Proper Eighth-Order Vacuum-Polarization Function and its Contribution to the Tenth-Order Lepton g-2

This paper reports the Feynman-parametric representation of the vacuum-polarization function consisting of 105 Feynman diagrams of the eighth order, and its contribution to the gauge-invariant set called Set I(i) of the tenth-order lepton anomalous magnetic moment. Numerical evaluation of this set is carried out using FORTRAN codes generated by an automatic code generation system gencodevpN developed specifically for this purpose. The contribution of diagrams containing electron loop to the electron g-2 is 0.017 47 (11) (alpha/pi)^5. The contribution of diagrams containing muon loop is 0.000 001 67 (3) (alpha/pi)^5. The contribution of tau-lepton loop is negligible at present. The sum of all these terms is 0.017 47 (11) (alpha/pi)^5. The contribution of diagrams containing electron loop to the muon g-2 is 0.087 1 (59) (alpha/pi)^5. That of tau-lepton loop is 0.000 237 (1) (alpha/pi)^5. The total contribution to a_mu, the sum of these terms and the mass-independent term, is 0.104 8 (59) (alpha/pi)^5.Comment: 48 pages, 6 figures. References are correcte

N-fold Supersymmetry in Quantum Mechanics - Analyses of Particular Models -

We investigate particular models which can be N-fold supersymmetric at specific values of a parameter in the Hamiltonians. The models to be investigated are a periodic potential and a parity-symmetric sextic triple-well potential. Through the quantitative analyses on the non-perturbative contributions to the spectra by the use of the valley method, we show how the characteristic features of N-fold supersymmetry which have been previously reported by the authors can be observed. We also clarify the difference between quasi-exactly solvable and quasi-perturbatively solvable case in view of the dynamical property, that is, dynamical N-fold supersymmetry breaking.Comment: 32 pages, 10 figures, REVTeX

Wealth distribution in an ancient Egyptian society

Modern excavations yielded a distribution of the house areas in the ancient Egyptian city Akhetaten, which was populated for a short period during the 14th century BC. Assuming that the house area is a measure of the wealth of its inhabitants allows us to make a comparison of the wealth distributions in ancient and modern societies

Impacts of the Fukushima nuclear power plants on marine radioactivity

Author Posting. © American Chemical Society, 2011. This article is posted here by permission of American Chemical Society for personal use, not for redistribution. The definitive version was published in Environmental Science and Technology 45 (2011): 9931–9935, doi:10.1021/es202816c.The impacts on the ocean of releases of radionuclides from the Fukushima Dai-ichi nuclear power plants remain unclear. However, information has been made public regarding the concentrations of radioactive isotopes of iodine and cesium in ocean water near the discharge point. These data allow us to draw some basic conclusions about the relative levels of radionuclides released which can be compared to prior ocean studies and be used to address dose consequences as discussed by Garnier-Laplace et al. in this journal.(1) The data show peak ocean discharges in early April, one month after the earthquake and a factor of 1000 decrease in the month following. Interestingly, the concentrations through the end of July remain higher than expected implying continued releases from the reactors or other contaminated sources, such as groundwater or coastal sediments. By July, levels of 137Cs are still more than 10 000 times higher than levels measured in 2010 in the coastal waters off Japan. Although some radionuclides are significantly elevated, dose calculations suggest minimal impact on marine biota or humans due to direct exposure in surrounding ocean waters, though considerations for biological uptake and consumption of seafood are discussed and further study is warranted.Funding for this work to KOB is from the Gordon and Betty Moore Foundation as well as the Chemical Oceanography Program of the US National Science Foundation

The Heun equation and the Calogero-Moser-Sutherland system V: generalized Darboux transformations

We obtain isomonodromic transformations for Heun's equation by generalizing Darboux transformation, and we find pairs and triplets of Heun's equation which have the same monodromy structure. By composing generalized Darboux transformations, we establish a new construction of the commuting operator which ensures finite-gap property. As an application, we prove conjectures in part III.Comment: 24 page

Finite-lattice expansion for Ising models on quasiperiodic tilings

Low-temperature series are calculated for the free energy, magnetisation, susceptibility and field-derivatives of the susceptibility in the Ising model on the quasiperiodic Penrose lattice. The series are computed to order 20 and estimates of the critical exponents alpha, beta and gamma are obtained from Pade approximants.Comment: 16 pages, REVTeX, 26 postscript figure

Tenth-Order Lepton Anomalous Magnetic Moment -- Sixth-Order Vertices Containing Vacuum-Polarization Subdiagrams

This paper reports the values of contributions to the electron g-2 from 300 Feynman diagrams of the gauge-invariant Set III(a) and 450 Feynman diagrams of the gauge-invariant Set III(b). The evaluation is carried out in two versions. Version A is to start from the sixth-order magnetic anomaly M_6 obtained in the previous work. The mass-independent contributions of Set III(a) and Set III(b) are 2.1275 (2) and 3.3271 (6) in units of (alpha/pi)^5, respectively. Version B is based on the recently-developed automatic code generation scheme. This method yields 2.1271 (3) and 3.3271 (8) in units of (alpha/pi)^5, respectively. They are in excellent agreement with the results of the first method within the uncertainties of numerical integration. Combining these results as statistically independent we obtain the best values, 2.1273 (2), and 3.3271 (5) times (alpha/pi)^5, for the mass-independent contributions of the Set III(a) and Set III(b), respectively. We have also evaluated mass-dependent contributions of diagrams containing muon and/or tau-particle loop. Including them the total contribution of Set III(a) is 2.1349 (2) and that of Set III(b) is 3.3299 (5) in units of (alpha/pi)^5. The total contributions to the muon g-2 of various leptonic vacuum-polarization loops of Set III(a) and Set III(b) are 112.418 (32) and 15.407 (5) in units of (alpha/pi)^5, respectively.Comment: 31 pages, 4 figure

Recommendations for the Determination of Nutrients in Seawater to High Levels of Precision and Inter-Comparability using Continuous Flow Analysers

The Global Ocean Ship-based Hydrographic Investigations Program (GO-SHIP) brings together scientists with interests in physical oceanography, the carbon cycle, marine biogeochemistry and ecosystems, and other users and collectors of ocean interior data to develop a sustained global network of hydrographic sections as part of the Global Ocean Climate Observing System. A series of manuals and guidelines are being produced by GO-SHIP which update those developed by the World Ocean Circulation Experiment (WOCE) in the early 1990s. Analysis of the data collected in WOCE suggests that improvements are needed in the collection of nutrient data if they are to be used for determining change within the ocean interior. Production of this manual is timely as it coincides with the development of reference materials for nutrients in seawater (RMNS). These RMNS solutions will be produced in sufficient quantities and be of sufficient quality that they will provide a basis for improving the consistency of nutrient measurements both within and between cruises. This manual is a guide to suggested best practice in performing nutrient measurements at sea. It provides a detailed set of advice on laboratory practice for all the procedures surrounding the use of 1 gas-segmented continuous flow analysers (CFA) for the determination of dissolved nutrients (usually ammonium, nitrate, nitrite, phosphate and silicate) at sea. It does not proscribe the use of a particular instrument or related chemical method as these are well described in other publications. The manual provides a brief introduction to the CFA method, the collection and storage of samples, considerations in the preparation of reagents and the calibrations of the system. It discusses how RMNS solutions can be used to “track” the performance of a system during a cruise and between cruises. It provides a format for the meta-data that need to be reported along side the sample data at the end of a cruise so that the quality of the reported data can be evaluated and set in context relative to other data sets. Most importantly the central manual is accompanied by a set of nutrient standard operating procedures (NSOPs) that provide detailed information on key procedures that are necessary if best quality data are to be achieved consistently. These cover sample collection and storage, an example NSOP for the use of a CFA system at sea, high precision preparation of calibration solutions, assessment of the true calibration blank, checking the linearity of a calibration and the use of internal and externally prepared reference solutions for controlling the precision of data during a cruise and between cruises. An example meta-data report and advice on the assembly of the quality control and statistical data that should form part of the meta-data report are also given

Multiinstanton ladders in Baryon Number Violating Processes

We estimate the contribution of a class of multiinstanton ladder graphs to baryon and lepton number violating processes in the standard model. We find that this contribution is negligible and does not alter the high energy behavior of the leading semiclassical approximation.Comment: 15 pages, 2 figures RevTe

On Associativity Equations in Dispersionless Integrable Hierarchies

We discuss the origin of the associativity (WDVV) equations in the context of quasiclassical or Whitham hierarchies. The associativity equations are shown to be encoded in the dispersionless limit of the Hirota equations for KP and Toda hierarchies. We show, therefore, that any tau-function of dispersionless KP or Toda hierarchy provides a solution to associativity equations. In general, they depend on infinitely many variables. We also discuss the particular solution to the dispersionless Toda hierarchy that describes conformal mappings and construct a family of new solutions to the WDVV equations depending on finite number of variables.Comment: 16 pages, LaTe