Generalized positive continuous additive functionals of multidimensional Brownian motion and their associated Revuz measures

We extend the notion of positive continuous additive functionals of multidimensional Brownian motions to generalized Wiener functionals in the setting of Malliavin calculus. We call such a functional a generalized PCAF. The associated Revuz measure and a characteristic of a generalized PCAF are also extended adequately. By making use of these tools a local time representation of generalized PCAFs is discussed. It is known that a Radon measure corresponds to a generalized Wiener functional through the occupation time formula. We also study a condition for this functional to be a generalized PCAF and the relation between the associated Revuz measure of the generalized PCAF corresponding to Radon measure and this Radon measure. Finally we discuss a criterion to determine the exact Meyer–Watanabe’s Sobolev space to which this corresponding functional belongs.     

Transport and focusing of a low-energy electron beam in low-pressure ionized argon

The transport and focusing of low-energy electron beams with effective transfer of stored energy in low-pressure ionized argon are investigated under the conditions of a high degree of charge neutralization in an external longitudinal magnetic field. It is shown that a nonuniform magnetic field provides the range of parameters where one can tightly stabilize the position of the maximum of the beam on the target and, if necessary, compress the beam. It is demonstrated that the parameters of the electron beam can be controlled by appropriately selecting the configuration of the magnetic field matched to self-fields.     

Stereocontrolled synthesis of the C79-C96 fragment of symbiodinolide

The stereoselective synthesis of the C79-C96 fragment of symbiodinolide is described in which the spiroacetalization and Kotsuki coupling are the key steps.     

The structure of liquid As2Se3 and GeSe2 by neutron diffraction

The liquid structures of As₂Se₃ and GeSe₂ have been investigated using the neutron diffraction patterns. In both cases the structure factor showed a low first peak maximum which follows a weak but apparent pre-peak at very low momentum transfer. It was also observed that the radial distribution function of both materials are characterized by the well-defined first neighbor shell because of the deep minimum on its right-hand side although in the liquid state. These results indicate that strong covalent bondings between unlike atoms in the solid state still remain when melting. Both the structure factor and the distribution curves of these alloys are, on the whole, similar to those in the amorphous phase which have already been examined. A slight difference in the coordination number, however, is found between amorphous and liquid phases of these materials.     

Robust particle image velocimetry using gradient method with upstream difference and downstream difference

In the first part of this paper, sub-pixel displacement detection methods in particle image velocimetry (PIV) measurements were discussed. Some schemes for calculating the spatial gradient in a gradient method, which is one of sub-pixel displacement detection methods, were evaluated. It was found that the second order central finite difference scheme tends to underestimate the gradient of the tracer-particle’s intensity. Consequently it leads to an overestimation of sub-pixel displacements. A first-frame upstream and second-frame downstream finite difference scheme was then proposed and evaluated for one-dimensional flow measurements. Furthermore, the proposed difference scheme was extended to apply to two-dimensional flows. It was shown that taking the direction of the sub-pixel correction into account and using fewer adjacent pixels are important for PIV images consisting of small tracer particle images. Finally, a robust procedure for the execution of the gradient method was proposed, which can eliminate the effect of noises. It was found that the proposed scheme is not only highly accurate but is highly robust to noise.