Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 13

Liczba wyników na stronie
first rewind previous Strona / 1 next fast forward last

Wyniki wyszukiwania

help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 1 next fast forward last
1
Content available remote

Determinant of Some Matrices of Field Elements

100%
Nakamura Y.
Formalized Mathematics
|
2006
|
tom 14
|
nr 1
1-5
EN
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.
2
Content available remote

Connectedness and Continuous Sequences in Finite Topological Spaces

100%
Nakamura Y.
Formalized Mathematics
|
2006
|
tom 14
|
nr 3
93-100
EN
First, equivalence conditions for connectedness are examined for a finite topological space (originated in [9]). Secondly, definitions of subspace, and components of the subspace of a finite topological space are given. Lastly, concepts of continuous finite sequence and minimum path of finite topological space are proposed.
3
Content available remote

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

64%
Nakamura Y., Ito H.
Formalized Mathematics
|
2008
|
tom 16
|
nr 3
283-288
EN
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.
4
Content available remote

Definition and some Properties of Information Entropy

64%
Zhang B., Nakamura Y.
Formalized Mathematics
|
2007
|
tom 15
|
nr 3
111-119
EN
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 Shannon's lemma, maximum property, additivity and super-additivity properties.
5
Content available remote

Determinant and Inverse of Matrices of Real Elements

64%
Tamura N., Nakamura Y.
Formalized Mathematics
|
2007
|
tom 15
|
nr 3
127-136
EN
In this paper the classic theory of matrices of real elements (see e.g. [12], [13]) is developed. We prove selected equations that have been proved previously for matrices of field elements. Similarly, we introduce in this special context the determinant of a matrix, the identity and zero matrices, and the inverse matrix. The new concept discussed in the case of matrices of real numbers is the property of matrices as operators acting on finite sequences of real numbers from both sides. The relations of invertibility of matrices and the "onto" property of matrices as operators are discussed.
6
Content available remote

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

64%
Zhang B., Nakamura Y.
Formalized Mathematics
|
2006
|
tom 14
|
nr 3
101-108
EN
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.
7
Content available remote

Complex Function Differentiability

52%
Pacharapokin C., Yamazaki H., Shidama Y., Nakamura Y.
Formalized Mathematics
|
2009
|
tom 17
|
nr 2
67-72
EN
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.
8
Content available remote

Cell Petri Net Concepts

52%
Jitsukawa M., Kawamoto P., Shidama Y., Nakamura Y.
Formalized Mathematics
|
2009
|
tom 17
|
nr 1
37-42
EN
Based on the Petri net definitions and theorems already formalized in [8], with this article, we developed the concept of "Cell Petri Nets". It is based on [9]. In a cell Petri net we introduce the notions of colors and colored states of a Petri net, connecting mappings for linking two Petri nets, firing rules for transitions, and the synthesis of two or more Petri nets.MML identifier: PETRI 2, version: 7.11.01 4.117.1046
9
Content available remote

The Real Vector Spaces of Finite Sequences are Finite Dimensional

52%
Nakamura Y., Korniłowicz A., Oya N., Shidama Y.
Formalized Mathematics
|
2009
|
tom 17
|
nr 1
1-9
EN
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
10
Content available remote

A Theory of Matrices of Real Elements

52%
Nakamura Y., Tamura N., Chang W.
Formalized Mathematics
|
2006
|
tom 14
|
nr 1
21-28
EN
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.
11
Content available remote

The Cauchy-Riemann Differential Equations of Complex Functions

52%
Yamazaki H., Shidama Y., Nakamura Y., Pacharapokin C.
Formalized Mathematics
|
2009
|
tom 17
|
nr 2
147-149
EN
In this article we prove Cauchy-Riemann differential equations of complex functions. These theorems give necessary and sufficient condition for differentiable function.
12
Content available remote

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

52%
Zhang B., Yamazaki H., Nakamura Y.
Formalized Mathematics
|
2006
|
tom 14
|
nr 4
225-229
EN
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.
13
Content available remote

Invertibility of Matrices of Field Elements

52%
Nakamura Y., Oniumi K., Chang W.
Formalized Mathematics
|
2008
|
tom 16
|
nr 2
195-202
EN
In this paper the theory of invertibility of matrices of field elements (see e.g. [5], [6]) is developed. The main purpose of this article is to prove that the left invertibility and the right invertibility are equivalent for a matrix of field elements. To prove this, we introduced a special transformation of matrix to some canonical forms. Other concepts as zero vector and base vectors of field elements are also introduced as a preparation.MML identifier: MATRIX14, version: 7.9.01 4.101.1015
first rewind previous Strona / 1 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.