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.     

Studies on the synthesis of proteinase inhibitors. II. Synthesis of cyclic nonapeptide fragments and analogs related to the reactive sites of soybean Bowman-Birk inhibitor

Several heterodetic cyclic nonapeptides modeled after the disulfide loops of Bowman-Birk inhibitor which involve either the anti-tryptic or anti-chymotryptic region have been synthesized by the conventional method. The inhibitory properties and the stabilities of these peptides toward trypsin and chymotrypsin, as well as the properties of dimers of the above nonapeptides, were examined.     

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.