Counting arithmetical structures on paths and cycles

Let $G$ be a finite, connected graph. An arithmetical structure on $G$ is a pair of positive integer vectors $\mathbf{d},\mathbf{r}$ such that $(diag\left(\mathbf{d}\right)?A)\mathbf{r}=0$, where $A$ is the adjacency matrix of $G$. We investigate the combinatorics of arithmetical structures on path and cycle graphs, as well as the associated critical groups (the torsion part of the cokernels of the matrices $(diag\left(\mathbf{d}\right)?A)$). For paths, we prove that arithmetical structures are enumerated by the Catalan numbers, and we obtain refined enumeration results related to ballot sequences. For cycles, we prove that arithmetical structures are enumerated by the binomial coefficients $\left(\genfrac{}{}{0ex}{}{2n?1}{n?1}\right)$, and we obtain refined enumeration results related to multisets. In addition, we determine the critical groups for all arithmetical structures on paths and cycles.     

A complex-analytic approach to the problem of uniform controllability of a transport equation in the vanishing viscosity limit

We revisit a result by Coron and Guerrero stating that the one-dimensional transport-diffusion equation

     

Minimising the number of gap-zeros in binary matrices

We study a problem of minimising the total number of zeros in the gaps between blocks of consecutive ones in the columns of a binary matrix by permuting its rows. The problem is referred to as the Consecutive Ones Matrix Augmentation Problem, and is known to be NP-hard. An analysis of the structure of an optimal solution allows us to focus on a restricted solution space, and to use an implicit representation for searching the space. We develop an exact solution algorithm, which is linear-time in the number of rows if the number of columns is constant, and two constructive heuristics to tackle instances with an arbitrary number of columns. The heuristics use a novel solution representation based upon row sequencing. In our computational study, all heuristic solutions are either optimal or close to an optimum. One of the heuristics is particularly effective, especially for problems with a large number of rows.     

A Multi‐Component Sensor System for Detection of Amphiphilic Compounds

Many biologically important compounds are amphiphilic in character. Glycolipids, for example, represent a biologically important class of amphiphiles. Receptors and sensors for such compounds must also be amphiphilic making them a challenge to prepare. Here, a cucurbit[8]uril (CB[8])‐based sensor system has been prepared and tested for detection of amphiphilic compounds. This multi‐component system consists: a CB[8], which acts as a hydrophobic lipid receptor, a hydrophilic pyridinium‐based carbohydrate receptor, and a fluorescent indicator. The system self‐assembles in aqueous solution. The pyridinium quenches the fluorescence of the indicator giving a strong turn‐on response when it is displaced by the analyte. The sensor system was characterized by NMR, X‐ray crystallography, and fluorescence titrations.     

Asymmetric synthesis of the (S)-1,1-dioxido-isothiazolidin-3-one phosphotyrosine mimetic via reduction of a homochiral (R)-oxido-isothiazolidin-3-one

[structure: see text]. The first asymmetric synthesis of the (S)-1,1-dioxido-isothiazolidin-3-one ((S)-IZD) pTyr mimetic, which has been incorporated into the recently reported potent protein tyrosine phosphatase 1B (PTP1B) inhibitors, is presented herein. The key reaction is the reduction of the (R)-oxido-isothiazolidin-3-one heterocycle with excellent regiochemical and stereochemical control (>98% ee; 82% yield).     

Hydrogen generation from weak acids: electrochemical and computational studies of a diiron hydrogenase mimic

Extended investigation of electrocatalytic generation of dihydrogen using [(mu-1,2-benzenedithiolato)][Fe(CO)3]2 has revealed that weak acids, such as acetic acid, can be used. The catalytic reduction producing dihydrogen occurs at approximately -2 V for several carboxylic acids and phenols resulting in overpotentials of only -0.44 to -0.71 V depending on the weak acid used. This unusual catalytic reduction occurs at a potential at which the starting material, in the absence of a proton source, does not show a reduction peak. The mechanism for this process and structures for the intermediates have been discerned by electrochemical and computational analysis. These studies reveal that the catalyst is the monoanion of the starting material and an ECEC mechanism occurs.     

Analytical method for assessing exposure of greenhouse applicators to procymidone by gas chromatography and whole body dosimetry

Summary An analytical method for the determination of the potential and actual exposure of agricultural workers to procymidone has been developed. The methodology is based on the whole body technique, using Tyvek Pro-Tech and Sontara as sampling media, and uses hexane extraction, GC-ECD analysis and GC-MSD confirmation. The validation of the analytical method has been carried out incorporating the matrix of coverall in all steps when calculating parameters such as retention time window, limits of detection and quantification, linear ranges and precision. A field sampling strategy has also been developed and the method has been applied to the evaluation of the potential and actual dermal exposure of an applicator and an assistant in normal working conditions.     

Theoretical calculations and experimental data on spectral,kinetic and thermodynamic properties of Se∴N and S∴N three-electron-bonded,structurally stabilized σ<Superscript>2</Superscript>σ* radicals

A complementary quantum mechanical and experimental study has been undertaken on the reactivity, formation and properties of Se∴N and S∴N σ²/σ* three-electron-bonded radical species, generated upon one-electron oxidation of selenomethionine, methionine and structurally related compounds. The quantum chemical calculations were based on density functional theory (DFT) hybrid B3LYP and BHandHLYP methods with basis sets ranging from 6-31G(d) to 6-311+G(d,p). Solvent effects, which play an important role concerning structure and energy of ground and excited states, were taken into account as dielectric continuum as well as explicit water molecules. They fully confirm new and previously obtained experimental results concerning the Vis/near-UV absorptions and thermodynamic stability. Special emphasis was put on a comparison between selenium and sulfur. The calculations clearly confirm the higher thermodynamic stability of the Se∴N radical species relative to the S∴N ones, and also corroborate the observed much higher kinetic stability of the former. Concerning optical absorptions, the calculations predict the Se∴N transients to exhibit a blue-shift by about 20 nm relative to the S-based analogues, confirming the few experimental data available so far. The theoretical study includes a comparison of various calculation levels and the influence of the solvent environment, by comparison with vacuum. New experimental data within the scope of this study have been obtained on intramolecularly-formed S∴N radical cation moieties, structurally stabilized by a rigid norbornane backbone. The methionine-related species, with an endo-2-amino, exo-2-carboxyl, and endo-6 methylthio substitution, for example, exhibits almost identical optical and kinetic stability properties as the corresponding species from free methionine. Its optical absorption depends on the protonation state of the carboxyl group, with λ_max at 410 nm for the carboxylate (zwitterionic) form and at 390 nm for the overall cationic form with the protonated carboxyl group. The fast exponential decays with t _1/2 of 490 ns and 2 μs pertain to the decarboxylation of the respective species. A much longer-lived S∴N species with t _1/2 > 500 μs and second order decay kinetics (λ_max 465 nm) was obtained from an endo-2-cyclohexylamino norbornane analogue which does not carry a carboxyl group. The methionine-based S∴N species is not stable anymore in vacuum and in low polarity solvents. This is explained by a decrease in stabilization energy of the 3-e-bond and a faster electron transfer from the carboxylate into the cationic 3-e-center. In conclusion, selenium enhances the thermodynamic and kinetic stability of its radical transients, relative to the sulfur analogues.     

怀菊花中微量铁的测定

为探讨邻二氮菲分光光度法测定怀菊花中微量元素铁含量的可行性,怀菊花的药理功效、食用营养价值与微量元素含量可能存在的关系,根据铁离子与特定显色剂显色产生可见吸收,采用混合酸y（HNO3）：V（HClO4）=4＋1对怀菊花样品湿法消化处理,在pH2～9的溶液中试剂与铁生成稳定的橙色络合物,并用分光光度法测定了怀菊花中微量元素铁含量。结果表明,所选的怀菊花中铁含量303．9～337．9μg／g,加标回收率为90．2％～100．6％。分光光度法操作简便、干扰离子少,测量快速、结果准确度和灵敏度高,易推广和 普及使用。