Abstract:
Microfluidic behavior of ternary mixed carrier solvents of water-acetonitrile-ethyl acetate (2:3:1 volume ratio) was examined by use of a microchip incorporating microchannels in which one wide channel was separated into three narrow channels, i.e., triple-branched microchannels. When the ternary carrier solution containing the fluorescent dyes, hydrophobic perylene (blue) and relatively hydrophilic Eosin Y (green), was fed into the wide channel under laminar flow conditions, the carrier solvent molecules or fluorescence dyes were radially distributed in the channel, forming inner (organic solvent-rich major; blue) and outer (water-rich minor; green) phases in the wide channel. And then, in the narrow channels, perylene molecules mostly appeared to flow through the center narrow channel and Eosin Y, which is distributed in the outer phases in the wide channel, flowed through the both side narrow channels. A metal ion, Cu(II) as a model, dissolved in the ternary mixed carrier solution was also examined. The Cu(II) showed fluidic behavior, transferring from the homogeneous carrier solution to the water-rich solution in the side narrow channels through the triple-branched microchannels.

Abstract:
Microfluidic analytical system was developed based on annular flow of phase separation multiphase flow with a ternary water-hydrophilic/hydrophobic organic solvent solution. The analytical system was combined with on-line luminol chemiluminescence detection for catechin analysis. The water (10 mM phosphate buffer, pH 7.3)-acetonitrile-ethyl acetate mixed solution (3:8:4, volume ratio) containing 60 μM luminol and 2 mM hydrogen peroxide as a carrier was fed into the capillary tube (open-tubular fused-silica, 75 μm inner diameter, 110 cm effective length) at a flow rate of 1.0 μL·min^{-1}. The carrier solution showed stable chemiluminescence as a baseline on the flow chart. Eight catechins were detected as negative peaks for their antioxidant potential with different detection times. The system was applied to analyze the amounts of catechin in commercially available green tea beverages.

Abstract:
Denaturation was examined for the first time in a ternary mixed solution of water/hydrophilic/ hydrophobic organic solvent using λ-DNA and a plasmid as models. The absorbance of λ-DNA and the plasmid at 260 nm gradually increased for several days up to 1.68 and 1.38 times the initial values, respectively, in a water/acetonitrile/ethyl acetate (15:3:2, volume ratio) mixed solution, whereas there was little change in a water/acetonitrile (15:3, volume ratio) mixed solution. The plasmid treated with the ternary mixed solution was also examined with agarose gel electrophoresis. These experimental data indicated that λ-DNA changed from a double helix structure to a single helix structure and that the plasmid partially transformed to generate a denaturation bubble in the structure. The new idea of using the ternary mixed solution first enabled the interaction of the hydrophobic organic solvent (e.g., ethyl acetate) molecule with the double helical structure of DNA, leading to specific slow-proceeding denaturation.

Abstract:
Capillary chromatography using an untreated open tubular capillary tube and a ternary solvent mixture consisting of water-hydrophilic/hydrophobic organic solvent as a carrier solution has been developed. The system is called tube radical distribution chromatography (TRDC). Separation performance of the TRDC system using a fused-silica capillary tube was examined through the phase diagram for the ternary water-acetonitrile-ethyl acetate solvent mixture. The TRDC system required homogeneous carrier solutions with solvent component ratios around the boundary curve between homogeneous and heterogeneous solution in the phase diagram. The data obtained using the fused-silica capillary tube were compared with those obtained using a polytetrafluoroethylene capillary tube in our previous study.

Abstract:
The diagonal argument is a very famous proof, which has influenced many areas of mathematics. However, this paper shows that the diagonal argument cannot be applied to the sequence of potentially infinite number of potentially infinite binary fractions. First, the original form of Cantor’s diagonal argument is introduced. Second, it is demonstrated that any natural number is finite, by a simple mathematical induction. Third, the concept of potential infinity, created by Aristotle, is presented. Typically, the natural numbers are considered potentially infinite. However, although any natural number is finite, there is also no limit to how large a natural number can be. Fourth, the concept of the potentially infinite decimal is introduced. Fifth, it is easily proven that the diagonal argument cannot be applied to the sequence of all n-bit binary fractions in the interval [0,1). Finally, the diagonal argument is shown to be inapplicable to the sequence of the potentially infinite number of potentially infinite binary fractions, which contains all n-bit binary fractions in the interval [0,1) for any n.

Abstract:
The derivative is a basic concept of differential calculus. However, if we calculate the derivative as change in distance over change in time, the result at any instant is 0/0, which seems meaningless. Hence, Newton and Leibniz used the limit to determine the derivative. Their method is valid in practice, but it is not easy to intuitively accept. Thus, this article describes the novel method of differential calculus based on the double contradiction, which is easier to accept intuitively. Next, the geometrical meaning of the double contradiction is considered as follows. A tangent at a point on a convex curve is iterated. Then, the slope of the tangent at the point is sandwiched by two kinds of lines. The first kind of line crosses the curve at the original point and a point to the right of it. The second kind of line crosses the curve at the original point and a point to the left of it. Then, the double contradiction can be applied, and the slope of the tangent is determined as a single value. Finally, the meaning of this method for the foundation of mathematics is considered. We reflect on Dehaene’s notion that the foundation of mathematics is based on the intuitions, which evolve independently. Hence, there may be gaps between intuitions. In fact, the Ancient Greeks identified inconsistency between arithmetic and geometry. However, Eudoxus developed the theory of proportion, which is equivalent to the Dedekind Cut. This allows the iteration of an irrational number by rational numbers as precisely as desired. Simultaneously, we can define the irrational number by the double contradiction, although its existence is not guaranteed. Further, an area of a curved figure is iterated and defined by rectilinear figures using the double contradiction.

Abstract:
What is number? This question is difficult to answer. Because the number is one of the most basic concepts, it is difficult to define the natural number with other concepts. Still, this problem is worth trying to answer. Now, everything is digitized and processed on computer. The importance of the number is increasing day by day. Now is time to consider what number is. Throughout the history of humankind, the ancient Greeks considered this question most profoundly. In particular, Plato defined the natural number one. The natural number one is equal, invariable and indivisible. These properties are intuitively acceptable. However, we have never seen or touched the natural number one itself. How can we know it? Socrates said that we know it before birth. This claim is called anamnesis. In this paper, we use a method, in which Socrates’ anamnesis is studied by the contemporary science. From a modern viewpoint, we could take Socrates’ anamnesis to mean that the natural number one is written in our genes. This article considers whether there is a biological entity corresponding to the natural number one. As a result, we find that a life itself is the prototype of the natural number one, and then properties of life make a critical base of DNA similar to the natural number one through natural selection. A life is an integrated and indivisible system, which resists the law of entropy. Furthermore, the basic properties of life enable natural selection, which conserves genetic information despite the law of entropy. The source of the power, which enables life to resist the law of entropy, is the genetic information. In conclusion, a life is a prototype of the natural number one. Furthermore, a life recognizes nature using natural numbers and resists the law of entropy using natural numbers.

Abstract:
Two new species of the interstitial ostracod genus Parvocythere, P. gottwaldi sp. n. and P. gracilis sp. n., are herein described. Although these two new species are clearly distinguishable by certain morphological differences in elements of the male copulatory organ, and the carapace, they share the following simplified characters of the appendages and male copulatory organ: antennular fourth podomere with no suture; reduced claws on the distal end of antenna; and asymmetric male copulatory organ. The morphological differences among known and new Parvocythere species suggest that the species of this genus can be classified into two groups by the presence/absence of the suture on the antennular fourth podomere. The “Group S” is characterised by the presence of the antennular suture, and all species of this group have a two-clawed antenna and symmetric male copulatory organ, characters which are generally seen in cytheroid ostracods. The species belonging to “Group N” are characterised by the absence of the suture, regarded as a pedomorphic character, show the following characters: two clawed or one clawed antenna, and symmetric or asymmetric male copulatory organ. The morphological variation within Group N includes reductive characters regarded as an adaptation to the narrow spaces of the interstitial environment of a sandy beach. These intrageneric morphological variations of the exclusively interstitial genus Parvocythere suggest the possibilities that Group N might be derived from Group S, and that some adaptive characters to an interstitial environment could have developed after the colonisation of these environments.

Abstract:
A new species of the genus Polycopetta Chavtur, 1981, Polycopetta quadrispinata sp. n. is described from the interstitial environment of Mihomasaki Beach in Japan. These observations showed some morphological peculiarities of Polycopetta quadrispinata sp. n. compared with its congeners; P. monneroni Chavtur, 1979, P. curva Chavtur, 1979, P. bransfieldensis (Hartmann, 1987), and P. pax Kornicker and Harrison-Nelson, 2005. Three characteristics are described for the first time: (1) a seta with serrated tip on the male antennula, (2) the endopodite of the fifth limb consisting of two podomeres, (3) the long spermatozoa in the male posterior body. More detailed observations of the type species are needed in order to update the generic diagnosis.

Abstract:
A random walk Metropolis-Hastings algorithm has been widely used in sampling the parameter of spatial interaction in spatial autoregressive model from a Bayesian point of view. In addition, as an alternative approach, the griddy Gibbs sampler is proposed by [1] and utilized by [2]. This paper proposes an acceptance-rejection Metropolis-Hastings algorithm as a third approach, and compares these three algorithms through Monte Carlo experiments. The experimental results show that the griddy Gibbs sampler is the most efficient algorithm among the algorithms whether the number of observations is small or not in terms of the computation time and the inefficiency factors. Moreover, it seems to work well when the size of grid is 100.