Writing an Escalation Contract Using the Consumer Price Index

[Excerpt] Each year thousands of people write contracts with escalation clauses that are tied to the Consumer Price Index (CPI). Escalation contracts call for an increase in some type of payment in the event of an increase in prices. These contracts are used in a wide variety of ways, from adjusting rent prices to adding cost-of-living adjustments to alimony payments and wage contracts. Unfortunately, many escalation contracts tied to the CPI are vague. For example, a contract may stipulate that “the Consumer Price Index (CPI) be used to escalate an apartment rent, but the Bureau of Labor Statistics (BLS) publishes thousands of CPIs each month, so a more carefully worded contract could minimize ambiguity and the likelihood of future disputes. This issue of BEYOND THE NUMBERS can help those who use the CPI to write escalation clauses to create a more comprehensive contract

A Concise Introduction to Perturbation Theory in Cosmology

We give a concise, self-contained introduction to perturbation theory in cosmology at linear and second order, striking a balance between mathematical rigour and usability. In particular we discuss gauge issues and the active and passive approach to calculating gauge transformations. We also construct gauge-invariant variables, including the second order tensor perturbation on uniform curvature hypersurfaces.Comment: revtex4, 16 pages, 3 figures; v2: minor changes, typos corrected, reference added, version accepted by CQ

The Power Spectrum for a Multi-Component Inflaton to Second-Order Corrections in the Slow-Roll Expansion

We derive the power spectrum $\mathcal P(k)$ of the density perturbations produced during inflation up to second-order corrections in the standard slow-roll approximation for an inflaton with more than one degree of freedom. We also present the spectral index $n$ up to first-order corrections including previously missing terms, and the running ${dn}/{d\ln k}$ to leading order.Comment: 11 pages, no figure. KAIST-TH 2002/0

Comments on gauge-invariance in cosmology

We revisit the gauge issue in cosmological perturbation theory, and highlight its relation to the notion of covariance in general relativity. We also discuss the similarities and differences of the covariant approach in perturbation theory to the Bardeen or metric approach in a non-technical fashion.Comment: 7 pages, 1 figure, revtex4; v3: minor changes, typos corrected, discussion extended; v4: typos corrected, corresponding to published versio

Modelling non-dust fluids in cosmology

Currently, most of the numerical simulations of structure formation use Newtonian gravity. When modelling pressureless dark matter, or `dust', this approach gives the correct results for scales much smaller than the cosmological horizon, but for scenarios in which the fluid has pressure this is no longer the case. In this article, we present the correspondence of perturbations in Newtonian and cosmological perturbation theory, showing exact mathematical equivalence for pressureless matter, and giving the relativistic corrections for matter with pressure. As an example, we study the case of scalar field dark matter which features non-zero pressure perturbations. We discuss some problems which may arise when evolving the perturbations in this model with Newtonian numerical simulations and with CMB Boltzmann codes.Comment: 5 pages; v2: typos corrected and refs added, submitted version; v3: version to appear in JCA

Vector and tensor contributions to the curvature perturbation at second order

We derive the evolution equation for the second order curvature perturbation using standard techniques of cosmological perturbation theory. We do this for different definitions of the gauge invariant curvature perturbation, arising from different splits of the spatial metric, and compare the expressions. The results are valid at all scales and include all contributions from scalar, vector and tensor perturbations, as well as anisotropic stress, with all our results written purely in terms of gauge invariant quantities. Taking the large-scale approximation, we find that a conserved quantity exists only if, in addition to the non-adiabatic pressure, the transverse traceless part of the anisotropic stress tensor is also negligible. We also find that the version of the gauge invariant curvature perturbation which is exactly conserved is the one defined with the determinant of the spatial part of the inverse metric.Comment: 21 pages. Appendix added and conclusions extended. Updated to match version published in JCA

Gauge invariant Boltzmann equation and the fluid limit

This article investigates the collisionless Boltzmann equation up to second order in the cosmological perturbations. It describes the gauge dependence of the distribution function and the construction of a gauge invariant distribution function and brightness, and then derives the gauge invariant fluid limit.Comment: 36 page

Temperature dependence of the spin and orbital magnetization density in Sm1−xGdxAl2Sm_{1-x}Gd_{x} Al_{2} around the spin-orbital compensation point

Non-resonant ferromagnetic x-ray diffraction has been used to separate the spin and orbital contribution to the magnetization density of the proposed zero-moment ferromagnet $Sm_{0.982}Gd_{0.018} Al_{2}$. The alignment of the spin and orbital moments relative to the net magnetization shows a sign reversal at 84K, the compensation temperature. Below this temperature the orbital moment is larger than the spin moment, and vice versa above it. This result implies that the compensation mechanism is driven by the different temperature dependencies of the $4f$ spin and orbital moments. Specific heat data indicate that the system remains ferromagnetically ordered throughout

Bilateral Serous Retinal Detachment as a Presenting Sign of Acute Lymphoblastic Leukemia

We present a case of bilateral serous retinal detachment (SRD) as a presenting sign of Philadelphia chromosome-positive acute lymphoblastic leukemia (Ph+ ALL). A 45-year-old woman presented with decreased vision and was found to have bilateral serous retinal detachment. Peripheral blood smears revealed leukocytosis of 53.9×103/µL with 64.6% lymphoblasts. A bone marrow aspirate revealed the presence of lymphoblasts. Cytogenetic and molecular genetic analysis detected a reciprocal translocation between chromosome 9 and 22, t(9;22) (q34;q11). A diagnosis of Ph+ ALL was made. Following systemic chemotherapy, the bilateral SRD resolved completely with full recovery of vision. The sudden appearance of SRD should raise suspicion for leukemia. Prompt recognition of this disease is important for early systemic treatment and restoration of visual function