The chemistry of 1,3,4-thiadiazoline-2-spiro-2'-fenchane

Diazomethane adds to one of the two faces of the sterically hindered thiofenchone furnishing the title compound which extrudes N₂ at 46°C with t_l/2 = 22 min; the thiofenchone S-methylide is intercepted by dipolarophiles and acts as a base in reactions with methanol, thiophenol and acetic acid, in the latter case accompanied by skeletal rearrangement.     

Local electronic structure of Cu2O,CuO and YBa2Cu3O7−δ

Cu 3d and O 2p electronic states of Cu₂O, CuO, and the highT _c compound YBa₂Cu₃O_7– have been probed by means of high resolution x-ray emission spectroscopy (XES). The CuL and OK XES bands are compared in detail with recently reported x-ray photoelectron and ultraviolet photoelectron spectroscopy (XPS and UPS) measurements and densities of states obtained by local density functional (LDF) theory. The XES data show that the hybridization between Cu 3d and O 2p states is completely modified in CuO and YBa₂Cu₃O_7–, whered-d correlation energy is large, as compared to LDF predictions. Such is not the case for Cu₂O where agreement between theory and experiment is good.The Cu 3d states are found to be highly localized in YBa₂Cu₃O_7– (though less so than in CuO). The O 2p states lie at lower binding energies than in the simpler oxides and are mainly situated above the Cu 3d states. The respective positions of the centre of gravity of the OK emission bands on an x-ray energy scale indicate that the oxygen sites are less well screened by the O 2p states in the highT _c compound. This provides indirect evidence for the presence ofd-like states at the oxygen sites.     

Invertibility in the Flag Kernels Algebra on the Heisenberg Group

Flag kernels are tempered distributions which generalize these of Calderón–Zygmund type. For any homogeneous group \(\mathbb {G}\) the class of operators which acts on \(L^{2}(\mathbb {G})\) by convolution with a flag kernel is closed under composition. In the case of the Heisenberg group we prove the inverse-closed property for this algebra. It means that if an operator from this algebra is invertible on \(L^{2}(\mathbb {G})\), then its inversion remains in the class.     

Protein Patterns and Oscillations on Lipid Monolayers and in Microdroplets

The Min proteins from E.coli position the bacterial cell‐division machinery through pole‐to‐pole oscillations. In vitro, Min protein self‐organization can be reconstituted in the presence of a lipid membrane as a catalytic surface. However, Min dynamics have so far not been reconstituted in fully membrane‐enclosed volumes. Microdroplets interfaced by lipid monolayers were employed as a simple 3D mimic of cellular compartments to reconstitute Min protein oscillations. We demonstrate that lipid monolayers are sufficient to fulfil the catalytic role of the membrane and thus represent a facile platform to investigate Min protein regulated dynamics of the cell‐division protein FtsZ‐mts. In particular, we show that droplet containers reveal distinct Min oscillation modes, and reveal a dependence of FtsZ‐mts structures on compartment size. Finally, co‐reconstitution of Min proteins and FtsZ‐mts in droplets yields antagonistic localization, thus demonstrating that droplets indeed support the analysis of complex bacterial self‐organization in confined volumes.     

Total Colorings of Graphs with Minimum Sum of Colors

The total chromatic sum of a graph is the minimum sum of colors (natural numbers) taken over all proper colorings of vertices and edges of a graph. We construct infinite families of graphs for which the minimum number of colors to achieve the total chromatic sum is larger than the total chromatic number.     

Novel stationary phases based on asphaltenes for gas chromatography

We present the results of investigations on the possibility of the application of the asphaltene fraction isolated from the oxidized residue from vacuum distillation of crude oil as a stationary phase for gas chromatography. The results of the investigation revealed that the asphaltene stationary phases can find use for the separation of a wide range of volatile organic compounds. The experimental values of Rohrschneider/McReynolds constants characterize the asphaltenes as stationary phases of medium polarity and selectivity similar to commercially available phases based on alkyl phthalates. Isolation of asphaltenes from the material obtained under controlled process conditions allows the production of a stationary phase having reproducible sorption properties and chromatographic columns having the same selectivity. Unique selectivity and high thermal stability make asphaltenes attractive as a material for stationary phases for gas chromatography. A low production cost from a readily available raw material (oxidized petroleum bitumens) is an important economic factor in case of application of the asphaltene stationary phases for preparative and process separations.     

Isolation of a furan fatty acid from Hevea brasiliensis latex employing the combined use of pH‐zone‐refining and conventional countercurrent chromatography

Furan fatty acids are valuable and bioactive minor fatty acids that usually contribute <0.1% to the fatty acid content of food samples. Their biological role still remains unclear as authentic furan fatty acid standards are not readily available and thorough experimental studies verifying the relevance of furan fatty acids are thus virtually impossible. An efficient protocol for the isolation of the furan fatty acid 9‐(3‐methyl‐5‐pentylfuran‐2‐yl)‐nonanoic acid from hydrolyzed and centrifuged latex of Hevea brasiliensis was developed using countercurrent chromatography. A first run using pH‐zone‐refining countercurrent chromatography provided 48.4 mg of 9‐(3‐methyl‐5‐pentylfuran‐2‐yl)‐nonanoic acid from 210 mg latex extract in a purity of 95%. The purity was increased to 99% by means of one second run in conventional countercurrent chromatography mode. The Structure and purity of 9‐(3‐methyl‐5‐pentylfuran‐2‐yl)‐nonanoic acid were determined by gas chromatography coupled to mass spectrometry and ¹H and ¹³C NMR spectroscopy.     

Multiple solutions and corresponding power output of a nonlinear bistable piezoelectric energy harvester

We examine multiple responses of a vibrational energy harvester composed of a verticalbeam and a tip mass. The beam is excited horizontally by a harmonic inertial force whilemechanical vibrational energy is converted to electrical power through a piezoelectricpatch. The mechanical resonator can be described by single or double well potentialsdepending on the gravity force from the tip mass. By changing the tip mass we examine theappearance of various solutions and their basins of attraction. Identification ofparticular solutions of the energy harvester is important as each solution may provide adifferent level of power output.     

Spectral Properties of Unbounded Jacobi Matrices with Almost Monotonic Weights

We present a unified framework to identify spectra of Jacobi matrices. We give applications of the long-standing problem of Chihara (Mt J Math 21(1):121–137, 1991, J Comput Appl Math 153(1–2):535–536, 2003) concerning one-quarter class of orthogonal polynomials, to the conjecture posed by Roehner and Valent (SIAM J Appl Math 42(5):1020–1046, 1982) concerning continuous spectra of generators of birth and death processes, and to spectral properties of operators studied by Janas and Moszyńki (Integral Equ Oper Theory 43(4):397–416, 2002) and Pedersen (Proc Am Math Soc 130(8):2369–2376, 2002).