On Edge Exchangeable Random Graphs

We study a recent model for edge exchangeable random graphs introduced by Crane and Dempsey; in particular we study asymptotic properties of the random simple graph obtained by merging multiple edges. We study a number of examples, and show that the model can produce dense, sparse and extremely sparse random graphs. One example yields a power-law degree distribution. We give some examples where the random graph is dense and converges a.s. in the sense of graph limit theory, but also an example where a.s. every graph limit is the limit of some subsequence. Another example is sparse and yields convergence to a non-integrable generalized graphon defined on \((0,\infty )\).     

Molecular-field splitting in S2p photoelectron spectra of dimethyl sulfide and sulfur dichloride

High-resolution S2p photoelectron spectra have been measured for sulfur dichloride and dimethyl sulfide. By means of efficient fitting procedures and theoretical analyses, the vibrational fine structure has been disentangled from the molecular-field induced splitting of the S2p_3/2 core-ionized level. The resulting molecular-field splitting is determined to be 177 meV in the case of SCl₂ and 104 meV for (CH₃)₂S. Ab initio calculations that include core–valence electron correlation are able to reproduce these values to within 3 meV. Theoretical predictions of the molecular-field splitting are presented for a series of related sulfur compounds, SX₂, where X=H, NH₂, CN, and F.     

Orthogonal signal correction, wavelet analysis, and multivariate calibration of complicated process fluorescence data

In this paper, multivariate calibration of complicated process fluorescence data is presented. Two data sets related to the production of white sugar are investigated. The first data set comprises 106 observations and 571 spectral variables, and the second data set 268 observations and 3997 spectral variables. In both applications, a single response, ash content, is modelled and predicted as a function of the spectral variables. Both data sets contain certain features making multivariate calibration efforts non-trivial. The objective is to show how principal component analysis (PCA) and partial least squares (PLS) regression can be used to overview the data sets and to establish predictively sound regression models. It is shown how a recently developed technique for signal filtering, orthogonal signal correction (OSC), can be applied in multivariate calibration to enhance predictive power. In addition, signal compression is tested on the larger data set using wavelet analysis. It is demonstrated that a compression down to 4% of the original matrix size — in the variable direction — is possible without loss of predictive power. It is concluded that the combination of OSC for pre-processing and wavelet analysis for compression of spectral data is promising for future use.     

Reverse juggling processes

Knutson introduced two families of reverse juggling Markov chains (single and multispecies) motivated by the study of random semi‐infinite matrices over . We present natural generalizations of both chains by placing generic weights that still lead to simple combinatorial expressions for the stationary distribution. For permutations, this is a seemingly new multivariate generalization of the inversion polynomial.     

Solution behaviour of a formate capped surfactant—the oxidation product of an alcohol ethoxylate

The solution behaviour has been investigated for an alcohol ethoxylate terminated with a formic acid ester. This compound has previously been reported to be an important degradation product in the auto-oxidation of alcohol ethoxylates. In this work we have investigated the solution behaviour of the formic acid ester surfactant C₁₂H₂₅(OCH₂CH₂)₄OCHO (C12E4---OCHO). The pure formate was found to be sparsely soluble in water with no clear point at 0.1%. The critical micelle concentration was found to be 129 μM at 35°C, compared to 50 μM for the parent surfactant C₁₂H₂₅(OCH₂CH₂)₅OH (C12E5). To mimic the behaviour of the oxidised surfactant, the formate was mixed in different ratios with C12E5 and the cloud point, surface tension and critical micelle concentration (cmc) of these mixtures were studied. The gradual increase of formate was found to shift the cloud point and isotropic regions to lower temperatures. The cmc of the mixture was found to be lower than for the pure surfactant. The favourable interaction was analysed according to the non-ideal model by Rubingh and the interaction parameter, β, was determined to be −4±0.53, which is unusually large for a mixture of two non-ionic surfactants. These results indicate that the reduction of cloud point observed during oxidation of non-ionic surfactants can in part be attributed to the formation of formate esters.     

Phase separation and crystallinity in proton conducting membranes of styrene grafted and sulfonated poly(vinylidene fluoride)

A series of proton exchange membranes have been prepared by the preirradiation grafting method. Styrene was grafted onto a matrix of poly(vinylidene fluoride) (PVDF) after electron beam irradiation. Part of the samples was crosslinked with divinylbenzene (DVB) or bis(vinylphenyl)ethane (BVPE). Subsequent sulfonation gave membranes grafted with poly(styrene sulfonic acid) and marked PVDF‐g‐PSSA. It was found that the intrinsic crystallinity of the matrix decreased in both the grafting and the sulfonation reaction in all the membranes. The graft penetration and the ion conductivity are influenced strongly by the crosslinker. The ion conductivity is considerably lower in crosslinked membranes than in noncrosslinked ones. Generally, the mechanical strength decreases with crosslinking. The membranes show a regular phase separated structure in which the sulfonated grafts are incorporated in the amorphous parts of the matrix polymer. The phase separated domains are small, of the order of magnitude of 100–250 nm. These were resolved on transmission electron micrographs and on atomic force images but could not be resolved with microprobe Raman spectroscopy. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 1741–1753, 1999     

Laboratory soft-x-ray microscope for cryotomography of biological specimens

Soft-x-ray cryotomography allows quantitative and high-resolution three-dimensional imaging of intact unstained cells. To date, the method relies on synchrotron-radiation sources, which limits accessibility for researchers. Here we present a laboratory water-window microscope for cryotomography. It is based on a λ=2.48 nm liquid-jet laser-plasma source, a normal-incidence multilayer condenser, a 30 nm zone-plate objective, and a cryotilt sample holder. We demonstrate high-resolution imaging, as well as quantitative tomographic imaging, of frozen intact cells. The reconstructed tomogram of the intracellular local absorption coefficient shows details down to ～100 nm.     

Intercalation of Coordinatively Unsaturated FeIII Ion within Interpenetrated Metal–Organic Framework MOF‐5

Coordinatively unsaturated Fe^III metal sites were successfully incorporated into the iconic MOF‐5 framework. This new structure, Fe^III‐iMOF‐5, is the first example of an interpenetrated MOF linked through intercalated metal ions. Structural characterization was performed with single‐crystal and powder XRD, followed by extensive analysis by spectroscopic methods and solid‐state NMR, which reveals the paramagnetic ion through its interaction with the framework. EPR and Mössbauer spectroscopy confirmed that the intercalated ions were indeed Fe^III, whereas DFT calculations were employed to ascertain the unique pentacoordinate architecture around the Fe^III ion. Interestingly, this is also the first crystallographic evidence of pentacoordinate Zn^II within the MOF‐5 SBU. This new MOF structure displays the potential for metal‐site addition as a framework connector, thus creating further opportunity for the innovative development of new MOF materials.