The reconstruction conjecture and edge ideals

Given a simple graph G on n vertices, we prove that it is possible to reconstruct several algebraic properties of the edge ideal from the deck of G, that is, from the collection of subgraphs obtained by removing a vertex from G. These properties include the Krull dimension, the Hilbert function, and all the graded Betti numbers β_i,j where j<n. We also state many further questions that arise from our study.     

Reconstituted Enzymes on Electropolymerizable FAD‐Modified Metallic Nanoparticles: Functional Units for the Assembly of Effectively “Wired” Enzyme Electrodes

Au nanoparticles are functionalized with thioaniline electropolymerizable units and mercaptophenyl boronic acid ligands. Flavin adenine dinucleotide (FAD) is linked to the boronic acid ligands and apo‐glucose oxidase, apo‐GOx, is reconstituted on the FAD cofactor units to yield enzymes in a structurally‐aligned configuration in respect to the Au NPs. Electropolymerization of the enzyme‐functionalized Au NPs on a thioaniline‐modified Au electrode yields a three‐dimensional bis‐aniline‐crosslinked Au NPs/reconstituted glucose oxidase matrix on the electrode that reveals effective electrical contacting with the electrode.     

Increasing the octane number of gasoline using functionalized carbon nanotubes

The octane number is one of the characteristics of spark-ignition fuels such as gasoline. Octane number of fuels can be improved by addition of oxygenates such as ethanol, MTBE (methyl tert-butyl ether), TBF (tertiary butyl formate) and TBA (tertiary butyl alcohol) as well as their blends with gasoline that reduce the cost impact of fuels. Carbon nanotubes (CNTs) are as useful additives for increasing the octane number. Functionalized carbon nanotubes containing amide groups have a high reactivity and can react with many chemicals. These compounds can be solubilized in gasoline to increase the octane number. In this study, using octadecylamine and dodecylamine, CNTs were amidated and the amino-functionalized carbon nanotubes were added to gasoline. Research octane number analysis showed that these additives increase octane number of the desired samples. X-ray diffraction (XRD), Fourier transforms infrared (FTIR), X-ray photoelectron spectroscopy (XPS), and thermal gravimetry analyses (TGA) were used for characterization of the prepared functionalized carbon nanotubes.     

Synthesis of diketopyrrolopyrrole (DPP) derivatives comprising bithiophene moieties

Herein we disclose an easily applicable method for the synthesis of diketopyrrolopyrrole (DPP) derivatives comprising bithiophene moieties, with different substituents on the nitrogen atoms (Me, n-octyl, 3,5-di-tert-butylbenzyl, Boc) and on the thiophene rings (C₆H₁₃, C₁₂H₂₅), in good yields and purities. A comparison is made between the previously described method from literature and our more efficient approach regarding number of steps, overall yields and ease of synthesis and purification.     

Kohonen classification applying ‘missing variables’ criterion to evaluate the p‐boronophenylalanine human‐body‐concentration decreasing profile of boron neutron capture therapy patients

The irradiation dose in tumor and healthy tissue of a boron neutron capture therapy (BNCT) patient depends on the boron concentration in blood. In most treatments, this concentration is experimentally determined before and after irradiation but not while irradiation is being carried out because it is troublesome to take the blood samples when the patient remains isolated in the irradiation room. A few models are used to predict the boron profile during that period, which until now involves a biexponential decay. For the prediction of decay concentration profiles of the p‐boronophenylalanine (BPA) in the human body during BNCT treatment, a Kohonen‐based neural network method is suggested. The results of various (20 × 20 × 40 Kohonen network) models based on different trainings on the data set of 67 concentration sets (profiles) are described and discussed. The prediction ability and robustness of the modeling method were tested by the leave‐one‐out procedure. The results show that the method is very robust and mostly independent of small variations. It can yield predictions, root mean squared prediction error (RMSPE), with a maximum of 3.30 µg g⁻¹ for the present cases. In order to show the abilities and limitations of the method, the best and the few worst results are discussed in detail. It should be emphasized that one of the main advantages of this method is the automatic improvement in the prediction ability and robustness of the model by feeding it with an increasing number of data. Copyright © 2011 John Wiley & Sons, Ltd.     

Photoreactive polymer brushes for high-density patterned surface derivatization using a Diels-Alder photoclick reaction

Reactive polymer brushes grown on silicon oxide surfaces were derivatized with photoreactive 3-(hydroxymethyl)naphthalene-2-ol (NQMP) moieties. Upon 300 or 350 nm irradiation, NQMP efficiently produces o-naphthoquinone methide (oNQM), which in turn undergoes very rapid Diels-Alder addition to vinyl ether groups attached to a substrate, resulting in the covalent immobilization of the latter. Any unreacted oNQM groups rapidly add water to regenerate NQMP. High-resolution surface patterning is achieved by irradiating NQMP-derivatized surfaces using photolithographic methods. The Diels-Alder photoclick reaction is orthogonal to azide-alkyne click chemistry, enabling sequential photoclick/azide-click derivatizations to generate complex surface functionalities.     

β-Nitro derivatives of iron corrolates

Two different methods for the regioselective nitration of different meso-triarylcorroles leading to the corresponding β-substituted nitrocorrole iron complexes have been developed. A two-step procedure affords three Fe(III) nitrosyl products-the unsubstituted corrole, the 3-nitrocorrole, and the 3,17-dinitrocorrole. In contrast, a one-pot synthetic approach drives the reaction almost exclusively to formation of the iron nitrosyl 3,17-dinitrocorrole. Electron-releasing substituents on the meso-aryl groups of the triarylcorroles induce higher yields and longer reaction times than what is observed for the synthesis of similar triarylcorroles with electron-withdrawing functionalities, and these results can be confidently attributed to the facile formation and stabilization of an intermediate iron corrole π-cation radical. Electron-withdrawing substituents on the meso-aryl groups of triarylcorrole also seem to labilize the axial nitrosyl group which, in the case of the pentafluorophenylcorrole derivative, results in the direct formation of a disubstituted iron μ-oxo dimer complex. The influence of meso-aryl substituents on the progress and products of the nitration reaction was investigated. In addition, to elucidate the most important factors which influence the redox reactivity of these different iron nitrosyl complexes, selected compounds were examined by cyclic voltammetry and thin-layer UV-visible or FTIR spectroelectrochemistry in CH(2)Cl(2).     

Stereochemical inversion of phosphonothioate methanolysis by La(III) and Zn(II): mechanistic implications for the degradation of organophosphate neurotoxins

The utility of phosphonothioate methanolysis to degrade organophosphate neurotoxins has prompted the stereochemical investigation of this useful transformation. The methanolysis of enantiomerically pure O,S-diethyl phenylphosphonothioate (5) was studied both in the presence and in the absence of metal ions known to catalyze the phosphonothioate → phosphonate transformation. This report outlines the syntheses of enantiomerically pure 5 and its methanolysis product O-ethyl O-methyl phenylphosphonate (7). Compound 7 results from exclusive P-S scission of 5, which is the desired mode of phosphonothioate methanolysis (E(a) = 14.5 ± 0.5 kcal/mol). The stereochemical analysis of the phosphonothioate methanolysis was done for the first time with β-cyclodextrin, and it shows complete inversion on the phosphorus center upon methoxide displacement of ethanethiolate. The presence of La(III) or Zn(II) complexes do not alter this S(N)2-like substitution which sheds new light on the mechanism of methanolysis of phosphonothioates.     

Click-chemistry for surface modification of monodisperse-macroporous particles

In this study, click chemistry was proposed as a tool for tuning the surface hydrophilicity of monodisperse-macroporous particles in micron-size range. The monodisperse-porous particles carrying hydrophobic or hydrophilic molecular brushes on their surfaces were obtained by the proposed modification. Hydrophilic poly(glycidyl methacrylate-co-ethylene dimethacrylate), poly(GMA-co-EDM) particles were hydrophobized by the covalent attachment of poly(octadecyl acrylate-co-propargyl acrylate), poly(ODA-co-PA) copolymer onto the particle surface via triazole formation by click chemistry. In the second part, Hydrophobic poly(4-chloromethylstyrene-co-divinylbenzene), poly(CMS-co-DVB) particles were hydrophilized by the covalent attachment of poly(vinyl alcohol), PVA onto their surface also via triazole formation by click chemistry. The presence of PVA and poly(ODA-co-PA) copolymer on the corresponding particles was shown by FTIR-DRS. After click-coupling reactions applied for both hydrophobic poly(CMS-co-DVB) and hydrophilic poly(GMA-co-EDM) particles, the marked changes in surface polarity were shown by contact angle measurements. Protein adsorption characteristics of plain and modified particles were investigated for both materials. In the isoelectric point of albumin, the non-specific albumin adsorption decreased from 225 to 80 mg/g by grafting PVA onto the poly(CMS-co-DVB) beads. On the other hand, the non-specific albumin adsorption onto the plain poly(GMA-co-EDM) beads increased from 50 to 400 mg/g by the covalent attachment of poly(ODA-co-PA) copolymer onto the bead-surface via click chemistry. The protein adsorption behavior was efficiently regulated by the covalent attachment of appropriate molecular brushes onto the surfaces of selected particles. The results indicated that "click chemistry" was an efficient tool for controlling the polarity of monodisperse-macroporous particles.