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On Ycompatible and strict Ycompatible functions
, 1997
"... Let Y 2 IR n . A function f : IR n ! IR k Y compatible, if for any Z 2 IR n , Z Y if and only if f(Z) f(Y ) and is strict Y compatible, if for any Z 2 IR n , Z ! Y if and only if f(Z) ! f(Y ). It is proved that for any Y 2 IR n , n 2, there is no Y compatible polynomial function f ..."
Abstract

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Let Y 2 IR n . A function f : IR n ! IR k Y compatible, if for any Z 2 IR n , Z Y if and only if f(Z) f(Y ) and is strict Y compatible, if for any Z 2 IR n , Z ! Y if and only if f(Z) ! f(Y ). It is proved that for any Y 2 IR n , n 2, there is no Y compatible polynomial function f : IR n ! IR k , 1 k ! n. It is also proved that for a strict Y compatible map f , J f (Y ) = 0, where J f (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 y 1 , y 2 , : ...