This review on "wave optics in gravitational lensing" includes a derivation of the diffraction integral formula for the lensed wave amplitude using the path integral ( §2), reduction of this formula to the geometric optics approximation in the short wavelength limit along with discussion on the condition that the wave effects become important ( §3), examples of wave effects for a point-mass lens and the fold caustic ( §4), and a numerical method of evaluating the diffraction integral ( §5). * ) To our knowledge this approach is new to the gravitational lens theory. at University of British Columbia on June 24, 2015 http://ptps.oxfordjournals.org/ Downloaded from

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The bipolar nebula IRAS 19312$+$1950 is a unique SiO maser source exhibiting both properties of young and evolved objects. To clarify the nature of this object, we made molecular line observations with the Nobeyama 45-m radio telescope. We detected emission from O-bearing ($\mathrm{HCO}^{{+}}\mkern-2.0mu$, SiO, SO, and $\mathrm{SO}_2$), C–and N-bearing molecules (CN, CS, HCN, HNC, $\mathrm{NH}_{3}$, $\mathrm{N}_{2}\mathrm{H}^{+}\mkern-2.0mu$, $\mathrm{HC}_{3}\mathrm{N}$, $\mathrm{H}_2\mathrm{CS}$, and $\mathrm{CH}_3\mathrm{OH}$), and their isotopic species (C${{17\atop} \mathrm{O}}, {{13\atop} \mathrm{C}}$${{18\atop} \mathrm{O}}$, and C${{34\atop} \mathrm{S}}$). The line profiles consist of weak broad ($\Delta v \sim 30 \,\mathrm{km} \,\mathrm{s}^{-1}$) and/or strong narrow ($\Delta v \lesssim 5 \,\mathrm{km} \,\mathrm{s}^{-1}$) components, depending on the molecular species. Strong time variations of $\mathrm{H}_2\mathrm{O}$ and SiO masers were also observed. Numerical modeling of the envelope with the LVG-code resulted in a good fit of the model with a mass loss rate of $2.6 \times10^{-4} \,{{{M}_{\odot}}} \,\mathrm{yr}^{-1}$ to the observed intensities for the broad-component lines. On the other hand, non-O-bearing molecules, which only have narrow profiles, were found to have abundances typical of those in cool dust clouds. No isotopic enrichment was found, indicating little evidence of the narrow cool component being ejecta of the central AGB star or a possible companion. These facts compelled us to conclude that IRAS 19312$+$1950 is an exotic mass-losing evolved star embedded in a low-mass ($\sim 20 \; \,{{{M}_{\odot}}}$) dark cloud.

We present the results of observations of cold IRAS sources in the Galactic disk area, −10 • < l < 100 • and |b| < 5 • , in the SiO J = 1-0, v = 1 and 2 maser lines. SiO masers were detected in 51 out of 143 observed sources; 45 were new detections in SiO masers. The selected IRAS sources were objects with dust temperatures of between 160 and 280 K. According to a confirmation using 2MASS near-infrared images, a majority of the sample are AGB or post-AGB stars, although dense cores in the starforming regions (or dusty Hii regions) are involved in part of the sample. Among new detections, two were candidates for post-AGB stars: IRAS 18450−0148 (W 43A), and 19312+1950. We found that the intensity ratios of the SiO J = 1-0, v = 2 to the v = 1 line of the objects clearly correlate with those IRAS colors. The detection rates of SiO masers tend to increase toward the Galactic center as well as the cases of previous SiO maser surveys of typical AGB stars. No strong associations of the objects to the spiral arms were found. The radial-velocity dispersion of the present sample is comparable with the dispersion of the SiO maser sample of typical AGB stars. These facts suggest that the present sample of cold IRAS sources with SiO masers has a kinematic property very similar with that of typical AGB stars.