Noncommutative Geometry and The Ising Model

The main aim of this work is to present the interpretation of the Ising type models as a kind of field theory in the framework of noncommutative geometry. We present the method and construct sample models of field theory on discrete spaces using the introduced tools of discrete geometry. We write the action for few models, then we compare them with various models of statistical physics. We construct also the gauge theory with a discrete gauge group.Comment: 12 pages, LaTeX, TPJU - 18/92, December 199

The Employment, Earnings, and Income of Less-Skilled Workers over the Business Cycle

In this paper, I examine the effect of business cycles on the employment, earnings, and income of persons in different demographic groups. I classify individuals by sex, education, and race. The analysis uses data from the Current Population Survey’s Outgoing Rotation Group data, covering the period 1979–1992, and March Annual Demographic File data, covering the period 1975–1997. Many different individual and family outcome measures are considered, including employment to population ratios, weekly earnings, hourly earnings, annual hours, annual earnings, family earnings, family transfer income, and total family income. The regression model is specified such that the key parameters measure how the labor market outcomes of less-skilled workers vary with the business cycle relative to the variability for high-skill groups. The analysis uses variation across MSAs in the timing and severity of shocks. The results consistently show that individuals with lower educational levels, nonwhites, and low-skill women experience greater cyclical fluctuation than high-skill men. These results are the most striking when examining comprehensive measures of labor force activity such as the likelihood of full-time, full-year work. Government transfers and the earnings of other family members decrease the differences between groups, resulting in more skill-group-neutral effects of business cycles on family income than on individual earnings. The paper examines the stability of these results by comparing evidence across the 1982 and 1992 recessions. The evidence suggests that the 1992 recession led to more uniform effects across skill groups than did earlier cycles.

Spin Structures on Kleinian Manifolds

We derive the topological obstruction to spin-Klein cobordism. This result has implications for signature change in general relativity, and for the $N=2$ superstring.Comment: 8 page

Coupled Mg/Ca and clumped isotope analyses of foraminifera provide consistent water temperatures

The reliable determination of past seawater temperature is fundamental to paleoclimate studies. We test the robustness of two paleotemperature proxies by combining Mg/Ca and clumped isotopes (Δ47) on the same specimens of core top planktonic foraminifera. The strength of this approach is that Mg/Ca and Δ47 are measured on the same specimens of foraminifera, thereby providing two independent estimates of temperature. This replication constitutes a rigorous test of individual methods with the advantage that the same approach can be applied to fossil specimens. Aliquots for Mg/Ca and clumped analyses are treated in the same manner following a modified cleaning procedure of foraminifera for trace element and isotopic analyses. We analysed eight species of planktonic foraminifera from coretop samples over a wide range of temperatures from 2 to 29°C. We provide a new clumped isotope temperature calibrations using subaqueous cave carbonates, which is consistent with recent studies. Tandem Mg/Ca–Δ47 results follow an exponential curve as predicted by temperature calibration equations. Observed deviations from the predicted Mg/Ca-Δ47 relationship are attributed to the effects of Fe-Mn oxide coatings, contamination, or dissolution of foraminiferal tests. This coupled approach provides a high degree of confidence in temperature estimates when Mg/Ca and Δ47 yield concordant results, and can be used to infer the past δ18O of seawater (δ18Osw) for paleoclimate studies

Rationale for UV-filtered clover fermions

We study the contributions Sigma_0 and Sigma_1, proportional to a^0 and a^1, to the fermion self-energy in Wilson's formulation of lattice QCD with UV-filtering in the fermion action. We derive results for m_{crit} and the renormalization factors Z_S, Z_P, Z_V, Z_A to 1-loop order in perturbation theory for several filtering recipes (APE, HYP, EXP, HEX), both with and without a clover term. The perturbative series is much better behaved with filtering, in particular tadpole resummation proves irrelevant. Our non-perturbative data for m_{crit} and Z_A/(Z_m*Z_P) show that the combination of filtering and clover improvement efficiently reduces the amount of chiral symmetry breaking -- we find residual masses am_{res}=O(10^{-2}).Comment: 25 pages, 4 figures; v2: typo in eqn. (37) fixed [agrees with published version

Quasi-exactly solvable quartic potential

A new two-parameter family of quasi-exactly solvable quartic polynomial potentials $V(x)=-x^4+2iax^3+(a^2-2b)x^2+2i(ab-J)x$ is introduced. Until now, it was believed that the lowest-degree one-dimensional quasi-exactly solvable polynomial potential is sextic. This belief is based on the assumption that the Hamiltonian must be Hermitian. However, it has recently been discovered that there are huge classes of non-Hermitian, ${\cal PT}$-symmetric Hamiltonians whose spectra are real, discrete, and bounded below [physics/9712001]. Replacing Hermiticity by the weaker condition of ${\cal PT}$ symmetry allows for new kinds of quasi-exactly solvable theories. The spectra of this family of quartic potentials discussed here are also real, discrete, and bounded below, and the quasi-exact portion of the spectra consists of the lowest $J$ eigenvalues. These eigenvalues are the roots of a $J$th-degree polynomial.Comment: 3 Pages, RevTex, 1 Figure, encapsulated postscrip

Non-extremal Localised Branes and Vacuum Solutions in M-Theory

Non-extremal overlapping p-brane supergravity solutions localised in their relative transverse coordinates are constructed. The construction uses an algebraic method of solving the bosonic equations of motion. It is shown that these non-extremal solutions can be obtained from the extremal solutions by means of the superposition of two deformation functions defined by vacuum solutions of M-theory. Vacuum solutions of M-theory including irrational powers of harmonic functions are discussed.Comment: LaTeX, 16 pages, no figures, typos correcte

Velocity Segregation and Systematic Biases In Velocity Dispersion Estimates With the SPT-GMOS Spectroscopic Survey

The velocity distribution of galaxies in clusters is not universal; rather, galaxies are segregated according to their spectral type and relative luminosity. We examine the velocity distributions of different populations of galaxies within 89 Sunyaev Zel'dovich (SZ) selected galaxy clusters spanning $0.28 < z < 1.08$. Our sample is primarily draw from the SPT-GMOS spectroscopic survey, supplemented by additional published spectroscopy, resulting in a final spectroscopic sample of 4148 galaxy spectra---2868 cluster members. The velocity dispersion of star-forming cluster galaxies is $17\pm4$% greater than that of passive cluster galaxies, and the velocity dispersion of bright ($m < m^{*}-0.5$) cluster galaxies is $11\pm4$% lower than the velocity dispersion of our total member population. We find good agreement with simulations regarding the shape of the relationship between the measured velocity dispersion and the fraction of passive vs. star-forming galaxies used to measure it, but we find a small offset between this relationship as measured in data and simulations in which suggests that our dispersions are systematically low by as much as 3\% relative to simulations. We argue that this offset could be interpreted as a measurement of the effective velocity bias that describes the ratio of our observed velocity dispersions and the intrinsic velocity dispersion of dark matter particles in a published simulation result. Measuring velocity bias in this way suggests that large spectroscopic surveys can improve dispersion-based mass-observable scaling relations for cosmology even in the face of velocity biases, by quantifying and ultimately calibrating them out.Comment: Accepted to ApJ; 21 pages, 11 figures, 5 table