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...

This paper presents a new approach to sensor placement based on diagnosability criteria. It is based on the study of structural matrices. Properties of structural matrices regarding detectability, discriminability and diagnosability are established in order to be used by sensor placement methods. The proposed approach manages any number of constraints modelled by linear or nonlinear equations a...

The control function approach (Heckman and Robb (1985)) in a system of linear simultaneous equations provides a convenient procedure to estimate one of the functions in the system using reduced form residuals from the other functions as additional regressors. The conditions on the structural system under which this procedure can be used in nonlinear and nonparametric simultaneous equations has ...

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...

System identification is important in science and engineering. This contribution proposes a simple yet elegant scheme for identifying a fractional order dynamic system based on its observed response to a standard excitation. Our approach consists in obtaining and solving a set of simultaneous linear equations connecting the parameters to yield the desired estimates. To minimise the effect of no...

Solving the incompressible Navier-Stokes equations for fluid flow using a semi-lagrangian method is a two step process [3]. In this paper we focus on the second step which involves the solution of a large sparse symmetric indefinite linear system of equations. Numerous numerical methods were used to solve this system. Here, the computation requirements of several are compared in hopes of findin...