Formalized Mathematics    (ISSN 1426-2630)
Volume 14, Number 3 (2006): PDF.
  1. Bo Li, Yan Zhang, Artur Kornilowicz. Simple Continued Fractions and Their Convergents, Formalized Mathematics 14(3), pages 71-78, 2006. MML Identifier: REAL_3
    Summary: The article introduces simple continued fractions. They are defined as an infinite sequence of integers. The characterization of rational numbers in terms of simple continued fractions is shown. We also give definitions of convergents of continued fractions, and several important properties of simple continued fractions and their convergents.
  2. Broderick Arneson, Piotr Rudnicki. Chordal Graphs, Formalized Mathematics 14(3), pages 79-92, 2006. MML Identifier: CHORD
    Summary: We are formalizing \cite[pp.~81--84]{Golumbic} where chordal graphs are defined and their basic characterization is given. This formalization is a part of the M.Sc. work of the first author under supervision of the second author.
  3. Yatsuka Nakamura. Connectedness and Continuous Sequences in Finite Topological Spaces, Formalized Mathematics 14(3), pages 93-100, 2006. MML Identifier: FINTOPO6
    Summary: First, equivalence conditions for connectedness are examined, for a finite topological space (originated in \cite{Nakamura:2}). 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.
  4. Bo Zhang, Yatsuka Nakamura. The Definition of Finite Sequences and Matrices of Probability, and Addition of Matrices of Real Elements, Formalized Mathematics 14(3), pages 101-108, 2006. MML Identifier: MATRPROB
    Summary: 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.
  5. Bo Li, Peng Wang. Several Differentiation Formulas of Special Functions. Part IV, Formalized Mathematics 14(3), pages 109-114, 2006. MML Identifier: FDIFF_8
    Summary: In this article, we give several differentiation formulas of special and composite functions including trigonometric function, polynomial function and logarithmic function.
  6. Bo Li, Yan Zhang, Xiquan Liang. Difference and Difference Quotient, Formalized Mathematics 14(3), pages 115-119, 2006. MML Identifier: DIFF_1
    Summary: In this article, we give the definitions of forward difference, backward difference, central difference and difference quotient, and some important properties of them.