On Y -compatible and strict Y -compatible

functions ?

Bojan Hvala, Sandi Klav?ar
University of Maribor, PF
Department of Mathematics
Koro?ka 160, 2000 Maribor, Slovenia
email: [email protected] [email protected]

Franc Novak
Jo?ef Stefan Institute
University of Ljubljana
Jamova 39, 1000 Ljubljana, Slovenia
email:[email protected]

Abstract

Let Y 2 IRn. A function f : IRn ! IRk Y -compatible, if for any Z 2 IRn, Z <= Y if and only if f(Z) <= f(Y ) and is strict Y -compatible, if for any Z 2 IRn, Z < Y if and only if f(Z) < f(Y ). It is proved that for any Y 2 IRn, n >= 2, there is no Y -compatible polynomial function f : IRn ! IRk, 1 <= k < n. It is also proved that for a strict Y -compatible map f , Jf (Y ) = , where Jf (Y ) denote the Jacobian
matrix of the mapping f in Y . These problems arose in studying data compression of analog signatures.

1 Introduction

This work was initiated by the problems of storage and processing of measured response data of analog circuits normally used by the fault dictionary techniques in fault localization [1], [2]. We explore the possibility of data compression of a series of real numbers representing given response data. In particular, we are looking for some data compression function that would enable us to determine for any two given responses y1, y2, : : :, yn and z1, z2,

?Published in Applied Mathematics Letters, Vol.10, No.1, 1997, pp.79-82.