Yatsuka Nakamura

A Theory of Matrices of Real Elements

A Theory of Matrices of Real Elements Here, the concept of matrix of real elements is introduced. This is defined as a special case of the general concept of matrix of a field. For such a real matrix, the notions of addition, subtraction, scalar product are defined. For any real finite sequences, two transformations to matrices are introduced. One of the matrices is of width 1, and the other is of length 1. By such transformations, two products of a matrix and a finite sequence are defined. Also the linearity of such product is shown.

The Definition of Finite Sequences and Matrices of Probability, and Addition of Matrices of Real Elements

The Definition of Finite Sequences and Matrices of Probability, and Addition of Matrices of Real Elements In this article, we first define finite sequences of probability distribution and matrices of joint probability and conditional probability. We discuss also the concept of marginal probability. Further, we describe some theorems of matrices of real elements including quadratic form.

Determinant of Some Matrices of Field Elements

Determinant of Some Matrices of Field Elements Here, we present determinants of some square matrices of field elements. First, the determinat of 2 * 2 matrix is shown. Secondly, the determinants of zero matrix and unit matrix are shown, which are equal to 0 in the field and 1 in the field respectively. Thirdly, the determinant of diagonal matrix is shown, which is a product of all diagonal elements of the matrix. At the end, we prove that the determinant of a matrix is the same as the determinant of its transpose.

Basic Properties and Concept of Selected Subsequence of Zero Based Finite Sequences

Basic Properties and Concept of Selected Subsequence of Zero Based Finite Sequences Here, we develop the theory of zero based finite sequences, which are sometimes, more useful in applications than normal one based finite sequences. The fundamental function Sgm is introduced as well as in case of normal finite sequences and other notions are also introduced. However, many theorems are a modification of old theorems of normal finite sequences, they are basically important and are necessary for applications. A new concept of selected subsequence is introduced. This concept came from the individual Ergodic theorem (see [7]) and it is the preparation for its proof.

The Relevance of Measure and Probability, and Definition of Completeness of Probability

The Relevance of Measure and Probability, and Definition of Completeness of Probability In this article, we first discuss the relation between measure defined using extended real numbers and probability defined using real numbers. Further, we define completeness of probability, and its completion method, and also show that they coincide with those of measure.

Complex Function Differentiability

Complex Function Differentiability For a complex valued function defined on its domain in complex numbers the differentiability in a single point and on a subset of the domain is presented. The main elements of differential calculus are developed. The algebraic properties of differential complex functions are shown.

The Real Vector Spaces of Finite Sequences are Finite Dimensional

The Real Vector Spaces of Finite Sequences are Finite Dimensional In this paper we show the finite dimensionality of real linear spaces with their carriers equal Rn. We also give the standard basis of such spaces. For the set Rn we introduce the concepts of linear manifold subsets and orthogonal subsets. The cardinality of orthonormal basis of discussed spaces is proved to equal n. MML identifier: EUCLID 7, version: 7.11.01 4.117.1046

Definition and some Properties of Information Entropy

Definition and some Properties of Information Entropy In this article we mainly define the information entropy [3], [11] and prove some its basic properties. First, we discuss some properties on four kinds of transformation functions between vector and matrix. The transformation functions are LineVec2Mx, ColVec2Mx, Vec2DiagMx and Mx2FinS. Mx2FinS is a horizontal concatenation operator for a given matrix, treating rows of the given matrix as finite sequences, yielding a new finite sequence by horizontally joining each row of the given matrix in order to index. Then we define each concept of information entropy for a probability sequence and two kinds of probability matrices, joint and conditional, that are defined in article [25]. Further, we discuss some properties of information entropy including Shannons lemma, maximum property, additivity and super-additivity properties.

The learning system of shinshu university graduate school of science and technology on the internet

Shinshu University Graduate School of Science and Technology on the Internet (SUGSI) is established in 2002 as the first Internet University in Japan. In SUGSI, students can learn every lecture using a CAI system featuring drills on the web, and get supervising about a masters thesis from faculty adviser via network. Therefore, students can complete a master course and get a masters degree without commuting to the school. We manage SUGSI on day school system, and we developed some student support systems as well as learning contents with CAI. In this paper, we mention about the learning system of SUGSI: its CAI contents, a student management system, and the profile of enrolled students such as their age structure and their learning style.

A self‐recovering communication buffer based on the concept of cellular automaton

This paper presents a self-recovering buffer memory for communication systems based on the concept of cellular automaton. The model proposed is a FIFO-type (First-in, First-out-type) memory which meets the conditions for a communication buffer and incorporates the principles of cellular automaton. By binding together a number of cells which can perform basic FIFO operations, it is found that each cell is capable of determining whether or not it is holding the first valid data in a queue based on information about its own status and it s neighboring cell. It also is observed that this model possesses a capacity for self recovery which always enables the buffer to return to a normal state in the event of an internal transient fault. Furthermore, by representing each cell with a sequential circuit, this buffer memory is prototyped with a gate array and its applicability is verified comparing it with existing FIFO design methods.