Gap-Free Set Partitions

A set partition is called “gap-free” if its block sizes form an interval. In other words, there is at least one block of each size between the smallest and largest block sizes. Let B(n) and G(n), respectively, denote the number of partitions and the number of gap-free partitions of the set [n]. We prove that      

Quantitative analysis of oxytetracycline and its 4-epimer in calf tissues by high-performance liquid chromatography combined with positive electrospray ionization mass spectrometry

Tetracycline antibiotics are commonly used in veterinary medicine because of their broad spectrum activity and cost effectiveness. Oxytetracycline (OTC) is one of the most important members of this antibiotic family. The purpose of this study was to develop and validate a method to determine OTC residues in edible tissues of calf. Extraction of OTC and its 4-epimer (4-epiOTC), in the presence of the internal standard demethylchlortetracycline (DMCTC), was performed using a liquid extraction with sodium succinate solution (pH 4.0), followed by protein removal with trichloroacetic acid and paper filtration. Further solid-phase extraction clean-up on an HLB polymeric reversed phase column was performed to obtain an extract suitable for LC-MS-MS analysis. Chromatographic separation of the internal standard, and especially OTC and its 4-epimer, was achieved on a PLRP-S polymeric reversed phase column, using a mixture of 0.001 M of oxalic acid, 0.5% (v/v) of formic acid and 3% (v/v) of tetrahydrofuran in water (mobile phase A) and tetrahydrofuran (mobile phase B) as the mobile phase, and at a column temperature of 60 degrees C. OTC and its 4-epimer could be identified using the MS-MS detection technique, and were subsequently quantified. The method has been validated according to the requirements of the EC at the MRL (maximum residue limit, 100 ng g(-1) for muscle, 300 ng g(-1) for liver and600 ng g(-1) for kidney), half the MRL and double the MRL levels, as well for OTC as for 4-epiOTC. Calibration graphs were prepared for all tissues and good linearity was achieved over the concentration ranges tested (r > 0.99 and goodness of fit < 10%). Limits of quantification of half the MRLs were obtained for the analysis of OTC and 4-epiOTC in muscle, liver and kidney tissues of calf. Limits of detection ranged for both components between 0.8 and 48.2 ng g(-1). The within-day and between-day precisions, expressed as RSD values, were all below the maximum allowed RSD values calculated according to the Horwitz equation. The results for accuracy fell within the -20% to +10% range. Recoveries were between 47 and 56% for OTC, and between 52 and 62% for 4-epiOTC, depending on the tissue. The method has been successfully used for the quantitative determination of OTC and 4-epiOTC in tissue samples of calves medicated with OTC by intramuscular injection.     

Sulfur K-edge XAS and DFT calculations on [Fe4S4]2+ clusters: effects of H-bonding and structural distortion on covalency and spin topology

Sulfur K-edge X-ray absorption spectroscopy of a hydrogen-bonded elongated [Fe4S4]2+ cube is reported. The data show that this synthetic cube is less covalent than a normal compressed cube with no hydrogen bonding. DFT calculations reveal that the observed difference in electronic structure has significant contributions from both the cluster distortion and from hydrogen bonding. The elongated and compressed Fe4S4 structures are found to have different spin topologies (i.e., orientation of the delocalized Fe2S2 subclusters which are antiferromagnetically coupled to each other). It is suggested that the H-bonding interaction with the counterion does not contribute to the cluster elongation. A magneto-structural correlation is developed for the Fe4S4 cube that is used to identify the redox-active Fe2S2 subclusters in active sites of HiPIP and ferredoxin proteins involving these clusters.     

En route to coordination chemistry under confined conditions in a porous capsule: Pr3+ with different coordination shells

The highly charged nanocontainer capsule of the type [pentagon]12[linker]30 identical with [(Mo)Mo5O21(H2O)6]12[Mo2O4(SO4)]30 with 20 nanosized pores and channels allows the entrance of cations like Pr3+: the latter are positioned at two different sites and have two different coordination shells, corresponding to a coordination chemistry under confined conditions; a fascinating aspect is that capsule encapsulated water shells fixed by hydrogen bonds act formally as polydentate ligands.     

Metal "capture" by a heterotrimetalloligand, heterometallic d(10)-d(10) interactions, and unexpected iron-to-platinum silyl ligand migration: a combined experimental and theoretical study

The heterotrinuclear chain complex Hg[Fe{Si(OMe)(3)}(CO)(3)(dppm-P)](2) (dppm = Ph(2)PCH(2)PPh(2)) 1 which has a transoid arrangement of the phosphine donors was used as a versatile chelating metallodiphosphine ligand owing to the easy rotation of its metal core about the Fe-Hg sigma-bonds. Its reaction with the labile Pt(0) olefin complex [Pt(C(7)H(10))(3)] yielded [HgPt{Si(OMe)(3)}Fe(2)(CO)(6){Si(OMe)(3)}(mu-dppm)(2)] 5 which resulted, after coordination of the dangling phosphine donors to Pt, from an unprecedented intramolecular rearrangement involving a very rare example of silyl ligand migration between two different metal centers, and the first one in metal cluster chemistry. The major structural differences observed between the heterometallic complexes obtained from 1 and d(10) Cu(I), Pd(0), or Pt(0) precursors have been established by X-ray diffraction. The bonding situation in the silyl migrated Pt complex 5 was analyzed and compared to those in the isoelectronic, but structurally distinct complexes obtained from Cu(I) and Pd(0) precursors, [Hg{Fe[Si(OMe)(3)](CO)(3)(mu-dppm)}(2)Cu](+) (2) and [Hg{Fe[Si(OMe)(3)](CO)(3)(mu-dppm)}(2)Pd] (4), respectively, by means of extended Hückel interaction diagrams. DFT calculations then allowed the energy minima associated with the three structures to be compared for 2, 4, and 5. All three minima are in close competition for the Pd complex 4, but silyl migration is favored by approximately 10 kcal mol(-)(1) for 5, mainly due to the more electronegative character of Pt with respect to Pd.     

Micellar shape change and internal segregation induced by chemical modification of a tryptych block copolymer surfactant

We report the detailed characterization of micelles formed by two nonionic, amphiphilic ABC triblock copolymers. Poly(ethylene oxide)-b-poly(styrene)-b-1,2-poly(butadiene) (PEO-b-PS-b-PB) triblock copolymer "OSB" forms core-corona spherical micelles in aqueous solution, and the two hydrophobic blocks S and B are mixed homogeneously within the micelle core. PEO-b-PS-b-PB:C6F13I triblock copolymer "OSF" was prepared by selective fluorination of the B block in OSB with n-perfluorohexyl iodide. Fluorination of the B block induces internal segregation into an inner F core and an intermediate S shell. Furthermore, the strong incompatibility that results from fluorination drives a shape change into an oblate ellipsoid. These micellar morphologies are confirmed by combined light, neutron, and X-ray scattering measurements, as well as TEM imaging.     

Improved access to 19-nor-7β, 8β-methylene-taxoids and formation of a 7-membered C-ring analog of doxetaxel by electrochemistry

A new route to semisynthetic 19-nor-7β, 8β-methylene taxoids, such as compound 8, from the 7-O-trifluoromethanesulfonyl derivative 6 is reported. Evidence for a dissociation of the triflate to form a carbocation at C-7 under the reaction conditions is presented. Electrochemical reduction of the cyclopropane taxoid 8 gives, besides the expected 10-dehydroxy-cyclopropane analog 10, the 7-membered C-ring derivative 11.     

The Coordination Chemistry of Iron with the 1,4‐Bis(2‐pyridyl‐methyl)piperazine Ligand

The behaviour of Fe^II and Fe^III ions in combination with the potential ligand 1,4‐bis(2‐pyridyl‐methyl)piperazine (BPMP) under anhydrous conditions has been investigated. BPMP has been reacted with FeCl₂, FeCl₃ and [Fe(OTf)₂(MeCN)₂]. This led to the isolation of four new complexes, which were fully characterized and structurally investigated by single crystal X‐ray diffraction. It turned out that in the presence of chloride co‐ligands Fe^III favours the tetradentate coordination mode of BPMP with the piperazine unit in a boat configuration, like for instance in [BPMP(Cl)Fe(μ‐O)FeCl₃] or [BPMP‐FeCl₂][FeCl₄], ( 1 ). However, the employment of FeCl₂ leads to the formation of a coordination polymer [BPMP‐FeCl₂]_n, ( 2 ), containing the piperazine ring in a chair configuration binding to two iron centres each. 2 can only be dissolved in very polar solvents like dmf which is capable of breaking up the polymeric structure under formation of [Cl₂(dmf)Fe(μ‐BPMP‐1κ²N,N:2κ²N,N))Fe(dmf)Cl₂]·2 dmf, ( 3 ). In contrast, using [Fe(OTf)₂(MeCN)₂] instead of FeCl₂ as the starting material leads to a mononuclear Fe^II complex with BPMP bound in the desirable tetradentate fashion: [BPMP‐Fe(OTf)₂], ( 4 ). Unlike other complexes with tetradentate N/py ligands the two residual ligands in 4 are bound almost trans to each other with the potential to adopt a cis orientation under oxidising conditions, and it will be interesting to exploit its catalytic properties in future.     

A quasi‐dynamic procedure for coupled thermal simulations

This paper outlines the development and adaptation of a coupling strategy for transient temperature analysis in a solid via a conjugate heat transfer method. This study proposes a quasi‐dynamic coupling procedure to bridge the temporal disparities between the fluid and the solid. In this approach, dynamic thermal modeling in the solid is coupled with a sequence of steady states in the fluid. This quasi‐dynamic algorithm has been applied to the problem of convective heat transfer over, and transient conduction heat transfer within, a flat plate using the severe thermal conditions of a solid propellant rocket. Two different coupled thermal computations have been performed. In the first one—referred to as the reference computation—the coupling period is equal to the smallest solid time constant. In the second one, a very large coupling period is used. The results show that the procedure can predict accurate transient temperature fields at a reasonable computational cost. The simulation CPU time is approximately reduced by up to 90%, while maintaining a very good accuracy. All the details of the numerical test case are given in the paper. This application illustrates the capabilities and the overall efficiency of this coupled approach in a solid transient problem using long term simulations of time dependent flows. Copyright © 2013 John Wiley & Sons, Ltd.