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.     

Subtilisin catalysis of substrate anchored in cyclodextrin

The N-benzoyl-l-tyrosine ethyl ester (BTEE) anchored in cyclodextrin (β and β-methyl CD) serves as an excellent substrate for subtilisin Carlsberg catalysis. The rate of hydrolysis was found to be approximately twofold higher than that of the methanolic substrate. The K_mapp and V_max values for the CD anchored substrates were significantly higher than the methanol-solubilized BTEE.     

Di(2-ethyl hexyl) butyramide and di(2-ethyl hexyl)isobutyramide as extractants for uranium(VI) and plutonium(IV)

The extraction of uranium(VI) and plutonium(IV) from nitric acid into n-dodecane was studied using two isomeric branched alkyl amides, di(2-ethyl hexyl) butyramide (DEHBA) and di(2-ethyl hexyl) isobutyramide (DEHIBA). The extraction ratios of Pu(IV) at relatively high acidities were higher than the corresponding values for U(VI) in the case of DEHBA. However, with DEHIBA the values for Pu(IV) were negligibly small. Pu(IV) was found to be extracted as trisolvate by DEHBA and as disolvate by DEHIBA. U(VI) was extracted by both the amides. From the study of the extraction reactions at different temperatures, it was shown that all the reactions in the present investigation were enthalpy favoured and entropy disfavoured. Separation of Pu(IV) from bulk of U(VI) was feasible. However, the purity of the separated plutonium was not satisfactory in batch extraction studies.     

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.     

Investigation of the complexation of essential oil components with cyclodextrins

The formation of inclusion complexes of six essential oil (EO) components (β-caryophyllene, cis-ocimene, trans-ocimene, sabinene hydrate (thujanol), γ-terpinene and α-terpineol) with six cyclodextrins (CDs) (α-CD, β-CD, γ-CD, HP-β-CD, RAMEB and CRYSMEB) was investigated by using static headspace-gas chromatography and UV–visible spectroscopy. Retention studies showed that CDs could efficiently reduce the volatility of EO components except for β-caryophyllene with α-CD. In this case, no inclusion complex was detected while for other compounds the formation of 1:1 inclusion complexes was observed. Results revealed that the inclusion stability mainly depends on geometric complementarity between encapsulated molecule and CD's cavity. Molecular modelling was used to investigate the complementarities between host and guest. Thus, CDs could efficiently be regarded as promising encapsulants for EO components leading to improve their application in cosmetic, pharmaceutical and agriculture fields.     

Biphasic kinetic investigations on the evaluation of non-salt forming reductants for Pu(IV) stripping from tributyl phosphate and N,N-dihexyl octanamide solutions in n-dodecane

The relative stability of different oxidation states of actinide elements is influenced by the nature of complexes formed and redox equilibria in aqueous/non-aqueous solutions. The reduction/stripping studies on Pu(IV) ions from loaded organic phases of 1.1 M tributyl phosphate and of 1.1 M N,N-dihexyl octanamide in n-dodecane were studied using organic soluble tert-butyl hydroquinone (TBH) and aqueous soluble reductants like acetaldoxime (AX) and hydroxyurea (HU). These studies were carried out as a function of reductant and nitric acid concentration (0.5–4 M HNO₃) and of time. The changes in Pu oxidation states were followed by spectrophotometry for TBH and by distribution ratio values for AX and HU as reductants. Spectrophotometric investigations using TBH as reductant showed that it was desirable to strip Pu(III) formed after reduction of Pu(IV) in the organic phase, which may otherwise be reconverted to extractable Pu(IV) by in situ generated HNO₂ from oxidative degradation of TBH to tert-butyl quinone. Similarly, the biphasic reduction/stripping of Pu(IV) using AX and HU as reductant rate was affected adversely with increased aqueous phase acidity. This data will help in the accurate simulation of Pu separation processes using these reductants in mixer-settlers/pulsed columns or centrifugal contactors.     

The effect of incorporation of ferrous titanate nanoparticles in sulfonated poly(ether ether ketone)/poly (amide imide) acid-base polymer for cations exchange membrane fuel cells

Journal of Solid State Electrochemistry - The sulfonated poly(ether ether ketone) (SPEEK) is one of the most promising aromatic proton exchange polymer membranes concerning fluorinated aliphatic...