐(thiophen‐2‐yl)quinoxaline were synthesized and polymerized potentiodynamically. Their electrochemical and spectroelectrochemical studies were performed, and the results were compared with those of poly(2,3‐bis(4‐tert‐butylphenyl)‐5,8‐bis(2,3‐dihydrothieno[3,4‐b][1,4]dioxin‐5‐yl)quinoxaline) (Gunbas et al., Adv Mater 2008, 20, 691–695). A blue shift in the polymer π–π* transitions revealed that the bandgap of such polymers with the same acceptor unit is related to the electron density of donor units. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011