On the oscillatory modes of quarks in baryons

The color bond structure of a quark-antiquark system is extended, in the long-range approximation, self-consistently to the baryonic three-quark bond structure for SU(3)_c and generally to the N-quark bond structure for SU(N)_c. The universal (N-independent) mass square eigenvalues for massless quarks are

$\text{M}{}^2\text{=(H}{}_{\mathrm{N}}\text{)}{}^2\text{?2m}{}_{\mathrm{\rho }}{}^2\text{∑}\text{α=1}\text{3N?3}\text{ν}{}_{\mathrm{\alpha }}\text{+}\text{constant}\text{, ν}{}_{\mathrm{\alpha }}\text{=0,1,2,…}$

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Radius of clusters at the percolation threshold: A position space renormalization group study

Using a direct position-space renormalization-group approach we study percolation clusters in the limits , wheres is the number of occupied elements in a cluster. We do this by assigning a fugacityK per cluster element; asK approaches a critical valueK _c , the conjugate variables . All exponents along the path (K–K _c ) 0 are then related to a corresponding exponent along the paths . We calculate the exponent , which describes how the radius of ans-site cluster grows withs at the percolation threshold, in dimensionsd=2, 3. Ind=2 our numerical estimate of =0.52±0.02, obtained from extrapolation and from cell-to-cell transformation procedures, is in agreement with the best known estimates. We combine this result with previous PSRG calculations for the connectedness-length exponent , to make an indirect test of cluster-radius scaling by calculating the scaling function exponent using the relation =/. Our result for is in agreement with direct Monte-Carlo calculations of , and thus supports the cluster-radius scaling assumption. We also calculate ind=3 for both site and bond percolation, using a cell of linear sizeb=2 on the simple-cubic lattice. Although the result of such small-cell calculations are at best only approximate, they nevertheless are consistent with the most recent numerical estimates.Supported in part by grants from ARO and ONR     

On uniform distribution of double sequences

In this paper a new notion of uniform distribution of double sequences is introduced. In the most elementary case a double sequence (x_mn)_{m, nN} is called uniformly distributed in this sense if all finite matrices of equal size appear with the same frequency as submatrices of the infinite matrix (x_mn). Some special double sequences with such a distribution property are studied and metric theorems are proved.     

Synthesis of PI3K inhibitor GDC-0077 via a stereocontrolled N-arylation of α-amino acids

An efficient synthesis of PI3K inhibitor GDC-0077, featuring two consecutive Cu-catalyzed CN coupling reactions, is reported. The described synthetic route involves a chemoselective Ullmann-type coupling of a chiral difluoromethyl-substituted oxazolidinone, a Cu-catalyzed N-arylation of l-alanine with high stereochemical integrity, and a high-yielding final amide bond formation step to produce GDC-0077 in >99.5 area % HPLC purity.     

Analytical characteristics and sensitivity mechanisms of electrolyte-insulator-semiconductor system-based chemical sensors—a critical review

Recent trends in research and development of electrolyte-insulator-semiconductor (EIS) field-effect chemical sensors (ion-selective field-effect transistors, light-addressable potentiometric sensors, capacitive EIS-sensors) with inorganic gate insulators (oxide, nitride and chalcogenide films) are reviewed. Physical properties of EIS systems and basic mechanisms of their chemical sensitivity are examined. Analytical characteristics and sensing mechanisms of EIS pH sensors with oxide and nitride films, as well as metal ions sensors with chalcogenide films, are critically discussed. Prospects of future research on EIS field-effect biosensors are briefly outlined.     

An improved CNDO/2 standard parametrization for bromine containing molecules

Bromine parameters are proposed, matching well the standard values of first and second row atoms, as introduced by Pople et al. This is shown by comparisons of geometries, configurations, conformations, and dipole moments, obtained with different approaches. The new parameter set was found in a very simple and efficient way that may also be useful for other tasks, e.g. in non-empirical calculations.     

A laser desorption fourier transform mass spectrometric study of dimethyl 8-acetyl-3,7,12,17-tetramethylporphyrin-2,18-dipropanoate

Laser desorption Fourier transform ion cyclotron resonance positive- and negative-ion mass spectra are presented for dimethyl 8-acetyl-3,7,12,17-tetramethylporphyrin-2,18-dipropanoate. The 248-nm laser ionization thresholds for both positive and negative ions are observed to be about 2.5 MW cm^?2. The M⁺˙ molecular ion is assigned to the base peak in the low-power spectra whereas it is the M^?˙ ion for the corresponding anion spectra. Increased intensities of [M + H]⁺ and [M ? H]^? are observed with increased laser fluences of up to 38 MW cm^?2. At high laser powers the negative-ion results reveal that a series of carbon-nitrogen cumulene and polyacetylene cluster ions are formed. Laser evaporation/multiphoton ionization/ and thermal evaporation/electron impact ionization/collision-induced dissociation experiments carried out on the porphyrin M⁺˙ and [M + H]⁺ ions over a range of translational kinetic energies and delay times after acceleration are compared and used to obtain mechanistic and structural information. In contrast to the electron impact experiments, which show only side-chain cleavage, the laser-based collision-induced dissociation experiments reveal that, in addition to side-chain cleavage, it is possible to cleave the porphyrin ring to various extents depending on the ion translational energy selected.     

Technical Procedures for the Syntheses of Carotenoids and Related Compounds from 6-Oxo-isophorone: Syntheses of (3R,3′R)-Zeaxanthin. Part I

Starting from the readily available, optically active (4R)-4-hydroxy-2,2,6-trimethylcyclohexanone ( 1 ), a new technical synthesis of (3R,3′R)-zeaxanthin is described. According to a 2(C₉ + C₆) + C₁₀ = C₄₀ construction scheme, the ketone 1 was first transformed with (E)-3-methylpent-2-en-4-yn-1-ol ( 5 ) into a C₁₅-intermediate which, by a three-step sequence, could be converted into the known olefinic C₁₅-Wittig salt 4 . Optimized conditions for the final Wittig reaction of 4 with the C₁₀-dialdehyde 3 are discussed. Based on 1 , the overall yield of the entire technical process is ca. 40%.