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.

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.

The aim of this
study is to clarify factors related to premature death among Japanese professional
baseball players by a case-control analysis. The subjects are two matching
groups of 622 Japan Professional Baseball (JPB) league players, those deceased
and those surviving. Cases and controls are matched by birth year. All players
debuted on the first string between 1934 and 2003, and are listed in The
Official Baseball Encyclopedia of Japan. To compare means and frequencies of
characteristics between deceased and surviving groups, t-tests and chi-square
tests were used. A logistic regression analysis was assessed contributions of
each independent variable on death. Significant differences between deceased
and surviving players were observed in this study; deceased players had
higher body mass indexes and longer careers. Furthermore, logistic regression
analysis confirmed that body mass index and career length were statistically significant determinants of death for baseball players. This is the first report to
examine factors of death for professional baseball players except employing data attained from Major League Baseball.

Nicotine and cotinine in hair
are good biomarkers for assessing long-term exposure to smoking. However, analytical
devices such as GC/MS are associated with high cost and are not widely used. HPLC/UV is used widely in laboratories, but is unsuitable for measurement of minor
constituents, except when using the column-switching method. Thus, we
aimed to establish a simple, inexpensive and sensitive method based on HPLC/UV
with column switching for measuring nicotine and cotinine in hair. First, we
compared the presence and absence of a column selection unit. We then measured
amounts of nicotine and cotinine in hair samples collected from the general
population, and compared both the corresponding levels and the detection
limits with those in previous studies. Finally, initial and running costs of
HPLC/UV were compared with other analytical methods. As one of the results, the
areas of nicotine and cotinine measured by HPLC/UV with column-switching method
were 12.9 and 16.9 times greater, respectively, than those without the
column-switching method. The amount of nicotine and cotinine in hair was significantly
correlated to number of cigarettes smoked per day (r = 0.228, p = 0.040). In
addition, the HPLC/UV method showed similar sensitivity and detection limit
(nicotine, 0.10 ng/mg; cotinine, 0.08 ng/mg) as reported in previous studies.
The cost of the HPLC/UV method is lower than that of other analytical methods. We
were able to establish a low-cost method with good sensitivity for measuring
nicotine and cotinine in hair. The HPLC/UV with a column-switching method will
be useful as a first step in screening surveys in order to better understand
the effects of smoking exposure.

Abstract:
It is controversial whether or not Japanese manufacturing is already in decline and the Japanese model of manufacturing that drove past decades of the industrial and economic growth has lost the power. It is though true that Japan needs to develop a new and innovative business model for manufacturing in the years ahead. The present paper aims at (1) arguing that Japanese manufacturing requires transformation from integral-technology-based to modular-technology-based as well as their co-existence and (2) visualizing strategies for supporting them in practical terms. We in particular claim that in the transformation Machine-Tool Trading (MTT) companies should play a crucial role in getting servitizatized and functioning as project producers. We discuss roles and functions to be expected from servitized MTT companies by using the value orchestration platform model with quality control 7 tools as a reference. We also illustrate a roadmap for an MTT company to be servitized based on some real observations as well as the authors’ experiences.

Abstract:
An LMI-based method for the integrated system identification and controller design is proposed in the paper. We use the fact that a class of a system identification problem results in an LMI optimization problem. By combining LMIs for the system identification and those to obtain a discrete time controller we propose a framework to integrate two steps for the model-based control system design, that is, the system identification and the controller synthesis. The framework enables us to obtain a good model for control and a model-based feedback controller simultaneously in the sense of the closed-loop performance. An iterative design algorithm similar to so-called Windsurfer Approach is presented.

Abstract:
In this paper, we discuss the K"ahlerian submersion with vanishing Bochner curvature tensor and prove that the Bochner curvature tensor of the base space vanishes. Also, we seek a sufficient condition with respect to the length of the Ricci tensor of each fiber that the Bochner curvature tensor of each fiber vanishes.

Abstract:
We show that necessary and sufficient condition in order that K- conformal Killing equation is completely integrable is that the Kaehlerian manifold K2m(m>2) is of constant holomorphic sectional curvature.