An Algorithm for constructing Hjelmslev planes

Projective Hjelmslev planes and Affine Hjelmselv planes are generalisations of projective planes and affine planes. We present an algorithm for constructing a projective Hjelmslev planes and affine Hjelsmelv planes using projective planes, affine planes and orthogonal arrays. We show that all 2-uniform projective Hjelmslev planes, and all 2-uniform affine Hjelsmelv planes can be constructed in this way. As a corollary it is shown that all 2-uniform Affine Hjelmselv planes are sub-geometries of 2-uniform projective Hjelmselv planes.Comment: 15 pages. Algebraic Design Theory and Hadamard matrices, 2014, Springer Proceedings in Mathematics & Statistics 13

An explanation of the Newman-Janis Algorithm

After the original discovery of the Kerr metric, Newman and Janis showed that this solution could be ``derived'' by making an elementary complex transformation to the Schwarzschild solution. The same method was then used to obtain a new stationary axisymmetric solution to Einstein's field equations now known as the Kerr-newman metric, representing a rotating massive charged black hole. However no clear reason has ever been given as to why the Newman-Janis algorithm works, many physicist considering it to be an ad hoc procedure or ``fluke'' and not worthy of further investigation. Contrary to this belief this paper shows why the Newman-Janis algorithm is successful in obtaining the Kerr-Newman metric by removing some of the ambiguities present in the original derivation. Finally we show that the only perfect fluid generated by the Newman-Janis algorithm is the (vacuum) Kerr metric and that the only Petrov typed D solution to the Einstein-Maxwell equations is the Kerr-Newman metric.Comment: 14 pages, no figures, submitted to Class. Quantum Gra

A rigorous treatment of O(α 6mc 2) QED corrections to the fine structure splittings of helium

Relativistic formulae for the energy level shifts due to electron self-energy corrections are derived within the external potential Bethe-Salpeter formalism. A rigorous treatment of QED corrections to the fine structure splittings of helium is carried out. Although some individual self-energy diagrams give contributions of order α 6mc 2, they are shown to sum to zero. In addition, the α 6mc 2 correction from vertex modifications in the presence of Coulomb photons does not contribute. Therefore, a rigorous treatment of all QED corrections of order α 6mc 2 to the fine structure splittings of helium now appears to be complete. © 1994 IOP Publishing Ltd

Calculations of polarizabilities and hyperpolarizabilities for the Be+^+ ion

The polarizabilities and hyperpolarizabilities of the Be$^+$ ion in the $2^2S$ state and the $2^2P$ state are determined. Calculations are performed using two independent methods: i) variationally determined wave functions using Hylleraas basis set expansions and ii) single electron calculations utilizing a frozen-core Hamiltonian. The first few parameters in the long-range interaction potential between a Be$^+$ ion and a H, He, or Li atom, and the leading parameters of the effective potential for the high-$L$ Rydberg states of beryllium were also computed. All the values reported are the results of calculations close to convergence. Comparisons are made with published results where available.Comment: 18 pp; added details to Sec. I

Fine Structure of the 1s3p ^3P_J Level in Atomic ^4He: Theory and Experiment

We report on a theoretical calculation and a new experimental determination of the 1s3p ^3P_J fine structure intervals in atomic ^4He. The values from the theoretical calculation of 8113.730(6) MHz and 658.801(6) MHz for the nu_{01} and nu_{12} intervals, respectively, disagree significantly with previous experimental results. However, the new laser spectroscopic measurement reported here yields values of 8113.714(28) MHz and 658.810(18) MHz for these intervals. These results show an excellent agreement with the theoretical values and resolve the apparent discrepancy between theory and experiment.Comment: 9 pages, 3 figure

Entropy/IP: Uncovering Structure in IPv6 Addresses

In this paper, we introduce Entropy/IP: a system that discovers Internet address structure based on analyses of a subset of IPv6 addresses known to be active, i.e., training data, gleaned by readily available passive and active means. The system is completely automated and employs a combination of information-theoretic and machine learning techniques to probabilistically model IPv6 addresses. We present results showing that our system is effective in exposing structural characteristics of portions of the IPv6 Internet address space populated by active client, service, and router addresses. In addition to visualizing the address structure for exploration, the system uses its models to generate candidate target addresses for scanning. For each of 15 evaluated datasets, we train on 1K addresses and generate 1M candidates for scanning. We achieve some success in 14 datasets, finding up to 40% of the generated addresses to be active. In 11 of these datasets, we find active network identifiers (e.g., /64 prefixes or `subnets') not seen in training. Thus, we provide the first evidence that it is practical to discover subnets and hosts by scanning probabilistically selected areas of the IPv6 address space not known to contain active hosts a priori.Comment: Paper presented at the ACM IMC 2016 in Santa Monica, USA (https://dl.acm.org/citation.cfm?id=2987445). Live Demo site available at http://www.entropy-ip.com

Characteristics of central collision events in Fe-nucleus interactions for 20 - 60 GeV/nucleon

A counter emulsion hybrid chamber in Japanese-American Cooperative Emulsion Experiment (JACEE-3) was flown on a balloon at the altitude (5.4 g/sq cm) in 1982 with the objective of probing the heavy nuclear collisions above 20 GeV per nucleon. In the energy region, it is suggested that nucleus-nucleus collisions provide dense collisions complex through compression and secondary particle production. In the lower energy region, an evidence of collective flow has been reported. And also, at higher energy region, it has been argued that nucleus has rather large stopping power. In this paper, the high multiplicity characteristics of Fe nucleus central collisions with energies 20 to 50 GeV/nucleon are presented. This is considered to be relevant to compressibility and collective flow of nuclear matter

Long-range interactions of metastable helium atoms

Polarizabilities, dispersion coefficients, and long-range atom-surface interaction potentials are calculated for the n=2 triplet and singlet states of helium using highly accurate, variationally determined, wave functions.Comment: RevTeX, epsf, 4 fig