Korn's inequalities for piecewise vector fields

Korn's inequalities for piecewise vector fields are established. They can be applied to classical nonconforming finite element methods, mortar methods and discontinuous Galerkin methods.

     

Embedding optimisation algorithms with Mosel

Algebraic modelling languages allow models to be implemented in such a way that they can easily be understood and modified. They are therefore a working environment commonly used by practitioners in Operations Research. Having once developed models, they need to be integrated inside the company information system. This step often involves embedding a model into a programming language environment: many existing algebraic modelling languages make possible to run parameterised models and subsequently retrieve their results, but without any facility for interacting with the model during the model generation or solution process.In this paper we show how to use the Mosel environment to implement complex algorithms directly in the modelling language.The Office cleaning problem is solved by a branch-and-cut algorithm, implemented entirely in the modelling language (including the definition of the callback function for the solver). Secondly, a cutting stock problem is solved by column generation, also implemented in the modelling language.AMS classification: 90Cxx, 65K05, 68N15     

Trace determination of volatile sulfur compounds by solid-phase microextraction and GC-MS

A method was developed for the simultaneous determination of the following nine volatile sulfur compounds in gas samples: carbon disulfide, carbonyl sulfide, ethyl sulfide, ethyl methyl sulfide, hydrogen sulfide, isopropanethiol, methanethiol, methyl disulfide and methyl sulfide. The target compounds were preconcentrated by solid-phase microextraction (SPME) and determined by gas chromatography combined with mass spectrometry. Experimental design was employed to optimize the extraction time and temperature and concurrent detection of the nine compounds was achieved by using an SPME fiber coated with Carboxen-polydimethylsiloxane (75 microns). Detection limits ranged from 1 ppt (v/v) for carbon disulfide to 350 ppt (v/v) for hydrogen sulfide and calibration functions were linear up to 20 ppb (v/v) for all the compounds investigated.     

Controlled formation of ag nanoparticles by means of long-chain sodium polyacrylates in dilute solution

A new tool is presented to control formation of Ag nanoparticles. Small amounts of silver ions were added to dilute solutions of long-chain sodium polyacrylates (NaPA). Four NaPA samples covering a molar mass regime of 97 kD < or = Mw < or = 650 kD have been used. With amounts of added Ag(+) as low as 1-2% of the COO(-) groups of the polyanionic chains, significant changes could already be induced in the NaPA coils with 650 kD. If the NaPA concentration was kept below 0.1 g/L, the coils with 650 kD exhibited a significant coil shrinking in stable solutions. At larger NaPA concentrations, addition of Ag+ initiates an aggregation of the polyacrylate coils toward compact structures. Coil shrinking and aggregation was revealed by means of time-resolved static light scattering. If exposed to UV-radiation, small Ag particles formed within the shrunken anionic polyacrylate coils. The Ag nanoparticles were identified by means of an enhanced light scattering and a characteristic plasmon absorption band around 410 nm. No such Ag particle formation could be observed even at 5 times larger concentrations of Ag(+) and NaPA if the two smallest polyacrylate samples have been used under otherwise equal conditions. This molar mass sensitive response of NaPA to Ag(+)-addition suggests an interesting phenomenon: if the coil size of the NaPa chains, which act as Ag(+) collectors, is large enough, local Ag(+) concentration in these coil-shaped Ag(+) containers exceeds a critical value, and irradiation with UV generates Ag nanoparticles.     

A comprehensive analysis in one run – in-depth conformation studies of protein–polymer chimeras by asymmetrical flow field-flow fractionation

Polymer-based protein engineering has enabled the synthesis of a variety of protein–polymer conjugates that are widely applicable in therapeutic, diagnostic and biotechnological industries. Accurate characterizations of physical–chemical properties, in particular, molar masses, sizes, composition and their dispersities are critical parameters that determine the functionality and conformation of protein–polymer conjugates and are important for creating reproducible manufacturing processes. Most of the current characterization techniques suffer from fundamental limitations and do not provide an accurate understanding of a sample''s true nature. In this paper, we demonstrate the advantage of asymmetrical flow field-flow fractionation (AF4) coupled with multiple detectors for the characterization of a library of complex, zwitterionic and neutral protein–polymer conjugates. This method allows for determination of intrinsic physical properties of protein–polymer chimeras from a single, rapid measurement.

Precise characterization of structural parameters and their polydispersities of protein–polymer conjugates is performed with rapid analysis using asymmetrical flow field-flow fractionation coupled with multiple detectors.     

Network information and connected correlations

Entropy and information provide natural measures of correlation among elements in a network. We construct here the information theoretic analog of connected correlation functions: irreducible N-point correlation is measured by a decrease in entropy for the joint distribution of N variables relative to the maximum entropy allowed by all the observed N-1 variable distributions. We calculate the "connected information" terms for several examples and show that it also enables the decomposition of the information that is carried by a population of elements about an outside source.     

Sequence Control in Polymer Chemistry through the Passerini Three‐Component Reaction

A new strategy to achieve sequence control in polymer chemistry based on the iterative application of the versatile Passerini three‐component reaction (P‐3CR) in combination with efficient thiol–ene addition reactions is introduced. First, stearic acid was used as a starting substrate to build up a sequence‐defined tetramer with a molecular weight of 1.6 kDa. Using an acid‐functionalized PEG allowed for an easier isolation of the sequence‐defined macromolecules by simple precipitation and led to a sequence‐defined pentamer in a block‐copolymer architecture. Importantly, this new strategy completely avoids protecting group chemistry. By following this strategy, a different side chain can be introduced to the polymer/oligomer backbone in a simple way and at a defined position within the macromolecule.