منابع مشابه
Closed Systems of Invertible Maps
We generalise clones, which are sets of functions f : A → A, to sets of mappings f : A → A. We formalise this and develop language that we can use to speak about it. We then look at bijective mappings, which have connections to reversible computation, which is important for physical (e.g. quantum computation) as well as engineering (e.g. heat dissipation) reasons. We generalise Toffoli’s semina...
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In this paper, we present a systematic method for finding all homoclinic orbits of invertible maps in any finite dimension. One advantage of this method is that it can also be used to order and classify all the homoclinic orbits, using symbolic dynamics, if a certain criterion is satisfied. We also present a more direct scheme, which quickly locates homoclinic orbits without, however, being abl...
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Let K be a commutative ring and K be an affine space over K of dimension n. We introduce the concept of a family of multivariate maps f(n) of K into itself with invertible decomposition. If f(n) is computable in polynomial time then it can be used as the public rule and the invertible decomposition provides a private key in f(n) based public key infrastructure. Requirements of polynomial ity of...
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A geometric characterization is given for invertible quantum measurement maps. Denote by S(H) the convex set of all states (i.e., trace-1 positive operators) on Hilbert space H with dimH ≤ ∞, and [ρ1, ρ2] the line segment joining two elements ρ1, ρ2 in S(H). It is shown that a bijective map φ : S(H) → S(H) satisfies φ([ρ1, ρ2]) ⊆ [φ(ρ1), φ(ρ2)] for any ρ1, ρ2 ∈ S if and only if φ has one of the...
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ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 1998
ISSN: 0196-8858
DOI: 10.1006/aama.1998.0584