Key Words: Division by zero, division by zero

calculus, singularity, derivative, differential equation, $0/0=1/0=z/0=0 $, $tan (pi/2) = 0$, $log 0=0$, infinity, discontinuous, point at infinity, gradient, Laurent expansion, extension of solutions of differential equations, reduction problems of differential equations, analytic geometry, singular integral, conformal mapping, Euclidean geometry, Wasan.

In order to see simply the results of the division by zero, we will show the simple results in the typical and fundamental object triangles and triangle functions. Even the case of triangles, we will be able to derive new concepts and results from the division by zero property.

One typical result is as follows:

$$

tan frac{pi}{2} = 0.

$$

The essential problems with the mysterious history of the division by zero were on the {bf definition} of the division by zero and the strong {bf discontinuity} of the fundamental function $y = 1/x$ at the origin. This discontinuity was not accepted for long years. One more problem for the division by zero is on the concept of the {bf division by zero calculus}; that is, the fractions and functions cases are different, as we showed clearly.

We have considered our mathematics around an isolated singular point for analytic functions, however, we did not consider mathematics {bf at the singular point itself}. At the isolated singular point, we considered our mathematics with the limiting concept, however, the limiting values to the singular point and {bf the values at the singular point } in the sense of division by zero calculus are different.

By the division by zero calculus, we can consider the values and differential coefficients at the singular point. We, therefore, have a general open problem discussing our mathematics on a domain containing the singular points.

Singular integral equations are presently encountered in a wide range of mathematical models, for instance in acoustics, fluid dynamics, elasticity and fracture mechanics. Together with these models, a variety of methods and applications for these integral equations has been developed.

However, what are singular integrals and why do appear singular integrals in many discontinuity phenomena? For singular integrals, we will consider their integrals as divergence, however, the Hadamard finite part or Cauchy's principal values give finite values; that is, from divergence values, we will consider finite values; for this interesting property, we will be able to give a natural interpretation by the division by zero calculus.

We would like to give some essential answers to those questions by the division by zero calculus that was born from the division by zero.

In the talk, we will introduce our recent results on the division by zero calculus and formulas that were obtained from the division by zero and we will give the interpretation for the Hadamard finite part of singular integrals and Cauchy's principal values by means of the division by zero calculus.

The real numbers were built from the counting numbers in a process using new definitions and symbols to graft new numbers on to already

existing numbers. The new numbers made possible something impossible with existing numbers. For example, defining fractions made possible dividing odd numbers by an even number and defining negative numbers made subtracting larger numbers from smaller numbers possible. Proposed here are new definitions and symbols to once more build on to the already existing real number system with one key difference. An existing number, zero, will be replaced with a new and improved zero as part of the process. In this paper, we will focus on the impossible task of making an additive identity that has a reciprocal - a reciprocal that is not a multiplicative inverse of zero. The benefits of defining division by the new zero such as unique quotients capable of constructing

spaces of dimensions higher than the complex plane have been explored more thoroughly in another paper

The common sense on the division by zero with a long and mysterious history is wrong and our basic idea on the space around the point at infinity is also wrong since Euclid. On the gradient or on differential coefficients we have a great missing since $tan (pi/2) = 0$. Our mathematics is also wrong in elementary mathematics on the division by zero. In this talk, we will show and give various applications of the division by zero $0/0=1/0=z/0=0$. In particular, we will introduce several fundamental concepts in calculus, Euclidian geometry, analytic geometry, complex analysis and differential equations. We will see new properties on the Laurent expansion, singularity, derivative, extension of solutions of differential equations beyond analytical and isolated singularities, and reduction problems of differential equations. On Euclidean geometry and analytic geometry, we will find new fields by the concept of the division by zero. We will show many concrete properties in mathematical sciences from the viewpoint of the division by zero. We will know that the division by zero is our elementary and fundamental mathematics.

The extended self-conception was first discussed 20 years before( Hidano (2002), Hidano and Muto (2006)) and has attracted an attention from various fields of studies including applied physics. Unlike to western world individualism, we proposed a united self not only within our body and mind and also multiple individuals as an extended self.  After showing the results of the game-theoretic theorem to identify the conditions to make an extended self, we argue how the extended self can be specially formulated in a collective art making a performance by taking several experiments. We discuss the possibility to utilize this conception to promote innovation in applied sciences. 

Cognitive computing and neuro-inspired information processing have been gaining immense interest in recent years. Increasing demands on computing, problems to maintain Moore’s Law much longer and the need for higher energy efficiency have been stimulating novel computational concepts. Their hardware implementation, adapted to the concept and to the targeted infrastructure in which it needs to be embedded, define a number of challenges. We follow a minimal design approach in optics, allowing for hardware efficiency, high speed, low energy consumption and compatibility with our optical communication infrastructure.

Using telecommunication-compatible hardware, we have implemented reservoir computing and extreme learning machine concepts and could demonstrate their attractive features in benchmark tests including classification tasks and nonlinear prediction. The real-world technological challenge we present here is, how to classify ultra-fast signals that are subjected to significant nonlinear distortions. In particular, we process optical fibre communication data. Fibre communication systems are range-limited due to transmission impairments that distort the propagating signals. For extended transmission distances, standard bit recovery techniques fail completely. We overcome this limitation by transforming the bit classification problem into a pattern recognition problem. We experimentally demonstrate a bit error rate improvement of 2 orders of magnitude compared to competing methods. The bit classification performance we achieve is a significant breakthrough since we can recover data at a high speed that otherwise cannot be recovered. Challenges regarding a full hardware and real-time implementation remain, but we show strategies how these challenges can be overcome

Gallium nitride (GaN) is currently the most ideal semiconductor for power transistors and other power devices.  It has been found that GaN has much better performances in comparison with silicon carbide (SiC) as well as Si from a viewpoint of condensed matter physics.  However, GaN power devices (power GaNs) have not yet been applicable to power electronics devices for inverters/converters, power conditioners, electric vehicles and other transportation systems, although theoretical calculations have revealed that the change from power Si to power GaN will bring about more than 90 percent cut of the energy loss to the society.  In the present work, we will discuss what disturbs the appearance of power GaN and draw an innovation scenario toward the society without energy loss from both aspects of physics studies and industry studies. 

Recently global climate change has been a critical issue for survivability of the whole life system on the globe. Monitoring and prediction of population and community stabilities are an urgent issue as a prerequisite for achieving sustainability of ecosystems. Example cases of population/community dynamics are presented during the course of invasion, eruption and establishment. Based on model applications population growth patterns are reported, showing the break points during the course of invasion and eruption. Community structure properties are additionally revealed in responding to various sources of natural and anthropogenic disturbances according to species abundance distributions. The responding patterns of communities were observed including a few dominant taxa in natural conditions and rapid decrease in species richness under stressful conditions of disturbances. Feasibility of mathematical models in population/community monitoring and management are further discussed in the presentation.

Perception and recognition means the assignment of objects to specific classes. Objects defined by the primary character ‘life’ are named ‘organisms’. Organisms are grouped into classes called ‘species’ according to homogeneities in shape and organization. Several species concepts have been developed. Like organisms, species are ‘individuals’ because being entities restricted in time (by originating and ending) and by space. A general explorative species definition must be used in the studies on evolution, phylogeny, ecology, biodiversity and biogeography. Species as evolutionary units show different forms of speciation. Measures for diversities used in ecology and biodiversity must be based on a general species concept otherwise apples will be mixed with oranges. Grouping of species into classes with decreasing character homogeneities leads to nested hierarchical class systems. Introduced by Carolus Linnaeus together with the binomial naming, two classification systems require representing the ‘natural system’. The phenetic system is a nested hierarchy of fixed classes called ‘categories’, named ‘genus’, ‘family’, ‘order’, ‘class’, ‘phylum’, ‘kingdom’ and ‘domain’. This ‘evolutionary system’ cannot directly show phylogenetic lineages due to different evolutionary rates within categorial classes. Furthermore, the fixed categories are arbitrary due to inconsistencies in the defining character sets. The phylogenetic system strictly reflects phylogenetic relations. Initially based on morphological characters weighted by apomorphies (novel evolutionary traits), molecular genetic sequences are used today. Both methods result in nested hierarchies named ‘phyletic systems’. The underlying phylogenetic system, which is an exclusive hierarchy with branching points becoming objects (species), cannot be reconstructed explicitly. Natural categories can be detected in nested hierarchies based on inconstancies in class building rates when identical character sets are used. Only the genus category with the lowest inconstant heterogeneity grade in monophyletic groups can represent a natural category. This is important for a consistent intersubjective identification of species by the binomen

Nursing Science is one of the integrative human sciences. The nursing theories are considered to be the structures reflecting thinking ways or philosophical ideas, which can explain the mutual relationships among human beings within nursing phenomena in a unified manner. Most nursing theories so far have been proposed in order to understand such mutual relationships on the basis of the general system theory and the problem-solving way according to Western scientific ideas.

The first nursing theory was presented by Florence Nightingale in her book, “Notes on Nursing: What it is and what it is not” published in 1859. She said that “Nursing is to alter the environment in such a way to obey the natural laws and at the least expense of vital power to the patient.” Nightingale’s vital power can be considered to be “resilient systems” in the present terminology. Resilient Systems have the Power that can rebuild autonomously and fluidly our own structure. In addition, the resilient systems have the meaning of recovery from the failure and/or recovery from the disability, illness, and some other dis-functions autonomously.

In the present study, the author proposed the new nursing model based on the Eastern Philosophy. The right-side figure shows the structure of a new nursing model named “The Mandala Nursing Model”. It was constructed on the framework of the “Self-Nonself Circulation Theory” proposed by Masatoshi Murase (2000). The data obtained from 10 persons with depression were qualitatively analyzed in order to identify 5 cognitive characteristics: (1) inharmonic body v.s. harmonic mind-body, (2) limit of energy v.s. increasing energy, (3) introvert relationship v.s. the extrovert relationship, (4) collapsing self v.s. redeveloping self, and (5) past life v.s. future life.

In addition, there were 5 different patterns of nursing care:  (1) nursing care of inherent ability within denial, (2) nursing care of the discovery of the meaning of life, (3) nursing care from parts to wholeness, (4) nursing care of pro-care (sympathetic care), and (5) nursing care of con-care (critical care).

The present figure indicates one of the developmental stages of nursing care.  As time proceeds, the structure develops in such a way that the whole structure and its parts are the same as each other. This is the important characteristics of the mandala structure. Because of this self-nested hierarchical structures, the mandala can indicate not only the goal of nursing care but also its current stage. From such a point of view, the author believed that we have a hopeful future on human caring as well as its education.