A Necessary and Sufficient Condition for the Existence of a Heterochromatic Spanning Tree in a Graph

We prove the following theorem. An edge-colored (not necessary to be proper) connected graph G of order n has a heterochromatic spanning tree if and only if for any r colors (1≤r≤n−2), the removal of all the edges colored with these r colors from G results in a graph having at most r+1 components, where a heterochromatic spanning tree is a spanning tree whose edges have distinct colors.     

THE DESIGNS OF HIGH EFFICIENCY LAUNCHER OF QUASI-OPTICAL MODE CONVERTER FOR HIGH POWER GYROTRONS

A high efficiency launcher of quasi-optical (QO) mode converters for high power gyrotrons have been designed and tested. A helical cut launcher radiates the RF power via its straight cut onto the first phase correcting mirror. The launchers have been optimized for the TE_31.8 mode at 170 GHz and TE_22.6 mode at 110 GHz by numerically optimizing a launcher surface. The helical cut of the launcher has been optimized by taking the taper angle into account. Further more, the amplitude of the surface perturbation have been optimized for improved focusing in order to reduce the diffraction losses at the helical cut. Low power measurement shows a good agreement with the design. High efficiency characteristics of the design have also been calculated on the assumption of frequency downshift due to the thermal expansion of the cavity and stepwise frequency tuning by changing the operating mode. Besides, the possibility of high efficiency launcher for higher mode is discussed, and these results give the prospect to high efficiency long pulse gyrotrons.     

Self-Restoration Properties of VWP Networks by Spare Wavelength Optimization

The self-restoration properties in VWP networks are investigated with optimization about spare wavelength by simulations. Rapid restoration can be achieved by selection of rerouting path with long delay and no delay-limitation for new routes.     

Endoscopic Observation of Tissue by Narrowband Illumination

We propose a new illumination method for a medical endoscope: narrow band imaging (NBI), in which the spectral bandwidth of the filtered light is narrowed. To confirm how the spectral specifications of the filtered light influence a reproduced image, an experiment was conducted observing the endoscopic images of the back mucosa of a human tongue. In addition, the effect of NBI on endoscopic images was investigated through preliminary clinical tests in colonoscopy and upper gastrointestinal endoscopy. It has been shown that NBI can enhance the capillary pattern and the crypt pattern on the mucosa. These patterns are useful features for diagnosing an early cancer.     

Slow cyclotron instability in a high-power backward-wave oscillator

The linear dispersion relation of a backward-wave oscillator (BWO), derived earlier by the authors, is modified to include effects of RF surface current at the beam-vacuum interface. This modified dispersion relation results in an unstable interaction between the slow cyclotron mode (SCM) and the structure mode in addition to the conventional Cherenkov instability caused by the slow space charge mode. Numerical analysis is then carried out using parameters of a BWO experiment at University of Maryland. Fine structure of the SCM instability is elucidated. The analysis indicates that BWO radiation would not be suppressed near cyclotron absorption in an infinitely long system.