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.     

One Spot Microwave Synthesis and Characterization of Nitrogen-Doped Carbon Dots with High Oxygen Content for Fluorometric Determination of Banned Sudan II Dye in Spice Samples

Journal of Fluorescence - A simple microwave-assisted synthesis of nitrogen-doped carbon dots with high oxygen content (O-N-CDs) was carried out with citric acid as a carbon source and...     

Liquid Chromatographic Determination of NSAIDs in Urine After Dispersive Liquid–Liquid Microextraction Based on Solidification of Floating Organic Droplets

An environmentally benign method of sample preparation based on dispersive liquid–liquid microextraction and solidification of floating organic droplets (DLLME-SFO) coupled with high-performance liquid chromatography with ultraviolet detection has been developed for analysis of non-steroidal anti-inflammatory drugs (NSAIDs) in biological fluids. A low-toxicity solvent was used to replace the chlorinated solvents commonly used in conventional DLLME. Seven conditions were investigated and optimized: type and volume of extraction solvent and dispersive solvent, extraction time, effect of addition of salt, and sample pH. Under the optimum conditions, good linearity was obtained in the range 0.01–10 µg mL⁻¹, with coefficients of determination (r ²) >0.9949. Detection limits were in the range 0.0034–0.0052 µg mL⁻¹ with good reproducibility (RSD) and satisfactory inter-day and intra-day recovery (95.7–115.6 %). The method was successfully used for analysis of diclofenac, mefenamic acid, and ketoprofen in human urine. Analysis of urine samples from a patient 2 and 4 h after administration of diclofenac revealed concentrations of 1.20 and 0.34 µg mL⁻¹, respectively.

     

Interaction of pyromellitic diimide derivatives with beta-cyclodextrin and anthracene-appended beta-cyclodextrin: rim binding vs inclusion complexation

Complex formation of pyromellitic diimide derivatives with beta-cyclodextrin and anthracene-appended beta-cyclodextrin was studied with use of induced circular dichroism and 1H NMR spectroscopies. It is revealed that pyromellitic diimides form rim-binding type complexes with beta-CD and in these complexes the pyromellitic diimides lie just outside of the narrow rim of the CD. With anthracene-appended beta-CD the pyromellitic diimides form true inclusion complexes. Implications of the formation of rim-binding type complexes are also discussed.     

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.     

Chemometric Optimization of Biologically Active Compounds Extraction from Grape Marc: Composition and Antimicrobial Activity

The article focuses on the optimization of the extraction process of biologically active compounds (BAC) from grape marc—a by-product of the wine industry. The influence of temperature, specifically 30 °C, 45 °C and 65 °C, and ethanol concentration in solutions, specifically 0–96% (v/v) on the extraction yield of polyphenols, flavonoids, tannins and anthocyanins, were investigated. The composition of individual polyphenols, anthocyanins and organic acids, antioxidant activity (DPPH and ABTS) and CIELab chromatic characteristics of the grape marc extracts (GME), were characterized. The microbiostatic and microbicidal effects in direct contact of GME with pathogenic microorganisms, Bacillus subtilis, Staphylococcus aureus, Escherichia coli, Klebsiella pneumoniae, were determined in vitro. The influence of extraction parameters on the total polyphenol content (TPC), total flavonoid content (TFC), tannin content (TC), total anthocyanin content (TAC) and their interdependencies were studied using information analysis. A mathematical model was developed on cubic spline functions. The analysis of individual compounds showed the presence of a wide range of flavonoids (procyanidin B2, procyanidin B1, hyperoside and quercetin), flavones (catechin), hydroxybenzoic acid derivatives (gallic, protocatechuic, p-hydroxybenzoic acids, m-hydroxybenzoic acid, syringic acid), hydroxycinic acid derivatives and ferulic acid methyl ester. The malvidol-3-glucoside was the main anthocyanin identified in the extract. A high amount of tartaric acid was also found. GME showed significant antimicrobial activity against Gram-positive bacteria and lower activity against Gram-negative bacteria.     

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.     

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.