427,736 research outputs found
Reflexivity and rigidity for complexes, II: Schemes
We prove basic facts about reflexivity in derived categories over noetherian
schemes; and about related notions such as semidualizing complexes, invertible
complexes, and Gorenstein-perfect maps. Also, we study a notion of rigidity
with respect to semidualizing complexes, in particular, relative dualizing
complexes for Gorenstein-perfect maps. Our results include theorems of
Yekutieli and Zhang concerning rigid dualizing complexes on schemes. This work
is a continuation of part I, which dealt with commutative rings.Comment: 40 page
Preserving affine Baire classes by perfect affine maps
Let be an affine continuous surjection between compact
convex sets. Suppose that the canonical copy of the space of real-valued affine
continuous functions on in the space of real-valued affine continuous
functions on is complemented. We show that if is a topological vector
space, then is of affine Baire class whenever the
composition is of affine Baire class . This abstract
result is applied to extend known results on affine Baire classes of strongly
affine Baire mappings.Comment: 10 page
Dynamics of transcendental H\'enon maps-II
Transcendental H\'enon maps are the natural extensions of the well
investigated complex polynomial H\'enon maps to the much larger class of
holomorphic automorphisms. We prove here that transcendental H\'enon maps
always have non-trivial dynamical behavior, namely that they always admit both
periodic and escaping orbits, and that their Julia sets are non-empty and
perfect
Unitary quantum gates, perfect entanglers and unistochastic maps
Non-local properties of ensembles of quantum gates induced by the Haar
measure on the unitary group are investigated. We analyze the entropy of
entanglement of a unitary matrix U equal to the Shannon entropy of the vector
of singular values of the reshuffled matrix. Averaging the entropy over the
Haar measure on U(N^2) we find its asymptotic behaviour. For two--qubit quantum
gates we derive the induced probability distribution of the interaction content
and show that the relative volume of the set of perfect entanglers reads 8/3
\pi \approx 0.85. We establish explicit conditions under which a given
one-qubit bistochastic map is unistochastic, so it can be obtained by partial
trace over a one--qubit environment initially prepared in the maximally mixed
state.Comment: 14 pages including 6 figures in eps, version 4, title changed
according to a suggestion of the editor
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