Apollonius tenth problem via radius adjustment and Möbius transformations

The Apollonius Tenth Problem, as defined by Apollonius of Perga circa 200 B.C., has been useful for various applications in addition to its theoretical interest. Even though particular cases have been handled previously, a general framework for the problem has never been reported. Presented in this paper is a theory to handle the Apollonius Tenth Problem by characterizing the spatial relationship among given circles and the desired Apollonius circles. Hence, the given three circles in this paper do not make any assumption regarding on the sizes of circles and the intersection/inclusion relationship among them. The observations made provide an easy-to-code algorithm to compute any desired Apollonius circle which is computationally efficient and robust.     

Approximation of fruit skin patterns using spherical Voronoi diagrams

In nature, there are many tessellation patterns on curved surfaces that look like Voronoi diagrams. Typical examples are the patterns found on fruit skins. Verifying that a given tessellation is a Voronoi diagram will be useful for constructing mathematical models of polygonal patterns. However, the data are usually obtained as a 2D projected image, and hence it is not easy to compare it with a Voronoi diagram on a curved surfaces. We propose a framework for using a photograph of a fruit to measure the difference between the pattern on its skin and a spherical Voronoi diagram. The problem of finding the spherical Voronoi diagram that best fits the fruit skin pattern is reduced to an optimization problem. The validity of this formulation is evaluated using jackfruit and lychee. We also propose generalizations of our problem for further research.     

Continuous reactor system of monosized colloidal particles

A reactor system, which continuously hydrolysed the metal alkoxide in an alcohol solution, was designed using an electromagnetic stirrer and an ageing tube. Several monosized colloidal particles were produced by this reactor system, which had high reproducibility and reliability for long-term production. The relation between powder characteristics and experimental parameters such as reagent concentration, mixing rate, ageing time, temperature, was investigated. These parameters had an effect on the particle size, size distribution, morphology and state of agglomeration. It is possible to control the particle size to between 0.1 and 1.0 μm by varying the experimental conditions. A narrower size distribution of powders was obtained by using an electromagnetic stirrer with greater flow rate. Physical and chemical properties of monosized colloidal particles obtained by this reactor were comparable to those of monosized colloidal particles obtained by the batch process.     

Semiautomatic leakage analyzing system for time series fluorescein ocular fundus angiography

An algorithm for measuring an index of leakage in fluorescein fundus angiography is presented. The number of pixels whose gray level exceeds an automatically determined slice level is calculated. An automatic blood vessel elimination technique is introduced. Further, a method of measuring the short term change of leakage from a time series of the fluorescein fundus angiographs is described. Our system can also deal with the time series images obtained on different occasions (long term change).The features of this paper are: (1) this paper deals with double time sequence images (short and long term); (2) an automatic blood vessel recognition algorithm is employed.     

Anisotropy and Superconductivity in the DMET-TSeF System

The electronic states have been studied in the quasi-one-dimensional DMET-TSeF system, which includes several superconductors and nonsuperconductors. The origin of the different ground states has been examined by using the tight-binding band calculation. The type of the superconductivity has been discussed, considering the electronic wave functions that constitute the Fermi surface.     

Flaw and modification of the iKP electronic payment protocols

We found that the 2KP/3KP electronic payment protocols as well as the 1KP electronic payment protocol do not possess a probably important property. The property is that if an acquirer authorizes a payment, then both the buyer and seller concerned always agree on it, which is called agreement property in this article. We also propose a modification to have 2KP/3KP possess the property.     

Low Temperature Study of the Mixed Donor System (TMTSF1-x TMTTF x )2PF6 : Crystal Structure, ESR and Transport Property

The phase diagram of the mixed donor quasi one-dimensional (Q1D) metallic system (TMTSF_1-x TMTTF _x )₂PF₆ has been studied. The study on the mixed donor systems helps us to establish not yet clarified phase boundaries in the Q1D system. We showed dependencies of properties on the donor mixing percentage for crystal parameters, resistivity, ESR(intensity and line width). ESR results show clear changes in the susceptibility and line width around 40 K. This result may indicate the existence of new boundary determined by the microscopic method on the Q1D phase.     

3D numerical analysis and test results of a short‐primary linear reluctance motor

A 3D boundary integral equation is applied to a model of a short‐primary linear reluctance motor. The model is a double‐sided construction where the primary member is surrounded by a set of secondary iron plates on both sides. Six kinds of different secondary geometries are calculated and their characteristics are discussed. For the confirmation of calculation results, a test machine is manufactured. Test results are compared with calculated ones. Furthermore, the static thrusts of a single‐sided machine and a coreless PMLSM are measured and compared with those of the double‐sided machine. © 2007 Wiley Periodicals, Inc. Electr Eng Jpn, 161(1): 58–65, 2007; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20390