Multiperfect numbers with identical digits

Let g?2. A natural number N is called a repdigit in base g if all of the digits in its base g expansion are equal, i.e., if for some m?1 and some D∈{1,2,…,g−1}. We call N perfect if σ(N)=2N, where σ denotes the usual sum-of-divisors function. More generally, we call N multiperfect if σ(N) is a proper multiple of N. The second author recently showed that for each fixed g?2, there are finitely many repdigit perfect numbers in base g, and that when g=10, the only example is N=6. We prove the same results for repdigit multiperfect numbers.     

Multi-component regio- and diastereoselective cobalt-catalyzed hydrovinylation/allylboration reaction sequence

The combination of a regioselective cobalt-catalyzed 1,4-hydrovinylation and the diastereoselective allylboronation reaction leads to a wide scope of functionalized hydroxydienyl esters in a one-pot reaction in excellent yields. With catalytic amounts of base, these products are easily converted either into α,β,γ,δ-unsaturated hydroxyl esters or complex tetrasubstituted tetrahydropyrans in chemo- and diastereoselective fashions. In addition, a high-yielding four-component one-pot reaction involving an acrylate, two different and unsymmetrical 1,3-dienes, and an unsaturated aldehyde is presented.     

Postprocessing of docked protein-ligand complexes using implicit solvation models

Molecular docking plays an important role in drug discovery as a tool for the structure-based design of small organic ligands for macromolecules. Possible applications of docking are identification of the bioactive conformation of a protein-ligand complex and the ranking of different ligands with respect to their strength of binding to a particular target. We have investigated the effect of implicit water on the postprocessing of binding poses generated by molecular docking using MM-PB/GB-SA (molecular mechanics Poisson-Boltzmann and generalized Born surface area) methodology. The investigation was divided into three parts: geometry optimization, pose selection, and estimation of the relative binding energies of docked protein-ligand complexes. Appropriate geometry optimization afforded more accurate binding poses for 20% of the complexes investigated. The time required for this step was greatly reduced by minimizing the energy of the binding site using GB solvation models rather than minimizing the entire complex using the PB model. By optimizing the geometries of docking poses using the GB(HCT+SA) model then calculating their free energies of binding using the PB implicit solvent model, binding poses similar to those observed in crystal structures were obtained. Rescoring of these poses according to their calculated binding energies resulted in improved correlations with experimental binding data. These correlations could be further improved by applying the postprocessing to several of the most highly ranked poses rather than focusing exclusively on the top-scored pose. The postprocessing protocol was successfully applied to the analysis of a set of Factor Xa inhibitors and a set of glycopeptide ligands for the class II major histocompatibility complex (MHC) A(q) protein. These results indicate that the protocol for the postprocessing of docked protein-ligand complexes developed in this paper may be generally useful for structure-based design in drug discovery.     

CYP2D6 genotyping by liquid chromatography-electrospray ionization mass spectrometry

Genetic polymorphisms can significantly affect the enzyme activity of the drug metabolizing enzyme Cytochrome P450 2D6 (CYP2D6; OMIM 124030). Accordingly, CYP2D6 genotyping is considered as a valid approach to predict the individual CYP2D6 metabolizing status. We introduce ion-pair reversed-phase high-performance liquid chromatography-electrospray ionization mass spectrometry (ICEMS) as method for the characterization of single base variants, small deletions, and insertions in the CYP2D6 gene. A two-step polymerase chain reaction (PCR) was developed for the simultaneous amplification of nine polymorphic regions within the CYP2D6 gene. Cleanup, separation, and denaturation of PCR amplicons were achieved by high-performance liquid chromatography. High-performance molecular mass measurements provided nucleotide composition profiles that principally enable the resolution of 37 reported CYP2D6 alleles. The developed assay was applied to the genotyping of 93 unrelated Austrian individuals. For validation, a selected number of samples and polymorphic sites were retyped by alternative genotyping technologies. The PCR-ICEMS assay turned out to be an accurate, robust, and cost-effective CYP2D6 genotyping strategy.     

Separation of short-chain branched polyolefins by high-temperature gradient adsorption liquid chromatography

A new separation principle was recently introduced into the analytical characterization of polyolefins by researchers from the German Institute for Polymers in Darmstadt. It was demonstrated that polyolefins can be selectively separated via high-performance liquid chromatography on the basis of their adsorption/desorption behaviours at temperatures as high as 160 °C. A Hypercarb? column packed with porous graphite gave the best results. The mobile phase consisted of a mixture of 1-decanol and 1,2,4-trichlorobenzene. In this work, the same chromatographic system is applied to the separation of ethylene/alkene and ethylene/norbornene copolymers. It was found that the elution volumes of the samples correlate linearly with the average chemical composition of samples. The elution volume is indirectly proportional to the concentration of branches in the ethylene/alkene copolymer. Branching shortens the length of continuous methylene sequences of the polymer backbone, thus decreasing the probability of orientation of a methylene sequence in a flat conformation on the graphite surface, which enables the most intensive van der Waals interactions between the methylene backbone and the carbon surface. An opposite trend in the elution order has been found for ethylene/norbornene copolymers. The elution volume of the ethylene/norbornene copolymers increased with the concentration of norbornene. It indicates pronounced attractive interactions between graphite and the cyclic comonomer.     

Thermorheological behavior of polyethylene: a sensitive probe to molecular structure

Recent investigations have shown that different topographies in polyethylene (PE) lead to either thermorheological simplicity (linear and short-chain branched PE) or two different types of thermorheologically complex behavior. Low-density polyethylene (LDPE) has a thermorheological complexity, which can be eliminated by a modulus shift, while long-chain branched metallocene PE (LCB-mPE) has a temperature dependent shape of the spectrum and thus a total failure of the time-temperature superposition principle. The reason for that behavior lies in the different relaxation times of linear and long-chain branched chains, present in LCB-mPE. The origin of the thermorheological complexity of LDPE might be the temperature dependence of the miscibility of the different molar mass fractions that differ in their content of short chain branches.     

Secure collaborative supply chain planning and inverse optimization – The JELS model

It is a well-acknowledged fact that collaboration between different members of a supply chain yields a significant potential to increase overall supply chain performance. Sharing private information has been identified as prerequisite for collaboration and, at the same time, as one of its major obstacles. One potential avenue for overcoming this obstacle is Secure Multi-Party Computation (SMC). SMC is a cryptographic technique that enables the computation of any (well-defined) mathematical function by a number of parties without any party having to disclose its input to another party. In this paper, we show how SMC can be successfully employed to enable joint decision-making and benefit sharing in a simple supply chain setting. We develop secure protocols for implementing the well-known “Joint Economic Lot Size (JELS) Model” with benefit sharing in such a way that none of the parties involved has to disclose any private (cost and capacity) data. Thereupon, we show that although computation of the model’s outputs can be performed securely, the approach still faces practical limitations. These limitations are caused by the potential of “inverse optimization”, i.e., a party can infer another party’s private data from the output of a collaborative planning scheme even if the computation is performed in a secure fashion. We provide a detailed analysis of “inverse optimization” potentials and introduce the notion of “stochastic security”, a novel approach to assess the additional information a party may learn from joint computation and benefit sharing. Based on our definition of “stochastic security” we propose a stochastic benefit sharing rule, develop a secure protocol for this benefit sharing rule, and assess under which conditions stochastic benefit sharing can guarantee secure collaboration.     

Determination of Nicotine in Dried Mushrooms by Using a Modified QuEChERS Approach and GC–MS–MS

Levels of nicotine higher than the maximum residue level were detected in edible mushrooms. Analyses of self-collected and purchased dried mushrooms were performed with a QuEChERS approach. A small amount (2.5 g) of dried sample matrix was mixed with 5 mL sodium hydroxide solution, 2.5 g of sodium sulfate/sodium chloride mixture (4:1) and 5 mL ethyl acetate. The organic phase was cleaned by using dispersive solid-phase extraction and analysed by GC–MS–MS. The linear range of the method was 0.01–10.00 mg kg^?1 and the limit of detection 0.006 mg kg^?1 on dry weight basis by using EURACHEM method.     

Syntheses and crystal structures of the closo-borates M2[B7H7] and M[B7H8] (M = PPh4, PNP, and N(n-Bu4)): the missing crystal structure in the series [B(n)H(n)]2- (n = 6-12)

Oxidation of [N(n-Bu(4))](2)[B(9)H(9)] with oxygen in a mixture of dimethoxyethane and CH(2)Cl(2) leads to salts of the [B(7)H(7)](2-) dianion. This is the first convenient synthesis for a seven-vertex hydro-closo-borate anion. Protonation with NEt(3)·HCl resulted in salts of the [B(7)H(8)](-) monoanion. Both closo-borate anions were isolated and characterized by (1)H, (1)H{(11)B}, (11)B, and (11)B{(1)H} NMR spectroscopy. The temperature-dependent (1)H{(11)B}, (11)B, and (11)B{(1)H} NMR spectra of [B(7)H(8)](-) were also measured. The structure of [B(7)H(7)](2-) as well as of [B(7)H(8)](-) were determined by single-crystal X-ray diffraction.