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.     

Increasing protein stability by engineering the n → π* interaction at the β-turn

Abundant n → π* interactions between adjacent backbone carbonyl groups, identified by statistical analysis of protein structures, are predicted to play an important role in dictating the structure of proteins. However, experimentally testing the prediction in proteins has been challenging due to the weak nature of this interaction. By amplifying the strength of the n → π* interaction via amino acid substitution and thioamide incorporation at a solvent exposed β-turn within the GB1 proteins and Pin 1 WW domain, we demonstrate that an n → π* interaction increases the structural stability of proteins by restricting the ϕ torsion angle. Our results also suggest that amino acid side-chain identity and its rotameric conformation play an important and decisive role in dictating the strength of an n → π* interaction.

Amino acid residues adopt a right-handed α-helical conformation with increasing strength of the n → π* interaction. We also demonstrate a direct consequence of n → π* interactions on enhancing the structural stability of proteins.     

Regioselective cleavage of the bis-benzylidene acetal of d-mannitol under oxidative and reductive conditions: a new approach to C2-symmetric chiral ligands

A highly regioselective oxidative cleavage of 1,3:4,6-di-O-benzylidene-d-mannitol was carried out using NBS and the resultant product was readily converted to the C₂-symmetric chiral ligand, (R,R)-3,4-dihydroxy-1,5-hexadiene. On the other hand, reductive cleavage of 1,3:4,6-di-O-benzylidene-d-mannitol was achieved in a highly regioselective manner using BF₃·OEt₂ and Et₃SiH to give a highly functionalized benzyl ether, which was converted to a synthetically useful C₂-symmetric bis-amino alcohol derivative.     

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.     

Gels dried under supercritical and ambient conditions: a comparative study and their subsequent conversion to silica–carbon composite aerogels

In present work, we have prepared gels with various compositions of methyltrimethoxysilane—3-(2,3-epoxypropoxy) propyltrimethoxysilane (MTMS-GPTMS) using a two-step acid base sol–gel process. To make a comparative study between the two common drying routes, we prepared gels under supercritical and also under ambient conditions. The density of the supercritically dried hybrid aerogels lies between 0.18 and 0.31 gcm^?3, while the density of the ambient dried ones ranges between 0.35 and 0.42 gcm^?3. The surface area of MTMS-0.25 GPTMS aerogel dried under supercritical conditions, has been found to be 464 m² g^?1 with a pore volume and average pore diameter of 1.24 cm³ g^?1 and 11 nm respectively. The same composition dried under ambient conditions is found to have similar properties i.e. a BET surface area of 439 m² g^?1, pore volume of 1.22 cm³ g^?1 and average pore diameter of 11 nm. The aerogels were later pyrolyzed yielding silica/carbon composite aerogels. The pyrolized aerogels possessed a surface area as high as 207 m² g^?1 with a total pore volume of 0.98 cm³ g^?1. The pyrolysed aerogels were also calcined to yield carbon free materials.     

Scalable bottom‐up assembly of suspended carbon nanotube and graphene devices by dielectrophoresis

Bottom‐up assembly by dielectrophoresis (DEP) has emerged in recent years as a viable alternative to conventional top–down fabrication of electronic devices from nanomaterials, particularly carbon nanotubes and graphene. Here, we demonstrate how this technique can be extended to fabricate devices containing carbon nanotubes and graphene suspended between two electrodes over a back‐gate electrode. The suspended device geometry is critical for the development of nano‐electromechanical devices and to extract maximum performance out of electronic and optoelectronic devices. This technique allows for parallel assembly of devices over large scale. (© 2015 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

Optimization of the Production of Thermostable endo-β-1,4 Mannanases from a Newly Isolated <Emphasis Type="Italic">Aspergillus niger gr</Emphasis> and <Emphasis Type="Italic">Aspergillus flavus gr</Emphasis>

The aim of this work was to establish optimal conditions for the maximum production of endo-β-1,4 mannanases using cheaper sources. Eight thermotolerant fungal strains were isolated from garden soil and compost samples collected in and around the Gulbarga University campus, India. Two strains were selected based on their ability to produce considerable endo-β-1,4 mannanases activity while growing in liquid medium at 37 °C with locust bean gum (LBG) as the only carbon source. They were identified as Aspergillus niger gr and Aspergillus flavus gr. The experiment to evaluate the effect of different carbon sources, nitrogen sources, temperatures and initial pH of the medium on maximal enzyme production was studied. Enzyme productivity was influenced by the type of polysaccharide used as the carbon source. Copra meal defatted with n-hexane showed to be a better substrate than LBG and guar gum for endo-β-1,4 mannanases production by A. niger gr (40.011 U/ml), but for A. flavus gr (33.532 U/ml), the difference was not significant. Endo-β-1,4 mannanases produced from A. niger gr and A. flavus gr have high optimum temperature (65 and 60 °C) and good thermostability in the absence of any stabilizers (maintaining 50% of residual activity for 8 and 6 h, respectively, at 60 °C) and are stable over in a wide pH range. These new strains offer an attractive alternative source of enzymes for the food and feed processing industries.