Cyclic acetal-photosensitized polymerization. VII. Photopolymerization of 2-vinyl-4-hydroxymethyl-1,3-dioxolane

In order to assess the effect of the methylol group at the 4-position of 1,3-dioxolane on polymerization, the photopolymerization of 2-vinyl-4-hydroxymethyl-1,3-dioxolane (VHDO) was carried out in benzene at 40°C. The reaction scheme of VHDO was considered to be the same as that of 2-vinyl-1,3-dioxolane (VDO). The rate of polymerization and the molecular weight of polymer were small because of the degradative chain transfer by allylidene group. Moreover, the rate of polymerization of VHDO was greater than that of VDO, whereas the molecular weight of polymer of VHDO was less than that of VDO.     

On Selection Criteria for the Tuning Parameter in Robust Divergence

Although robust divergence, such as density power divergence and γ-divergence, is helpful for robust statistical inference in the presence of outliers, the tuning parameter that controls the degree of robustness is chosen in a rule-of-thumb, which may lead to an inefficient inference. We here propose a selection criterion based on an asymptotic approximation of the Hyvarinen score applied to an unnormalized model defined by robust divergence. The proposed selection criterion only requires first and second-order partial derivatives of an assumed density function with respect to observations, which can be easily computed regardless of the number of parameters. We demonstrate the usefulness of the proposed method via numerical studies using normal distributions and regularized linear regression.     

Dilatation and pattern formation of cells in internally heated convection

The dilatation and the pattern formation of convection cells in natural convection driven by internal heat generation, first investigated during the 1970s, are reexamined in this paper using an improved experimental apparatus in order to reduce uncertainties as much as possible. The convective motion in the fluid layer was visualized using reflecting particles (Kalliroscope). Cell dilatation was confirmed in the improved experimental apparatus and then investigated quantitatively by extracting the pattern wavenumber from Fourier analysis of the images recorded by a digital camera. The pattern wavenumber was found to decrease with increasing Rayleigh number. We compare our results with earlier investigations and discuss the influence of the thermal boundary condition at the bottom of the fluid layer on the variation of the wavenumber. Two different structures were observed in the same fluid layer at a relatively high Rayleigh number; an additional cell appears in the original cell (Double cell structure) and the descending flow region around the center of the cell expands laterally like a spoke of wheels (Spoke-like structure). Factors for the formation of such complex structures are discussed.