The non-solvability by radicals of generic 3-connected planar Laman graphs

We show that planar embeddable -connected Laman graphs are generically non-soluble. A Laman graph represents a configuration of points on the Euclidean plane with just enough distance specifications between them to ensure rigidity. Formally, a Laman graph is a maximally independent graph, that is, one that satisfies the vertex-edge count together with a corresponding inequality for each subgraph. The following main theorem of the paper resolves a conjecture of Owen (1991) in the planar case. Let be a maximally independent -connected planar graph, with more than 3 vertices, together with a realisable assignment of generic distances for the edges which includes a normalised unit length (base) edge. Then, for any solution configuration for these distances on a plane, with the base edge vertices placed at rational points, not all coordinates of the vertices lie in a radical extension of the distance field.

     

A monopole mass filter with a hyperbolic V-shaped electrode

In this article we compare the classical monopole mass filter of von Zahn and the monopole mass filter with a hyperbolic V-shaped electrode. The experimental results and those of computer simulation for both mass spectrometers are presented. We show that the replacement of a conventional 90 degrees V-shaped electrode by an electrode with a hyperbolic profile substantially improves the peak shape of any given mass, and increases the mass resolution by a factor of 3-4 and the abundance sensitivity by a factor of 100. The potential of high analytical performance combined with electroforming techniques for electrode manufacture indicate future practical uses of such instruments. Copyright 1999 John Wiley & Sons, Ltd.     

Synthesis and Solid-State Structure of 2,6-Trip2C6H3Tl (Trip=2,4,6-iPr3C6H2): A Monomeric Arylthallium(I) Compound with a Singly Coordinated Thallium Atom

A “one-legged thallium” is observed in the arylthallium(I ) compound 2,6-Trip₂C₆H₃Tl (Trip=2,4,6-iPr₃C₆H₂), which was synthesized from the corresponding organolithium compound and thallium chloride. X-ray structure analysis reveals that 2,6-Trip₂C₆H₃Tl is monomeric in the solid state and contains a singly coordinated thallium atom (see space-filling model on the right).     

非共沸混合物微翅管内强制对流蒸发换热计算

分析了非共沸混合物在水平微翅管内强制对流蒸发换热的传热传质的特点,考察了影响非共沸混合工质强制对流蒸发换热的主要影响因素,建立了考虑相界面传质阻力和微翅管二次流效应的换热系数的计算模型,利用本文模型的计算结果与实验数据进行了比较,吻合较好。在高质量流量和高干度(x>0.3)下,理论预测值与实验值的平均偏差不大于10％。     

Addition of Hydrogen or Ammonia to a Low‐Valent Group 13 Metal Species at 25 °C and 1 Atmosphere

Mild‐mannered : The low‐valent aryl gallium(I) species :GaAr′ (Ar′=2,6‐(2,6‐iPr₂C₆H₃)₂C₆H₃) undergoes addition to H₂ or NH₃ at room temperature and one atmosphere of pressure to afford 1 or 2 (see scheme), which were characterized by X‐ray crystallography and NMR and IR spectroscopy.

     

Ab initio quantum chemistry calculations on the electronic structure of heavier alkyne congeners: diradical character and reactivity

The electronic structure of the heavier congeners of alkynes has been studied with emphasis on characterizing their extent of diradical character. Four orbitals play a crucial role in determining the electronic structure in planar trans-bent geometries. Two are associated with an out-of-plane pi interaction, pi and pi, and two are associated with in-plane interactions and/or in-plane lone pairs, LP(n-) and LP(n+). The ordering of these orbitals can change depending upon geometry. One extreme, corresponding to the local minimum for Si-Si and Ge-Ge, is a diradicaloid multiple-bonding configuration where LP and pi are nominally occupied. Another extreme, corresponding to a local minimum for Sn-Sn, is a relatively closed-shell single-bond configuration where LP and LP are nominally occupied. This ordering leads to predicted bond shortening upon excitation from singlet to triplet state. For the heavier elements, there appears to be very little energy penalty for large geometric distortions that convert from one ordering to the other on the singlet surface. The implications of these results with respect to experimental observations are discussed.     

Kinetics of spontaneous change in the localized motions of D-sorbitol glass

The dielectric relaxation spectra of D-sorbitol glass have been studied in real time during annealing at 221.1 K, which is 47 K below its T(g) of 268 K. As the glass structurally relaxes during annealing, features of the Johari-Goldstein (JG) relaxation change with time: (i) the relaxation strength decreases, (ii) the relaxation peak at 48 Hz shifts to a higher frequency, and (iii) the relaxation spectra become narrower. All seem to follow the relation p proportional, variant exp[-(kt)(n)], where p is the magnitude of a property, k the rate constant, and t the time. The parameter n may well be less than 1, but this could not be ascertained. It is proposed that shift of the relaxation peak to a higher frequency and narrowing of the relaxation spectra occur when local, loosely packed regions of molecules in the glass structure collapse nonuniformly and the relaxation time of some of the molecules in the collapsed state becomes too long to contribute to the JG-relaxation spectra. Consequently, the half width of the spectra decreases, and the relaxation peak shifts to a higher frequency. Molecules whose diffusion becomes too slow after the local regions' collapse would contribute to the alpha-relaxation spectra and thus the net relaxation strength would increase on structural relaxation. It is argued that these findings conflict with the NMR-based conclusions that motion of all molecules in the glass and supercooled liquid contributes to the faster relaxation process.     

Orientation polarization from faster motions in the ultraviscous and glassy diethyl phthalate and its entropy

Dielectric spectra of the beta relaxation in glassy and ultraviscous liquid diethyl phthalate show that its relaxation strength Delta epsilon(beta), the distribution of times, and the relaxation rate are more sensitive to temperature T in the ultraviscous liquid than in the glassy state. The Delta epsilon(beta) against temperature plot has an elbow-shaped break near T(g) of approximately 181 K, which is remarkably similar to that observed in the entropy, enthalpy, and volume against temperature plots, and in the plot of Delta epsilon(beta) against the liquid's entropy minus its 0 K value. The ratio of Delta epsilon(beta) to diethyl phthalate's entropy, after subtracting the 0 K value, is 1.08 x 10(-3) mol K/J in the glassy state at 120.4 K, which decreases slowly to 0.81 x 10(-3) mol K/J at 176 K near T(g) and thereafter rapidly increases to 1.57 x 10(-3) mol K/J at 190 K. Variation in Delta epsilon(beta) parallels the variation of the entropy. A change in the activation energy of the beta process at T>T(g) indicates that its rate is also determined by the structure of the ultraviscous liquid. Features of beta relaxation are consistent with localized motions of molecules and may not involve small-angle motions of all molecules.