TRYING TO FIT AN OVAL SHAPED ISLAND INTO A SQUARE CONSTITUTION: ARGUMENTS FOR PUERTO RICAN STATEHOOD

This Comment focuses on the limits placed on Puerto Rico under the United States Constitution and concludes that Puerto Rico must become the 51st state to improve its status under the Constitution. It explores Puerto Rico\u27s relationship with the United States and its unusual position under the Constitution. This Comment then examines the voting rights issues facing Puerto Ricans, including a First Circuit case which denied Puerto Ricans the right to vote in presidential elections. The Comment concludes that this case was correctly decided and the Supreme Court, in other decisions, has only recognized a limited right to vote under the Equal Protection Clause. Based on this case law, the Comment argues that Puerto Rico must become the 51st state to alleviate these voting rights issues

Russian Doll Renormalization Group and Superconductivity

We show that an extension of the standard BCS Hamiltonian leads to an infinite number of condensates with different energy gaps and self-similar properties, described by a cyclic RG flow of the BCS coupling constant which returns to its original value after a finite RG time.Comment: 4 pages, 2 figs, RevTex

Systematic Analysis of Majorization in Quantum Algorithms

Motivated by the need to uncover some underlying mathematical structure of optimal quantum computation, we carry out a systematic analysis of a wide variety of quantum algorithms from the majorization theory point of view. We conclude that step-by-step majorization is found in the known instances of fast and efficient algorithms, namely in the quantum Fourier transform, in Grover's algorithm, in the hidden affine function problem, in searching by quantum adiabatic evolution and in deterministic quantum walks in continuous time solving a classically hard problem. On the other hand, the optimal quantum algorithm for parity determination, which does not provide any computational speed-up, does not show step-by-step majorization. Lack of both speed-up and step-by-step majorization is also a feature of the adiabatic quantum algorithm solving the 2-SAT ``ring of agrees'' problem. Furthermore, the quantum algorithm for the hidden affine function problem does not make use of any entanglement while it does obey majorization. All the above results give support to a step-by-step Majorization Principle necessary for optimal quantum computation.Comment: 15 pages, 14 figures, final versio

The Foundations of Saint Vincent de Paul

By tracing history of the Congregation’s establishments and houses, how they were made, and how they were supported, we can appreciate Vincent de Paul as an organizer and administrator and understand the Congregation’s development. Vincent’s principles for foundations were to never take the initiative in establishing them, to accept only stable ones, and to start with small ones to build up larger ones. He was careful to ensure that the Congregation and its works would be self-sufficient. Initiative for foundations came largely from bishops, but also from wealthy laity, teams of founders, and royalty. Foundations replicated the Congregation’s initial one, focusing on missions and retreats for ordinands and seminaries’ direction. The Congregation’s income and the chronological pace and geographical distribution of foundations are examined

Self-replicating cracks: a collaborative fracture mode in thin films

Straight cracks are observed in thin coatings under residual tensile stress, resulting into the classical network pattern observed in china crockery, old paintings or dry mud. Here, we present a novel fracture mechanism where delamination and propagation occur simultaneously, leading to the spontaneous self-replication of an initial template. Surprisingly, this mechanism is active below the standard critical tensile load for channel cracks and selects a robust interaction length scale on the order of 30 times the film thickness. Depending on triggering mechanisms, crescent alleys, spirals or long bands are generated over a wide range of experimental parameters. We describe with a simple physical model the selection of the fracture path and provide a configuration diagram displaying the different failure modes