Bounds on some van der Waerden numbers

For positive integers s and k₁,k₂,…,ks, the van der Waerden number w(k₁,k₂,…,ks;s) is the minimum integer n such that for every s-coloring of set {1,2,…,n}, with colors 1,2,…,s, there is a ki-term arithmetic progression of color i for some i. We give an asymptotic lower bound for w(k,m;2) for fixed m. We include a table of values of w(k,3;2) that are very close to this lower bound for m=3. We also give a lower bound for w(k,k,…,k;s) that slightly improves previously-known bounds. Upper bounds for w(k,4;2) and w(4,4,…,4;s) are also provided.     

Proficiency testing scheme for the harmonization and comparability of analytical measurements

According to the experience of the successful implementation of proficiency tests (PT) by using the certified reference value as the assigned value, a new scheme of evaluation is presented by suggesting the use of the uncertainty associated with the certified value. The technical performance of laboratories is evaluated by the parameter quadratic mean error (QME), which is the square root of the sum of the square of the bias and that of the standard deviation of the laboratory. This parameter is considered as the estimate of the measurement uncertainty of the laboratory and is compared to the uncertainty (U) associated with the certified value provided by an NMI. Considering that the calibration and measurement capability, known as the CMC, is recognized among NMIs, the ratio QME/U enables us to compare the PT relative to the CMC of an NMI, and, consequently, to any other comparison results based on the CMC of signatories of the mutual recognition arrangement (MRA) of the International Committee of Weights and Measure (CIPM). Presented at BERM-11, October 2007, Tsukuba, Japan.     

Beauveria bassiana ATCC 7159 Containsan L-Specific a-Amino Acid Benzamidase

 Biotransformation of a series of racemic N-benzoyl α-amino acids by the fungus Beauveria bassiana ATCC 7159 results in isolation of the corresponding D-amino acid benzamides in high enantiomeric purity and yield.     

Viscosity of n-alkyl-3-methyl-imidazolium bis(trifluoromethylsulfonyl)amide ionic liquids saturated with compressed CO2

The viscosity of imidazolium-based ionic liquids (ILs) saturated with gaseous, liquid and supercritical carbon dioxide (CO₂) was measured by a high-pressure viscometer at three different temperatures (25, 50, and 70 °C). The high-pressure viscosity of 1-ethyl-3-methylimidazolium ([EMIm]), 1-n-hexyl-3-methylimidazolium ([HMIm]), and 1-n-decyl-3-methylimidazolium ([DMIm]) cations with a common anion, bis(trifluoromethylsulfonyl)amide ([Tf₂N]), saturated with CO₂ was measured up to a maximum of 287 bar. As CO₂ pressure is increased the viscosity of the IL mixture dramatically decreases. While, the ambient pressure viscosity of 1-alkyl-3-methyl-imidazolium [Tf₂N] ILs increases significantly with increasing chain length, the viscosity of all the CO₂-saturated ILs becomes very similar at high CO₂ pressures. From previous vapor–liquid equilibrium data, the viscosity with concentration was determined and found to be the primary factor to describe the fractional viscosity reduction. Several predictive and correlative methods were investigated for the mixture viscosity given pure component properties and include arithmetic mixing rules, the Irving (Predictive Arrhenius) model, Grunberg equation, etc. The modified Grunberg model with one adjustable parameter provided an adequate fit to the data.     

Design and synthesis of 6-amino-5-oxo-1,2,3,5-tetrahydro-3-indolizinecarboxylic acids as β-sheet peptidomimetics

6-Amino-5-oxo-1,2,3,5-tetrahydro-3-indolizinecarboxylic acid was designed as a novel scaffold that can effectively mimic the extended conformation of a peptide. The key reaction in the synthesis of the scaffold involved a [3+2]-cycloaddition of a dicarbonyl stabilized isomünchnone intermediate. Its effectiveness as a β-sheet mimetic was demonstrated by the preparation of a potent HCV NS3 protease inhibitor.     

Singlet and triplet potential surfaces for the O2+C2H4 reaction

Electronic structure calculations at the CASSCF and UB3LYP levels of theory with the aug-cc-pVDZ basis set were used to characterize structures, vibrational frequencies, and energies for stationary points on the ground state triplet and singlet O(2)+C(2)H(4) potential energy surfaces (PESs). Spin-orbit couplings between the PESs were calculated using state averaged CASSCF wave functions. More accurate energies were obtained for the CASSCF structures with the MRMP2/aug-cc-pVDZ method. An important and necessary aspect of the calculations was the need to use different CASSCF active spaces for the different reaction paths on the investigated PESs. The CASSCF calculations focused on O(2)+C(2)H(4) addition to form the C(2)H(4)O(2) biradical on the triplet and singlet surfaces, and isomerization reaction paths ensuing from this biradical. The triplet and singlet C(2)H(4)O(2) biradicals are very similar in structure, primarily differing in their C-C-O-O dihedral angles. The MRMP2 values for the O(2)+C(2)H(4)→C(2)H(4)O(2) barrier to form the biradical are 33.8 and 6.1 kcal/mol, respectively, for the triplet and singlet surfaces. On the singlet surface, C(2)H(4)O(2) isomerizes to dioxetane and ethane-peroxide with MRMP2 barriers of 7.8 and 21.3 kcal/mol. A more exhaustive search of reaction paths was made for the singlet surface using the UB3LYP/aug-cc-pVDZ theory. The triplet and singlet surfaces cross between the structures for the O(2)+C(2)H(4) addition transition states and the biradical intermediates. Trapping in the triplet biradical intermediate, following (3)O(2)+C(2)H(4) addition, is expected to enhance triplet→singlet intersystem crossing.     

Palladium-catalyzed benzylation of N-Boc indole boronic acids

The direct benzylation of indole 2-boronic acid can be efficiently achieved using trans-PdBr(N-Succ)(PPh₃)₂, alleviating the need for strong bases or toxic organotin reagents. Under these reaction conditions substituted indole-2-boronic acids and substituted benzyl bromides are cross-coupled to afford aryl(indolo)methanes in good yield.     

Concerted C-N and C-H bond formation in a magnesium-catalyzed hydroamination

Coordinatively saturated To(M)MgMe (1; To(M) = tris(4,4-dimethyl-2-oxazolinyl)phenylborate) is an active precatalyst for intramolecular hydroamination/cyclization at 50 °C. The empirical rate law of -d[substrate]/dt = k'(obs)[Mg](1)[substrate](1) and Michaelis-Menten-type kinetics are consistent with a mechanism involving reversible catalyst-substrate association prior to cyclization. The resting state of the catalyst, To(M)MgNHCH(2)CR(2)CH(2)CH═CH(2) [R = Ph, Me, -(CH(2))(5)-], is isolable, but isolated magnesium amidoalkene does not undergo unimolecular cyclization at 50 °C. However, addition of trace amounts of substrate allows cyclization to occur. Therefore, we propose a two-substrate, six-center transition state involving concerted C-N bond formation and N-H bond cleavage as the turnover-limiting step of the catalytic cycle.