Signature of relations in mapping class groups and non-holomorphic Lefschetz fibrations

We introduce the notion of signature for relations in mapping class groups and show that the signature of a Lefschetz fibration over the 2-sphere is the sum of the signatures for basic relations contained in its monodromy. Combining explicit calculations of the signature cocycle with a technique of substituting positive relations, we give some new examples of non-holomorphic Lefschetz fibrations of genus and which violate slope bounds for non-hyperelliptic fibrations on algebraic surfaces of general type.

     

Ion cyclotron drift instability driven by cross-field current

An ion cyclotron drift instability is excited by a cross field current due to E_r × B drift of electrons and ion heating is observed in a plasma column in a magnetic field when a dc radial electric field E_r is applied.     

Stereocontrolled synthesis of 7-hydroxy- and 7-acetoxy-PGI2: New stable PGI2 analogues

Stable analogues of PGI₂, 7-hydroxy- and 7-acetoxy-PGI₂, were synthesized from protected PGI₂ methyl ester $\text{1b}$via sulfoxides $\text{6a}$, $\text{6b}$ through stereocontrolled sulfoxide-sulfenate rearrangement.     

Preparation and electrical resistivities of tetrathiafulvalen (TTF) and tetraselenafulvalen salts with the [SnR2Cln]2-n anions (n = 3 or 4: R = Et or Ph) and X-ray crystal structure of [TTF]3[SnEt2Cl4]

Tetrathiafulvalen (TTF) and tetraselenafulvalen (TSF) salts with diorganochloro-stannate anions, [TTF][SnEt₂Cl₃] (1), [TTF]₂[SnPh₂Cl₄] (2), [TTF]₃[SnEt₂Cl₄] (3), [TTF]_3.3[SnPh₂Cl₄] (4), [TSF]₂[SnPh₂Cl₄] (5) and [TSF]_3.3[SnPh₂Cl₄] (6), were prepared by the reactions of [TTF or TSF]₃[BF₄]₂ with SnR₂Cl₂ (R = Et or Ph) in the presence of [Ph₃PCH₂Ph]Cl and by electrocrystallization of TTF or TSF in acetonitrile containing SnR₂Cl₂ and [Ph₃PCH₂Ph]Cl. All the salts behave as semiconductors with electrical resistivities of the order of 10–10⁸ Ω cm as compacted samples at 25°C. Electronic reflectance spectra of the simple salts 1, 2 and 5, show a band due to the dimeric(TTF⁺)₂ or (TSF⁺)₂ unit in the 12,200–12,800-cm^?1 region. The complex salt 3 exhibits a TTF⁺/TTF° charge-transfer (CT) band at 8700 cm^?1, and the remaining complex salts, 4 and 6, both display CT bands between the radical cations and between the radical cation and the neutral donor molecule. The crystal structure of 3 was determined by a single-crystal X-ray diffraction. The tetragonal crystal, space group I4cm, has cell dimensions a = 11.710(3) Å, c = 25.242(7) Å, and Z = 4. The structure was solved by the heavy-atom method and refined to a final R value of 0.082 for 479 independent reflections with >F_° > 3σ(F). TTF molecules exist as trimers, in which a slight lateral shift from the eclipsed TTF overlap occurs, although TTF molecules are arranged with equal spacing between them. The trimer units are located perpendicularly to each other, forming a two-dimensional layer. The [SnEt₂Cl₄]^2? anion is disordered with respect to the two SnEt and two SnCl bonds.     

Studies of lattice dynamics in 2HTaS2 by Raman scattering

Raman spectra are presented in the high and low temperature phases of 2H-TaS₂. In the normal phase at 380 K one A_1g- and two E_2g-modes have been observed at 400, 27 and 286 cm^-1, respectively. In the charge density wave state two extra peaks appear with strong scattering intensity in E_2g- symmetry and weak in A_1g-symmetry. The E_2g peak grows and hardens toward 50 cm^-1 with decreasing temperature. The temperature dependence is very similar to the E_2g-mode in 2H-TaSe₂ of similar 3a₀ × 3a₀ superstructure. Other peaks observed in 2H-TaSe₂ in the commensurate phase are not observed. This suggests the incommensurability of the charge density wave state in 2H-TaS₂.     

Effects of surface roughness of a moving test body on laser-interferometric displacement measurements

Displacement measurements by laser-homodyne or laser-heterodyne methods are dicussed analytically with respect to the relevant surface roughness. Expressions of the output signal and its signal-to-noise ratio are derived on the basis of gaussian statistics of the roughness. The roughness does not impose restrictions on the measurable minimum displacement but degrades the signal-to-noise ratio of the output signal.