Detecting squarefree numbers

We present an algorithm, based on the explicit formula for $L$-functions and conditional on GRH, for proving that a given integer is squarefree with little or no knowledge of its factorization. We analyze the algorithm both theoretically and practically, and use it to prove that several RSA challenge numbers are not squarefull.Comment: 31 pages, 3 figures, latest versio

Nodal domain distributions for quantum maps

The statistics of the nodal lines and nodal domains of the eigenfunctions of quantum billiards have recently been observed to be fingerprints of the chaoticity of the underlying classical motion by Blum et al. (Phys. Rev. Lett., Vol. 88 (2002), 114101) and by Bogomolny and Schmit (Phys. Rev. Lett., Vol. 88 (2002), 114102). These statistics were shown to be computable from the random wave model of the eigenfunctions. We here study the analogous problem for chaotic maps whose phase space is the two-torus. We show that the distributions of the numbers of nodal points and nodal domains of the eigenvectors of the corresponding quantum maps can be computed straightforwardly and exactly using random matrix theory. We compare the predictions with the results of numerical computations involving quantum perturbed cat maps.Comment: 7 pages, 2 figures. Second version: minor correction

A note on the evaluation of a beta-casein variant in bovine breeds by allele-specific PCR and relevance to β-casomorphin

peer-reviewedThis work was supported by Enterprise Ireland and by a Teagasc Walsh fellowship to A.F. Keating.Two genetic variants of the bovine β-casein gene (A1 and B) encode a histidine residue at codon 67, resulting in potential liberation of a bioactive peptide, β-casomorphin, upon digestion. An allele-specific PCR (AS-PCR) was evaluated to distinguish between the β-casomorphin-releasing variants (A1 and B) and the non-releasing variants. AS-PCR successfully distinguished β-casein variants in 41 of 42 animals as confirmed by sequence analysis. Overall, while the incidence of the homozygous A1 and B animals (i.e., homozygous for the histidine residue; 21.4%) was lower than that for animals without the histidine residue (30.9% respectively), 69% of animals carried at least one allele for the histidine residue at codon 67.Teagasc Walsh Fellowship ProgrammeEnterprise Irelan

Integrated Online Media Management Systems For Media Centers: A Model For Selection And Effective Use

The researcher proposed to advice in the selection of an Integrated Online Library System (IOLS) for use in the 103 school media centers in the Palm Beach County Schools, Florida. This was accomplished by evaluating the two finalists of those vendors who answered the district\u27s Request for Proposal (RFP). Of the five vendors who responded to the RFP. CLSI and SIRSI were selected as the systems most likely to meet the needs of the media centers of the school district. An overview and definition of IOLS was first discussed. This overview then related itself to the needs of the school district as presented in the RFP. A selection criteria was then designed from previous research on the subject to help find the ideal system. The history and development of an Integrated Online Library System was important in seeing where the systems have originated in contrast to the systems in the Eighties to the also revealed the present time. Literature IOLS principles of operation. The Request for Proposal reflected the needs assessment discussed over several years of committee meetings of representatives from various schools. The committees explored IOLS automated options and compared these options. The RFP outlined the system requirements. Thoughts on staff attitudes while planning for a system were also considered. Each system was evaluated with the criteria outlined in the RFP. The background and capabilities of both systems were explored. This exploration took place where by the benchmark tests, on-site demonstrations systems were in use daily, conferences with the vendors, systems. And reading literature reviews on both systems. Evaluation guidelines and criteria were found in library resources. The functions required for terminal access requirements, process for data conversion, vendor background and reliability, contained in these library resources. And the cost were contained in these library resources. The results of this study culminated in the official recommendation of the SIRSI to be purchased by the district\u27s school board. It was the expectation of the author of this document to see the purchase of the recommended system by the school board and have it implemented in all the schools in the district within a three year period following the submission of the recommendation

The Relative Influence of Social Structure and Family Role Variables on Voluntary Association Participation of Men and Women

Sociology has long claimed to be an objective, value free science (Hinkle and Hinkle, 1954; Bates, 1967i Caplow, 1971). The research process is expected to be unaffected by the personal values, hopes,and prejudices of the researcher. Superficially, such claims can simply refer to professional ethics in gathering, analyzing, and presenting data. Violations at this level, albeit unintentional, are usually sufficiently manifest to be detected in professional review and replication attempts

Method and apparatus for attaching physiological monitoring electrodes Patent

Adhesive spray process for attaching biomedical skin electrode

Fractional ℏ\hbar-scaling for quantum kicked rotors without cantori

Previous studies of quantum delta-kicked rotors have found momentum probability distributions with a typical width (localization length $L$) characterized by fractional $\hbar$-scaling, ie $L \sim \hbar^{2/3}$ in regimes and phase-space regions close to `golden-ratio' cantori. In contrast, in typical chaotic regimes, the scaling is integer, $L \sim \hbar^{-1}$. Here we consider a generic variant of the kicked rotor, the random-pair-kicked particle (RP-KP), obtained by randomizing the phases every second kick; it has no KAM mixed phase-space structures, like golden-ratio cantori, at all. Our unexpected finding is that, over comparable phase-space regions, it also has fractional scaling, but $L \sim \hbar^{-2/3}$. A semiclassical analysis indicates that the $\hbar^{2/3}$ scaling here is of quantum origin and is not a signature of classical cantori.Comment: 5 pages, 4 figures, Revtex, typos removed, further analysis added, authors adjuste

Stability of the Period-Doubled Core of the 90-degree Partial in Silicon

In a recent Letter [N. Lehto and S. Oberg, Phys. Rev. Lett. 80, 5568 (1998)], Lehto and Oberg investigated the effects of strain fields on the core structure of the 90-degree partial dislocation in silicon, especially the influence of the choice of supercell periodic boundary conditions in theoretical simulations. We show that their results for the relative stability between the two structures are in disagreement with cell-size converged tight-binding total energy (TBTE) calculations, which suggest the DP core to be more stable, regardless of the choice of boundary condition. Moreover, we argue that this disagreement is due to their use of a Keating potential.Comment: 1 page. Submitted to Comments section of PRL. Also available at http://www.physics.rutgers.edu/~dhv/preprints/rn_dcom/index.htm