Local partial regularity theorems for suitable weak solutions of a class of degenerate systems

A partial regularity theorem is established for a particular class of weak solutions to the systemu/t– div(K(u)u)=(u)¦¦², div((u))=0 on a bounded domain inR ^N . Under our assumptions, (u) may exhibit exponential decay, and thus the system may be degenerate. Our proof is based upon a blow-up argument.This work was supported in part by NSF Grant DMS9424448.     

Transition metal 1,2-bidentate thiolates as building blocks and their construction into cluster complexes

Simple fragments of transition metal 1,2-bidentate thiolates, the so-called building blocks of the general compositions ML₃, ML₂, ML, M(O)L₂, ML₂L, MLL, etc. have been proposed to constitute the di-, tri- and tetranuclear complexes concerned in this review. Structureal regularities and characteristics have been discussed and summarized according to the thiolato ligands edt and pdt, bdt and tdt, mp, and mpo, and mpp, respectively.Abbreviations H₂mpo o-mercaptophenol - Hmpo 2-mercaptopyridine-N-oxide - R₂dtc N,N-dialkyldithiocarbamate - Haet 2-aminoethanethiol - H₂bdt o-benzenedithiol - H₂pdt 1,2-propanedithiol - H₂tdt toluene-3,4-dithiol - Hmpp-mppH bis-(3-hydroxy-2-pyridyl)disulfide - Hmp-mpH bis-(2-oxyphenyl)disulfide - H₂edt 1,2-ethanedithiol - dppe 1,2-bis(diphenylphosphino)ethane - H₂tedt 3,4,5,6-tetrachlorobenzene-1,2-dithiol - H₂tpdt 3-thiapentane-1,5-dithiol - H₂mnt maleonitriledithiol - Him imidazole - Bz benzyl - py pyridine     

IMEP in support of the comparability of measurement results across the Romanian chemical metrology infrastructure

On the basis of quantitative chemical measurements many important decisions are made in support of legislation or in industrial processes or social aspects. For this reason it is important to improve the quality of chemical measurement results and thus make them comparable and acceptable everywhere. The measurement quality is important to enable an equivalent implementation of the European Union regulations and directives across an enlarged EU. In this context, the European Commission–Joint Research Centre–Institute for Reference Materials and Measurement (EC-JRC-IRMM) set up a programme to improve the scientific basis for metrology in chemistry (MiC) in EU candidate countries in the framework of EU enlargement. Several activities were initiated, such as training, fellowships, sponsoring of seminars, conferences and participation in interlaboratory comparisons. To disseminate measurement traceability, IRMM provides through its International Measurement Evaluation Programme (IMEP) an interlaboratory tool to enable the benchmarking of laboratory performance. IMEP emphasizes the metrological aspects of measurement results, such as traceability and measurement uncertainty. In this way it has become a publicly available European tool for MiC. The Romanian Bureau of Legal Metrology – National Institute of Metrology (BRML-INM) actively supports the participation of Romanian authorized and field laboratories in IMEP interlaboratory comparisons. This paper describes the interest of Romanian laboratories participating in this programme, the analytical and metrological problems that became relevant during these exercises and some actions for improvement. The results from Romanian laboratories participating in IMEP-12 (water), IMEP-16 (wine), IMEP-17 (human serum) and IMEP-20 (tuna fish) are presented. To conclude, the educational and training activities at national level organized jointly by the Romanian National Institute of Metrology (INM) and IRMM are also mentioned.     

A MORPHOLOGICAL STUDY OF POLY（DIVINYLBENZENE-co-ACRYLIC ACID） IN CROSSLINKING PRECIPITATION POLYMERIZATION

Divinylbenzene-80 （DVB-80） and polar monomer acrylic acid （AA） having hydrogen bonding at a total monomer loading of 5 vol% were precipitated-copolymerized in a variety of organic solvents with 2,2＇-azobis（isobutyronitrile） （AIBN） as initiator. The experiments were investigated from a two-dimensional matrix, i.e., the actual crosslinking degree of DVB varying from 0 to 80% and the solvent composition varying from 0 to 100% of toluene mixture with acetonitrile, when the mixture of acetonitrile and toluene was used as the reaction solvent. Under various reaction conditions, six distinct morphologies including soluble polymers, swellable microgels, coagulum, irregular microparticles, and nano-/micrometer microspheres were formed and the structures of these polymer architectures were described. A morphological map was utilized to discuss the effects of both crosslinking degree of DVB and composition of solvent on the transitions between morphology domains. The results demonstrated that the microspheres are formed by an internal contraction due to the marginal solvency of the continuous phase and the crosslinking of the polymer network through the covalent bonding from DVB as well as the interchain hydrogen-bonding between the carboxylic acid units.     

EFFECTS OF COUPLING AGENTS ON THE CRYSTALLIZATION BEHAVIOR OF PP/T-ZnOw COMPOSITES

The objectives of this paper are to understand the crystallization behavior of polypropylene(PP)composites with surface modified tetra-needle-shaped zinc oxide whisker(T-ZnOw).T-ZnOw was surface modified with different coupling agents,such as silane coupling agents(KH-550,KH-560)and titanate coupling agent(NDZ-105),in order to improve the compatibility between PP and T-ZnOw.DSC and POM were used to characterize the melt and crystallization behavior and the crystalline structures of the composites,respectively.The results show that the surface modified T-ZnOw acts as a nucleating agent of PP crystallization,depending on the coupling agent used for modification.KH-550 and KH-560 have more apparent role in improving the interfacial interaction than NDZ-105 and induce PP crystallization at higher temperature and with smaller spherulites size.The results also suggest that the crystallization behavior depends on not only the content of coupling agent,but also the content of the surface modified T-ZnOw used in the composites.     

RATE OF INTRA-MOLECULAR CONTACT FORMATION IN SHORT TWO-DIMENSIONAL COMPACT POLYMERS CHAINS

It is important to know the rate of intra-molecular contact formation in proteins in order to understand how proteins fold clearly. Here we investigate the rate of intra-molecular contact formation in short two-dimensional compact polymer chains by calculating the probability distribution p(r) of end-to-end distance r using the enumeration calculation method and HP model on two-dimensional square lattice. The probability distribution of end-to-end distance p(r) of short two-dimensional compact polymers chains may consist of two parts, i.e. p(r) = p1(r) p2(r), where p1(r) and p2(r) are different for small r. The rate of contact formation decreases monotonically with the number of bonds N, and the rate approximately conforms to the scaling relation of k(N) ∝ N-α. Here the value of α increases with the contact radius a and it also depends on the percentage of H (hydrophobic) residues in the sequences of compact chains and the energy parameters of εHH, εHP and εPP . Some comparisons of theoretical predictions with experimental results are also made. This investigation may help us to understand the protein folding.     

ADSORPTION OF 2,4-D ON MODIFIED HYPERCROSSLINKED POLYSTYRENE （NDA-99） AND XAD-4 RESIN

The adsorption behavior of pesticide 2,4-dichlorophenoxyacetic acid (2,4-D) in aqueous solution has been investigated using a hypercrosslinked polystyrene adsorbent (NDA-99) modified by dimethylamine group as well as a nonionic macroporous adsorbent (XAD-4). The Langmuir and Freundlich isotherm models were employed to fit the experimental data to describe adsorption mechanism. It shows that NDA-99 resin exhibits an adsorption affinity for 2,4-D higher than XAD-4 resin owing to its exceptional micropore structure and the amine group of the hypercrosslinked matrix.Further studies indicate that the hydrogen bonding interaction and the stronger π-π conjugation play a significant role in the course of the adsorption of 2,4-D on NDA-99 resin, which is in agreement with the IR spectroscopic results and the △E values of HOMO (the highest occupied molecular orbit) of adsorbent and LUMO (the lowest unoccupied molecular orbit) of adsorbate calculated from the MINDO/3 model.     

Practical aspects of the uncertainty and traceability of spectrochemical measurement results by electrothermal atomic absorption spectrometry

The determination of trace elements concentration in water by electrothermal atomic absorption spectrometry (ETAAS) is a common and well established technique in many chemical testing laboratories. However, the evaluation of measurement uncertainty results is not systematically implemented. The paper presents an easy step-by-step example leading to the evaluation of the combined standard uncertainty of copper determination in water using ETAAS. The major contributors to the overall measurement uncertainty are identified due to amount of copper in water sample that mainly depends on the absorbance measurements, due to certified reference material and due to auto-sampler volume measurements. The practical aspects how the traceability of copper concentration in water can be established and demonstrated are also pointed out.     

High speed liquid chromatography with small bore columns

Using a specially designed column system, we have systematically investigated the effect of mobile phase velocity on column efficiency. The performance of small bore columns operated at different linear velocities of mobile phase was examined for three different types of injection system. Using the value of H^∞/u or n^∞/t${}_{\text{r}}^{\text{º}}$ as a criterion of a high speed separation, we calculated values of n/t${}_{\text{r}}^{\text{º}}$ for different solutes according to the equation \documentclass{article}\pagestyle{empty}\begin{document}$ {{\rm n}\mathord{\left/ {\vphantom {{\rm n} {{\rm t}_{\rm r}^ \circ }}}\right. \kern-\nulldelimiterspace} {{\rm t}_{\rm r}^ \circ }} = {{{\rm n}^\infty } \mathord{\left/ {\vphantom {{{\rm n}^\infty } {{\rm t}_{\rm r}^ \circ }}} \right. \kern-\nulldelimiterspace} {{\rm t}_{\rm r}^ \circ }}\left({\frac{{1 + {\rm k'}}}{{{\rm k' + }\beta }}} \right)^2 $\end{document}; the results obtained are in agreement with the experimentally determined values. These systematic investigations culminated in the separation of seven compounds in less than 10 s; the respective chromatogram is shown.     

Some results on regularity in vector optimization

In this paper we suggest an approach to regularity in, vector optimization which extends the one given in [9]; some necessary or sufficient regularity conditions are given for a wide class of nondifferentiable vector optimization problems which embraces the convex ones.