Graphs with at most one crossing

The crossing number of a graph $G$ is the least number of crossings over all possible drawings of $G$. We present a structural characterization of graphs with crossing number one.     

Preparation of Benzylidene Barbituric Acids Promoted by Infrared Irradiation in Absence of Solvent

Several benzaldehydes were condensed with barbituric acid under infrared irradiation, in absence of solvent, affording the corresponding 5-benzylidene barbituric acids.     

Excess Molar Volumes of Binary Mixtures of 1-Heptanol or 1-Nonanol with n-Polyethers at 25°C

Excess molar volumes V ^E _m at 25°C and atmospheric pressure over the entirecomposition range for binary mixtures of 1-heptanol with 2,5-dioxahexane, 2,5,8-trioxanonane,5,8,11-trioxapentadecane, 2,5,8,11-tetraoxadodecane,or 2,5,8,11,14-pentaoxapentadecane, and mixtures of 1-nonanol with 2,5-dioxahexane,3,6-dioxaoctane, 2,5,8-trioxanonane, 3,6,9-trioxaundecane, 5,8,11-trioxapentadecane,2,5,8,11-tetraoxadodecane, or 2,5,8,11,14-pentaoxapentadecane are reportedfrom densities measured with a vibrating-tube densimeter.V ^E _m curves are nearlysymmetrical at about 0.5 mole fraction. Excess molar volumes are usually positive,indicating predominance of positive contributions to V ^E _m from the disruption ofH bonds of alcohols and from physical interactions. When chain lengths ofboth components of the mixture are increased, the contribution from interstitialaccommodation appears to be sufficiently negative, such that V ^E _m becomes negative(e.g., l-nonanol + 5,8,11-tetraoxapentadecane).     

Event detection, multimodality and non-stationarity: Ordinal patterns, a tool to rule them all?

In this work, we apply ordinal analysis of time series to the characterisation of neuronal activity. Automatic event detection is performed by means of the so-called permutation entropy, along with the quantification of the relative cardinality of forbidden patterns. In addition, multivariate time series are characterised using the joint permutation entropy. In order to illustrate the suitability of the ordinal analysis for characterising neurophysiological data, we have compared the measures based on ordinal patterns of time series to the tools typically used in the context of neurophysiology.     

Micellar electrokinetic capillary chromatography as an alternative method for the determination of dexamethasone, trimethoprim, and polymyxin B

A micellar electrokinetic capillary chromatographic method is presented which enables quantification of dexamethasone, polymyxin B and trimethoprim in synthetic mixtures and pharmaceutical products. Separation was carried out at 25?°C and 30 kV, with 10 mmol L^–1 borate–phosphate buffer adjusted to pH 8 as electrolyte, with 50 mmol L^–1 sodium dodecyl sulfate. Under these conditions separations were performed in 10 min. The limits of detection and quantification were approximately 2 mg L^–1 for each component, except for polymyxin B. The method was applied to different commercial formulations.     

Rhenium-mediated coupling of acetonitrile and pyrazoles. New molecular clefts for anion binding

The reaction of fac-[ReBr(CO)3(NCMe)2] (1) with either pyrazole (Hpz) or 3,5-dimethylpyrazole (Hdmpz) in a 1:2 Re/pyrazole ratio affords the known complexes fac-[ReBr(CO)3(Hpz)2] (2) and [ReBr(CO)3(Hdmpz)2] (3). Using a 1:1 ratio, MeCN as solvent, and longer reaction times led to a mixture in which the major components are the pyrazolylamidino complexes fac-[ReBr(CO)3(HN=C(CH3)pz-kappa2N,N)] (4) and fac-[ReBr(CO)3(HN=C(CH3)dmpz-kappa2N,N)] (5). The complexes fac-[ReBr(CO)3(Hpz)(NCMe)] (6) and fac-[ReBr(CO)3(Hdmpz)(NCMe)] (7) (along with 2 and 3) were found to be minor components of these reactions. Analogous reactions of fac-[Re(OClO3)(CO)3(NCMe)2] yielded fac-[Re(NCCH3)(CO)3(HN=C(CH3)pz-kappa2N,N)]ClO4 (8), fac-[Re(NCCH3)(CO)3(HN=C(CH3)dmpz-kappa2N,N)]ClO4 (9), fac-[Re(Hpz)(CO)3(HN=C(CH3)pz-kappa2N,N)]ClO4 (10), and fac-[Re(Hdmpz)(CO)3(HN=C(CH3)dmpz-kappa2N,N)]ClO4 (11). The X-ray structure of 11 showed the perchlorate anion to be hydrogen-bonded by the N-H groups of the pyrazole and pyrazolylamidino ligands. The behavior of the compound fac-[Re(Hdmpz)(CO)3(HN=C(CH3)dmpz-kappa2N,N)]BAr'4 (13) (synthesized by reaction of [ReBr(CO)3(Hdmpz)2] (3) with (i) AgOTf and (ii) NaBAr'(4)/MeCN) as an anion receptor has been studied in CD3CN solution. In addition, the structure of the supramolecular adduct fac-[Re(CO)3(Hdmpz)(HN=C(CH3)dmpz-kappa2N,N)].Cl (14), featuring chloride binding by the two N-H groups, was determined by X-ray diffraction.     

Numerical and analytical studies of the electrical conductivity of a concentrated colloidal suspension

In the past few years, different models and analytical approximations have been developed facing the problem of the electrical conductivity of a concentrated colloidal suspension, according to the cell-model concept. Most of them make use of the Kuwabara cell model to account for hydrodynamic particle-particle interactions, but they differ in the choice of electrostatic boundary conditions at the outer surface of the cell. Most analytical and numerical studies have been developed using two different sets of boundary conditions of the Neumann or Dirichlet type for the electrical potential, ionic concentrations or electrochemical potentials at that outer surface. In this contribution, we study and compare numerical conductivity predictions with results obtained using different analytical formulas valid for arbitrary zeta potentials and thin double layers for each of the two common sets of boundary conditions referred to above. The conductivity will be analyzed as a function of particle volume fraction, phi, zeta potential, zeta, and electrokinetic radius, kappaa (kappa(-1) is the double layer thickness, and a is the radius of the particle). A comparison with some experimental conductivity results in the literature is also given. We demonstrate in this work that the two analytical conductivity formulas, which are mainly based on Neumann- and Dirichlet-type boundary conditions for the electrochemical potential, predict values of the conductivity very close to their corresponding numerical results for the same boundary conditions, whatever the suspension or solution parameters, under the assumption of thin double layers where these approximations are valid. Furthermore, both analytical conductivity equations fulfill the Maxwell limit for uncharged nonconductive spheres, which coincides with the limit kappaa --> infinity. However, some experimental data will show that the Neumann, either numerical or analytical, approach is unable to make predictions in agreement with experiments, unlike the Dirichlet approach which correctly predicts the experimental conductivity results. In consequence, a deeper study has been performed with numerical and analytical predictions based on Dirichlet-type boundary conditions.     

Structure assignment, total synthesis, and antiviral evaluation of cycloviracin B1

The first total synthesis of the antivirally active glycolipid cycloviracin B(1) (1) is described. The approach is based on a two-directional synthesis strategy which constructs the C(2)()-symmetrical macrodiolide core of the target by an efficient template-directed macrodilactonization reaction promoted by 2-chloro-1,3-dimethylimidazolinium chloride 14 as the activating agent. Attachment of the lateral fatty acid chains to the lactide core thus formed features not only one of the most advanced ligand-controlled addition reactions of a functionalized dialkyl zinc reagent to a polyfunctional aldehyde, but also a highly demanding Julia-Kocienski olefination of a tetrazolyl sulfone bearing electrophilic and base-labile beta-hydroxy ester motifs. By virtue of the flexibility of this synthesis plan, it was possible to prepare a series of macrodiolide cores differing only in the absolute stereochemistry at the branching points as well as a host of model compounds for the fatty acid appendices of cycloviracin. Comparison of these derivatives with the natural product allowed us to establish the as yet unknown absolute stereochemistry of 6 chiral centers of 1 as (3R,19S,25R,3'R,17'S,23'R). Thereby, the (13)C NMR shifts of the anomeric position of the beta-glycosides residing at those positions turned out to be excellent probes for the absolute configuration of the attached aglycones. The concise set of data thus obtained also makes clear that the proposed structure of the fattiviracins, a seemingly closely related family of glycoconjugates, is not matched by the published data. Finally, the biological activity of synthetic 1 and some of the key intermediates obtained en route to this natural product was investigated, showing that the entire construct is necessary for appreciable and selective antiviral activity.