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.     

A capillary electrophoresis and off-line capillary electrophoresis/electrospray ionization-quadrupole time of flight-tandem mass spectrometry approach for ganglioside analysis

A systematic study for the optimization and implementation of high-performance capillary electrophoresis (HPCE) in conjunction with negative ion electrospray ionization-quadrupole time of flight-tandem mass spectrometry (ESI-QTOF-MS/MS) for the analysis of complex glycolipids is described. The performance of the capillary electrophoresis (CE) and off-line CE/ESI-QTOF-MS approach has been explored for screening a complex ganglioside mixture from bovine brain. All instrumental and solution parameters demonstrated to require special adjustment and to have the most substantial effect on the CE separation, abundance of product ions produced in a low-energy collision-induced dissociation (CID) process and their detection by MS/MS, when attempting to identify and sequence single ganglioside molecular species from CE eluted fractions. Upon optimization of the experimental parameters, an efficient methodology emerged providing the general basic requirements for combined CE/ESI-MS analysis of this type of complex glycoconjugate.     

Structural characterization of chondroitin/dermatan sulfate oligosaccharides from bovine aorta by capillary electrophoresis and electrospray ionization quadrupole time-of-flight tandem mass spectrometry

An analytical approach based on high-performance capillary electrophoresis (CE) in conjunction with electrospray ionization quadrupole time-of-flight tandem mass spectrometry (ESI-QTOF-MS/MS) has been developed for providing the basis to obtain new insights into the domain structure of the glycosaminoglycan (GAG) moiety of proteoglycans. The feasibility and performance of the off-line CE/ESI-QTOF-MS approach in GAG oligosaccharide analysis were assessed by screening a chondroitin/dermatan sulfate (DS) oligosaccharide mixture obtained from bovine aorta by enzymatic depolymerization by chondroitin B lyase. The CS/DS mixture was analyzed by CE using 50 mM ammonium acetate, pH 12.0, dissolved in aqueous methanol (2:3; v/v), as a CE carrier. Structural identification of the GAG components was achieved using off-line CE/nanoESI-QTOF-MS and-MS/MS experiments. ESI-QTOF instrumental parameters were found to play an important role in the MS screening of the CE-separated GAG species. By optimizing the ESI conditions, oligosaccharides differing in chain length and degree of sulfation could be detected. The building block composition, the size of the carbohydrate chain, as well as structural features of the repeating HexA-GalNAc, HexA-GalNAc(S) units, have been determined using MS/MS by applying collision-induced dissociation at low energies. Cleavage of GAG chains by chondroitin B lyase occurs with formation of structural markers useful for identification of IdoA-containing domains.     

Glycoscreening by on-line sheathless capillary electrophoresis/electrospray ionization-quadrupole time of flight-tandem mass spectrometry

An analytical approach based on sheathless on-line coupling of capillary electrophoresis (CE) and electrospray ionization (ESI) quadrupole time-of-flight (QTOF) mass spectrometry (MS) has been developed for providing new insight into the characterization of carbohydrate mixtures. The home-built sheathless CE/     

Thin chip microsprayer system coupled to quadrupole time-of-flight mass spectrometer for glycoconjugate analysis

A thin chip polymer-based microsprayer has been coupled to a hybrid quadrupole time-of-flight mass spectrometer (QTOF MS) and introduced in carbohydrate research. The feasibility of the approach is demonstrated for mapping, sequencing and structural elucidation of glycoconjugates originating from human body fluids and tissues such as a glycopeptide mixture from normal human urine and an isolated and purified GT1 ganglioside fraction from normal adult human brain. The optimization procedure required by each glycoconjugate category is described and the advantages of the system in terms of flexibility and adaptability to QTOF MS, stability of the ESI MS signal, carbohydrate ionization and sequencing, sensitivity, speed of analysis and sample consumption are 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.