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1.
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. 相似文献
2.
A. Salahouelhadj F. Abed-Meraim H. Chalal T. Balan 《Archive of Applied Mechanics (Ingenieur Archiv)》2012,82(9):1269-1290
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. 相似文献
3.
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. 相似文献
4.
Mirela-Fernanda Zaltariov Angelica VladMaria Cazacu Sergiu ShovaMihaela Balan Carmen Racles 《Tetrahedron》2014
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. 相似文献
5.
Aliona Ghendov-Mosanu Daniela Cojocari Greta Balan Antoanela Patras Ildiko Lung Maria-Loredana Soran Ocsana Opri Elena Cristea Rodica Sturza 《Molecules (Basel, Switzerland)》2022,27(5)
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. 相似文献
6.
7.
A stable high-order Spectral Difference method for hyperbolic conservation laws on triangular elements 总被引:1,自引:0,他引:1
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. 相似文献
8.
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. 相似文献
9.
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. 相似文献
10.