2,693 research outputs found
A dynamical pairing between two rational maps
Given two rational maps and on \PP^1 of degree at least
two, we study a symmetric, nonnegative-real-valued pairing
which is closely related to the canonical height functions $h_\varphi$ and
$h_\psi$ associated to these maps. Our main results show a strong connection
between the value of and the canonical heights of points which
are small with respect to at least one of the two maps and .
Several necessary and sufficient conditions are given for the vanishing of
. We give an explicit upper bound on the difference between the
canonical height $h_\psi$ and the standard height $h_\st$ in terms of
, where denotes the squaring map. The pairing
is computed or approximated for several families of rational
maps
Local Distinguishability of Multipartite Orthogonal Quantum States
We consider one copy of a quantum system prepared in one of two orthogonal
pure states, entangled or otherwise, and distributed between any number of
parties. We demonstrate that it is possible to identify which of these two
states the system is in by means of local operations and classical
communication alone. The protocol we outline is both completely reliable and
completely general - it will correctly distinguish any two orthogonal states
100% of the time.Comment: 5 pages, revte
Alien Registration- Dube, Lucien J. (Dexter, Penobscot County)
https://digitalmaine.com/alien_docs/11385/thumbnail.jp
From Scopes to Edwards: The Sixty-Year Evolution of Biblical Creationism in the Public School Classroom
Few issues have generated as much controversy as the scope of the religion clauses of the first amendment to the United States Constitution within the setting of the public schools. Indeed, as Justice Brennan once stated, the courts have encountered few issues more intricate or more demanding than that of the relationship between religion and the public schools. This controversy is not surprising in light of the important role played by the public schools in shaping the nation\u27s thoughts, beliefs and institutions. It is a controversy without end; for as long as the public schools maintain their primary role in educating future generations and American society moves farther away from the traditional religious convictions of its forefathers, the controversy will continue
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