Sum-free sets and Ramsey numbers

In this note we obtain new lower bounds for the Ramsey numbers R(5, 5) and R(5, 6). The method is based on computational results of partitioning the integers into sum-free sets. We obtain R(5, 5)?42 and R(5, 6)?53.     

Cavity-enhanced absorption spectroscopy for shocktubes: Design and optimization

Cavity-enhanced absorption spectroscopy (CEAS) has generated much interest in shocktube kinetics studies because of its recent success in achieving improved sensitivity and high time resolution with robust optical alignment. While recent progress demonstrated experimental schemes including off-axis scanned-wavelength approach and on-axis ps-pulsed laser approach, that both successfully suppressed the laser-cavity coupling noise, this paper develops a theoretical model to predict the CEAS sensor performance that can be used as a design tool applicable to more generalized cases. The method models the optical field in the cavity based on the decentered Gaussian beam model, from which the cavity transmission spectrum and the laser-cavity coupling noise can be numerically calculated. The simulation results predict sensor performance for different cavity configurations and laser characteristics, including various degrees of laser-cavity mode-matching, laser linewidths, scanning rates, and cavity filling conditions. Simulation with example wavelengths in the ultraviolet, near-infrared, and mid-infrared showed increasing mode-matched beam waist size for increasing wavelengths. An off-axis alignment scheme was found to be capable of suppressing the coupling noise by two orders-of-magnitude at a moderate laser linewidth of 1?GHz. Coupling noise level on the order of 1e-5 for scanned-wavelength off-axis alignment case with a narrowband mid-infrared laser was obtained by model calculation and agreed with experimental results within acceptable uncertainty range. The developed method can serve to guide future design and optimization of CEAS system in shocktube studies.     

Using external coils to correct field errors in tokamaks

Non axisymmetric correction coils can be highly effective at canceling the low order magnetic islands generated by magnetic field errors. Correction coil currents which, by themselves, mould produce an island of the same size and opposite phase as the error field, will result in cancelled magnetic islands. In computing the magnetic island sizes and toroidal phases of perturbations, the use of a straight-cylinder approximation can cause substantial error. An n=1 error with arbitrary phase can be corrected at a single resonant surface with one set of four correction coils. Correcting higher n harmonics requires more coils toroidally. Correcting same-n errors at more than one rational surface requires more correction coil sets     

New zinc phosphates decorated by imidazole-containing ligands

Four new zinc phosphates [Zn(HPO4)(C6H9N3O2)] (1), [Zn(HPO4)(C4H6N2)].H2O (2), [Zn2(HPO4)2(C14H14N4)].2H2O (3), and [Zn(HPO4)(C14H14N4)] (4) were synthesized in the presence of d-histidine, 1-methylimidazole, 1,4-bis(imidazol-1-ylmethyl)benzene (L1), and 1,2-bis(imidazol-1-ylmethyl)benzene (L2), respectively, and their structures were determined by X-ray crystallography. The inorganic framework of compounds 1, 2, and 3 is composed of vertex-shared ZnO3N and HPO4 tetrahedra that form four rings, which, in turn, are linked to generate a one-dimensional ladder structure. In 1 and 2 the organic groups (monoimidazole ligand) are located at each side of the ladders, while in 3 the bisimidazole ligand, 1,4-bis(imidazol-1-ylmethyl)benzene, links the ladders together to form a novel 2D structure. Compound 1 is the first zinc phosphate framework to be templated by an N-bonded chiral amino acid. In 4 the zero-dimensional four rings are joined together by the linear bridging ligand, 1,2-bis(imidazol-1-ylmethyl)benzene, to generate a one-dimensional framework with a new face-to-face structural motif. The 3D structure of compound 4 is stabilized by hydrogen-bonding, pi-pi interactions, and C-H...pi interactions. The approach of incorporating multifunctional ligands into zinc phosphate frameworks and linking the inorganic zinc phosphates subunits by an organic ligand provides opportunities for the design of new inorganic-organic open frameworks.     

Solid-phase synthesis of metal-complex containing peptides

We report the synthesis of Fmoc protected single amino acid chelates (SAAC) and their metal complexes. The modified amino acids are suitable for solid-phase peptide synthesis. The use of 4-hydroxymethylbenzoic acid AM (HMBA-AM) resin allows the nucleophilic cleavage of the peptide-metal complexes from the resin without decomplexation.     

RAMPED-UP NMR: multiplexed NMR-based screening for drug discovery

The crucial step in drug discovery is the identification of a lead compound from a vast chemical library by any number of screening techniques. NMR-based screening has the advantage of directly detecting binding of a compound to the target. The spectra resulting from these screens can also be very complex and difficult to analyze, making this an inefficient process. We present here a method, RAMPED-UP NMR, (Rapid Analysis and Multiplexing of Experimentally Discriminated Uniquely Labeled Proteins using NMR) which generates simple spectra which are easy to interpret and allows several proteins to be screened simultaneously. In this method, the proteins to be screened are uniquely labeled with one amino acid type. There are several benefits derived from this unique labeling strategy: the spectra are greatly simplified, resonances that are most likely to be affected by binding are the only ones observed, and peaks that yield little or no information upon binding are eliminated, allowing the analysis of multiple proteins easily and simultaneously. We demonstrate the ability of three different proteins to be analyzed simultaneously for binding to two different ligands. This method will have significant impact in the use of NMR spectroscopy for both the lead generation and lead optimization phases of drug discovery by its ability to increase screening throughput and the ability to examine selectivity. To the best of our knowledge, this is the first time in any format that multiple proteins can be screened in one tube.     

Synthesis, structural characterization, and multifrequency electron paramagnetic resonance studies of mononuclear thiomolybdenyl complexes

Reaction of Tp*MoVSCl2 with a variety of phenols and thiols in the presence of triethylamine produces mononuclear, thiomolybdenyl complexes Tp*MoVSX2 [Tp* = hydrotris(3,5-dimethylpyrazol-1-yl)borate; X = 2-(ethylthio)phenolate (etp), 2-(n-propyl)phenolate (pp), phenolate; X2 = benzene-1,2-dithiolate (bdt), 4-methylbenzene-1,2-dithiolate (tdt), benzene-1,2-diolate (cat)]. The complexes have been characterized by microanalysis, mass spectrometry, IR, EPR, and UV-visible spectroscopic data, and X-ray crystallography (for the etp, pp, bdt, and cat derivatives). The mononuclear, six-coordinate, distorted-octahedral Mo centers are coordinated by terminal sulfido (MoS = 2.123(1)-2.1368(8) A), tridentate facial Tp*, and monodentate or bidentate O/S-donor ligands. Multifrequency (S-, X-, Q-band) EPR spectra of the complexes and selected molybdenyl analogues were acquired at 130 K and 295 K and yielded a spin Hamiltonian of Cs symmetry or lower, with gzz < gyy < gxx < ge and Az'z' > Ax'x' approximately Ay'y', and a noncoincidence angle in the range of beta = 24-39 degrees . Multifrequency EPR, especially at S-band, was found to be particularly valuable in the unambiguous assignment of the spin Hamiltonian parameters in these low-symmetry complexes. The weaker pi-donor terminal sulfido ligand yields a smaller SOMO-LUMO gap and reduced g-values for the thiomolybdenyl complexes compared with molybdenyl analogues, supporting existing crystallographic and EPR data for an apically coordinated oxo group in the active site of xanthine oxidase.     

A two-dimensional cationic lattice built from [Zn6(HPO4)2(PO4)2]2+ clusters

A unique cationic zinc phosphate cluster linked by neutral bifunctional rigid ligands to form a two dimensional framework was synthesized and structurally characterized.