A Note on Caterpillar-Embeddings with No Two Parallel Edges

Let G be a set of n points in general position (i.e., no three points are on a line) in the plane, and let C be a caterpillar on n vertices. We show that one can always find a rectilinear embedding of C in the plane such that the vertices of C are the points of G and no two edges of C go to parallel segments. This proves a conjecture of Robert E. Jamison.     

Growth of Sb-Bi gradient single crystals

The growth conditions and structural quality of Sb-Bi gradient single crystals with Bi content from 2 to 18 at %, grown by the Czochralski method with solid phase feed, are investigated. Bi distribution in the crystals along their pulling direction are studied by electron probe microanalysis and the change in the interplanar spacing is analyzed by double-crystal X-ray diffraction. It is established that the pulling rate and feed mass affect the Bi distribution in Sb-Bi single crystals.     

At Least n – 1 Intersection Points in a Connected Family of n Unit Circles in the Plane

Let C be a family of n different unit circles in the plane. We show that C determines at least n - c intersection points, where c is the number of connected components in ∪_{C ∈ C}C. This proves a conjecture of A. Bezdek.     

On the effect of montmorillonite in the curing reaction of epoxy nanocomposites

The procedure for the fabrication of epoxy-based polymer layered silicate nanocomposites is important in respect of the nanostructure that is developed. To further our understanding of this, the influence of an organically modified clay (montmorillonite, MMT) on the curing kinetics of an epoxy resin has been studied by differential scanning calorimetry. Clay loadings of 10 and 20 mass% are used, and isothermal as well as dynamic cures have been investigated. For both cure schedules the effect of the MMT is to advance the reaction. Kinetic analysis yields values for the activation energy, but shows that the reaction cannot be described simply by the usual autocatalytic equation. The glass transition of the cured nanocomposites is lower than that for the cured neat resin, a result that is attributed to homopolymerisation taking place in addition to the epoxy–amine reaction.     

First seco-C oleananes from nature

[structure: see text] The triterpenes 8,14-seco-oleana-8(26),13-dien-3beta-ol (1) and its acetyl derivative 2 were isolated from Stevia viscida and Stevia eupatoria, respectively. Their structures were elucidated by 2D NMR, including carbon-carbon connectivity experiments, and confirmed by X-ray diffraction analysis of ketone 3. The absolute configuration was determined by NMR analysis of the Mosher esters of 1. The biogenetic implications of the new substances are discussed.     

New physically adsorbed polymer coating for reproducible separations of basic and acidic proteins by capillary electrophoresis

In this work, a new physically adsorbed coating for capillary electrophoresis (CE) is presented. The coating is based on a N,N-dimethylacrylamide-ethylpyrrolidine methacrylate (DMA-EPyM) copolymer synthesized in our laboratory. The capillary coating is simple and easy to obtain as only requires flushing the capillary with a polymer aqueous solution for 2 min. It is shown that by using these coated capillaries the electrostatic adsorption of a group of basic proteins onto the capillary wall is significantly reduced allowing their analysis by CE. Moreover, the DMA-EPyM coating provides reproducible separations of the basic proteins with RSD values for migration times lower than 0.75% for the same day (n = 5) and lower than 3.90% for three different days (n = 15). Interestingly, the electrical charge of the coated capillary wall can be modulated by varying the pH of the running buffer which makes possible the analysis of basic and acidic proteins in the same capillary. The usefulness of this coating is further demonstrated via the reproducible separation of whey (i.e. acidic) proteins from raw milk. The coating protocol should be compatible with both CE in microchips and CE-MS of different types of proteins.     

Statistical thermodynamics models for polyatomic adsorbates: application to adsorption of n-paraffins in 5A zeolite

Experimental adsorption isotherms of five n-paraffins (ethane, propane, butane, pentane, and hexane) in 5A zeolite were described by means of a statistical thermodynamics model for linear adsorbates (MLA) developed by Ramirez-Pastor et al. (1999) and compared with the well-known multisite Langmuir model (MSL) of Nitta et al. (1984). The experimental data, obtained by different authors in a wide range of temperatures and pressures, were correlated by using an algorithm of multiple fitting. Two main conclusions were drawn from the analysis of experimental data: (i) for small molecules (ethane, propane), MLA is the more accurate model, validating the hypothesis of the linear rigid character of the adsorbate and reinforcing previous results obtained from the analysis of computational experiments developed for dimers and linear trimers; (ii) for large molecules (n-butane, n-pentane, n-hexane), the better performance of the MSL model suggests that the admolecules adsorb in a nonlinear structure. The isosteric heat of adsorption dependence on the number of carbons obtained from our study, ranging between 23.84 kJ/mol for ethane and 59.26 kJ/mol for hexane, showed a very good agreement with previous results reported in the literature, confirming the consistency of our analysis.     

Comparison of the fragility index of different eudragit polymers determined by activation enthalpies

The present study aimed to apply fragility index (m) of polymers in the determination of the optimal amount of plasticizer in polymer films. The fragility index of different Eudragit polymers (RS, RL, EPO) was assessed by differential scanning calorimerty (DSC), applying the Arrhenius connection (logq–1/T _g). The fragility of Eudragit EPO films proved to be the highest, while in the case of RS and RL, the increase of the alkyl-chain length caused the increase of fragility. Studying the effect of plasticizer (triethyl citrate, TEC) on the m value of Eudragit RL and RS films, a near linear reduction of the fragility index could be observed between 5–30% TEC concentration, but above 30%, this value leveled out to constant.