Abstract: A system for rejecting second and subsequent copies of an informationally-equivalent card or badge asserted into a client/server system by processing only those cards having transaction histories recorded thereon by comparison matching a history recorded in a central repository and then rewriting the history on the card and in the repository. The rewritten histories include the current transaction. Counterfeit cards, informationally equivalent to the original card prior to the transaction update of the original card, will be rejected when asserted into the system since their histories mismatch that recorded in the repository.

Abstract: A modulator apparatus for modulating arrays of input data V.sub.in to be stored in a holographic recording medium is disclosed wherein the final output data array V.sub.out has frequent transitions from light to dark and from dark to light in either dimension across the data page and has the total amount of illuminated regions throughout the entire data page held constant. These two constraints are achieved by a first set of control arrays obtained from two fixed sets of m.times.n binary arrays {A.sub.0, A.sub.1, . . . , A.sub.n } and {B.sub.0, B.sub.1, . . . , B.sub.m } which in turn are obtained from fixed sets of binary control vectors {a.sub.0, a.sub.1, . . . , a.sub.n }, {b.sub.0, b.sub.1, . . . , b.sub.m }, respectively. The control vectors a.sub.0, a.sub.1, . . . , a.sub.n are any n+1 fixed elements of the inverse mapping, .phi..sup.-1 (C.sub.1), of the (t-2) error-correcting code C.sub.1 of length m. The control vectors b.sub.0, b.sub.1, . . . , b.sub.

Abstract: This invention relates to a reversible display device based upon the electrochromic properties of triaryl pyrazoline compounds when used in conjunction with a complementary redox material.