Construction of Antimagic Labeling for the Cartesian Product of Regular Graphs

An antimagic labeling of a graph with p vertices and q edges is a bijection from the set of edges to the set of integers {1, 2, . . . , q} such that all vertex weights are pairwise distinct, where a vertex weight is the sum of labels of all edges incident with the vertex. A graph is antimagic if it has an antimagic labeling. In 1990, Hartsfield and Ringel conjectured that that every connected graph, except K ₂, is antimagic. Recently, using completely separating systems, Phanalasy et al. showed that for each k 3 2, q 3 \binomk+12{k\geq 2,\,q\geq\binom{k+1}{2}} with k|2q, there exists an antimagic k-regular graph with q edges and p = 2q/k vertices. In this paper we prove constructively that certain families of Cartesian products of regular graphs are antimagic.     

Nucleophilic aryl fluorination and aryl halide exchange mediated by a Cu(I)/Cu(III) catalytic cycle

Copper-catalyzed halide exchange reactions under very mild reaction conditions are described for the first time using a family of model aryl halide substrates. All combinations of halide exchange (I, Br, Cl, F) are observed using catalytic amounts of Cu(I). Strikingly, quantitative fluorination of aryl-X substrates is also achieved catalytically at room temperature, using common F(-) sources, via the intermediacy of aryl-Cu(III)-X species. Experimental and computational data support a redox Cu(I)/Cu(III) catalytic cycle involving aryl-X oxidative addition at the Cu(I) center, followed by halide exchange and reductive elimination steps. Additionally, defluorination of the aryl-F model system can be also achieved with Cu(I) at room temperature operating under a Cu(I)/Cu(III) redox pair.     

Selective Ortho‐Hydroxylation–Defluorination of 2‐Fluorophenolates with a Bis(μ‐oxo)dicopper(III) Species

The bis(μ‐oxo)dicopper(III) species [Cu^III₂(μ‐O)₂(m‐XYL^MeAN)]²⁺ ( 1 ) promotes the electrophilic ortho‐hydroxylation–defluorination of 2‐fluorophenolates to give the corresponding catechols, a reaction that is not accomplishable with a (η²:η²‐O₂)dicopper(II) complex. Isotopic labeling studies show that the incoming oxygen atom originates from the bis(μ‐oxo) unit. Ortho‐hydroxylation–defluorination occurs selectively in intramolecular competition with other ortho‐substituents such as chlorine or bromine.     

Poly(ethylene glycol)‐based amphiphilic model conetworks: Synthesis by RAFT polymerization and characterization

Poly(ethylene glycol) (PEG)‐containing quasi‐model amphiphilic polymer conetworks (APCNs) were prepared by reversible addition fragmentation chain transfer (RAFT) polymerization using α,ω‐bis(2‐cyanoprop‐2‐yl dithiobenzoate)‐PEG as a bifunctional RAFT macrochain transfer agent (macro‐CTA) and stepwise additions of a hydrophobic monomer and a crosslinker (crosslinker: macro‐CTA = 10:1, reaction time 24 h). Three different types of monomers, methyl methacrylate (MMA), n‐butyl acrylate and styrene, were employed as the hydrophobic monomers, whereas ethylene glycol dimethacrylate, ethylene glycol diacrylate and 1,4‐divinylbenzene served as the respective crosslinkers. PEG homopolymer hydrophilic quasi‐model networks were also prepared by RAFT‐polymerizing the three crosslinkers directly onto the two active ends of the PEG‐based macro‐CTA. From the three ABA triblock copolymers prepared, the MMA‐containing one was obtained at the highest polymerization yields. The crosslinking yields of the three ABA triblock copolymers with the corresponding crosslinkers were higher than those of the PEG‐based macro‐CTA with the same crosslinkers. The degrees of swelling (DSs) of all conetworks were measured in water and in tetrahydrofuran (THF). The DSs of the APCNs in THF were higher than those in water, whereas the reverse was true for the DSs of the hydrophilic homopolymer networks. Finally, the aqueous DSs of the APCNs were lower than those of the corresponding hydrophilic homopolymer networks. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 7556–7565, 2008     

Bit-parallel -matching and suffix automata

(δ,γ)-matching is a string matching problem with applications to music retrieval. The goal is, given a pattern P_1…m and a text T_1…n on an alphabet of integers, find the occurrences P^′ of the pattern in the text such that (i) , and (ii) . The problem makes sense for δγδm. Several techniques for (δ,γ)-matching have been proposed, based on bit-parallelism or on skipping characters. We first present an O(mnlog(γ)/w) worst-case time and O(n) average-case time bit-parallel algorithm (being w the number of bits in the computer word). It improves the previous O(mnlog(δm)/w) worst-case time algorithm of the same type. Second, we combine our bit-parallel algorithm with suffix automata to obtain the first algorithm that skips characters using both δ and γ. This algorithm examines less characters than any previous approach, as the others do just δ-matching and check the γ-condition on the candidates. We implemented our algorithms and drew experimental results on real music, showing that our algorithms are superior to current alternatives with high values of δ.     

Synthesis of caffeic acid and p-hydroxybenzoic acid molecularly imprinted polymers and their application for the selective extraction of polyphenols from olive mill waste waters

Using caffeic acid and p-hydroxybenzoic acid as templates, two molecularly imprinted polymers (MIPs) were prepared that were used for isolation of polyphenols from olive mill waste water samples (OMWWs) without previous pre-treatment. For the preparation of the caffeic acid MIPs 4-vinylpyridine, allylurea, allylaniline and methacrylic acid were tested as functional monomers, ethylene glycol dimethylacrylate (EDMA), pentaerythritol trimethylacrylate (PETRA) and divinylbenzene 80 (DVB80) as cross-linkers and tetrahydrofuran as porogen. For p-hydroxybenzoic acid 4-vinylpyridine, allylurea and allylaniline were tested as functional monomers, EDMA and PETRA as cross-linkers and acetonitrile as porogen. The performance of the synthesized polymers was evaluated against seven structurally related compounds by means of polymer-based HPLC. The two polymers that presented the most interesting properties were further evaluated by batch rebinding and from the derived isotherms their capacity and binding strength were determined. Using solid-phase extraction (SPE), their ability to recognize and bind the template molecule from an aqueous solution as well as the pH dependence of the binding strength were explored. After establishing the best SPE protocol, an aqueous model mixture of compounds and a raw OMWWs sample were loaded on the two best polymers. The result of the consecutive use of the two polymers on the same sample was explored. It was concluded that acidic conditions favour the recognition abilities of both polymers and that they can be used for a quick and efficient isolation of the polyphenol fraction directly from raw OMWW.     

A small molecular size system giving unexpected surface effects: alpha-Cyclodextrin + sodium dodecyl sulfate in water

Maximum drop volumes (MDV) and the resultant surface tension values (sigma) of alpha-cyclodextrin (alpha-CD) + sodium dodecyl sulfate (SDS) aqueous mixtures have been determined over a broad concentration range of both solutes at 283.15, 293.15, 303.15, 313.15, and 323.15 K. Drops significantly larger than those of pure water (up to approximately 25% larger) were observed at low temperatures for solutions with [alpha-CD]/[SDS] concentration ratios, approximately > 2, producing unexpectedly high surface tension values. Our results indicate that at certain solute concentration ratios and temperatures, the drop volume method provides wrong values for equilibrium surface tensions. This is due to the high viscoelasticity of the surface film whose effect is important even though the injection rate of the drops was slow and the solutes molecular sizes are small.     

Readily Accessible Bulky Iron Catalysts exhibiting Site Selectivity in the Oxidation of Steroidal Substrates

Bulky iron complexes are described that catalyze the site‐selective oxidation of alkyl C?H bonds with hydrogen peroxide under mild conditions. Steric bulk at the iron center is introduced by appending trialkylsilyl groups at the meta‐position of the pyridines in tetradentate aminopyridine ligands, and this effect translates into high product yields, an enhanced preferential oxidation of secondary over tertiary C?H bonds, and the ability to perform site‐selective oxidation of methylenic sites in terpenoid and steroidal substrates. Unprecedented site selective oxidation at C6 and C12 methylenic sites in steroidal substrates is shown to be governed by the chirality of the catalysts.     

Electrophoretic, size-exclusion high-performance liquid chromatography and liquid chromatography-electrospray ionization ion trap mass spectrometric detection of hemoglobin-based oxygen carriers

Hemoglobin-based oxygen carriers (HBOCs) are blood substitutes based on hemoglobin of either bovine or human origin and they can potentially be misused in elite sports to improve endurance performance. Recently, three methods have been proposed in doping control analysis to allow HBOCs screening and identification by application of electrophoresis, size-exclusion chromatography coupled with HPLC and LC coupled with tandem mass spectrometry (LC/MSMS). In view of the Athens 2004 Olympic Games, modifications were introduced in order to increase the specificity of these methods. The sample preparation protocols of the electrophoretic and SEC-HPLC methods were modified with the introduction of sequential ultra filtration steps to remove all heme containing material below 100 kDa, thus leaving only HBOCs material for analysis. Furthermore, a modification of the LC/MSMS methodology was introduced to allow full scan MS-MS spectra of peptide segments arising from the tryptic digestion of bovine HBOCs. These relatively simple methodological modifications have major impact, as far as time and cost effectiveness is concerned in doping control procedures, because they provide a useful tool in order to identify which suspect samples from the initial visual screening are due to hemolysis and exclude them from further analysis.     

Structural and kinetic study of reversible CO2 fixation by dicopper macrocyclic complexes. From intramolecular binding to self-assembly of molecular boxes

A study of the reversible CO2 fixation by a series of macrocyclic dicopper complexes is described. The dicopper macrocyclic complexes [Cu2(OH)2(Me2p)](CF3SO3)2, 1(CF3SO3)2, and [Cu2(mu-OH)2(Me2m)](CF3SO3)2, 2(CF3SO3)2, (Scheme 1) containing terminally bound and bridging hydroxide ligands, respectively, promote reversible inter- and intramolecular CO2 fixation that results in the formation of the carbonate complexes [{Cu2(Me2p)}2(mu-CO3)2](CF3SO3)4, 4(CF3SO3)4, and [Cu2(mu-CO3)(Me2m)](CF3SO3)2, 5(CF3SO3)2. Under a N2 atmosphere the complexes evolve CO2 and revert to the starting hydroxo complexes 1(CF3SO3)2 and 2(CF3SO3)2, a reaction the rate of which linearly depends on [H2O]. In the presence of water, attempts to crystallize 5(CF3SO3)2 afford [{Cu2(Me2m)(H2O)}2(mu-CO3)2](CF3SO3)4, 6(CF3SO3)4, which appears to rapidly convert to 5(CF3SO3)2 in acetonitrile solution. [Cu2(OH)2(H3m)]2+, 7, which contains a larger macrocyclic ligand, irreversibly reacts with atmospheric CO2 to generate cagelike [{Cu2(H3m)}2(mu-CO3)2](ClO4)4, 8(ClO4)4. However, addition of 1 equiv of HClO4 per Cu generates [Cu2(H3m)(CH3CN)4]4+ (3), and subsequent addition of Et3N under air reassembles 8. The carbonate complexes 4(CF3SO3)4, 5(CF3SO3)2, 6(CF3SO3)4, and 8(ClO4)4 have been characterized in the solid state by X-ray crystallography. This analysis reveals that 4(CF3SO3)4, 6(CF3SO3)4, and 8(ClO4)4 consist of self-assembled molecular boxes containing two macrocyclic dicopper complexes, bridged by CO32- ligands. The bridging mode of the carbonate ligand is anti-anti-mu-eta1:eta1 in 4(CF3SO3)4, anti-anti-mu-eta2:eta1 in 6(CF3SO3)4 and anti-anti-mu-eta2:eta2 in 5(CF3SO3)2 and 8(ClO4)4. Magnetic susceptibility measurements on 4(CF3SO3)4, 6(CF3SO3)4, and 8(ClO4)4 indicate that the carbonate ligands mediate antiferromagnetic coupling between each pair of bridged CuII ions (J = -23.1, -108.3, and -163.4 cm-1, respectively, H = -JS1S2). Detailed kinetic analyses of the reaction between carbon dioxide and the macrocyclic complexes 1(CF3SO3)2 and 2(CF3SO3)2 suggest that it is actually hydrogen carbonate formed in aqueous solution on dissolving CO2 that is responsible for the observed formation of the different carbonate complexes controlled by the binding mode of the hydroxy ligands. This study shows that CO2 fixation can be used as an on/off switch for the reversible self-assembly of supramolecular structures based on macrocyclic dicopper complexes.