Normalizers of Irreducible Subfactors

We consider normalizers of an irreducible inclusion $N\subseteq M$ of $\mathrm{II}_1$ factors. In the infinite index setting an inclusion $uNu^*\subseteq N$ can be strict, forcing us to also investigate the semigroup of one-sided normalizers. We relate these normalizers of $N$ in $M$ to projections in the basic construction and show that every trace one projection in the relative commutant $N'\cap$ is of the form $u^*e_Nu$ for some unitary $u\in M$ with $uNu^*\subseteq N$. This enables us to identify the normalizers and the algebras they generate in several situations. In particular each normalizer of a tensor product of irreducible subfactors is a tensor product of normalizers modulo a unitary. We also examine normalizers of irreducible subfactors arising from subgroup--group inclusions $H\subseteq G$. Here the normalizers are the normalizing group elements modulo a unitary from $L(H)$. We are also able to identify the finite trace $L(H)$-bimodules in $\ell^2(G)$ as double cosets which are also finite unions of left cosets.Comment: 33 Page

Eliminating the Hadronic Uncertainty

The Standard Model Lagrangian requires the values of the fermion masses, the Higgs mass and three other experimentally well-measured quantities as input in order to become predictive. These are typically taken to be $\alpha$, $G_\mu$ and $M_Z$. Using the first of these, however, introduces a hadronic contribution that leads to a significant error. If a quantity could be found that was measured at high energy with sufficient precision then it could be used to replace $\alpha$ as input. The level of precision required for this to happen is given for a number of precisely-measured observables. The $W$ boson mass must be measured with an error of $\pm13$\,MeV, $\Gamma_Z$ to $0.7$\,MeV and polarization asymmetry, $A_{LR}$, to $\pm0.002$ that would seem to be the most promising candidate. The r\^ole of renormalized parameters in perturbative calculations is reviewed and the value for the electromagnetic coupling constant in the $\overline{\rm MS}$ renormalization scheme that is consistent with all experimental data is obtained to be $\alpha^{-1}_{\overline{\rm MS}}(M^2_Z)=128.17$.Comment: 8 pages LaTeX2

Tully Knoles of Pacific: Horseman, Teacher, Minister, College President, Traveler, and Public Speaker

https://scholarlycommons.pacific.edu/pacific-pubs/1003/thumbnail.jp

Are the Earth and the Moon compositionally alike? Inferences on lunar composition and implications for lunar origin and evolution from geophysical modeling

The main objective of the present study is to discuss in detail the results obtained from an inversion of the Apollo lunar seismic data set, lunar mass, and moment of inertia. We inverted directly for lunar chemical composition and temperature using the model system CaO-FeO-MgO-Al2O3-SiO2. Using Gibbs free energy minimization, stable mineral phases at the temperatures and pressures of interest, their modes and physical properties are calculated. We determine the compositional range of the oxide elements, thermal state, Mg#, mineralogy and physical structure of the lunar interior, as well as constraining core size and density. The results indicate a lunar mantle mineralogy that is dominated by olivine and orthopyroxene ( 80 vol%), with the remainder being composed of clinopyroxene and an aluminous phase (plagioclase, spinel, and garnet present in the depth ranges 0–150 km, 150–200 km, and >200 km, respectively). This model is broadly consistent with constraints on mantle mineralogy derived from the experimental and observational study of the phase lationships and trace element compositions of lunar mare basalts and picritic glasses. In particular, by melting a typical model mantle composition using the pMELTS algorithm, we found that a range of batch melts generated from these models have features in common with low Ti mare basalts and picritic glasses. Our results also indicate a bulk lunar composition and Mg# different to that of the Earth’s upper mantle, represented by the pyrolite composition. This difference is reflected in a lower bulk lunar Mg# ( 0.83). Results also indicate a small iron-like core with a radius around 340 km.The Carlsberg Foundation, NER

Jointly selecting for fibre diameter and fleece weight: A market-level assessment of the QPLU$ Merino breeding project

The QPLU$ Merino breeding project began in the early 1990s. The aim of the project was to demonstrate the efficiency of using a selection index to achieve breeding objectives. A number of selection lines were created from three strains of Merino sheep. During the ten-year course of the project, selection of each line was undertaken using an index based on measurements of fleece weight and fibre diameter. Different emphases were placed on each trait in each selected line. This paper estimates the potential aggregate returns of the project to the Australian sheep and wool industries using an equilibrium displacement model.Australian sheep and wool industries, equilibrium displacement model, cross-commodity relationships, R&D evaluation, Livestock Production/Industries, Research and Development/Tech Change/Emerging Technologies, Research Methods/ Statistical Methods,

Multistep self-assembly of heteroleptic magnesium and sodium-magnesium benzamidinate complexes

Reaction of the magnesium bis-alkyl Mg(CH2SiMe3)(2) and the sodium amide NaHMDS (where HMDS = N(SiMe3)(2)) with benzonitrile yields the homometallic heteroleptic complex [PhC(NSiMe3)(2)Mg{mu-NC(CH2SiMe3)Ph}](2) (1). It appears that at least six independent reactions must have occurred in this one-pot reaction to arrive at this mixed benzamidinate ketimido product. Two benzonitrile solvated derivatives of Mg(CH2SiMe3)(2) (5a and 5b) have been synthesized, with 5a crystallographically characterized as a centrosymmetric (MgC)(2) cyclodimer. When, the components of 5a are allowed to react for longer, partial addition of the Mg-alkyl unit across the C N triple bond occurs to yield the trimeric species (Me3SiCH2)(2)Mg-3[mu-N=C(CH2SiMe3)Ph](4)center dot 2N CPh (6), with bridging ketimido groups and terminal alkyl groups. Finally, using the same starting materials as that which produced 1, but altering their order of addition, a magnesium bis-alkyl unit is inserted into the Na-N bonds of a benzamidinate species to yield a new sodium magnesiate complex, PhC(NSiMe3)(2)Mg(mu-CH2SiMe3)(2)Na center dot 2TMEDA (7). The formation of 7 represents a novel (insertion) route to mixed-metal species of this kind and is the first Such example to contain a bidentate terminal anion attached to the divalent metal center. All new species are characterized by H-1 and C-13 NMR spectroscopy and where appropriate by IR spectroscopy. The solid-state structures of complexes 1, 5a, and 7 have also been determined and are disclosed within

Starting on the Path to a High Performance Health System: Analysis of Health System Reform Provisions of Reform Bills in the House of Representatives and Senate

Compares the reform bills' reform provisions, with a focus on closing the coverage gap by creating an insurance exchange of public and private plans, strengthening Medicare, and expanding Medicaid. Examines implications for the budget and coverage rates