Thermal and photochemical reactions of a stable thiobenzaldehyde, 2,4,6-tri-t-butylthiobenzaldehyde

Thermal and photochemical reactions of the title compound gave benzothiolane $\text{2}$ in high yield; the reaction with free radicals also afforded $\text{2}$ along with some other products.     

An X-ray diffraction study of anharmonic thermal vibrations in the ionic conductor,barium chloride fluoride (BaClF)

Integrated intensities of X-ray reflections from a barium chloride fluoride single crystal were measured at 24, 180, 289, 402, 467 and 610°C. The intensities were used for the determination of the anharmonic potential parameters up to the third order. Harmonic potential parameters for each ion were obtained from the temperature dependence of thermal parameters, and anharmonic potential parameters were determined by the least-squares procedures, utilizing the temperature factor formalism based on the cumulant expansion. As a result, it has been found that the Ba²⁺ and Cl^? ions show an anharmonicity, while no significant anharmonic effect was detected for the F^? ion. From the potential calculated around the Cl^? and F^? ions, it was found that both Cl^? and F^? ions diffuse more easily within the (001) plane than along the c axis.     

The cycloadducts of hexafluoroacetone and -thioacetone with diphenylketene

Hexafluoroacetone reacted with diphenylketene in the presence of potassium fluoride to give a 1:1 cycloadduct of β-lactone structure. On the other hand, hexafluorothioacetone, liberated from 2,2,4,4-tetrakis(trifluoromethyl)-1,3-dithietane by potassium fluoride, reacted with diphenylketene to give a “reverse” cycloadduct, a 3-thietanone derivative. Several reactions ofthe above product, including a reductive desulfuration of the 3-thietanone derivative were carried out.     

Recoil effects in high-energy photoemission beyond single-site approximation

Recoil effects of photoelectrons excited by high-energy X-rays are studied beyond the simplest approximation where elastic scatterings of photoelectrons are completely neglected (single-site approximation). At first we have shown that the simple free atom energy shift is accurately obtained within the harmonic and the single-site approximations. Beyond the single-site approximation, this simple formula does not work, but still simple classically acceptable formula can be used to explain the recoil energy shift. Illustrative numerical calculations show that the energy shifts caused by the photoelectron diffraction amounts to 5–8 meV for graphite-like carbon and about 100 meV for LiI₆${\text{LiI}}_6$ cluster at _?k=5${?}_k=5$–7 keV, and show oscillations as functions of the photoelectron energy. Furthermore we discuss the recoil effects in photoemission from extended levels by use of the tight-binding approach. Our approach naturally provides not only Debye–Waller factors but also the recoil factors. In addition to the phonon excitation, we also study the recoil effects associated with plasmon losses where intrinsic and extrinsic processes can interfere each other. Only the latter can contribute to the recoil energy shift.     

Sparse quasi-Newton updates with positive definite matrix completion

Quasi-Newton methods are powerful techniques for solving unconstrained minimization problems. Variable metric methods, which include the BFGS and DFP methods, generate dense positive definite approximations and, therefore, are not applicable to large-scale problems. To overcome this difficulty, a sparse quasi-Newton update with positive definite matrix completion that exploits the sparsity pattern of the Hessian is proposed. The proposed method first calculates a partial approximate Hessian , where , using an existing quasi-Newton update formula such as the BFGS or DFP methods. Next, a full matrix H _k+1, which is a maximum-determinant positive definite matrix completion of , is obtained. If the sparsity pattern E (or its extension F) has a property related to a chordal graph, then the matrix H _k+1 can be expressed as products of some sparse matrices. The time and space requirements of the proposed method are lower than those of the BFGS or the DFP methods. In particular, when the Hessian matrix is tridiagonal, the complexities become O(n). The proposed method is shown to have superlinear convergence under the usual assumptions.      

Measurements of velocity distributions with a laser doppler imaging system

A laser Doppler imaging system with a TV camera has been constructed and velocity distributions of fluid flow in cross sections of a rectangular channel have been measured. Consequently, it has been found that the system has some advantages in comparison with usual laser Doppler velocimeters, for example, the visualization of flow can be easily achieved.