A dynamical pairing between two rational maps

Given two rational maps $\varphi$ and $\psi$ 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 $\varphi$ and $\psi$. 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 $\sigma(x)=x^2$ denotes the squaring map. The pairing $$ is computed or approximated for several families of rational maps $\psi$

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

Public Accommodation Statutes and Sexual Orientation: Should There Be a Religious Exemption for Secular Businesses?

This Article examines the issue of whether there should be a religious exemption for secular businesses from public accommodation statutes that protect prospective patrons from discrimination on the basis of sexual orientation. The Article examines this issue in the context of protecting free exercise of religion versus offering services to all members of the public equally and without distinction. The Article concludes that the perceived threat to religious liberty posed by such statutes is exaggerated, that the consequences of granting exemptions would be harmful, and that state-sanctioned discrimination is contrary to the fundamental principles of justice and equality underlying the U.S. legal system

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