Timelike Minimal Surfaces via Loop Groups

This work consists of two parts. In Part I, we shall give a systematic study of Lorentz conformal structure from structural viewpoints. We study manifolds with split-complex structure. We apply general results on split-complex structure for the study of Lorentz surfaces.In Part II, we study the conformal realization of Lorentz surfaces in the Minkowski 3-space via conformal minimal immersions. We apply loop group theoretic Weierstrass-type representation of timelike constant mean curvature for timelike minimal surfaces. Classical integral representation formula for timelike minimal surfaces will be recovered from loop group theoretic viewpoint.     

Lightness Change as Perceived in Relation to the Size of Recognized Visual Space of Illumination

According to the concept of the recognized visual space of illumination (RVSI) the lightness of an object surface is perceived in relation to its conceptualized size. To prove this proposition the lightness of gray test patches was judged when they were located at various positions inside an illuminated space composed of two rooms in the depth direction from a subject. No retinal image arrangement was changed in the test patch and its immediate surroundings, but the front room had walls, floors and furniture lower in lightness by the amount of N1.5 than the back room to make the RVSI of the former smaller despite the illuminance in the entire space being the same. The results showed that the apparent lightness of the patches was perceived higher by amount of about 13 in L units for the N4 test patch and about 20 for N6 when the patches were located in the front room, in accordance with the prediction. It was stressed that the experiment of lightness judgment should be conducted in a three dimensional space rather than two dimensional plane as done by several investigators.     

Common-path achromatic interferometer-coronagraph: nulling of polychromatic light

A three-dimensional common-path interferometer is proposed, which can achromatically null out an on-axis source while it maintains the detectability of an off-axis source. A geometric phase in the three-dimensional interferometer introduces an achromatic pi-phase shift to the light from the on-axis source, such that destructive interference nulls out the axial light at one of the ports of the interferometer. Light from the off-axis source, which is exempt from the pi-phase shift, comes out from both ports with equal intensity. The common-path scheme makes the system highly immune to environmental disturbances.     

Geometrical Form Factor Improvement for Receiving System of Infrared Lidar

Improvement of an infrared light detection and ranging (IR-lidar) system for a short range (0–1000 m) and with high resolution is studied to enhance a geometrical form factor. Theoretical modeling of Mie scattering echo signals agrees with the experimental results. Introduction of a lens in front of the detector is effective for increasing the geometrical form factor, and a significant improvement in the received signal intensity is achieved, especially for short-range measurements around 100 m. This is useful for the IR-lidar system with a detector diameter of less than 1 mm. In the theoretical model, a ray-tracing technique was applied and a transmitting laser beam with Gaussian profile was considered for better accuracy.     

Fringe formula for projection type moiré topography

The rays that form moiré fringes in projection type moiré topography are discussed. It is shown that the nodal-ray formula conventionally used in projection type moiré topography gives erroneous results for an object located close to the lenses. An alternative formula based on principal rays is proposed and compared with the conventional nodal ray formula. The principal ray formula proposed can be applied to a wide class of optical systems, including a telecentric system.     

Mechanical and dielectric absorption of poly(vinyl chloride) and some related polymers

The mechanical and dielectric low temperature absorptions of poly(vinyl chloride) (PVC) and several modified PVC's have been studied over the temperature range from ?60 to +60°C. with some tests extending to ?150°C. and others to +170°C. The results indicate that the low-temperature absorption near ?50°C (β₂ absorption) decreases in intensity with chlorination, while the absorption at a higher temperature near 0°C (β₁ absorption) decreases in intensity with hydrogenation. The apparent activation energies of the β₁ and β₂ absorptions were calculated to be 16 kcal/mole and 10.7 kcal/mole, respectively. Besides, the β₂ absorption markedly decreases in intensity with addition of plasticizer, while the intensity of β₁ absorption is not much affected by increasing plasticizer content. From these results, the β₁ and β₂ processes are concluded to be the results of molecular motion in crystalline and amorphous region in PVC, respectively. For samples of reduced Cl content, another low-temperature absorption was located near ?120°C (γ absorption) and attributed to the presence of short sequences of ethylene units. It has also been observed that the temperature location of the high temperature absorption near 100°C (α absorption) shifts linearly to higher temperature with increasing chlorine content and to lower temperature with increasing hydrogen content.