Mathematical norms are important cultural knowledge of mathematical activities. This paper reports an analysis of mathematical norms in ten consecutive lessons taught by an eighth-grade Japanese teacher. The lessons were located in the unit of simultaneous linear equations. The videotapes of the lessons, their transcripts, and the interview data were analyzed qualitatively. Several major mathem...

University of Caifornia/Davis 93.

Let e and Σ be respectively the vector of shocks and its variance covariance matrix in a linear system of equations in reduced form. This article shows that a unique orthogonal variance decomposition can be obtained if we impose a restriction that maximizes the trace of A, a positive definite matrix such that e Az = where z is vector of uncorrelated shocks with unit variance. Such a restriction...

We will denote intervals and interval vectors by Latin letters a, b, e . . . . (with or without index), interval matrices by capital Latin letters A, B, C , . . . Real vectors and matrices will be denoted by Latin letters with lower dots q, .b,e.,..., A., B., C . , . . . Endpoints of intervals and of interval vectors will be denoted by a_, ~ (lower and upper endpoims, respectively), real n u m ...

This article is a short supplement to our previously published paper, in which we proved that each semialgebraic set can be represented as a projection of a solution set of some system of interval linear equations with dependent coefficients. The new result says that interval occurring can be chosen as narrow as wanted. The new result is proved by a simple linear transformation.

We study the use of binary variables in reformulating general mixed-integer linear programs. We show that binary reformulations result in problems for which almost all the binary variables replacing a general integer variable need to be explored during branching. We also give computational results on the performance of such reformulations in solving the mixed-integer programs, which support our...

Article history: Received 4 April 2010 Received in revised form 27 June 2011 Accepted 27 June 2011 Available online xxxx

In this paper , some results about the index of matrix and Drazin inverse are given. We then explain applications of them in solving singular linear system of equations.